Untitled

Transcription

Untitled
STATNTICSAND
DAIA ANIALYSN
IN GEOLOGY
Secondedition
JohnC.Davis
KansasGeologicalSurvey
[xc. C.[anuc
CTATI,ICTHTIECKWI'.I
AHAJIH3 AAHHbIX
B TEGJXOTMVT
flepeeo4
c anr;rnrZcxoro
Aor(Tcpa
$usuxo-:r'':lT eivlaTHLjecKrIx Hav K
B.-4. {'o.rrx_{.ieoou
lI o g 1''-' laxtf uLri"l,qolt"oija
f €OJIOf O-t':IHIlepaJ-IOfi{rleCKllX ItayK
/1.A. Poduouoea
B AByX K;rlrfAx
KHP,II-A 1
JohnWiley and Sons
New York ' Chichester' Brisbane
Toronto ' Singapore
re
" 1990
MOCKBA "HE"II,PA
NPENVCflOBI,lE
EEK 26.3
Ag+
v"AK550.8.053:519
PexoMegroeaHo I{ li3raHlilo
P, H. Koeanou.
AenncAx. C.
D,g4
A-'B
Crailrcrttqecrttll
xaHAr.rAaro)r f eoilofo-MlllleparoflicecKI{x
HaIIi
aHa;rll3 ;lal;F;Ijx B feoJ-IofllH:- fi_ep. c aHr.I..
2-in./flep.n-.A. fony6eeofi;Ilo'r pel' A' A' PoArtoHoea'
K H .1 .- I \ . : H e l P a ,1 9 9 0 ' 3 1 ' :c ' : L r ' : r '
ISBN 5-217-02122-3
a;rre 6'
ar itcrnxu II
VIsJloxeHbl MeroAbI MareMarl'Iqec(oi! cr
YaT!-l:.Hori
p b ] , n p u M e H n e M b ] e _ B c o B p e M e H H b l x r e o . ! o | l l q e c K l t x u c c f l e ! , o B aoH IHopMsJb,Iqx.Paccvor.
npoBepKu xr3-iltcrltrlecKltx rllnore3:
perlbl I't3BecrHora*p"ttpii"
rt 'rp'
Mauua-)'urnrr
onuepa'
Crrrol9l.a'
HoM pacnpeA"n.u"'", xi"'epu"
M e T O A a Mc T a T l l c T l l q e c K o H
e
n
a
p
a
l
r
l
e
T
p
h
t
i
e
e
K
l
l
M
boaluioe u"r"unu"'yi"nerio
roaHanH3aAaHHbIx'onucanrtflpoueJ.yDLra:f.allnganoc,'IeAoBaTe.]Iluocteil
A a H H b r x : " " , . p n u n " u , n - , o p T o | o H a n b i ] a l . - n c . ] I i ' j o M l lBaaJpI bn H
e rMpbeIc' c$Iu, nI frfr'p3ao'H H .
o rapfapM
ana"iirg'
;;;J.;O;;u;q"cneKrparbriuii
;;;;;;;;,
I{Hfi H TpeHA'
3l i i l i M a r o q r . r x c n o 6 p a 6 o r x o i r x o ; i u .x,'llt reo'loros Bcex cneuuaJlbuocrell'
qecrBeHIJbIX n * uuaarue""otx p e3y'qbraroB n a o'rrol.eultii'
4i3#iilFry35-s0
tsBN 0-47I-08079-9
ISBN 5-247-02t21-5
ISBN 5-247-02122-3
66K 26.8
bY John \\'ileY a n d S o n s ,
O
' A1986
ll
: 1973,
'
r i g h t s r e s e r v e d Published
inc.
in Canada
sernulianeous-lY
A. Io'
@ fleperoa ua PYccrufinaux B.
1990
.rv6eeofi.
B 1973 f., KorAa BbrrrrrronepBoe HsAaHHegroii xulrn, llcfio'ltb30BaHIIe feoJrofaMll BbIrlilc,'IitTe,'rbHbIx
cpeAcTB Haxo.ltlr'iocb Ha KaqecrBeuHo uHoNrvposHe, qeM ceiiqac. 3ro 6rr.ro Bpe\,rffMaccrrBHbix
3BM, cocpe4orouesgsrx B Bbrqr.rcirHTeJrbHbIx
ueHrpax, Aocryn K
KoropbtM ocyqecrBJrflJrcs qepe3 oKotrrKo B 3aKpbrrbrx lnepax. I*Ipn
3TOM pe3yJIbTaTLICCJIeAOBaTe,'Ib
nO,'ryqa,1B JtyqIIleM Cryqae qepe3
Hecxo,rlxo ageti.
Ten_epl 6o,rluHscrBo reorToroB r.r\.IercTHefiocpeAcrseHHslfi-locTylI I{ 3BM vepes repMrrHa,'rrr,qrrI( MrrHlr-rio}tiibtorep\:,rir.tHI{}relor
tra)Ke nepcoua.nr,ulrfi KoMnbrorep. I(ourrrrorep cra.ir o6nr4eunoft
BeUbIo B )Krl3HlrreoJrofa. I( ueuy o6parqanrcfl iiar HoBr.lqr(u,TaK
l i n p o Q e c c u o H a ! ' r bBr H a , ( e ) r ( A en o B b r c r . r r ab $ Q e N r l r n H o c r uc n o e f r p a 6orrr.
K c o x a n e u a r c , , r e r x u f i A o c r y f l r i K o N { r r L , r o r e p aH\ re o 6 e c n e q ; r e a _
e r , t e r K o f o n o r y q e H l l q s H a H r . t i oi r o M , q r o c t n i N r j e " T a r b . I J n q
l{Horlrx feo,'rotoB ata[rrg [oBepxHocreri rpesna 1.ai<irie Ma,,ro uo_
H f l T C HK
, a K H l 0 , r e r H a J a n . T o l < c M o ; . r { Hcor i ar t r b r r o d a x r o p 'a
H O M a H a J I I ' I S e6.0 " ' I e e r o f o , r r o f l B I r J I L i cebu r e 6 0 n e e e n : o . r t , q e c n , i e
TpyAHO AOCTynHbre
nreroxL,r.Heo6xo4ruocrb B o6vqeuun reoJroroB
rio.[[iqecrBeHHoMyaHaJrnsy 6u,ra oqeBHAHayx(e B lg73 r., To ]Ke
B e p n o r r c e l i q a c . B o r n o q e u v H a n r { c a H a3 T a K H f i r a ,
B orser Ha Mr{orHe 3aMeqaHrrfl,Koropble fl IIo!'rvqtJl noc,rle
H 3 A a H l r f lK H u r H e 1 9 7 3 r . , a r a K x i e , y r r l r r j B a f l c o 6 c r n e s u n f t o n t t r
npenoAaBaHufl,fl BHHMare,lbHonepecMoTper'txHufv ,Irq HoBorC u3i ea r e p i l a d ' I ac o x p a H e H o ,o H O H a r l l r H a e r c f lc
A a H l I f l . P a c n o , ' r o > t < e H tM
ocHoBHbIXnoggrt{fi r.t 3aKaHr{rrBaercflaHaJI}r3OMnoc.[eAoBare,lbHoc t e t ? , x a p r , M H o r o M e p H b r xs a 6 . n r c A e s l r r l . T a x x a i i 6 o n l u r u H r : r s o
cryAeHroB _c{y_r!a.el orlrr HrrH 6o.nee KypcoB no @OpTpAHy-, ro
r.raBa o OOPTPAHe e eroN{ rl3AaHlrrlorcyrcrB}'er.
14s,roxegue HaqflHaeTcr c ocHoB reopuri n-epolrHocrefi, oveHl
Bair(Hbrx B aHaJ'[r3e/laHHbrx. !,o6an.leir Hoesrrt pa3,le.r o HeilapaMerpHqecKr4xMeroJ,ax, r{oropbre npeAcraB,'rrr}oTCfl
60"ree IIpr.rfoAH b r M l rA l T f l f e o J r o r t i q e c K a xA a H H b I X .T e u a < < C o 6 c r n e H u b l3eH a q c H t r f l
tr co6creeHHbreBer{TopbI>>
ocraerca rpy4Hor? Ar'Irt reo.rtofoB, rI ro3 r o M y o H a s a r p a r r r B a e r c r r A B a ) K A b r :B p a 3 A e J r e< < M a r D a q g a f la . { _
r e 6 p a > >H B p a 3 A e " ' r a x n
, o c B f l x r e H H b r xQ a x r o p u o n y a H d , r u s y . p a c _
cMorpega raKN(e cBfl3b npoqeAyp uaxoxAeHrrq co6creeHHtrx :JHa_
'leHnii li co6crneHHrJx BeriropoB c MeroAoM f,IraBHbrx
KoMtroHeHT,
R - r r Q - n a e r o A a M r(rr a x r o p u o r o a H a , ' r r r 3 aa, H a d , r [ 3 ac o o r B e r c r B a r r .
Helioropble reMbl aHa,'IH3aAaHHbIx B nocJleAHfie HecKo.irbKo
. a e r r p u o 6 p e r a J r H s c e 6 0 r r ' u e e H 3 a q e H r . rBe H a y K a x o 3 e u r e . T e o puq peflioHaJrn3oBaHHbrx
nepeMeHHr,rxnpr.rBJreKaercfl
celiqac
Anfl
o6rscseHuq [pocrpaHcrBeHHbrx csoiicre feodrrofnqecKrrx[epeMeHHL,rxMHOrr{MriHcc,rreAoBareJrflMr.
I_[eHrpa,rluy]o poJrb s erol? reo-
pIlH uf parcr [oJryBapr{orpaMMbr H KparlraHr. Ora MeroAbr
nDe.],cTaBJeHbr B HacToflrl{eMH3AaHI-rA.leosasaxn
nonflJrpr saxuvro
poJIL cIIeKTpar'lbHoroaHaJIH3a; oqeBHAHa [oJre3Hocrb 3Tnx
MeroA O B n p l r p e u e H u H .M H O T H X
A p y f r . t x 3 a A a q , H a q r . r H a ,o T r i p e A c K a 3 a Hriff 3ellJrerpaceuuri H KoHqafl Onr]caH[eM
sopuu llcxonaeuux ocrarl{oB. Pas4e,r o pflAax <Dypre H3Jrafaercfl c vqeroM 3TrrX
H3Meaeunri.
Pr,l ra6nHu ri p'cyHr{on e eroli KHr.rreBocnpori3BeAeHbr pa3c
p e u e H u r r a B r o p o B ( s r a A e n s q e B a B r o p c K r . r xn p a - n ) . t r 4 c r o v u u x
4;rx
riax<roir ra6,rrru,i,r ri pI4cyHKa yKa3arL B r{Ba,4parHbrx
cxo6xax,
: r i l o . r H a f c c L , r J r Kn
ap U B o A U T C R
B C n r r c r ( a x. { H T e p z i r y p b rx x a x A o l i
f i l r D e . l ' a 6 , ' u t q u r2 . 1 0 , 2 . 2 2 , 2 . 2 5 y 2 . 2 6 s n n n x t i o . o O . r u " H H o c r b r . o
r r 3 ; a . r e . r r b c r n {ar i t o u V a r i , r l r u C r , t u o e l s I n c . , r a 6 , , i u i l u 2 .
11. 2.14
r r 2 . 1 8 - c o 6 c r e e H H o c r b r ol l u u r s r { r i , 6 y x L t d , ' u , I . r O n l r u o i
+.gO Lr
4 . 3 1 - A u e p n x a u c K o f o x r M r . i q e c K o r oo 6 u l e c r e a .
B c e o g - _ ,t s o c r r o o I 1 3 B e . l e H bcr c o o r B e r c r B y r o u l u x p a 3 p e u e H f l i r . r i a c r l
ra6.nnq b.O_
,,o6crBesuocrn AvepuxascHofi ciarlcrtroecnofi
accoi1trari.r.rur
li Apy-
l'rasa I
BBEAEHHE
Btrt ltorcere lta'.ilepurbro' o 4eJi1
<(...ec.7u
truc'
eosopure, u pe3unblur BbtPA3Urb
o3l7(ttiller,qI.) BttL ti'c'J-4To
lo.n,3ro
3Heere o nped.ucre pa32c6opa; Ho ecJlu
BdL ue uoc0ere oxapaKTepu3olarb 3Tor
npedner qilc-'tort,To uJ- 3To2o crle()Aer,
qro Batuu sHaHufl cxu)naL u xegAoaaHu itoeAT 6otrO
. l e T E o p u T e r ' L b t l t Lu,
ornpaeuoi ro'txori npotlctil noronto
3HAH!!fr>.
JIop,q Ke'nsrrtn
rrHcrHryra 6uo,rorn,recxHxHa).K;
:i:.^::.::1_.1_y.quIrHcKoro
ra6"ruU
cAe,taHoc ilx pa3perleHHrr. Ta6,rarfbr
5o;\l0llllpoBaHIIe
nlercraB.rrflror co6creeHHocrs AxaAeunx flpecc
Inc
?( J* r^oi ir_l f?o_Hy),
L t d i l B o c [ p o t r 3 B e A e r r bcr H x p a 3 p e u e H u s . p u ' c . S . 2 l _
.o6crseHuoc'b
Alreplrxaucxor? crarncrnqecxorl
accoqaaqrJri,
a pirc. 5.25_ co6crseHuocrt Xapxypr Epcric tZo"rno"nq"Inc,
o6a
p n c j ' H K a B o c i r p o i r 3 B e A e Hcb r c o o r B e r c r B y r o r j r r x p a s p e r u e u u r i .
5 Tel{cre' B orBer Ha t'tHoforific.neHHble
Ilo}Ke,'raHLIfiqttrare.neri
c A e , r r a H oM H O f o u : l r e u e u r i i i , r r c n p a B J e H x r l ,
406aa,,re""ri nap"r"ai
JffTb rex, KTo llanflca"ryr.{Fre,irer cMbtc,Ta. tix 6,rarotraprc.'B
fl
,:or I o J H e H u cI ( T e M , x r o 6 u . , t H a 3 B a H B I
H::.."g.,
ii:i:l:::;
nuy.r,on'pB!X
Aoriropy
J';liJ#;' "fJ,:,"#l
A ) I { I l r l \ ' K e . v n o c J I J Vl z A o x r o p y -KEe;i;i;r,y' n p oTpeepcHceop y s , i , . x n o u o u _ t b .
M o r r p ' e u e u 3 e H r b ra, o n t g n n ; ? ;
epaux Orpri4x
tt npocfieccopLxu-aH @eur, c4e"tad,rr{N{Horo qenHbrx^
Hcnpae,reHrru.r
R OiioHqaTe"rtbHoM TeticTe.
I { H o r o q H c , u e H H b r 4e o 6 a a , r e u a a 6 u n n c A e " r a H b r
r i o , t J e fa M r r r r 3
KaHsaecxoii feorToruqecxoii cny>r<6br,BKdirroqarAor{ropa
Aarieirra
Ko.'r.''irrsa '' tro.Topa Ka,rusa (D_eprrccoHa
rr Moero [oMolr{Hrr^a no
' ' e p B o \ { y r 3 A a H r ] f o r l r r r c r e p ap o 6 e p r a C s 1 4 n c o H a .
Tpoe us Mo'x
rKrHBHoe\rqacrne B Harrrcasuu xilrru:
Ij.i.ill^"pllHfl,'rrr
AoKrop
pa3Aerr no perfioHa,'ril3oBaHHbrN{nepeMeHHbnr,
::13L"":,reJ.Jo)'
Aor..rop
pasAe/'r o co6crneuHtrx sHaqeHrrsx
Arr
u Aorirop
.II,NoH !,onelou, xoi_opuii ,r!o6csHo npeA,rro]KH,,r
MHorfle rr3 \,spairis e H r , f i H r p r r M e p o - Bs o e c e r i K H r f e u ' x o r o p u r ?
MHe Ha
B c e x c r a A u n x p a 6 o r s r . H a x o u e q , s o c o 6 e n H o n p"r;r;n; ;r;r;a" r a H
[{oe],{}.
accrr-creHTy' HCCJreAoBare.rrrc
r.r KoM''aHboHy Mr,ccHC nxo
Sirs
,[.e-fpgQQeirpafi4, 6es rrogep)KKr.rKoropofi ,]H*or sror? *-r."
onu3a,lct 6ot ueeo:iuox{HblM.
f,trcou C. f,seuc
Eule sa 3ape craHoB"leHIiflreo,;lorHu Hel{oropble reoJlorll IIoJIbC IT, O
Nb' I A T C M A T i l I ] C C K M
IIM
I A A M HH.A N P H U C P f' O P H b I EH H X ( C '
3OBA.TIIIC
HepbIIIfeo,rIo|IiCoTHtIjIeTHa3aAnoAcqIITbIBaJIII3anacbInopeB pyAe no"Ie33\'JbTaTai\,ronpo6osaHufl II oUeHltBaJIllCoAeplKaHI4e
r n r , t xx o n n o H e H r o B .O t t u e p [ 2 ] o r U e u a f l , q r o p a g q " i e H e H l ' irep e T I ' I q H o f o r l e p H o A a, r l a r i e l e M H a o c H o B eo T H 6 c r i T e . n l n o rpj a c n p o c T p a H e H H O C r r rc o B p e M e H H b r o
x p r a H H 3 N , r O6eH n O C r a t n c r u q e c i i o i i n p o l l e A y pori. Illrronofu eule B Haqar'te3Tolo crorrlerllfl ll3yqa"rlll pa3Mep 3eo e H n l r x o q e p r a H I I q , K o r o p b t e n p e A c r a B " r g , r t tc o 6 o t i B a ) K H b l eI { c ioqHr.rKureofiorfir{ecr<oiiuuQopua[H]4. Taxne HayKll o 3eu,re. xax
l e o x n N r u r , r e o Q u s u x a I I f u A p o r ' t o f u a ,r p e 6 y r o r n p o q H o r o 1 4 a T e M a r H qecrioro QyH4aueura, xorfl ucnoJlb3yeMbreLIMU npueMbl nepBoHat r a J I b H o6 n n n p a s p a 6 o r a u u H e H a o c n o B e r e o J I o f H H .T o q g o r a K ) l i e
\ l r l H e p a , l o f r r n x p H c T a , r . n o r p a Q ur r c n o , ' t b 3 y l o T
MareMart4qecxafa
i nnapar rpnsnuecxofi H aHaJrrlrr,rqecxor?
xal,{riu.
XorR arr pa3Ae,rTbr
r4Melor BaxHoe 3HaqeHHeB cneq[IaJM3LIpot s a l l H b r xo 6 , t a c r R x , o H L I H e f f B r f l I o r c q n p e A M e r o M p a c c M o r p e H t t r
aroj't tinrru. Ha,ruuaq c KoHua 50-x roaoa HaIIIero BeKa Bbrquc,'rHTe.IbHbreMalrrrrHbrcraJnl txfipoKo IrpprMeHfrbcflB yHHBepcHTeTaxH
r . o p n O p a U H t XB
, p e 3 y J I b T a T eq e r O f e O J I O f t i3 H a r { u T e , r b HqOa I I e C T a . , l t n p u 6 e r a T b I ( N { a T e M a T t r q e c K nM
Me T O I a M a H a J I I I 3 aI a H H b I X , K o 'tc)pbre
o H r I 3 a H N { c r B o B a J Itu{ 3 p a 3 J l r . r q H b r o
x ,c o 6 e H H o r e x H r { q e c K ! t x ,
H a - V I iI r n p x M e H q , ' r i xl n n 6 o u y p a 3 A e r r y H a y r { o 3 e l u t l e , e r o 6 o l e e
o6que MeroAI.iKH,qeM Hcllor'ib3yeMbre
o6uqno. feo.norHg caMa no
c e 6 e n p H n e . r a r i H e K o r o p o r n 1 ' c n e x a MB B b I q r { c ! ' I I r r e J r b H bHIaXy t ( a x ,
oco6euHo s o6,'raclu no-crpoeHurrpaQuxou, BKrroqafl Kaprbr w
o x o H T y p H B a l t r r eO. A u a x o H a t t r a H a y K a B b t f a A a d ' I a6 o " t n u e , l t e M n o xeprBoBa,'ra e o6lueH Ha Ko.rillqecrBeHHble
Mero,Itbr.
HeQrnuue KoMttaHHHCruA, BeAyrqre 6o.ttruue reoJrofopasBeAoqHbrepa6orn (He cqr.rras rrpaBr.rreJrbcrBerrHbrx
yupex4enuii),
ul{poKo HcnoJrb3yror Bbrqacrr4rerbHbreMatrruuur. flosroMy orpoMHuii uHrepec, lroropufi nporB/'rflIor ora opraHr.r3auuuK feoMaTeMaT r . i q e c K u MM e r o A a M , 3 a K o H o M e p e s O
. n Bbrpaxaercfl raKxe B -vBer ' r r r r i e l r r rpuo J r u r 3 b r K o Bn p o f p a M M u p o B a H i { qr r M a r e M a r r r q e c r r o jnt o ! rorcBr{rr npn o6yueunI{ feo,'rofos. I( co)KaJ'reHuto,
He cyx{ecrB}'er
I x H p o r ( o p a c l i p o c r p a H e H H b r xr p a 4 u q H r l ? r c l t o J r b 3 o B a r r HMf la r e M a r r r l r e c x c t o a H a J r u 3 aB f e o J r o r [ r i ; 6 o n e e r o r o , Q t o p u r r p o B a H r {ceo o r B e r crB\:ior{Hx nporpaMM o6yueula npoticxoAlJro ro/'rbrio B Hexo,ropbix
IlHcrrrryrax 6,raro4apl ycu,rlrsM orreJrbHbrx yqeHbrx. Bcero .nurus
qTOHeCIiO!'Iblio
nliOJI npeycneJlo B 3TO\1HaIIpaBJ-teHitft
HaCTOJTbKO,
6u rr,'"Ietl rtpaBo cqHTarbctr rlzoHepal{rr B Iio,rtjqecrseHHoti feovrror u H . O 6 y u e n r . r e] ' H u x o c H o B a H oH a n p o q H o N {Q y u 4 a r v r e u r ef e o J r o llll.i, l{aTeMaTHKHII CTaTHCTHKLI.
.\'lgorux reoJroroB Bblqricr'iaTe,'rbHafl
peBoJrrorlufl3acTaJ'taBpacn,,rox: BocriHTaHHbIe
B TpaAutlrrflx, Koropbre rpe6yior nor'ryqeHur{KaqecTBa 3a cr{eT KoII{qecTBa, oHI{ OKaSaJIIlCbnJIoxo IroAroToBneilHbr\{H MareMarfiqecriI,tH HesHaKoMb]x,rr.r
co crarucrr.rKoii. Ho aaxe
oHu 6ucrpo oIIeHIIJIIt rIoreHuI{a,'IbHbreB03t\{oxrrocril ai{a,'rrrrlrqecKHX I'teTOAOB,KOTOpbIeBbIr{ucd'iuTer'IbHafl
TexH}il{a cAe"{a,'Ia ,IIefKo
Aocr),flHbIMu.tr{Horne opraHH3arIHn,r{aK r(oMMeprlecr{He,
TaK r.r ro.
c y . ( a p c r B e H H b r ec, o 3 A a J r Ho 6 u r u p H t r e 6 u 6 , l u o . r e l i l r n p o f p a M M A n t
3 B 1 1 , n p e r H a 3 H a r r e H H b r xA J r n p e a J r H 3 a r l r l H r e o M a r e M a r r q e c K H X
npoueAyp. 14cxvueure HCnoJrb3oBarborrl nporpaMMbr cJrurrlKoM
cr,rrbHo, AalKe HecMorpfl Ha ro r{To lrx ocHoBa He Mo)Ker 6uT6
flcHo oco3HaHa.
[IJHpoxoe BHerpeHHe nepcoHaJrbHbrxKoMrrbrorepoB npaBeJro K
)'crr,'reHnlo3rHX reHAeHquii. B Hacroqrlee BpeMfl se6onnune roMrraHrii{,rpynilbr KoI{cyJrbTaHToB
r.r Aaxe oTAeJrbHbre
Hcc,leAoBaTeJIHfeoJofH noIyrII.t/'In AocTyrI K BbIqaCJIHre,rlnoftTexHI,IKe,IIp14MeHeHile r(oTopofi scero ,'rrlrIIrbHecKoJrbKoJIeT Ha3aA 6bI.[o npnsu;lerueft
6o,rrurux xopnopaqnl'r a yHnBepcnreroB. MHorux reo.uoioe ceiiqac
MolxHo yBI{Aerb sa co6crseHHblM KoMnbrcTepoM,Aa)Ke rex, o KoTopbrx Herrb3q 6lr"to no4yMarb, qro oHu 6yAyr HyxAarbcr B HeM
r . r r r n p o c r o l r M e r b r r o B o A e t o H c n o J r b 3 o B a r b .M s o r n u
u3 grux
feo,qoroB, ecJrr.IoHrI yMeror npr.rMeHqrbux s cgoefi npo$eccuoua.nru o t i p a 6 o r e , t ( a x ( e T c f l ,v r o p a 6 o r a c K o M n t r c T e p a M Ho 6 e u l a e r r r u
6o,rrLire, qeM onepHpoBaHue cJroBaMHu QtrrHaucoBbre
fioAcqerbl.
J T a K H u r a q a c r u q H o n p e A H a 3 H a q e r a! , J r f l ,r o r o , u t o 6 u l r o M o r { b
teo,lofaM, KoTopbte co3HaIoT, qTo MaTeMaTr{qecK[eMeToAbI MofJII.t
6r,1 6url ulvl noJle3HbrB HccJIeAoBaHHqx,
Ho HeAocraroqHo floAfoToB,reHbrK sroMy. I(oHeuuo, oHlr MorJrI{ 6u npocnyurat, Qopua"ulHuli liypc reopr.rl BepoflTHocrefi,ctatrtcraKI,I, rlricr'IeHHotoaHaJIH3a
rJ npofpaMN{npoBaHlfl c nocr'reAyroqeripa6oroir no4 pyKoBoAcrBoM
o r r b l r H O f Or e o N l a r e M a T r r x ao. A s a x o H a n p a K T r r K e 6 i l s a e r u H a q e ,
nu6upanr cnorl nyrt Hauryr{ufiM
u 6o,rtruuscrBo Hcc"reAosare,'rer2
a
svTafl, cilpauIIIBaf' yqacb Ha cBoBo3MoxHbiM A.rltl HIIx cnoco6olu:
He tBrfierct
crreAylor'
3Tx
xoropE'IM
rtx ouru6xax. flyrl,
"lIoAI'l
IleTo]llqecl{xnpofpeccllBHblr'II'13-3aTOfO'tlToIipII3TOMBCTOpOHe
OHlt BO3BpaUIalOTCfl
oc.faroTcrr NIIlOfIle Ba)KHblC BOnpOCbl. O6ltqtlO
MHeK
o
roobie' ro ux
M
C
T
o
A
b
I
'
r
e
H
a
B
i
l
I
l
M
a
H
i
l
c
ria3ar, o6pauiar
g u r c , t r a r r 6 o , t e e n p r r M e H u M b r B r i x I I C C , ' I e A O B a H I . I f l Xp, a S p a 6 o r i t a x ,
pa6ore. 3areu 6HI1 qyBcrBylor [po6eJIbI B rloArorc3oii.purn""oir
qe,leli
TeXHrilIeCKIIS
tie rr nbrratOrCfl I]pilCnOCO6lrrl LJIfl ITHX Xe
riDrreN{br o6pa6orr<H AalIHbIX. 3ro uey;1onr'lerBopH"r'c,'lunuliil't -iaxe
oOvqeHlleNI
onacuufi ubro1 o6yueHlrl, B03MoitiHo cpanttuultri c
O
i
L
i
l
l
l
l
\
' lI I 3 I l v T e i j ,
t
l
B
.
I
j
t
e
T
C
t
l
O
L
I
p
a
6
O
'
t
'
t
O
,
l
u
a
l
r
O
.
n
p
O
I
l
.
e
C
C
e
B
BitJqti
rro iiol'opoMlr Ilptl.\oAII'l'Cf IIJTII MHOfllNl feo.[ofaill. 3ra xriura ltoi r i c T r r O M O r l bO O f a H i t . j O B a T bU p O q e c c C a N I O O a ) \ ' t l e H I Taf l , l l N { e H H O: l u l e T B O : J i v i o ) K H O CC
T b, r ( e . [ a T bI I e p B b l e u a f u l i n C ) 3 H a H I I I OO ] l l l C i l H i l i r ] ] iB
BIIeuHe
\leHee
r i e u a , r r o p n r M o B . L { t l r a t e J l t o I I p u ! . e T c f l o c B o Hi b
aQQelirrinubrc relrtbI, cocraB"rflrcurtte Q1'H4auenr, lla i(olopo11 IIo{ira'{,'fl)oerrbrH
, i t r r P I r M e l )C, ( ' l i o B l , ri c o i r l l H l l o B e p x H o c l c i i r l l e t t t a l l
T O p H O | Oa H a J I l l 3 a .
3ta xulrra rrpcAFia3IIalIerIa ralix(e nitq cr)'/rl,eHToB,ti3\rqarcI1ILix
c 1 ' a r r r c T r . r r { yr r i r p o f p a M M l r l ) o B a i l i l e . T a x i l e K y p c b l B C e t r a u { e c T a H o nnrcfl o6fl3arc!'rbHbrMH B ar\reDi.rKaHcrinx u eepoleticxttx yHuBcfcnTerax. K Hecqacrllo, oHn o6bIIIHo qHTaIorcq JrHuarlllr, NIa,To 3Haiio\,rbu\{u c reo,'rorueli lr npoS;rL'NfaMu Hayri o 3eu.ne. Csggt grax
IIpeAMeToB c OCHoBHOIi reirrarutioi.i 06y'reHHfl cTyAeHToB oCTaerCg
IIeflcHorl. 3ro u1'ncrno ocJrolKHflerct orcyrcrBr,teM
MareMartir{eci{Hx npir,'io)KeHnr? eo Mnofux teo,'IorxqecKux tiypcax. B ro BpeMf
riaK cTyAeHTbI Hy>KAaio'fcg B criellltaJII.rcTe, r.lx vriltTelI9 3aqacTyro.
r B r r r r o r c r J r r o A b M l r , r r o d r r v q a B r r r H u uo 6 p a s o B a H H e A o 6 y p H o r o p a 3 Br.tTlrfl KoJrr.rqecTBeHHbIXMeToAoB i.I, c,'IeAoBaTe,'rbHO,He rIonfo.roB_
KHHfe ql,iTareJlb,
"iteHHbIMIi B 3TOM HailpaB,reHlrH. B Hacroaulefi
uafiAer He roJrbKo o6rUnrl Kypc Bbrq[c,rrr]Ter'rbHbrx MeroAoB,
Ho,
'l'al{x{e
MHoroqlcr'IeHHble npIrMepbI HX rlpHMeHeHHg B
reorof iltj..
KoueuHo, Mbr HaAeeMcs, qro Lr cryAeHTbr, H npenoAasarer[
Hari.r.,Yr B 3TOfi KHrrfe qro-,1n60 riHTepecHoe, pr oHa 6y4er cnoco6creoB A T b P A C N P O C T P A H C H HTFCOX O C H O BS H A U H I ? ,K O T O D b I CM b I H A 3 b I B A E M {
reou arelt aruxorl.
06 sTOH KHHI'E
BrrpaBc 3r{arb c caMofo Harrar,ra,riyAa H no KaKoMy.
_- _Jurare,rrb
nyTH
BeAeT efo aBrop, a TaKxe qTo oT Hero rpe6yeTcq, TaK KaK,
npeAIIoJIOxeHuflo nOAroToBKe,HHre-.
iBrop Aer'IaeTOlpeAe,'IeHHbIe
pecax
H BO3MO)KHOCTSX
csoefi ayl?Topur4. 3ra rsura riocBsxdeHa
XO"lUqecTBeHHbIM
MeTOAaM
aHaJIUga
f e O J I O fH T I e C K H X
AaHHbIX,.
a_Hr4eHHopasAe,'ry HayK o 3etune, xorOpurl
B HacToflrqeeBpeMfl
H a 3 b r B a e r c f lr e o M a r e M a r u x o i i . o p u e H T a r { H r
KH}rfu-MeroAo.rrofaqecKat, T. e. <<KaK
HaAo Aenartu. Teopnn yAenrrercnMano BHHMa_
Hln ilO HeCiio,'rbKIIM nptit{IIHaN{. AeIO S TOM IITO MHOIHe I€Or'IOIH
c T p e M f T c t 6 r t r l n p a r t v t a T I I K a M r l I I I I O 3 T O N { y} l H T e p e C } ' i o T c f lp e 3 y n b tloJe3HbIX IIpoTaraMLr 6o.nrrue, qeM Teoplleft, a 6o"rlurHHcrBo
o6ocreopernqecKoro
coorBercrByloulefo
He
LIMeer
Bce
eue
ueAyp
qacH O B a H H r r .T e O p e r u u e c K L I . I O C T a T O q H Op a 3 p a 6 O T a H H b l e M e T O A b l
KoTopble
OfpaHl.IqeH!flx,
To ocHoBaHbI Ha cHr'lbHbIX CTaTIICTUqeCK[X
nptt IICC,'IeAoBaHtlI{reOJIOrllqeCKHX AaHHblX'
06bl,lt{o He BiJIitOJ'tHIlMbt
Xorq e KHrrre I{ 06cyx{Aalorcfl 3,'IeNIeHTapHbIeacIIeKrbI reopilH BepoffTHocreir u ottucL'IBaeTcfl 6o,'IblullHcTBo craTI'lCTHqeCKI.{XKpI'lTepHeB, BCe >Ke noApo6Hoe L{3,'IOX<eHAefeOCTarHcrI'lqecKoft TeopI'IH
npeAocraB,lff ercfl ApyrllM aBTOpaM.
B csqstt c reN{ rtro caMbte c!'Iox{Hble aHa.rtHTHqecKUe[poqeA]'pbl
Mo)KHO npe;craBIlrb Kaii nocJIeAoBare!tbHocrb orHoci{TeJIbHo llpocTbrx MaTerraTlrqecKHx AeiicTBHft, yaeJiIrM oco6oe BHlIMaHlle onepal{rrflM. 3ru onepaqHr.r 3aqacry}o BbIpa}Kalorct B TepMHHax MaTpuuuofi aJrre6pbl, qro B cBolo oqepeAb npuBeAer K paccMorpeHlIlo
3ror-o npeAr\IeTa.
llepnan h:areropnfl oxBarbtBaer Bce KJIaccbl 3aAaq, AJIfl l{oropbrx AaHHbre co6llpalorcfl HelpepblBHo IIo BpeMeHI'l H,'ll{ [o JIHH]IK.
K nefi orHocrrcfl saAaqlr aHaJILI3aBpeMeHHbtx ptAoB, crparl]rpaQtiuecxtix pa3pe3oB I{ nr{repnperalruIl rpaQHxoo. Bropan KarefoKoopAHpur o6r,e4rrHqer saAar{rI, )'sIIrblBslglqrl€ reorpaSttuecKlle
sarr,i sa6erc:ieHHiJ: KaprtIpoBaHHe, aHaJIrr3 floBepxHocrefi rpeHAa,
xpaflruur rr -{,p. HaKoHeu} rperbq I(arefopl.ir HMeer AeJIo c aHailwKJIaccHQI4Kal{uefi I,I llcc,,leroBaHI'I30M fpyIIII (x,racrep-aHa,lusolt),
eM BHyrpeHr{rrx cBfl3efi BHyTDH na6opos AaHHbIX, B KOTOpbIX IIOIOx e H r i e n p o 6 u H a K a p r e I . I J I I {n p o Q u J l e H e p a c c M a r p n B a e r c f l . 3 a A a qI{ H3yrieHtlf naJIeoHTod'IofHqecKLlx, feoxIIMaqecKHx AaHHbIx r{acTO
orHocflTcf ti 3TOri KarefoDlil.t.
Marepria.ri B KHI4re n3,IIo)KeH no npriuullny or npocrofo K cJIolKHOMy, np[qeM KaxAafl nocJleAylolllatl TeMa cTpol{Tctl Ha ocHoBe
rpeAbIAyrrIHx. TaK, BOrrpocbl MHO}KeCTBeHHOfiperpeCCUH, I'I3JIafaeHa pe3y,Ilbrarax, no'ryqeHHblx B r,r. 5 (cu.
ML,te B rJr. 6, OCHOBaHbT
riH. 2) [pnMeHr.rreJrbHo r( TpeHA-aHarlLl3y, KoTOpbIM B CBOI]OOtlepeAb
ilpelnecrByer orr.{caHHeHenrzHefiHoftperpeccnu (cu. rn. 4). OcH O B H a rur c r r o J l b 3 y e M a fI l] p H S T O MM a r e M a r H q e c K a f ni p o q e A v p a o n H MeroAoB peIIIeHHff cucreM ypaBrrecaHa B r.n. 3 npx rz3Jro)KeHHH
s l r i i . a c r a r r i c r r r l r e c K u eo c H o B b Ip e r p e c c H o H H o r oa H a , ' r r r 3 aB t r e p B b r e
paccMarpHBa.rlt{cbe r,r. 2. /{pyrHe Merolbr rr3r'rox(eHbr
fio aHa,'ioII,IIIHO'i CXCMC.
l l e p n a x r e M a , p a c c M o r p e l l H a q B 3 r o r i K H I l r e ,- 3 J r e N r e H T a p u o e
B crarllcruKy, a noc,'IeAHqt- Qaxroputtfi aHaJII,I3.
BBeAeHr4e
Mexay
roropofi rpe6yer HecKoJrb3TirMr.rTeMaMr.{fiponacrb, npeoAoJreHr.re
Kr.tx,'Ier H3yqeHIIr coorBercrByloulux KypcoB. fcHo, uro e oAHoii
KIIltfe Mbr He Mo)KeMocyuecrBllTb nepexoA or nepnoft TeMbI K rrocaeAHeft,He onycKafl ttpn 3roM sHaqnTetrbHofoMarepr{ana. B cBr3r.r
c oTI{M Mbr [oxeprBoBaJIH ocHoBaMHcrarr.rcrliqecKoftreopnn, Aeral0
TO,'lr,KOcoBep 111eHHoHe.riE rvrH M aTeM aTuqecKI.{X Onep aqufi , COXpaHfl fl
U yTOr{HeHI{tMI'I'KOTOyCOBepIXeHCTBOBaHHTML
BceMH
I,I
O6xonUylte,
CTaTHCT}lqeCKHenpOOCHOBHbIe
COnpoBOX{Aa}OTCn
orrr\.r11o6uqso
aJIropH-rYlI:u'l-o_{1ttln"B
u"rypot. Coxpaueuu @yu4auenra,llbHble
Mex(Ay pa3cooTHoIueHI{u
xa;riirrii BvA a1ailL6a, paccMOrpeHI.Ie
Hx
.ltrqHbrMrr KO,'IHqeCTBeHHbIMIIMeTOAaMH H IIpocTble ilpIIMepbi
3
a
A
a
r
{
'
p
e
u
e
H
H
H
ilp
' l r M e H e H H t lB
B 3ToM I'l3AaHIllt*' TaK KaK
nporparurra He npllBoAtrcs
Texctlt
rrr{rr cga6XeHbI I\4HorHe6u6nuoreK}I nporpaMM, [peAHagHaqeHHbIX
HaqtiHar c cynepKoMtiblorepoB H KoHlIafl Ha.r..rfl JIro6bIX 3BM,
coAep)Kar
6tt6luorexu
croJIbHbrMpr MIiKpOKaJIbIiy,IIflrOpaMI;1.3ru
rn6xHe,
flporpaMN{br, 3HaqHTe,'lbHo 6oJlee coBeplxeHHble i{ 6o'lee
lier"I ;Io6arr r.r3 nporpaMM, Koropylo MbI MofJIH 6lt npltnecrll B SToll
r;lrrrre. Orgaxo, rIT06r'I noMoqb qurarer'Ilo B oBrIIaAeHI,titnepcoHanbHbrM KOMnblOrepoM, K aHrJIHfiCr{OMy H3AaHH}O i(HIIrn npHJIO}KeHa
.irrcKeTa, r{a xoropofr 3anucaHbr rrpofpaMMbr e.rieveHrapHoii cTa'.LlCTLrKLl11 N{arpHqHOfi a"Ure6pU.
npeAHa3HaqeHa ,lJIf
,fl,ucXera
iiepcoHa,'rbHoro r{oNlnbrorepa cpuprrau IBM-PC
I.I coBMecTHMa c r\raiUfiHaMH, IrCrroJ'ib3ylounMU lroly'TqpHyrO
Onepaq}IoHH]rn
cIIcTeMy
-i!S - DOS. llo,ruan 6u6nworeKanpofpaMM 6onruruncrBarpoii.er,yp,o6cyx4eHurrx s erofi Kurlre, TaKX(eAocryrrHaA"rs 6o,rrrxrrHcrBatrepcoHaJrbHbrx
KoMrrbroTepoB;
uHQoptrauufl no 3ToM,v
:triBo.u,!
npIIBeAeHa
e llpunoxeunn.
Mu cqlrraeM, qro NieroAbl liorrl[qecrBeHHofo a*a$u3a B reo!'ro-.
irru Moryr 6srrt gecrua notegHblMl{ B HccJleAoBare,'rbcriofi
pa6ore:
r.'HHAaIOT He CTOJIbKO
HJIII nOATBep)KAeHHq
feo!'Io-.
AOKa3aTeJlbCTBa
i n q e c K H x t 1 4 n o r e 3 ,n u p a 6 o r a u H b t x L i H T y I { q u e f tc, x o " r b r ( o K p H T H q e c 1.Ceilccd'teAoBaHHe
flBJ'teHrrflH npoHr.rKHoBeHHe
B efo cyxlHocTb..
C6op aaHHbrx coorBercrByrourero KariecrBa H B AocraroqHoM Ko.:iuqecrBe A.its qe,reii qr.IcJieHHoroaHail:asa npr.rBoAr.trx 6o.tee no.nlioLIeH_HoMy
I.I3yqeHuroo6terra, rreM Apyf[e cnoco6u ltcc.rleAoBa-.
rnls. HecouneHHo, qro naJieHToJrof,TluareJrbHo HsMepffIorqnftcor, r l t o 6 p a : r q o B H e r { o r o p o r o o p r a H u 3 M a . M o T K e Tr ' r y q u e o r l e H r i T br p a l i l l l i b l e c r e c r B e H H o r oI I 3 M e H e H I l fIl' l 3 l ' l e p f l e M b lxxa p a K T e p t i c r L I Kq, e M :
rlc.loBeri, iioropltfi rrpocro riccd'reAyer
I,Ix. Toqgocrl u o6'beKTI4B-.
llocrb, rpe61'evar Ko,T[qecrBeHHofiuero4o,tornefi, MorKer orqacrrl
r ^ o \ { I r e H C i l p o B a rrbr H T Y u q r r r cu o n b I T , K o T o p b I e
attpa6arunaIoTCfl
:oia\'{r.r pa6oru. B ro xe BpeMa AHcrIHn,'rr.rHa,
Heo6xo;1,trMafl
rJrr;
l l i ' l l l o ' - l F l c t l l l t l i o J l l l t t c c ' r B C H H b t xI t c c . 1 e , 4 . o n a u t t i iy, c K o p f l e T
TBoprlggli,tt-t
l r ) c T , I t H a c T ) ' n J r e H I I e3 p e , ' I o c T Hy q e H o r o .
vl3MepeHrrfl rr aHarrH3 AaHHbrx MofyT rrpr.rBecTrrri BbtBoAaM,
He,
Bno,IiHe IIOHflTHL,IMH!'Ir.i OqeBHAHbIM nplr
HCnoJIb3OBaHI.iltApvfHx.
* B pyccxou
nepeeo.learoil K l r t l r H M L ' l c o q n n [ e n e c o o 6 p a s n u v n p n B e c T a n o n r
H a f l 3 b r K e OOPTPAH,
,rrc6esuo ilpeAocraB,'reHHbr€HdM iB:
r o p o v ( l l p u v e u .n e p . ) .
llble Tel\CTbl npOrpaMM
l,U
MeroAoB HccJreAobaHHfl.
MHofoNfepHbreMeroAbr, Ha[pl{Mep, Ilo3BorflIoT o6beAr.rr{flTbo6rexrrt B fpylrlbl, Koropble HaxoAffTctt B corJIacr.rHc [pr{Hrrrbrulr x.raccltQIzKaqHsMH,oAHaKo oHI.r Motyr yKa3arb Ha HeoxlrAaHHbrecoorHorrreHuqMexAy nepeMeHHul.tu.I4gor4a rpe6y,el,roeo6a'rcHeHne orofo Qaxra He Mo)Ker 6ltru uaiiAeso,
a B A p y f f i x c J r v r { a r x , u a o 6 o p o r , M o r y r B o 3 H H K a r bH o B b I er e o p H L I ,
Koropbntra HHaqe npene6pernn 6u.
Bo3Mo>r<uo,qro uau6onnuufi a$QeKT or Kor'rlrqecrBeuHbrxMeT o A o B 3 a K , r r n q a e r c qH e B u x c n o c o 6 H o c r H n o K a 3 a r b , r { T o B e p H o ,
a c K o p e e B T o M , q r o 6 u n o r ( a 3 a r b ,q r o H e B e p H o 3. r u M e r o A b rM o r y T
yKa3arb Ha HeAocraror{Hocrb AaHHbrx, o6unue g,onyureHnft,MaJroe
K o . n r r q e c r B oi t r $ o p n a u u u , u a x o r o p o r ? 6 a s u p y e r c r 6 o r n u u u c r e o
r e o r ' t o f r r q e c r i r r iXl c c r t e , ( o s a u t r r ?f .l p u n u H l r a r e r ' r b H o Mu 6 e c n p n c r p a cTIIOM aI{aJIlr3e N'iHOfi]efeo!'roffiqecKue BbIBoAbInpeBpail{aIOTCflB
H a 6 o p . l o r a A o r { } i n p e A [ o / r o ] x e u u f i , o c H o B a H H b t xH a o q e H b H e 3 H a qllt e,'lbHoM Ko.rlfiqecrBe AaIlHbIX, 6o,tltuaq qacrb KoropbIX LIMeer
rrpoTuBopeqr.rBVro
il Hesar\oHqeHuyrosopuy. Ec.nu 6u
feo,rofrrfl
6lr,ra excnepriMeHTarrbHoir
uayxoii, noAo6so xr.rMr4uu Qusure, r4e
ria6,rr.oAeulrfl\,ro)KHorrpoBeprrrb Ha otrblTe, To ynot\{flHyrbre [poruBopeqfiff MoxiHo 6u,ro 6tr ycrpaHr.rrb. OAsaxo Mbr lrMeeM Ae,lo c
o[ucarc,rrbHoii Hayxoli, H np[MeHeHile rorrHbrx KoJIHrIecrBeHHbIx
MeT o I o B q a c r o H a r o M n H a e r H a M o H e c o B e p l x e H c r e eu a 6 " ' r r c a a r e r e r 1 ,
KaKoBbINIUMbr lBrt{eMcn. B cauol{ Ae,rre,cK,'IoHHocrbK Hayr{HoMy
c K e I i T t i u r r 3 M ) ' - o . l H ar r 3 o n a c H o c r e r i ,x o r o p a f l q a c r o i t o . t c r e p c r a e r
reoMareMarrixoe. 14N,rqacro ceoficrBeHHa noAo3pHTer'rbHafl
r.r nporueo6opcrnyrcuar no3Hrlnrr rro orHolrreHrllo K ycraHoBuBlruMcg B
reor'IofaH rpaAHur.rflM.OAsaxo HaAo llpH3Harb, r{To raxofi qr.rHrl3M
3ar{acryro uMeer onpaBAaHHe. leo"lorn o6yuanrca
sa6.lrcreslrrc
o6pasoe H crpyKryp B npnpoAe. leolrareuaruqecKxe
MeroAbr
qro6u
06ec[eqfiBaror o6texrnBHocrb, ueo6xo4auyn,
ae6exart
cyulecrBoBaHHs rex o6pason, co3AaHI{e Koropblx olpaBAaHo roJrr,xo coo6paxeHrrsMr.ro6urero roprAKa.
TEOCTATI,ICTIIKA
Bce MeroAbl KoJrHr{ecrBeHHoro
reo,'tofaqecKoro aHaJrH3a,pacc M a r p r i B a e M s r ee e r o f i K H a r e , M o l K H o o r H e c r l i r ( p a s p f l A y c r a r i r c qeCKHX>>
qeKBa 3HCTaTIZCTII
THqecKIJX,UHOfAa <<
II Jtr4 <<np
oTocTaTI{cTIt
q
a
c
r
b
n
p
o
u
e
n
y
p
.
Bo,rrruaq
cKI]x>)
H X H e A O C T a T O q UpO
aSpa6oraua
H He Mo>Ner6trrl ilcfror'rr,3oBaHa
npn crporoii npoBepKe crarr.rcruqecKLIxfufrore3. Hn o4tttt H3 3TI{x MeroAoB HeJIb3flcrlnTarb aneKBarHo orBeqarculau o6qeii reopr.rH feoJror[qecKHx coBoKynnocreft.
OAsaxo, noAo6so crarucrrrqecKnM Kprlrepr.tflM,MeroAbI MareMarlrrlecKori reoJrofHH ocHoBaHbrHa [peAnocbrJrKe,qro utt$opmauuro o
MOX{HOnOnyqHTbB pe3yJIbraTe r.rCCJreAOBaHr4fl
flBJreHLit{
tr4anOftSnr6oprn, oro6paHuoft H3 3Haqr{re.nsHo6onlurero MHo}KecrBa norenqr.IanbHo Bo3Mo)KHbIxsa6lroAesHfi ugyqaerrroro flBreHr4rr.
L2
crpyKryp np11
P a c c v r o r p u u s a r a q Y K a p r H p o B a H H nr ' r y 6 u u u b l x
3roM AaHHbIe
npn
ne$rH'
I4syuaerrlue
no"a*u* lretropoN4eHlttt
ns cxeaxnn, pa:6pocaHHblx Ha HeKoropoii n'roulaAn
[oc,'IeAoBaTer'IbHocTbcrpautrpas_nqecKrlx fo",{t OnDOHlr3btBaroilIux
"putt."
EruHuquoe ua6,rrcAeuue rpeAcraB"Iqer co6orl a6coltor'
;r;;;;;;
S OAHOfiH3 CKBa'
HVro oTNleTKyKpoB"r[ fopH3oHTa' 3aMepeHHyI,O
tIucJIo cKBa;irru. Ecnlr 6or utt MorJIIznpo6ypurl HeorpaHIIqeHHOe
MHO)KSCTBO
6eCrOUeqUOe
nOnyqLITb
6U
,11HH,ro 3ro Ilo3BOJIIa.nO
Olua'
rop'3oHra'
xpon,ru
orMerl(H
AaHHofo
a6co,rrcruofi
.oir.po"
Kc s Aei1clenrelbnocrll MbI ofpanlzqesbl y>l<enpo6ypeuHuMl{ cKBa'
ec,,'iII3TO 6yAer onpaBAaHHO, npO6ypnn',t
}KHHaMlr rr, B03NlOll{HO,
qttCJIO
fIO sTIIM AaHHbIM MbI AOJIXAO1OIHITeJ'I6U61X.
He6o,'rbrloe
o6pasoM orrncarb xoHQurypaqHlo KpoBJII{rOpH3OHHbr Har4fi\.quruHr
Ta Me)K.{}' cKBaXLiHaMU.?ra 3Al.aqa aHalofnqHa CTaTHCTHqeCKOMV
AHAd'III3\" HO, B OTJIiIqNC OT CTATI{CTIIKI{' MbI HC MOXCM
COCTA-
rnrl orr6opoqgutl irJIaH H!li{ KoHTponu_poBarb cfioco6, KoropblM
HMeroruriecflAaHHbIe6u.nu non,v,IeHH.OAHaKo MbI MoxeM ucnoJlbKaprHpoBaHHfl, KOTOpbIeTeCHO
3OBaTb N{ero.1,bIKoJIuqecTBeHHOrO
[pHMbrKaroT K crar]]crriqecKl{M npoueaypaM, Aaxe B cJlyqae ecnn
He BCe QOplta.nluue crarHcTllqecKHe rpe6oBaHHs.
Bbrfro,'rHeHbr
B npoilreono,'roxHocrb 3Tolly MoxHo paccMorperb raKx{e ropi{o-npoxo.1,iecnuep a6orbi }r npou,eccgKcfinyaraqufi MecropoxAenus.
B reqenrie N,rHorrrxJer fopubre riH)KeHepblI{ reoJlor[ paspa6atu,1 6ypeHltr u IpoBOAI{JII.I
Ba.rrfi;fera.{bHbre cxeNrsr onpo6ona:Hr4f..
crarrrcrrrr{ecxnri asa.rlr: ua6,rrcAesuft. B nocneAHee BpeMq qrrcJlo
n r - 6 l a x a q r r r ?n o r e o p a n o n p o 6 o n a n u a x a r a c r p o Q H q e c x r . r p a c r e r .
Hx anropu, co3AaBan reoperl.rqecxyrc 6aey AJIn rrpnN(eHeHuxQopNia,'rbHbrxcrarllcTI{qecKLIx KpuTepHeB, npeAJIafatoT A,'tfl orII{caHI,rfl
rr3r,reHqriBocrrrcoAep)KaHrrir pyau prA cJIoxHbrx crarHcrrrqecKHX
pacrpere,'reHr.iri.Tau, rA€ reor'rofir KoHrponnpyrcr o16op npo6, oulr
Mofyr 6orcrpo ou6uparr, yao6nyrc cncreMy orpa6orxn. tr4x ycnex
e paspa6orr{ax MecropoxAeslrfi cBuAereJrbcrByero ca!'re 3Tux MeTOJ.OB.
K co;xaneHnlo, 6orb[rriHcrBo feoJrofoB BbrHvx(reHbl6parl cnon
npo6u ro,rrbKo raM, fAe aro Bo3MoxHo. ,fl,auHsre ro
neQrRnul,r
.rro6H o16poczrt
ciiBalKHHaN{cJIIIrIIKor,{46porn AJIfl Toro,
Hx
ro"rrbKofroroMy, qro oHlt He yKJIaAbIBanrcg B cxeMy onpo6oeanan.
llareoHTo,'Iofll BbIHV)KAeHbIAoBolrbcrBoBarbcfl ficKonaeMbIMII ocraTKaMr{ opfaHr43MoB,B3tTbrMrr lis o6HaxeHHrr, KoToprie, 6yAyun
lorpe6euHnMr.r, HHKorAa 6u ne 6sr.na AocryriHbr rrccJreAoBaHr{ro.
[1po6u Mofyr 6trrt raxxe oro6paHu ?r3 ar]HKaJrbunxqacreft nurll\i3HBoB,BcKpbrrbrx B ecrecrBeusux o6saxeHr.rflx. Ilpo6u r{s KopHeBbrxqacrefi Tex xe ren 6esHaAexHo rny6oKo cKpbrrbr s setuuofi
rope. Pe4rH cJlyqan, KotAa B oAHoM Mecre co6pano oqeHb Mnoro
qaHHbrx. tlaute ux 6Hsaer HeAocraroqHo. Haun
ua6.un4enna,
cBg3aHHIIec HccJIeAoBaHIzeM
3eu.nu, cJrr{IrrKoMAoporn, .rro6rr It[4H
:MoxHo 6u.no npeHe6peur. Mu Ao.nxsH sHqcHaib, KaKHe cBeAe.
l3
HIit MbI MOXieM r.1g Hrrx tr3BJreqb,
H3)'rturb
HHfi H BbrqB[Tb HMeroxlaecs reHAeHq].jli.
HeAocTaTKH STHX cBe,[e_
ony6nrixonaHuuepa6orbr nocBrurenbrBorrpocaMn.[a.
.,-__{Ho."a
HlrpoBaHHs
crar'crrr{ecKorosKCrep'MeHra. cpaa"-""1-"u"oo"ree
riHrepecHareoJrorliqecKarr
qacrb xurirrr
_fpaQ$nfca, ; xoropcri
paccMarpriBaercq
Bonpoco B.i*rffHurr
er,r60pni.r'nu
pL=pbrarbr 'cnonb3oBaHr.rfl
crarircrHrrecKExxpureproe. Xora riprrioapo,fpH0$urca Bsqrbr 13 ocaAoqHorineriroroirrn, ," ;.r{eMeroAbrnpHMeHH_
paBHoti
MbI
B
lteoe II K rnvrrrv- n^.r
nprInIlCbIBaIOTcfl qllCJIeHHbIe sHaqe'
CnCcO6, KOropbIM sa6"rnAenttrc
Iloc,leAFIflfl B cBolo oqepeAb
It3llepeHut?.
IIIKaJIy
,*i"", onp"aeJter
C
.rnnererfleT TIIII aHafiil3:1. i':OTOpbIftN{O}KeT 6Strl OCyUSCTBJIeH
;;,i;;';;;"srrrrr.
ri:uepeHuii, rpHrleM
Cyucc,rB].erqerbrpe rrrKar'rbI
qe1{ npeAblAylqag, u 6O.nee
KairiAafl nrcJelyrcqiiq 6l;ee TOrIHa,
- 3 T o H O M L i H a , ' I b H aut n o p q A K o B a f l
n
3
e
[
e
p
a
o
l
g
r6r$opvarrrena.
KaI(
1r.,i,'rr,,, B KOTOpbIXlI3t'IepeHits nOrrpOCTVii"racCltSuUHpyIOTCg
n
o
c
J
IeLK
a
T
e
f
o
p
l
l
l
l
.
A
B
e
.
4
p
)
'
f
A
p
y
f
a
. n E e 8 3 : i x N l H Oi l c K ! ' I I O l l a m u ? l e
- flBJIgI'OTCtl
oTHouIeHHIl
II
lIIKa"]a
rlHTepBa,'Ib[iafl
Hfie IIrKaJrbr
K i . t r ip a 3 T e t { , q r o u i ' l c 6 u q H o c q l r T a e ! \ {< < l I 3 M e p e H H f M HT>a>K, K a K
oHtr gari,rioolelorB ce6e ltst"tepeHuflBe,'lnquHnpl'l3HaKa.
HolrlrrrIa,tIlilafluKa,'In tt.:rtepeHati ocHoBaHa ua x,raccuQI'IKaqHIl
I(arefopHll
na6.nlo-resli't so esaltlriHc iiali,lloqarculHe Apyf Apyra
O6OsuaqeHbI
NIOf]'T
6Hrs
I':arerOp]ll.l
UBeStlI
Tlt11a.
i).IrrHariOBot-O
ral,pr, Ha1rprr:Iep,Kpacust;1, se,reuuii, ro,rv6oft unu cIrMB9JIaMI.{
Orgaxo qlICr'laMofyr I{crIoJIb3oBarbttrl't riiIC.l1aMI{,
.(Arr, ..Brr, <.:C>>,
r. e. \{oxer He cyxrecrBoBarb
IIAeHrttQttlii;opst,
riar(
3fl npocro
cocruouretrits <<2sABoe So,ttue 1>>tt"'ill <<56o.nuue 4>. I(naccu0no c T a T l i o Bn o r u I I a M - n p H M e p H o M U H a J I b H b I X
riaur{fl iicr.:onae\{bIX
'rr:uepeui.rii. OrHecelrlte tlAI{t{r IIcKoirae\{bix ocrarKoB x 6paxnonoq , a ) { ,a r p } - f r r x - K l i p H l { c t { t e s ! I H t i q e f o H e f o B o p l r r o 6 o r H o c n 're,]r,Hor,{3HaqeHUI{lIJil.IBe,liilr{HHe
Tex II Apyfl4x.
Moxgo cocqrirarb qrrr"To sa6.nroresnft xaxAoro rLIrIa B HoMHna;runoli crrcrel,ren 3areM r.rcloJIb3oBarbAJIfl rlx o6pa6orKH KaKHel r r 6 o u e u a p a N r e r p r r q e c K r .Li e: p l r r e p L r u I. ( n a c c H q e c x u i i n p H M e p A a H HLr.{ groro rrilla, r(orcplrii rttu 6yAeu qacro paccMarpl4Barb HLI)r{e,- norB,rreHHerep6a
n"'rrr peur(H rtpta 6pocauIaH MoHerbI.
flpriuepon reo.lofrrqecriorir 3riBuBaJreHra3THx AaHHbrxMoxer cnyrr(HTbnoflEJreHrre3epeH Ill'ra-Bofo Ix|IaTa HJILIKBapua BAonb llepec e ' - { e H t r gu r r x $ a . K n a p u r r i ] o " { e s o f i u r u a i o S p a 3 v r c r A B e B 3 a [ M H o
{rcK,]rcqarcturreoIHa ApJrir}r:tiiaTeropl{u, KoTopble HeJ.tL3qHHKaKHNt
lr6p
p aHxI-{poBarb.
' a:olt oa\rbrcJreHHo
1 4 s o r : . r p a u > N u p - o n r <svl 6 " r r c r e u l l f t u o x i r o n p o B e c r r r H e p a p x H qecr(rzMcnoco6or,r. llf li.l;:a rBepAocrlr Mooca - qerxllft npnMep
nopngrioecii utr.a.rllr. Xorn iaeplocrb r\{rrHepaJloB
B rIIKaJIe,HMerou{eii Aecnli, Je.reriuri (rr ! ;o l0), r'se,ruurrBaercflc rroBbrrrreHr.reM
pasrr-r1)aHra, lla3Hocru Me>r{AvcccerHHIlIrr ypoBHrMri pa3Jrr.rqHbr.
,rrre MeiriAy a6co,rnrnoii rBe.r)Aocrbroa,rrMa3a (paur g)
6or'rb[Je,
qert{ pa3,[rrqrre\reN<rv Bcer/rirocraJrbHbIMII paHraMLr (or 0
ao 9).
t \ u a n o r l r q s o l r e r a l r o p $ r r r l e c r { H ef l o p o A b r M o x H o p a H x ( r r p o B a r b r r o
c r e r i e H r r I ' r e r a l i o p Q l r 3 M a ,i i o r o p a f l o r p a x { a e r t r H T e H c u B H o c r M
b erat ' t c p $ r r u e c x c r o I r 3 M e H 3 s r i a .O A s a x o I I e p e x o l b l M e ) K 4 v p a 3 H b r M r I
TeM"\'plBHar'riiHe orpax(anr elnriofi 3aKoHoilIepHo'Jrurr3N{eHeHufl
reparypbr rr AaB.rreHr{ff.
I(ari u AJrr AaHHbIX HollrlHarnsoitr rfiKa,.rbr, xonrrqecrgenguft
a H a r ' r H 3r r o p a A K o B b r xH 3 M e p e H H i t O r p a H l r u e u f J r a B H b r M o 6 p a s o u
TloIcqeroM rlllcd'taHaS,rrcAegiritn pa:,rtruHblx cocrofluugx. OAgaro
i".,[xt,:";3]i:,"?"?..J-1;
$.'llT^*i,'05if,"01##:"y,.JTf
gs"IeHI'rI1, ocHoBaHHyIo
Ha Iiciro,'IL'3oBaHlilr
cril'I'IicrrirrecKHx Mero-
r'{o)K'opeKor{eHAoBarb
reM, Kro rpr rpoBereHrir feo,rrorH191-.
-!"
r{ecKoro
sKCnepHMeHTa
r{oxer oc},il{ecrBxricrporuri KoHrpo,rrb
Har.
nPOL(eccov
B3flTHfl.npo6. Tax Kari srn Boilpocbr BMeCTe
c Bbrrrr]cJ,rHnporDaM-\{oii no4po6rio ocBeiueHbi
B i{H}.iie fpuQQurca
u
ran]r{e
[a],
'ol59l?r.ia"
u , r a H a p o a a Hfp"6pi,r.u
ira -axcnepu
, u OsAprrNa
eHros
[b], nru H€
6 y a e l r K a c a r b "c q
g eror? KHafe.
Bn'tecro 3Toro Mbr ocraHoBliMcs Ha 6o"ree
cJroxHbrx cr.iryarl'rx,
Kor,qa cxeMa Bsflru_fl
("ul6o c,r,r.uariHcr,nnai io_np06
HAXOAI,ITCflBHC HAIIICTO KOHTPOJI'I.
O T H A X O 3 A M E ' C H C , . q"e"eaen"ro;
TO HCKOHTrentsofi
ponupyeMbrri
excneprrnreHr
(i. e. rarcii axcnepuu""r,'n"p" noro_
poM l.rccd'IeAoBare!'IbHe Moxier
B,r'fiffTb Ha Mecra
B3gr'rrl
ripo6),
o6uqso BbrBorr'rr Hac 3a par{r{H xraccliqecxorri
crarricr'rir{.
3ro.
o6,racrl <<KBa3HCTa
o?;".'#' "'ll.
rrreHrrn 6op' u,o oliu'##;:''1;l#
;:
I il'i^
"
6esoronopouso.
B r3g1_9_0"r.*
"#'".
"t:tt";
Bro,rHe
paepa6o_
TaHHbrx KpHTepr.reB
""-.u*..r"yer
npoBepKrr fnnore3,
H ,lyquee, Ha qTo Mbr Mox{eM HaAeqrbcfl,- 3ro rlcrroJrr,3oBaHHe
li3BecTHbrx nporleAyp BO
BcrroMorare'rbrrblxr{edrtx' npri{reM
B KOHeqHoMao"re
pe[eHHg npeAocTaB,'Ifl
eTcq ucc/IeloBaTe..rrc.
"or60p
C H C T E M bII' 3 M E P E H 1 4 N
Ko,raqecrneHHbreMeToAbIB reo.riofriii rpe6vrcr
6o,tee r,,iy6oxux
3HaHHli, qel{ noBepxig:T:ra cBel1eHus,
rcnoJrb3yeMbrenpil pa6ore
c KoMIrbloTepaMu.Tax xax BbIBoJbr,noJyrreHHLIe
c no\,{oxlblo K."IIkqECTBCHHbIX MCTOI.OB,
OCHOBAHbI XOrg
6IT qACTIIgHO HA BC!'I,,qI,IHAX,.
B pesyJrbrare I{3Mepeuufi, reoJ]or
l9JryqeHHbrx
npeACTaBJ'IeHr.re
O npkpOAe Cucrert quc,
AoJrxeH
'Merr,
usuepeu'x.
vqerJfi,r.lr.ovr"r"o' i.T;r", iilT:tJ T."":#J;:
noHr'rMarb feoJIOr',qecliat? cnnrtc,rt
3a'HCbiBaeMbIx nepeMeHHbix,
HO
TaK)Ke qyBcrBoBarb MareMarriqecxr.tri
cMbrar,l nctrodlrb3yeMbIX IXKaJI
zsuepennfi. 3ra reua
cJolKHaq,- qeM M.xier [oKa3arbc,
_60,'Iee
Ha
nepnur?Bs.,rrsA.Ee noApo6nou
u oHo,,raoifa6 Hfl nprrBe,1eHbr
B Kunre r{epuiueuaa paryrua
"uno*.lye
IrJlreo,rorlau.-.,1#.ropo"u
-'- " '\!'!\aa L
BonpocaorpaxeHa B crarbe fpraqiqrarch
ibt.
Heuepenne- gro npunucdnai,moe
qncro, orpa_
xarcqee BenHqHHyHrrH 3HaqeHHeuexoropofi
"a.onroAeHnrc
;up;;;.;.
,HKH_
t4
l5
MbI MOX{eMTarix{e paccMoTperb crroco6, hoTopbll\r }'noprAoqeHb}
pa3JrHqHbrenopffAKoBbrer{Jraccbr,c.leA}'}olll}re oAuH 3a ApyfHn"
JTO AeJ'laeTCfl,HaIIpllN,{ep,IlpI{ Onpe.lerl€,H}iltTOI.C),IIMeIOTJI]I COcrofHLrt, llofiBr'IflrorullecrrHeo6btqHoe qticflo pa3, TeHAeHIIHIoc.']eAOBaTb3a Ha[6o,1ee lrJILrHarIMeHeeqacTbtMHcocTogHI{gMIInopgJ,.
r(oBoii turia,rrbr.
I4Hrep o anrH afi III rta,Ta - IIIKaTa, r.xe AJIIIHa [ocjIe,II,oBare!'tbHb]x
E H r e p B a J r o Br i o c r o a H H a_. H a u 6 o . , r e ep a c l t p o c r p a s e u H t r r i n p r . r M e -p
TeMnep^a^r-ypHafl
uria.[a. Vee,'rltqeuaere\lfieperypbr B HHTepBa.[eor
l 0 a o 2 0 o C r o , r H o r a K o e x ( e , K a K v s e r l i i . i e g l l el a - e x t t , 1 1 0 ; 1 2 0 . C "
o A H a x o H H T e p B a n b H a tI T I K a J I aH e r r l l e e r e c r e c r s e H r i b r o H y J l s , r r r r l t
To!ri(u, fAe BeJrHqrdHa
rrBJrrrercflHecyx{ecrB,vrouleri.
Taxlttrl o6pasov,
oTplilIaTe,'rbHbiereMnepaTi/pbr- 3To ilpocTo TeMriepaTvpbr HHxe
yc,'ronHofo uynr. IiauaJbnail roqria orc{lel.it A,rff crorpaAycsori
l l r K a J I b I6 t r , r a n u 6 p a H a I I p o f i 3 B o r t b t { o]!i a } i r o l l r i a 3 a M e p 3 a H i } f fB o 4u. B a6co,rrcrsoft uKad're KeflteriHa roqlia 0 K o6o:riaqaer rel,!|Iepary-py' ripri rioropoli ocraHas,'rHBaerce Mo,,leriylrspHoeABrr;'I(er i r ' r e .H u l i a x a f l T e M I ] e p a r y p a H e M C i r i e r 6 r , r r u s r r x < e ' s r o r ? . T a x l r M
o6paeolr, uriaJia Ke"rneaHa rBJfiercg He uHTepBer.ar,soli
ruxa,ror?.
a uria,ror'r orgorneHLtfi
LUxarra o'rHourerrniir.iMeeTrr€ To.rbrrcroauHaKoBbIenpnpaureHHfi
}ICXAY
OTACJIbHbIM]i IPAAAqI,IflMH,
HC ]I JtCl'IlHHYIO
HYNCBYIO TOI]KY.
I,IsuepeHrzx A,rrr.rHbr
orHocrrcr K sroMy rnry. A,rrzira i au" e,l"HHrIbrBABoe rpeBocxoArrr Ar'trlHy B oiHv eAUHrrrly.He cyulecrryer
o6reKros Hy.rrenoii AJrurHbr.O6rqenpHHaro, rrro orpuu,are,trutrx
He uoxer 6sIft,.
,u,JIHH
lllxa,ra orHouesHi'r- HarrBbrcuat $opua usuepeuHr?.C ee noMOXIbIO MO)KHO OCYXIECTBHTb BCC TIINb]
MEHTAMH' -
qe'$
<Vro ltoitcer 6oLro oepaHu!rckHee,
aaod ue^eepnau6auuttx o 38t'l u HausHAn HAOe?fiOA tO.1lqUTb gTOqHenHOe HA-
X,TATCMATI]qECKI{XH CTATH-
craqecriIrx onepaqnii. Xors riHrepBaJbHafl rrriiaJra reoperuqecKn
MeHee uuQopuaraBHa, qeM rlrKadraorHo[reHnli, g.na uHoiltx qe.reft
o6e uoryr 6lrrs trcno.lb3oBaHbrc onuHatioBbrMvcriexoM. Eo.ulnaxcTBo reoJ'rofrrqecKuxu:nepeHar? ocyurecrBr'rreris sa rrrKaJreorHoueuuii, rloroMy_trTo oHH cocrogr us lrelrepeutrfi .u,arII,IHbI,
o6rer,ta.
Maccbr l,t r. n. B cnelyrcqux rJraBax Mbr npe)KAe scero 6yAeM KaCATbC' AHAJIH3AIIHTepBa,'IbHbIx
H oTHocIITeJIbHbIX
AaHHbIx. Mex4y
HI.tMr.IHe 6yaer AeJrarbcs HuKaKoro pa3JnlqHt; 6orree rofo, Hx
MOI{HOCOBMeCTHO
I{cnorb3oBarb npri peueHHA OAsOfilt rot? x{e 3a_
4aur. Taroro poAa nplrMep Bcrpeqaercfl B aHaJra3enogeDxHocreil
rpeHAa' r4e QyHnrrr'rflMoxer 6Hrl Hsr\.{epeHa
no uKad're orHo[JeHl'ui, ror4a KaK reofpaQuuecxue rioopAlrHarbr, rBJrgrourHecffapryNO HHTCPSA,'IIHOI? IXKA,IC, TAK I(AK HAIIAJIO KOOPAI]HAT.
Hofi cetrn Mox{Ho ou6part
cylqecrBylourne
Bblpaxa}or
Hocrb, B Het{oropou npu6.ltlxeunH
cooTHolueHHfHocHoBaHbI'KaK3ToIlplIHflTocI]ItTaTb'HaHeno|pe.
qTo Bbtr{Hc'IIHTe,'lbHble N!ail-lHHbI
3aMerul,l,
ul1,{brx lpoueAypax.
aQQexrlteHOe CpeAcrBo 3aII]rH'
O
q
e
H
b
K
a
K
r
{
c
f
i
o
J
r
b
3
O
B
a
T
b
]{O}KHO
q1ICJISHHbIx
MaccHBOB C TOqHOCTbig,Il.O
Barilrfl. Tax, npeACTaBJleHl.le
yl\'1bI MHCillX ,'IlOnOAaB"IfleT
O6HqHO
3HaKOB
BOCbXIIIAeCflTIIqHbIX
feo.uortt,{ecKi{ft
cxerrrr{IIil3\{.
npupoAuliir
yrBepxAaeT
Hx
u
-teii
H IlepenO.'IHeH-tori.{aA, IrCnOiIb3ylgqttii lrareuaTHr{eciilie Tep}'lIlllbI
B
C
eX, iipOile He,
{
r
t
C
,
'
I
e
H
H
b
t
t
{
}
I
O
T
f
i
}
;
r
l
l
B
a
e
T
O
6
o
t
u
H
O
AaHHStltU,
Htiii
]IHo|HxI{pI,iTHKoB'HAa)KeTe'KTonoHI.IMaeTe|olIMo;'IieTj.aTb
r r O l s C H e s l i s , A e J I a I o T 3 r O H a H e n p O Q e c c H o H a d i l b H o 1y{p O B H e . I 4 r a x "
yr'1bI npeAllo".]riaP},1oI}
'I AoKJiaA' II lipI,1TI4KanpoxoA'iT cIiBC3b
I4Cc!'Ie;IOBareJlff
OnaCHoCTb
.lJfl
nau6OnlUas
OAgarO
a]'!,HTOpI.iH.
tlN{erb .I'e'i'J C
[p]IxoAIITCfi
iraxoArrrcfl B HeM CaMON{. ECnn euy
nepeCTa'ib
I(OX(eT
OH
MaIltlliiOii,
itOOCTBeHHOtiBlt,{IlC,'i['re.nlsOii
L p i l l r 4 q e c l i r i a H a J I 1 4 3 l . l p O B a TCbB O I I A a H H b I e I i M e T O A b I H X H H T ( : p i i i l e , e BIIAg HI{qef6 3a iipet i i r I H g , 3 a r U n l l O r U S I t p O n a t r H U U t t u C d I a N { HH
K canpufira
oH
Moxer
,ra6oparopHI'I,
i.e,raMr.I BbIqlicJiI{T'eJILriofi
Bcerra HMerb B BIIAy
libl\I Hei'IenblN{ 3aKd'IIoqeHIztM' Heo6xoAuuo
l3peqeHrre, O6lt.IHO IlMercUIeeCf Ha CTeHaX KaXAOIO BbIqHC,IIITe,'IbilOfO UeHTpa: <(tlTOnOCeetUb' iO U IIOX(He[I],>>.
HaqHHaiIacl c oAsoti IrHrarbI, saxoHqliNl ee Apyroii.
frasa
c,'IoBa 6uIril ocrasr'IeHbI Ha MoelI cro"ie Hel{3BecrHbIN{
C.'le.lynque
i..plrTLrKoM.
>.
no,/teoHoB
cKoepeweuue?
M a i i o p A . r e t c c u . r pf L , [ e
CNIZCOKTI,iTEPATYPbI
deiinitions and ihe1. ClrurchmanC. lY/. and.P. Ratooslt,eds.,^N{easuremeut:
o r i e s :J o h n W i l e y a n d S o n s ,I n c . , N e w Y o r k , 1 9 5 9 , 2 7 4p .
2. Fislrcr R. A. The expansionol statistics:Jour. Ro1'alSlaiistical Soc., 1953,
seriesA, l16, p. l-6.
3. Grif fitis "/. C. Some aspectsof measurementin tire geosciences:Pennsl,ll a n i a S t a t e U n i v . M i n e r a l I n d u s t r i e s ,1 9 6 0 , 2 9 ,n o . 4 , p . 1 , 4 , 5 , 8 .
4 . G r i f f i t h s . I . C . S c i e n t i f i cm e t h o d i n a n a l l s i s - o l s e d i m e n l sM c G r a r v - H i l l ,
IIrt., New York, 1967,508 p. I4ueercr pyccxuii nepeBo,t:lput\$urc.{cr. Havvnue
MeroabrlrccJ'reAoBagrlfl
ocaAoqHbrxnopo,l. t\i\.,Mup, 1971.
npon3Bonbno.
JIOXHAq YBEPEHHOCTb
pry rnaay l\4o)Kno 6u.no 6u 3aKonqr{rb
cneAyroqr.rM npeAy_
npex<AeHr..rerra.
flpnrrtensfl MaTeMaTL{qecKHeMeTOAbr, MO)KHo sany_
Tarbct B Tex n3 HHx' Koropble HMeIoT Hel{y]o [pereH3Hro Ha roql6
Ceeelcxr.r
2- 2 0 1
f.rasa 2
3JI EillE HTAP HAfl CTATI{ CTI,tKA
Hecnrorpx Ha ro, qro He[oCpeACTBeHHbre
gaS,rroAeuur feoJrofoB
ofpaHrrqeHbi notsepxHocrnrc selrgori Kopbr, c r4x rloMourbro rrbrraIorct BbtrcHurb nprrpoLy tApa rr NlaHTuHa
,
Tat(xe r,ry6rtHHux
c,roeB eeN{uoii xopu. Kpolre rofo, lisyqarorcfl npoqeccbl esorrordr.rur
J e M J r r { rT a r i H e ,x a i i r o p o o 6 p a 3 o B a H H ei l p a 3 B H T H ef i O H T t r H e H T oH
t se, AocrraeNrbreJ,JrRnpffN,rofouccJieAoBaHHs.Ec.na He cqlrrarb acrDo_
HoMoB, ro He ci'u{ecrByer Apyroii fpynrbr yqeHbrx, 6o.nee yaanbn_
HbIX or npeA\'lera IICC,leroBaHrtflIt rlluelourrrx N{eHbIxHeBo3r\Io)KHocrr gKCllepriN,relrtrpoBarb
Ha.r{HlM, qel{ feoJlorll. feo,rorug B 3Haqtre.nluoir creileHrrocraercfl nayxoit, ocuosaHHor?
ua ua6lrc4euu-
9X, B qACTHOCTII HA TAI(HX, IiOTOPbIE COACPX(AT 6O,TIUYIO
AOJIIO HC.
o n p e r e " r e H r { o c r r rB
. c e r r s r r c 3 T H r { C T a r l c f i r r ( e r I p e A H a 3 H a q e HH
Of p a r b o i p o l ' r r j \ ' i o l r c J b g n o A o 6 H H : i r r c c J l e A o B a u l r n .H
t : .e c N r o r o q H a
To' qro IIepBoHaqaxbHorepMI,rH <<crarlicrlrKa>>
il\{er'r orHolueHHe K
r r o A c q e T Vr l l t c r t o B b r xx a p a K l e p i l c T i r K , r i a K , H a I I p r i : r e p , I I p r r r r f p e
B
6 e f i c 6 c n , c e i i q a c o H a n p t r M e H f l e r c qr A J r f l a H a , , n r 3 aA a H H_.rLau*
b r x ,o c o Sesuo B yc,roBrrflx Heonpe-re,rreirHocrrr.crarucrrrqe&ira
cKpbITo I{,111fiBHo Bcrperla}orcfi 'ra\{, fAe corepirilrrcfl 3.iieMeHT
c,ryqarinocrri. leolorrr AoJrlKHbrriiderb npeACTaBreHrie o6 orgx
3all.aqe-\II o Tex crarllcrliqectilrr Irplier.rilx,rioropbre I]o3Bo,'rrrror
I]x
peuarb.
qllcJarlll or 0 ao f
Vqeuue o6uqso Bblpaxarcr BepoflrHocrb
q x c , r o u n P o l r e H r o eo r 0 A O 1 0 0 v 0 ' E c n n M b T
t l , i t r l3 K B H B a J e H T H b I M
yoeAO)KAfl 3aBTpa 0, ltlt a6co',rrcruo
ioBoprir'1. qro BepoETHOCTb
MbI foecJIlI
oAUaxo
riro
He
6yAer'
3aBTpa.
AolKAs
lcHbl B ToNr,
yBepeHbl B ToMn
r,rlrrlNI.r{To BepottrHocrb ,ll,oxAa 1, MH a6conrcrrio
r
a
BepoarHocrb, Bbrpa)KeHHar KIrIl cnoco6ou'
?la.t.
:,5' ;;*t;
o npruaonoAb6nn co6ltrus' A6colrorsoft
roJoSsa -"r".p*A."nd
...aepcHuOirrrcoOTBeTcTeyOrxpairHlle 3Haqe'Ilfl l',iia.rlbl' a pa3JIHq- n p o l { e } K y r o u u u e ' H a n p i l } 1 e p ' e c " t nr { b l
soii crencull lBepeuHocill
(a sHauur'
q
r
o
B e p o f l r H o c r bA o x A f l 3 a B r p . a p a a u a l i 2
loBoprr\{,
'ro>re 1/2), ltli
cBOtO
BblpaiKaelu
He
6.vAer,
ti roro, "iro JolKAfl
MbI
bc"III
ToqKV 3peHIIfi c Hal'IMeHbuleficreneullo )Bepe.HIlocru' qro
rofo,
n'oiliAfi
(a
3!4
paBHa
rrro
BepoflrHocrb .l,o>x!,tl
foBoDrir.r,
HeyBepeHHocrll'
i l r 6 ' \ - . l c r , I ' 1 ) , I ' r u r B b l p a ; K a e Ml 4 e H b u y l o c r e n e H b
TO|O'
raii ]iali BepofTHOCTlAoxaq n 3 pa:a 6o"rr'ue BepotTHOCTl'I
ri'io .lo;Ii,ltt ue 6-vAer,
nOfiBiIelIIlf .loiKif llofvT 6ltrl ocHauil or{eHrirrBepoflTHOCTtr
H o B a H L IH a l t H o f l l x r ] l a x r o p a x , a r a l i T l i e n a c v 6 r ' e t i r i l B g b l x o q y u e no3Bc'[faitn.x. .\1r,t, oJHario, 6yaen'l llcfioJb3oBarl' .u.p1'roi'lnoJXoA'
TatBJIeHIIq'
noBe!,eHilfl
npe/(ulecTByIOIIIero
ocHoBaHrru
Ha
rculrii
6
1
'
,1,ya
n
o
B
e
J
,
e
H
t
i
e
e
f
o
r , . o r o , r i a n l ) n \ { e l l , r i a K n o r o . r . a ,n p e A B r r J . e T b
q
e
p
e
3
<
<
o
r
H
ocllB
e
p
o
t
r
H
o
c
r
l
l
I
i
o
i
l
p
c
l
A
e
J
e
l
l
u
l
o
u r c , a t .T a , ' o i r l o ; t x o , r
Te.']bHL]eqaCToTbI>>i{FITyi]TuBHonpIleN{,'IeNireo,Iora}IH'TaKKaK3Ta
l i o } [ t e x u t r ' r e c H o c B r 3 a H a c [ o H f T I I e M O A H O p O A H O C TBn . H e K O T O pbr-\ c.rYqatx 6slsalor rIoJie3HbIApyrfie [oAXoAbI K o[peAereHl{Io
e e p o n r H o c r H ,I I O N { b IU e 6 v A e l t H a H r r x o c T a H a B r ' l l l B a T b CTfal ,K K a K
l KHIlrax Ouruepa [10] ii Qou Nlx:eca
r - , u r rn o : p o 6 H o u 3 . r o i K e H b B
[ 3 1.J
BEPO'THOCTb
Hecuorpt Ha ro, qro c}'x{ecrlt),er lrHoro pyKoBoAcrB rro
reop r i r l n e p o R t H O C r e i rn, p e A c T a B J r e r c f l i r o r e 3 H b r r . l0 c r a H o B U , r . b c f l
Ha
ToM, t.aK oflpere,rflercrr Beporrr{oe co6urlre qepe3 Bo3Mo)xHoe.
I'
JIFJOOM'IBJ'ICi]IIII CYIIICCTBYCT HEI{OTOI]OE MHO}KECTBO
(UUOrlA
6ecxoHeuuoe) rJ03Mox*rbrxIrcxoAoB, iioropbre Haxo!,rrcff B
BepogruoctHoir 3aBficHMOCrLr,
OIIrrcbrBaeuoiiqacrorori BCTpeqaeMocrH.
AHaalt:apyg BeporrHocrr.r 3Tr.ix ricxoAoB, r{oiriHo ouen}rrb
rroBeAe_
HHe H3)'qaemoro o6rexra v.ilH co6urr.rl B ilpolxd'ror{rr,ru 6yAyuelr.
Kaxauft Hs Hac rr[.{eer rrHT}'rrrrrBr]oe
npeAcraBJreHHeo BeporrH o c r t r . H a n p H v e p , e c , r r rB
r a c c n p o c a r , 6 1 , , t e r r H 3 a B r p a A o ) K A b ,B b i
orBerure c HeJioroporl crereHbro yBepcHHocru, qro
AoxAt ,rli6o
Bo3MoxieH,utri6o Heao:tvro)r{eit,
It,Tn B peAKoN{cr,IyrJae,rITo A9;KAr-,
6yael o6ssare,rlno, rJrr, Hao6opcr, qro Ao)Kxfl HaBeprrrrKa
rre 6r.ner. OnHuu us cnoco6oB Bbrpa;^rieHrrs
Haueil y".p."n'o-i;".";;";;
cf nHC,'IoBafl1lrKaJa, HattprrMep,npoueHTHafl.
lc.rru MbI rro,rrafaer.r,
qro BeporTHocrb Tofo, rrro nofiAer
Ao)r(Ab 30%, ro BeporrHocrb
roro, sro AoxAfl ue 6yAer, paana T00ls.
l8
florrrteo c ,l.olK.[,eMflBrrfercr AllcliperrlblM' T:ll( KaK 3Aecb
: o r n : o u o j r i e r 6 t i r t , a M o x i e r t t g e 6 r , l r l . K n a c C l i q e c t i u i l4 l l c x p e r rir,rii npirvep, npHBoAIntltrieo BCex pylioBoICrBax r]o reopilr Bei ir,.li,t.o-ttic 6;Op g l r u o c r c i i , c n a ' : a u c 6 p o c a u r r c \ t n i ) a B r r i t b t i c . rt tf o
y
c
x
o
A
a
:
t
i
o
r
o
p
L
, r cp a B H o B e p o f l T i l l , l .
p
e
u
(
a
,
r
{
r
e
p
6
a a H l r e r r \ { e e T, t B a
I l o a r o l t y B e p o f l r H o c r bB b I [ a A e H I i ar e p 6 a p a B H a 1 2 . 3 t o , x o H e q H O ,
c s H a q a e r i t e r o , q r o B K a x < A o r {B T o p o N {6 p o c a H t t i r n l t n a 4 e ' r r e p 6 ,
i ctiopee ro, tITo npII Aocraroqgo 6ortltuoxl ql'lc're6pocaHrlft npua-r,,rrisure,rlHo
no,'IoBuHa ltcxoAoB- rep6t,t. Epocanite MoHerbIoIieHb xoporuttit rpIiNIep Ar'Ifl I'l"l,IIrccrpaIIrltroilpeAer'leHHflBepotrllocTii. co6urue ul\{eer ABa IlcxoAa, Ii gAHH Ii3 HI1X oofl3are,'ibHo
l\'.ler II\rerb Mecro; cc,'rlt He )IqllrblBarL' oqeHb rla.ryrc BepotlrHocrb
':CTO,
I I T O ] \ { O H C T A M O } K C T B C T A T b P C 6 P O I T ' T ,T O B C C f J A
BbINAAET
ilIT"
,.c rep6, ,'rli6o peufiia.
Ha ocHose cxeMbl 6pocaHul MoHerbI Mo)Kllo nocrpouTb HHTeilecHlro nocreAoBare,'Ibnocrb neporruocreft. Ec,ru BepoflTHocrb
I r b r n a A e H u sr e p 6 a p a B H a l 1 2 , r o B e p o r r H o c r b B b I n a A e H I ' I f lA B y x
rcp6on ilpr.rAByx 6pocaunrx paBHa l12.l12:114. !,anee Bepoarl t o c r b B b r r r a A e H I . I qr p e x r e p 6 o n n p n r p e x 6 p o c a H r n x p a B u a
2'
19,
'112.112.1
2:l/8.
O 6 o c H o B a H H ee r o r ? n p o r p e c c n r . rn p o c r o e . B n e p _
i B o M 6 p o c a H r r . rB e p o f l r H o c r bB b r i l a l e H r { r r e p 6 a l l 2 . T a x r ( a K
ricxoA
B T O p O f o6 p o c a n u a H e 3 a B r i c l r o r n e p B o f o , H a u r r B o 3 M o ) K H O C T I i
n o J r y q r { r br e p 6 n o B r o p o M 6 p o c a H l l u c H o B a l 1 2 . l l o r c 6 H o 3 r o M y ,
T p e r b e 6 p o c a H r r eH e s a B H C r r ro r n p e l b r A \ . u l r . { xt,r B e p o a r H o c r b
Bbr_
r r a A e u r i f lr e p 6 a B r p e r b e M 6 p o c a H l r u c n o s a p a B H a i 1 2 . L 4 r u n ,
aepoflTIiOCTbBbrnaAeHlif rpex rep60B COCTetB.rrfler
<<t.to,10BI]HV
ro.{oB H H b l I I O J ' l O B I . { H b) >
l.
qro re[epb HaN{ H}'x(Ho oflpeAe,rrrrrb
llpelnoroxr,M,
tsepoflrH O C r bB b r n a . l , e H r .rioq. r r b r i oo A H o r o r e p 6 a e r p e x 6 p o c a s u s x .
hne_
I o r c f l c J r e A ) ' r o u r l rB
e o 3 r { o ) K H b rlei c x o A b r ( f _ r e p 6 ; ' p _ p e u r r i a ) :
ftr
fPf
Pfl'
.llt
Ii-Rp1 iPi]f l
PPP
ll]rPi
B cxo6rta.r 83firEr te rrorr6uHaqlrir, rtoropbre
)..t,oB,,rerBop,qlor
jraluirilI rpe6onauUalvl,T. e. oHrr
co.lep)r(aT.r.o,rtbr(o
o;rru rep6.' Tar<
K a r i I I M e e r c R B p a s , : i t . l s r , r xt i o l r 6 l r u a q r r i i , B C p o r ] T H o t r o
nonVu"",r"
T o " r b i i oo , [ , H o f or e p 6 a n p l r r p e x 6 p o c a n r r a x p a e H a 3 , / g .
i ro.{yqeHHoe HaL'{lrqlrc.[o ''p.ACTaBJ]Aerco60ri {,,cr-ro
Bo3N,ro)Kn u x r i o u 6 l . r u a q n i rr r 3 r p e x n o o i l r r o l i \ , . O 6 o 6 u a "
uroi
n1r,,no"p,
t v l o x i H oo n p e A e . r r ' r r br l i l c J r oe o : r t o x H t t - i c o , r e t a H l r i ru 3
/2 3,1e\reHTOB
lo r. 3ro qr4c,'IocuNrBo,{r.rqecxu
lrso6parxaercfl Tar{ ( )
Moxuo
r paBHo
A o r i a 3 a r l . q T o r r l { c . [ o c o q e r a n t t u t t s t z 3,rleMeHTOB no
lt.
(2.1)
;1,''"
Bclcx,ruqarentguli srrax o6ogsaqaet
u n! ecrb rrpoQairroprta,r,
::l3BeAeHHe
n nOC!,leAOBaTe,lbHbrx
qe,tbrx ql:l Ce,II:
n!:1.2.3...n.
3 H a , r e H n 3e ! p a a H o3 . 2 . 1 : 6 .
(2.2)
cKoJbKo
Toe6veuue rou6ugaqu B3tlrbl e cKo6xu' Haxoseil''
rpI{
coAepxar
6pocaHnxx
rpex
nprz
uorub**ot* tiolt6ttHaquri
a?
neP6
't
3!
, - 3 ' 23' l' 2
i 3 t _(l) -1.
\si
3l(s-3)l
'{tzcro 0! paBHose sv.rtrc,a l.
.lauerrltrl, tlro no olpeAenenuro
6pocaHIlflx He
Hatioseq, ocraerct Bo3Mo)KHocrb'KorAa rIpH r p e x
qficJlo raKI{x riou6r.rnaqHfi 6ylet
H
rep6a,
HII
oAHofo
BbtraAaer
ptiBHO
3'2'l -1.
3l
-1 3 \ _o
)
l
l
(
3'2'l)
o!(3\o/
BO3T a r , u M O 6 p a s o * r ,n p l . { T p e x 6 p o c a u H n x M O H e T bLI I M e e T C of fA H a
rloBo3MoxHocrIJ
TpI'I
rep6a,
oAHoro
HH
He
no.[yqllrb
MoxHocrb
[o,'IyqHTb ABa rep6a H oJ.Ha
nyquTb oauH rep6, Tpu BO3MOX(HOCTil
eosMoxuocrr, no;lyullrb rpu rep6a. Sror pesy'{b-Tar Mox{Ho ll3o6 -p a s n r r r p a S l l u e c x l l ,K a K 3 T o c A e n a H on a p l l c . 2 ' l '
O6ntee qprcJlo BO3MOiKHbIXIICXOAOB,
Mu Mo)t(eM IOACTTUTaTb
a
3
a
T e M n p e O 6 p a s O n a T bq a C T O T 6IIj o f B J I e K O T O D OD
e a B H OB O C b M I i ,
u l l s b r A e . r r o u r , r xc o 6 t r r u r i e e e p o n r H o c r r r . 1 4 u a q e f o B o p s , B e p o q r H O C r bo r c y r c r B r r r r c p 6 o r f i p r r r p e x 6 p o c a u t i l x , r . e . B e p o f i r H o c T b
BbrnaAeHHflo.lnoit xortl6vgair,ull cpeAll BocbMH Bo3Mo)KHbIX'paBHa
1 i 8 . f l p e o 6 p a 3 y e N 1r e r l e p b r H c r o r p a M M y p H c . . . 2l., o r x . n a r b l B a q I l o
BepTlKa"ribHOitOCtr BMSCTOrIliCrTaxOlr6UgaqUl'tnepOnrHOCTIICOOTBeT(-rB].OUlix c06oltlli. Mu noJIyqIlM AucKperHoe pacnpele,{eHi.re
n e p c o t t t o c ' t e f i 'r p a Q l r x K o r o p o r o n p e A c r a B " I e HH a - p i l c ' 2 ' 2 ' O 6 a a s
cyMMa Bcex Bepoflrllocreii paBHa B/B el,ru 1- TaNuu o6pa3oM,
c b 6 o t t r e , 3 a K , E I o q a l o u { e e cBt t T o l u , q r o r a x a g - , r H 6 o x o l ' l 6 u g a q n g
n p n T p e x 6 p o c a u l t t t x o c y q e c r B l l T c q , f l B J I f l e r c t IA o c r o B e p H s r v ' f p a -
B u a r u e f i3 a A a q e
t
:
\o
./ 3 \, :
\l/
3:
l!(3_l)r-
3.2.1
l.(:,1)
6
-,"
^
2
20
_
- s.2.t _
- 6_e- "
2 . t( r )
z
PPP
IfPfI
Pfp
iprri
PPf-
2
F
o
a
F
o
q
o
T. e- rlMeeTcf rpri Bo3Mox(HbieKoM6riHaqHH, coAepxaque
OAI,1H
rep6. Tax xe BbrrrrrcrnM qncro Bo3MoxrHbrx*orOirnurl,lri,
coAepx(atrllrx 4na rep6a:
3l
/3)_
\ 2 1 2 t ( 3- 2 ) t
fff
IffPl
rPP
0,375
s
J
o
o
1
c.25C
0,1?5
O
cO
s
J
U
UIL9
'l
*
{i
fi
0,0c0
.a?
t l Nc l o
reP6oa
Psc. 2.1. 3aurpuxonaHuafl o6.racts
ua rpaQnxe noKa3blBaer quc,'ro pa3JhrrHbtx cnoco6os no,qyqeHr.rfl3araHHofo qficra rep6oe npn rpex 6poca-
0123
Ll l4ctc
i-eP60B
Pnc. 2.2. !,r.icrperuoe pac[peAeneHlre,
noKa3brBaro[lee
BepoqrHocrbnonyqeHlrfl
3a,laHHorovrlcaa rep6on npr rpex 6pocaHllfx
MoHerbl
HTT'X MOHCTbI
2l
pjcnleAgreH-HflxapaKrepa3yerBepoerHocrb
f11 _Ayrnur.ru
Bbrna.ueHas
Naxori-nu6osa4auHoiixorrl6Hu aqar.r.
6pocaHr.rflMoHeru o6,ra4aer rrerbrpbMsoco6eH_
,,^^?_1:-1:p"nreHr
HOCTfMH:
l) n xax4oM r.rcrrbrraHnn
(nnu 6pocauua) uMeercrr
rorTbKo .{,B?
Bo3Mo)iHbrx
rrcxona (ua:oneu Hx <<ycnex>>
rr,rH <<Hey4ava>>)
;
2) HCxoEKaX(AOro
HCnbrTaHHrr
He 3aBHCHTOr IIpeAbrlvul[x rrcxo.loB;
3) neporrnocrbycnexa H C M C H q C T C g
OT IiCIIbITAHI,IS
Ii iICNbITA-
HIIIO;
3l "1tj:::::::
qncnopa3.
^""_"iop"rorcr3aAaHHoe
l';xo,T'i"'i1'",::3.:il"?.':t;^;;';;;;;;;ffJ;)'ria3.,HHo1{v
sKcnepr{Me'ra,
HasbrB
aercq 6aHoiurlin' nl
;;;;p;;1
;l;tfl J""u
JCHHCM,
,\rfiHyrb npe,4cr{a3aHrreBeposrHocrr{
yclex a npu 6yp."n;',,;$;;_
Hbrx ri ra3oBbrx
nepennc,reHurrx ebrrre xapaKre"*:lT_T^._,{erbrpe
prrcnrr{H noJ'r)KHbrnpe4ronararrba
clrpaBeAJrrrBbrMr.r:
AofiyrueHLrE
noro6soro poAa r{a)Kyrcq Har.i60,ree
npHeMreMbrMHflprr rrcrroJrb3'_
BaHHIrMeTOAa<nHxot't Koruni.i)>
npH pa3Belfie B cpaBHrrre,,rbHo
Ma_
.ilo 143yqeHHolr6accefiHe. C,reaoiarenrrro,
6uHol.lira,ryino"'pu"npa_
qacro
Ie,'IeHIIe
HCnOrb3yeTCflI,Tfl flpexcK a3allrl
pe3],JrbTaroe6V_
peHHfl Ha rpanrlue o6,racru
uJru 3a np"oanu*n Konrleccrrrr.
B npegnonox{eHu* o cnpaBeA,,r,,r"o'.r.n
ou"onruuinJio, pr"np._
IeJreHHfl i<axAsrfi
npnMeHeHr{flMeroAa <<AlrxofiKotrrKH>)
\ I o l x e r 6 n r m K r ' l a c_pe:ynlrai
c n Q i i q r r p o a anna 6 o r a r
< o r r i p b r r r r e > (>< J r c n e x > )
.ra6o
rax r\.crancr,iaxusa (d.),A;";;t.
ffi!;;uli..lono,.
rbITaHIl-q nperno"IafaroTcfl
He3aBuctrl,trrlrn, T. e. ycnex
lr,rtr
J;J,aqa s oirHofi cr{Ba)KI,IHe He B,rrHger
B Apyroir
cr\Bax{r.r'e._l5r;
;;"y*;;r;. "'rJ;;Xi"tffi
n._
He-
"i]:
T{HOTHM O6CTORTC.ISCTBAM,
TAK KAK OTI{PbiTHE O6ITqHO
B,lIIflCT HA
pe3y,'brarl,I
IIccdlie4oBaHHq cr'IeAyroI,.HX
cr{Ba}KrH.
,'oqg,Teulre
ro_
C J I C I O B A T E , T I b H O C T } I' ' Y C T b I X
CN'AXiUH TAKX{C NPI]BOAI,T
I{ II3MCHCHI,}O
lrporpaMMbr
":Xl::::,
p a 3 B e A K r . r . )H. a x o u e u , 6 a H o v r u a , l r r , H o e
pacilpeAeJIeHHc
OXA3bIBAETCfi IIOAXOAflIII]]M'
ECJIII
qHC,lO
QTTr<CAPONAHHOE
CKBAX{iIH
6y4er npo6ypeuo B/-l!_oueccepo.n,i4n,
HJtr4B rerrenue errrHrlqHoro
r e p n o r a B p e M e H r .(rH a n p a u e p , 6roArxersoro ulrx"la
), aril,roropo.o
npoBeAeHO
npofHo3r{poeaHHe.
Ja BepoqrHocrb p orKp-blr'g ue@rruoro
rr,rrrJra3oBoro r\,r€cropo)KAeHHrrMeroAoM <<Auxor?
Ko[Il{k)) ]
IrIflpoKo rrcrroJrb3)relvrbre
B rrpoN{b[r].reHHocr]r o."o:nl:-1-l]aIorcff
ycrex6yp
euua,
io.opu,.6una'na6.,r;fl?1i";niXtil::iTil"#,;
B aHa"'Iofr{qHbrxpefrroHax, un,
aHarofrrq'bre orHOUreHr,",nirnyoa"Hbte rioMnaHr4,s,Mw,
AeJlaIoqI.IMll o{€HKH,-HIH x(e npocro
cy6tex_
r'BHbre aHa,rof'qHhre xapaKrepHcruKH.
l{.nr onpegd;;;;
""po"r_
oae'n
n
o;"* ov!t np.ilnX"f.;r,tJf."fi'ff'fi1Tr-r'r
"'p" "tao
",in
22
qe-
l ) BepoflTriocrb <(yclrexa>>6ypenna cKBa]KllHbl o6o:gaqslt
pe3 p,
2) neporruocrt < < H e y A a q l l6>y>p e H l r a o 6 o : s a q n u u e p e : l - p , 3) nepoaruocruTO|O, qTO B pe3y,[bTaTenocJ'leA0eare'rtUorO6yBce oKaxyrcr
f e H H f l t z c K B a ) K l i i {MeronoM <<Azxot'iI(oulliu)>
e
c
r
b
MH,
P:
nycrbl-
(l -p)";
4) eeponruocrt Toro, rrro n-r npo6ltpeHHarcKBaxHHa oKa>Kernpe4uAyx{llx cKBaMuHoKaxyrcr
C n n p O . I , ) ' l i r i l B H O rf li 'p u r r e M n - l
n,vcrblMl'I,paBHa
P:(1-p)n-tp;
g
5 ) e e p o a r n o c T b n o s B J r e H u qO A t r o i ' {n p o A y l ( r l l B H O i tc x S a x u H H
n cKBa)KlrH,npo6ypenHblx N{eTOAOU<<Altxoir
nocJleaoBaTeJrbHOcrrr
ecTb
I(oluKI,I>>,
P:n(l-P)'-tP;
TaKKat{[poA,vKTIIBHoftuoxeroKa3arbcflt:ro6ani]3/1cl(Baxl'lH;
6) eeponruocrb roro, vro 6yAer npo6ypeuo /u-r n)'crtlx cliBaxuH, 3a KoTopbIr{il ilocJIeAyeTr npoA}'l(TIlBHblX'eCTb
P:
(l-P)"-'P';
fiycr.brx cKBa)KriH[i r [poAyKrllBHbIX cKBaxiliH
n
cnoco6aMII,ltJIH, r{ro 3iiBIiBar'IeHTHo'
Moryr 6urr nu6paHtt (
)
nl
p a s d ' I I I q H b I Mcl zu o c o 6 a l t t t . T a x , B e p o f l T H o c r bTOto, qro
( n - r \ t .r i cpeAI{ N C I ( B A ) K H H
KoIlIi(H>>
B nporpaMMe 6ypennn MeroAoM <<.ry.rixoit
t o r y q H N l r n p o A y K r i l B H b l x p, a B H a
p:
.. nt
(2.3)
. , ; ( l _ p ) " - ,p ' .
(n-r):r:
7) olnaro
n-r
3ro - $opuy"ra 6rscraHa;rtHoro pacnpeAeJlenllfl, 3a'r,arcu,as Bepon ' f i t o c ' I ' b r i o . r l y q e H i r qr y c i l e x o B B n o c l e A o B a T e I L I I O C T i l n H e 3 a B I I C f i ll.-iibrranufi, eepofrHocrb yclexa B IiaxAoM ii3 l{oropblx paB,^,ib1.x
Ha p.
(2.3) lvro;^r{HorroHriMarb KaK ypaBHeHIle, Koropoe
Pasei{crso
l,rox(er 6urr peueno, T. e. Moxer 6ttrt onpeg,eJleuaBeposrHocrb
rrosBJreHtrfirro6oir saAaHHoii tiona6uuaqnH ycnexoB I.i HeyAaI{ npH
; r r o 6 o n r3 a A a H H o NTr I I I C J IIez c l l t r a H u i i u s a A a u n o t ?B e p o q r H o c r u . S r t t
a'Jpor'r'Hocruyxe BbtqlicJleHblIl sara6y.ulipoBaHblA!'Is MHo|LIXKoMSrrHai{rrrin, r il p. Vcnonnzyx gro ypaBHeHI{e}tJlt't ony6.nuronauslte ra6,ruqbr, TaIiHe,KaK, HaIIpllltep, ra6nHqbl B KHllfe XanuAa
[ 1 5 ] , r r , r o x H oA a r b o r B e r H a & r H o r n eB o f l p o c b l .H a n p t t v e p , t t p e A l t o qTo MbI XoTI,IMOIIpeAe,lllrb BepoflTHocrll, coorBeTCTByIO"{o)KItM,
u { r l e n p o r p a M M e p a 3 B e A [ ( HB M a , ' i o u 3 y q e H s o u6 a c c e f i H e , c o A e p ] K a -
23
--
ycflex
IqeM ntTb CXBaxtIitH,npHLIeMorHO[IeHHe,XapaKTepI.r3yIOUee
l
0
%
.
B
e
p
.
o
f
l
r
H
o
c
rrbo f o '
KaxoBa
B e r O M p e f H o H e ,p a B H o n p u M e p H o
He no'
gro BCs nporpaMMa
vlt
H
rloJlHocrblo
6esycneuHofi
$1:;1€T
-oAitofi
npo,4yKrHBHoiicl{Ba}KHHlt?Taxoit pe3.v,Israr Haur.r
,'r),'quNr
3bIBaeTCfl
nOlTHbIM KpaXOM
nO
A"'IbHOC BbIP A)KCIIH C COACPiKIIT
n:5;
p:._
't-
OqeBIIAHL'IM rIpHrIIlHaM,
C"'IEAYIOuIUC qJICHbI
H
6rlilr.rl'tlt-
p:0,10;
r:0;
l u ; . o , t o o . ( 1 - o , l o ) {a
':
t.o,g[i': l. t.o,b9i:tr ,,lij.
roro, qro B pc3\)',lbTere pa3Bc.qlol He ^6^i.lel rio.rirqeBeDogrlccrb
Ho HHIiaKrtx ilpoAvt{TI'{BHbIx cliBa,'KIIH' paBna noqrll 600/0. ECJIq lOnlrig OAHa CI;BillKltHa OIia)lieTgff IlpO!,yliTl4BHCII, TC elg
M O r y T O K , V n a r b C s B C e 3 a r p a r b l B f i p o u e c c e p a 3 B e r : l K H .l \ a l i o B a B e pOSTHOCTbTO|O, IITO OAHa CI{BaiI(IIHa OKa)KeTCfl npOAVIiltlBr'ioit B
npoqecce Pa3BeAI{ll c IIflTbio cxnaxiitnavlt?
p : 1 5 ) . 0 . 1 0 ' . 1 10- .-1 0 t-' - q . . g , 1 g . r t , 9 0: a; ' 0 , 1 0 . 0 , 6 5 r - i - - O , l i l r .
' .I I
4'.ll
I4cno.nrsyn nu6o 6uHoMIiaJIbHoeypaBHeHHe nu,6o ra6lnuy
6uHol,rua.nr,HoropactrpeAeJIeHHfi,Mo>xno safirg BepoqrHocru BCex
IIgXOAOBB IIpofpaMMe 6ypennl c 11ffrbloCKBaiKnH;lltfI.l'
BO3Mox{HbIX
O H u n p e 4 c r a B , t e H l lu a p n c . 2 . 3 .
0,60[
ocHoBHbIeAoIIv3aAarlax' B KoropbIX
B 4pyrux npaKruqecKltx
6urr ncnOltb3oBaHbl
ynurrnnbrx BbI[Ie, Moryr
sr,eHHf orr,ruqHbro,
ileAeneHlit' fl perno;to'
l:;;;;;;;;i:l{^,g:.
Ha'MepeBaerlpYil' e AilcKperHbre
qro iLono'opu'BeJoqHafl xoM'.aHI'Ifl
npeA'
xnnt, HanpHMep,
6accefige',
I'i3VqeHHOM
Ma'Iio
noJlfl B
cro"lbxo
cg cTi(pbiTb auu nouot"
lpo6ypHTb
H nuo,ttptuuttcn
'o,lefaeMoM naptnt*i'"HblM'
uro6bl Aocrliqb eror
noipeOye"o
Itro Arfl sTofo
311-::to'
.liBr),Klitt, cKoJIbKo
BepoqrHocTb Toro'
,rc.'tu. MuI Mox(eM
roro xax 6y'
"tt'iteti""'b
pa3Ber'oqxu*'Jtluu*"" {o
i i o r p e 6 y e r cs 2 , 3 , 4 . . ' , i o n
Aoil'\/cMoxtio
-y*o"'o'
cKBa>KIIHu'
a"Jipo'i'yxrusHblx.
ler o6napy*."o
Koroptil^e- 6t'uti't
xe
re
or'
rrlriJ, qro rpe6yercn-"a'"o"i""o
pacnpeAereHl'Iq' IicKrloqag
AJIfl 8""o*"'no*loro
He tB"Ifl'
flel,reqI'Ic,leHbl
renepb
I(oropoe
yc'rosue'
Hoc.qiueecsn '"tny ii-nurauriir
o"'
uee r aKoMv
ercrBvIo
"" t iJl;'"'11""?Xtlou.nl"lll.ll'il ilLcoorB6ugotvtlianlHblM'
I'{ ero
o'p'uarerbHblM
3 l{c[ep]lMeHr.,"
oilpeAeJIeHHe-6uHolunallHoro
"u'o'ulerca
ottDe.[.ereHlnaou"no^-nanouunaer
ilpllN{epe' p ecrb -BeporrflpeAblAyurer"r
qI.ICro <<ycre'
,u.npeAe;lenuq. I(ax H B
cxnaxutrlr r'r r ecrb
qrlcrlo
nocri uossJleHl{tr;;;;i;""!rori
HcnbIraHHH'
oLsaxo n'
;;;;*""-^
uro 6y'
xoB)> rI.lIrI npooyntit'Jfo1;'
Toro'
nafirn *eponi*toctb
tox"o
r
He saAaHo. Buecro
cAeJIaHo
6yAer
uell
p-aHlure'
"o'o
cKBaxlIH
HMeer
aer lpo6ypeHo .r nyt"o'*
o"no*ua.llluoe pacnpeAereHl'le
orrpltrnil' orp"uuiJni"ot
BIIA
(2.1)
p:('+'t-r)rt-nl'n
0 . 59
I
I
r\{exAyrlly--.vpi::" " i:x x3:" ";l "?:.l?iJ ]
3ar,rer.u c:xoAcrBo
t;il ;;;a' ;e;1i.u': ": "
i
;;11,"';T,
I,sof
lliliril;'
"d;il;;)'
I
oonuvrv
, 0,40l-
^i3::'1yi
r-* i::t%:;
6st'o l-:"
vcrexoNt'
";cKBaxLIH'
AoJIxHa
BIIAe:
BIIA.:
cJIeAyIoueM
B crleAyloueM
"oo||fii""nnotx
npeAcraBi'Irb B
(2.4) tont"o
uox<no npeAcraBi'Irb
ii.+i'
p:
3i
('+
(r -
_ p), p..
":,1)rl fl
(2.5)
l)! tl
:l
; o,3o
i-RI
f lpe.4noraran,qrou9P9,"tn-9:1"-.y:.:::u'.:,",o;""tJ,t:"';:#ii-#i;
-
,o":."3,"#;1,"""J;
";;J;:i";;","i6v''1""1^L"l::X"."":u1'i,of
npo'p-1Y
iff *" "'.o
""#u#'.';;fi
l{'};;
i3
Y.1..
:..*?y
-'-1"i
3r*'.a
ru.%T:
ax#
cxe
"'iu"o"I
u nx""
n,
*', oov
"#" " L1,"Jp.;1;#;"
b-l
col
o,2o
iI
I
0,r0
r
;ilt
;",?,tH
B e p o e r H O C r bp a B H a
:
012345
'
'i7:
i-*
l
' i ' o , 9 o o ' 0 , 1 01' -' 1 ' o , o- l o , o l '
l:0,
\.{HC'lO rlCnexOB
3aAalouleeBeposrHocrb ycnexa B npoll]lMPuc. 2.3. ,Il,ucxperuoepacnpeAe,'leHlle,
ue 6ypeHun nqrn cxsaxuH rtpll yctoBl'l]I' rITo BepotrHocrb yc[exa pauua 100/6
9d,
""
p _ ( 2 + o - l ) ! . ( l _ 0 , 1 0 ) 0 . 0 , 1 0: 2
(2- l)l ol
I
I
0 ,0 0 L
",i
uue'
n p o f p a M M a M H6ypeuua,
BeooqrHocrll, cBfl3aHublec ApylIrMlI
HAHTH AHAJIOII.tqHbIM
loT DA3II-IqHbIC
IIHCJIA CKBAXI'IH'
H HX MO}I(HO
25
o6pa3oM.BepoarHocrb roro, r{ro Ar'rsAocrr.rxeHttrr
}'cnexa B AByx
HcnbITaHHfl..r
rpe6yglss rtqrb criBar(HH,paBHa
p-
( 2 + 3 - l ) . ( l - 0 , 1 0 ) . . 0 , 1:0 '
+ . 0 , 7 1 9 .-0' , -1:)0l ','c 2 g .
(2- l):3!
1.6
B u q H c , r e H g b l eB e p o g r H o c r HH H 3 K HI r o r o M y , q r o o H I r c B r 3 a H b rc B o 3 MO)r{HOCrbro
rroflB"rreHrrs
AByx npoAyKTriBHbrxH B TorrHocrn l; nycT b I X C K B a l K l t Hf.l o , r e s H e ep a c c M o r p e r b p a c n p e f e , r e H r r eB e p o r r H o c r r t
Toro, qro 6o.nee # cKBa)KLrHAo,rI)KHo6urs tpo6\-ilcrro fo
roro
KaK IIeJIb' cocroslqafl B notIBJIeHI'IH
/' [poAyKTIiBHbir ctiea;xttH, 6yAeT AOCTltfHyra.3ry BepoflTHocrb Mo)KHOno,rysilTb, ec,;rr cHaqaJra
Ilocrpourb
pacflpe.leJreHrre
B Ky.orpr{rlarenbHoe 6usorr.ruHa.nbHoe
-roro,
t',ty.narnnrioflQopue, Aaroqee BepoqrHocTb
.lro 6yAer AocrufHyro JBa ycnexa npu 6ypeHult (x*r rrJru \reHee cxna>raH),,
KaK aro ltso6paxeuo Ha pltc. 2.4. Btl,ruttf .{,3r'rceKa)KAyroH3 grnx
BeporrHocreft us 1,Q nolyvuN{ xeJraeMoe pacilpeAeJrenueBeporruocreli (puc. 2.5). orpuqareJrbHoe
pacnpeAeJreHHe
.6uHor,rHa,rlHoe
O y A e r p a c c M o r p e H oc H o B a e r . , 1 .5 , r A e c e r o n o M o u l b r o 6 1 , 4 e r
o l l u c a H a B a x { H a q M o A e , / r bp a c n p e A e J r e H r r ro q e K B n p o c r p a H c r B e "
I4lrerorcq u Apyrne AucKperHbrepaclpeAeJreuua, r-oropbre npn_
MeHgIOTCflB npaKTIiqecKHx 3aAar{ax, aHa!,IofHqHbIXT€N{,1,rls 9|It1_
c a H r r s r i o r o p b r x r r c n o J l b 3 y e r c s6 u s o l f i r a J l b H o ep a c n p e A e r e u l r e . T a KoBo, HanpriMep, pacnpeAeJreHHeflyaccona, r;oropoe c,rre.{yer r.ic_
[oJIbSOBarb BMecro 6nuonflra"rrHofo, ecJrfi p, BepofiTHoCTbycnexa.
o l r e H 6 N I a , r a . l I ) t a c c o u o B c r { o ep a c n p e A e , ' r e H } rpea c c \ r a r p u B a e r c R L 1
r.r. 4, r1e oHo ripnMeHeHoK awanizy peAr{HXi,ry.iariuux co6ursri
B O B p e M e H H ( : e u , r e r p x c e u u i t w n u u y n x a u u u e c K i l X r r 3 r v r e H e u u f i )r,i
B rJ. 5, oHo ucro,yrb3oBaHo4na nocipoeuna uo4e.neit o6beKToB.
c,ryuairuo pa3MerqeHHbrx n npocrpancroe. leouerpHvecxoe pac_
IIpeAe.neHrre,fBr'rflIouIeecfi qacTHbrM c,ryqaeM oTprirlareJrbHoro
6]t,
HoMHar'lbHof
o' I{cloJIb3yercfl B Tex cJlyqaflx, KofAa LIHTepec HanpaB"IeH Ha qilcJ.lollcnuraHHt?, IlpeAlxccrByrouru.xnepBoMy yc[exy.
llo.qu Hov u a rbHoe p acnpeAerreHue- ero odooureu"e'ol,
aJrbH
o.
ro pacnpeAe"'reHriflua c,ryuari, KorAa uMeercfl 60.ree
"o'"H
B3aHMHc
AByx
HcKJrr.qaiourrx HcxoAoB 3KC[epHMeHra. 3rH
Bonpocbl rx'poxo
npeACTiB,reHHS 60,'ilrulrHcrBe KHH| rro reopal] BepoflTHocTefi,
rarinx, r(ali KHvtru llapsena u.nr Aua
[3].
IJAX.HbII\{ CBOHCTBOM BCCX
YNOM'HYTbIX
B'IITE
,AHCKPCTHbIX
ACnpeAe,rreHHr?
rBJrsercflTo, qro neporiuocrb ycnexa ocraercflP noctosHHofiB npoqecceucnuragr.rfi.B craracra,.e paccMarpr.iBarorcg
npocrbresKcnepuMeHrbr,
gtr6opxgli I so:spaqeHReM,
Ha3brBaelrsre
B IiOTOpbr-\3TO yC.rrOBIic
crpofo Bbrlo,'IHeHo. Harr60,ree'rttnHqirslfi
g K c f l e p x r { e H rr a K o r o p o A a M o ) r { H on p o B e c r u
c yprroti, stnorH€HHoji
r ( p a c u b r \ r r rr i 6 e u r u u H u a p a r r r r ; e c , ' l r . u
r ay.ra,{ au6HpaeTcn oAHg
Iuap, To BepOsTHocTbTofo, qTo oH 6yA_erKpacHb]M,paBHa
OTHOIITeHHrOqlrc,rraTaKr.txuapoB B ypHe x o6rqeuy qHCJy uapoB.
Ec.nu
3areM 3ror rxap Bo3Bpauaerc, B ypHy, To npollenrs6e
orHorrezo
1,00
0,90
'
, ,BQ
,irrn
onAn
!( ;,.rv
O. AA
r
-,JU
4.20
--,10
,:,c0
45678
'1vic,no cKBarxkH
Puc. 2.4.
;;;;.;;;
pacnpeae,IleHlre'3aAalouee
xyMy"IrrlIBH!'Io Bep0flrHocrb
!,rrcxpernoe
ABavcrexaBoBpeM'u,o:lll (1':llro trero)'(au'
ofryr''aonrorirrcd
- 'ltofi
paBHa luY0
cKBa)I{l'lHbe
l ,c , l u B e p o t l r H o c r b ) ' c n e \ a
1,00
0,90
j 0,80
c,7o
3
=
^.^
- Li,DU
Tncn
i-:'i:
i,cU
.J...,1
t
0,00
2
3
4
5
t - {H c r o
6
7
8
I
10 ...
c KBa-}fiHH
aarculeeBeporrHocrbroro' qro 6y'rer npo'
Puc- 2.5. ,[,ltcxperHoepacnpeae,'IeHue,
ycneivceuo 6crlure 3alauHofo qucJa cKBaxuH,,q.rqroro. utogol lg*y"l'rrb.u,Ba
r]ro BepotrHocrbycnexs paBHa lu%
xa, npH )'CJ1oBI{[,
Hi,ieAByXIIBeTOBBypHeocTaeTcflHeI{3MeHHbIM'HBepo'ITHocTb
lorrBJreHrifi r{pacHoro ruapa nppl noBropnOnt nu6Ope OcTaeTCfl He'
IIOr13MeHHOft.3ia nepOnrHOcTb Tal{)Ke ocTaeTcg IIp146JII.I3lrTeJIbHO
qVc,'IO UapOB B ypHe' L3CTOSHHOIi,eCJTIIIIMeeTCq OqeHb 6O.nluOe
ir{e B ToM cflyr{ae, ecd'III AeJlaercn nu6op 6es aoeopauleHl'Ifl, raK
MaJIOMy II3MeHeHtlIO
iiax nU6Op 111apanptrBOAIIT Ii 6ectlogeqgO
nponopuliri cpe.r,IIocralournXcsuapoB. 3ro uocleAsee ycnoBne
o6r,rqnb npe.I,flo,'IafaeTCf BbIIIo"'IHeHHblN{npH leoJlorI,tqecKIIx noIICli;tx,KOfAaeCTecTBeHHOI.iCnOJIb3OBaTL'AHCKperHbIep,aCnpeAe'Ie- 3To f eo,roruqecKl'Iii 6accel'ln'
n,,,o. B HauelI I]ptlN{epe <<ypHa)>
a KpacHbIM I'I 6erblM lrlapaM ccB rioropo\l npoBo.I,flrcq pa6oru,
3adiIeXtII
tt nyCTbIe SJIOIIIaAtt' .II,O TeX
O-tBeTCTB)IOTHeoTiipbtTbIe
o'7
nop, noKa rrHcro He noABepfHyTbtx 6ypeHuro yqacrKoB BeJirrr(o,
a qHc,'Io onpaB/t,aBlxllx ce6s B pe3yr'rbraTe 6_vpenlra nporHo3oB
.
(IxapoB, H3Br'reqeHHbrx
H3 ypHbr) irla.to, npeArrono)KeHrreo rocrogHcrBe BepoflTHocruorKpbrrnfl KalKercrr otrpaBAaHHbIM.
OAsaxo
ecna su60poqsuii sKcrrepr{MeHTocyUrecrBJlqercr c MaJrbrMHcxoAHbiMqr.rc,roM
p a c x p a n e H r J b r xr x a p o B B y p H e , H o H u n u 6 H p a r c r c n u s
ypuur 6e: Bo3BpauIeHHfl,To oqeBr.rAHo,
q'ro BepolrHocrb II3MeHflercfl rroc"'rerial.r{Aoronu6opa. Taxofr 3KcrrepflNreHT,
Ha3rrrBaeuurlnsr6opolr 6es nosaparueHrrr, onucbrBaercfi AlrcKperHbrr{ r[nepfeo\rerpHrrecr{uMpacilpeAereHlreu. feo.irorrrqecKr.te 3aJ.aqu, B KoroDbtx
qe.neco_o6pa3Ho
ero Hcno!'Ib3oBaHrre,
BecbMa cneUrrQuvulr, u r\lax
fpeft [25] npriBoArrr np'Mep, ceq:auHlrir c reocpn:lr'uecK'Mr.r
]reroA a r { r r p a 3 B e J . x uu e $ r n u b r x M e c r o p o x 4 e H u i r .
B u e r i o r o p s r x c j ' r y q a r x M o l K H o o n p e A e , T n r bp a 3 M e p c o B o K y n H o crll, B I]peAenax xoropofi BeAercfl nor]cK. flpelno.;roNlrM. qro rioHqeccrzfl B_orKpr,rroM uope o6HapylKnd,ra
Aecflrb rBHbrx asonra"ryirfi,
npuvrtuoli- xoropblx rBJIfltOTCr,BO3MO,*HO,nepeMerreHrit cotlr Ha
r,'ty61q9. I1: onura rpeAbrAyulux l.{ccJreAoBaur,?
c,re4yer, qro orio.ao 400/s raxux cericrrnqecrnx asoua.ruii yrassrnntfr'"l
Harfiqne,
npoAyrirriBHbrx crpyKryp. flpu peanr.{3ar{Hr{
rporpaMMbr pa3BexoqHnx pa60r_B crJJ'ryorpaHr{qeHHocrr.I
cpeAcrB Her BO3MOX{HOCTH
OcyrlecrBrirb 6ypeHne B MeCTax npoflBJreHr.rfl
arionannft. ,[l,rx oqenxH
B e p o r r H o c r a T o f o ' u r o 6 y A e r o 6 H a p y x e n o 3 a p a n e e 3 a A a H H o eq r c Jro 3a'rre)Keir,ec.ra roJrbKo uexoropu-e H3 Ilpe.qcKa3aHHL,Ix
llepcrIeKrHBHbrx n"roulageft 6yayr pas6ypeuu, rnroxer 6'rn Hcno.lb3oBaHoi
rr.rIIepfeoMerprrqecKoep acnpeAeJleHlre.
,bnHoMrla,'rbHoe
pactrpeAe,'reHr.ie
Anfl peIUeHuq eroti 3aAaqn HerprrfoAHo, TaK KaK,BeposrHocrr
^o6napyxeH'fl ?r3Me'rrercfl rrpH
riax(Aor.{c,uyuafiuonrIIcnbrraHr.:ra.
Ec.na HMeercq qerbrpe 3aJrex{I{,.
KaX(Aaq II3- IiOTOpbrXBXOAT.IT
B qIIC"rOAeCqTLtn,rOqaAet?, [p,eACr<a_
3aHHbr.\ceiicr.ui,recxt.rr,tllMero,{aMlt, To orxpr]ITIie
oJnoii ,r, Hux
\rMeHbuIaeTIIIaHCbIorKpbITI'{t
TaK KaK ocraercq Mer{bue
.Apyfofi,
o6rexron, r(oropbre Aonx{Hbr 6r,irl o6Hapy}KeHbr.Hu;6;;;",
c6sa_
PY}KCI]IIE NYCTOIi CXBA}K],IHbI HA OCHOBC CCHCMIIIICCKNX
I]HbIX
A
VBC.
.{rr{rrBaerBepoflrHocrb
roro, qro ocraBrrr[ecs uenpo"epeu"iu"n
crpvrirypbr 6yayr rpoAyKrHBHbrMa,
rroroMyqro oAHa irenpb4ynrn"_
Has crp)-nT):pa ylKe ncKr'rrortcHa
I]3 cOBOKynHocTH.
Blr'rrrc.DeHrrerrrrepfeol,rerprrqecfioii neponrHocrH
cocrorT npo_
cro B Haxo)KneHur{BCex Bo3Mo}r{HbIxxonr6nsau,nii
npoayr<rzgHHx
rr nycrbrxcrpyKryp-B"-y:l11:gugxyrHocri.r
r.r3areM n6penn"re_
'o6HapyHHr{ rex xorur6ir'aquil, xoropue 4aror rpe6yenaoe q'c,10
"
xesufi. BepoaruocrbocyqecrB/reHu,
i oi"upy",.nnii'ipi
oi,puHVH n CXBaX{r'rH,
ec"rr' AeJraercs nu60pxa i.r3- coBoKyniiocrpr
N
g";reMeHToB,
S us troropbrx, Bo3Mo)KHo,coAepxar
3aJlexb, paBHa
P:(:)(;_-;)
lc)
28
(2.6i.
I eH c , l a x o l t 6 u r i a u u f i I t : q l l c , r a s a r e x e i i n o '
9 r o e c r u n p o H 3 B e A e H I 'q
qflc,ty o6uapyxeuuft sa ill'Icr'Ioxou6usalrHli us n,vcrntx agoltanuir
AeregHoe Ha qllc.lo l<ou6usaunit' uz
no qrcJly nycrblx cKBa>KI'tH,
B c e - \ I I p e A c l i a 3 a H H b Iox6 l e t ' r o s n o o 6 q e M ) t q l l c ' ] y c K B a x ( l I HB r l p o '
rpaxlMe 6ypeuua.
llliepreouerpr.iqecKoe BepottrHocrHoe pacnpeAe,leHIie Moxer
6url npiiueHeHox sarueii xoHlleccllll B orrpblroM Mope' lioropa*
coJeplKr.rr Aecflrb ceficltu'lecxHX aHoMaJIrlii, uerupe ns KoTopbIx'
Bo3Mo)KHo,coAeplKar 3a,tej'l{ti.K coxa.nesulo, MbI 3apauee He sHaeu, 6ypeHtte naxnx Ir3 qerbtpex anoua.lxli Aacr no.noxnre.rllsuft
pe3yJlbrar. EcJlla s reKyI{eM ce3one 6rcArxerslte orpaHuqeHl'Iflno'
3BoJifllor ocyurecrBl{Tr 6ypeHne roJIbKo rpex cKBaxHg' MbI Mo>KeNl
CBfl3aHHbleC KaIKAbIMH3 BO3MOX{HbIX
BepoflTHOCrH,
onpeAeJrr4Tb
ficxoAoB.
Kanoea Beposruocrb roro, qro npofpartlta 6ypeuul norepirHT
no;iuur? trpoBaJi,T. e. He 6yrrer Iloryr{eHo sli orrioii npoA}rxrl'iBHofi
c K B a x f i H b Ic p e A l r r p e x n p o 6 y p e u u u x ?
/4\ 16\
o: J$*L _+#:0,167.
\ s,/
ii
B e p o r r u o c r b r r o J l u o f oK p a x a p a B H a n p u i u e p H o 1 7 0 / e .
Kaxosa BepoerHocrb roro, uro 6yAer cAe''iaHo oAHo o6uapyxeglte?
o:
/ a \ i 6r
"/'uti'-#-0,50.
t,t/
Bepoaruocrb roro, uro 6y,ner uatl4eua oAHa ltpoAyKrltBHafl cliBairiuHa, p anua 50 o/e
.
Moxuo nocrpor.irb fllcrofpaMMy, Ha Koropoii 6yayr npeAcraBHCXO'
.reHbI BCe BepofiTHocTIl,cBfl3aHIIbIeCO BCel\IHBo3MOIKHbIN{II
.falnr B arorl pasne4oultoft3aAar{e (puc. 2.6). 3aMetzM, qro Bepoflrnocrb ycnexa paBHa ( 1,00-0,17), nnu 83 70.
flpeauayuruii npnnep orHoct4JrcsK c,Ilyqato, riorAa ItMeercg
'ioJrbi(o
ABa Bo3Mo)KHbrxr{cxoAa: [ycras cKBa)KLIHau.nrr o6napyx(cHlre ueQrir. Ec.uu ue$rr Haft4eHa, cKBaiKLIHaHe uoxer 6urt
n1-cror?,H o6paruo. Co6uruR, B Koropbtx qacrora norBJIeHI.tfloAHofo ucxoAa rro3BOJIfeTnpeAcKa3aTb qacrory rIoflBneHIIq lpyroro
rlcxoAa, Ha3brBanrcg B3anMHo ucr,'IrcqarculllMli Apyf Apyra. Bepo,qrHocrb roro, qro npoHsofiAer oAHo r.rJrrrApyfoe co6Htue, ecrr
c 1 ' r r M aB e p o q r u o c r e r l n o s s r e H u t K a x A o f o i r 3 H l t x ; r . e . p ( o 6 u a ( o 6 n a p y x < e n a r )* p ( n y c r o f t
p)-)Keurq uru nycroft creaxuHu):p
cnnaxauu). 3ro - trpaBnJ'Ioc,'roxeHufl aepoarxocretl.
29,
960
Pnc. 2.6. .{ucxperHoe pacnpe1e,leulre,3a.tarcu{ee BeporTHocTb 4 ycflexoB B Tpex cKBa]Kr.rII3.\ H3 ,qecrT!, ecJlt qeTbrpe H3 ,lecfTtt neDecex,ru ue$rrn)'rc 3a.Texb
AEN
0,5a
,F
o
? 0A0
F
q
n1{1
c,10
a1?3
thcno
gcnexoB
suLrrr,\rvrJr
co6nrrr q He o6fl -rareJlbH o E B,'Iflrorcfl B3aHMHo rrcri,rroqauou-r
t{:,{ir.
F l a l p u v e p , r r i ) r { p a - 3 B e A o q H o M6 y p e u r ' l H a u e Q r r H
fa3 rroflBJreHpre
3a.lexiil c ]lor]rrcrbr\i recrJaHrilioM ]roxr]ro Il]irerilperrioBarb
Iiaii
aHrr{r';d'rr{Ha,'rbHvto
crpyr{Typy, HcxoAfl. ttg cerictvtH,{ecxux J,ariHbr.
3rtr Asa r{cxo.!.a,noirilcrirt nu"uu"tunu 6ypeure no- ,"r",rrrrHa,qri.
He flB.rrqrorcr B3ailN{HO HcKJrroqarculriMH
Apyf Apyfa, Tari riaK l\{br
BCTpeqaeM Hx onHoBpeMeHHo. flocl<o,,tlxy Ha,rlHrlrre
[ecqaHr.rKa v,'paB"'rrrercs Saxroparril,
xoropbre Aer"rcrsoga,,rH Bo Bperin o6paio
tsaHI'ltl NlecropoiK-leHI'Ifl, I{ IIocKo,]rbr(y trogBJIeHHe
aHTr.rri"rrrHa,lbHorr
c K . r j a A h ' l i n p e . l n o " ' I a r a e r c t c B r r 3 a H H E ' r Mc r e K T o H I { q e c r { r r } l i
vc"ioBI;t_,rtrl n 6o,ree no:truliir nepuoA, 3TrI ABa ilcxoAa ,BJlflIorcq
Hects,i3arr_
I{bl\4H Hr'IH He3aBI{CIlMbIir.tn.Ec,rlt ASa CO6HTLIfl He
,B,,IflIoTCff IrCh:flIoqarcrrliMH, Ho fl'BJI,Iorc' He3aBIIcHMbIMII, To
coB\{ecrHarr Bepo'THocrb rofo' qro oHlI IloflBflTcfl oAHoBpeMeHHo,
ecrb nporr3BereH H e B e p o q r H o c r e i r r ] x r r o f l B , ' r e H r r sT
. o ecir p (necuauuxa'ri,rrr ari-
: p) ( n e c v a u u r < aX
rriKJrr{HaJrH
) p (asrr.rx,rurianirl. Oro * npaBri,rD
v MH o ) K e H H rere p o a r H o c r e r l .
-[[ea co6srirrq ruofyr 6Hrr csggaHbr HeKoropul,t o6pasc\{. ririi
'r{To I'rcxoA o.{Hofo
0Tqacr' 3aBHCIlr OT l]cxoAa Ap1'roro. Coglrec._
Harr BeporrHocTb rar(Hx co6sruili I{a3brBaercfl
1.b.roeno11. Taxr,t
co6srrlrs oqeHb BarKHbrB feoJlofr.rH,Tar{ IiaK oAi{o
Ir3 CO6rrrtrir uc_
x<er 6url [pr]tro .locrvnHo ua6.trcnesHro, a
np)rroe npfl
sro.,t
MolKer 6srrr cxpuro. Ec,ra oHli o6l,c,ronneHsr
aiyr
.lp!,ron, ro
r { a c r o r a H a 6 " r r o l a e u - o r oc o 6 r t u r n f o B o p H T
HaM rioe-qro o eepoa:H O MC O C r O f H r r cr rr ( p b t r o r o o 6 r e x r a . I { a n p u u e p , H 3 B e p ) K e H r r e
}rir\1-.r
I13 KAMCPbI BV,lI{AHA,
AHAJ'IO|HIIHOTO
iioJ'Ie6aHIrl: Mo'
(lio"'Ie6aHufi) lioj'Ie6aHI'1fl, rI p
ByrrlKaHHqecKoro
(xole6a; r 3 B e p x ( e H r,r r rl o p ( x o , r e 6 a H r r r il r n l r u s e e p x < e H l l rt)' p
8
3
a
u
N
I H y l o0 6 '
(
r
i
:
e
e
p
x
e
u
H
n
)
,
u
\
I
e
l
o
r
uHii) Xp
ec.nu4na co6urul
vc,rtoB"'IeHHocrb.
V c ; i o s H a q B e p o f r H o c r b T o r o , q r o n p o l t 3 o f i . 1 e rl t a n e p i K e H l l es, z l e o,'Ie6aHHg 6u.itit 3attllcaHbl,
I a H r I a a r e M , r r r o f a p N 4 o H I r q e c r { i 1K
) . a r o l t n p l l N l e p ey c o 6 o r u a u a e r c n p ( u s a e p ; x e u r r r T n o " r e 6 a H u aB
JoBHafl BeporrHocrb u3BeplKeHlts6o.tnue, ucr,t 6esl'cJIoBHatlBepos r H o c r F , L ' 1 . i tp1 \ ( u : n e p ; x e u l l r ) , r i o r o p a f l e c r b I l p o c r o B e p o fr H o c r b
roro, qro npoirsoii,ler rr3BepilieHrre6es xaxofi-",llt5o .qonoJ'tHureJlbaofi r.rurlopi\raurtro Ap)-fr1x co6brrtrflx. fipyrue
:;c.r]oBHbleBepoflr-
o ^-^
O- U.,JU
o'
0c0
o6)cJoBneHHocrb, To IIoflBJIeHlte rapMoHttr{eciill.\
xer nolloqb npeACKa3arb [3Bep]I(eHHe. Ec,ru p
BepoflTHocrb rofo, qro IIo9BflTcfl fapMoHI'lqecli]le
Iloc,'IeAyloqero
(useep>xeullfl)-BepofiTHocrb
BYJIKAHY
CS'1TOI1 E,,ICHbI
B
BauHsrroae, no o6uleMy MHeHrrro,.,prrBorxprrK f ap\roHriqecKri\{
rore6aHfigl,r, HanoMHHarox-tr.rM
3eM,'rerpflcesne.Mrt ua'*ornu, np"_
l t o H a 6 . n r o n a r ba K r r B H o c . r . bM a f ' a r r r q e c x o r t * o " . p o i ,
;il;r"
,obr
MOXeM Ha6rn4arr 3an'c' Ceticuuqecxolr aKTHBHO.TH,
cnrsaHHoli
c By.[KaHoM.Ec,rH MexAy 3TIIMrrrBJieHrisMrrcyulecrB],er
B3auNrHan
.30
,^
BepogTHocTri
Ha II.1OIIIa:I.I
At t-,
w o r r o M e H b i I I e , q e N { C O O T B C T C T B y ; S L U l { e6 e S y C l O n U U e
LIcKOriaeMoro
(BepoflTHocTb Haxo)KAeHHq HeKorOp0fo
B)r/"IKaHIIqeCliOlO IpOITCXO)KA€HU9 3HaI]ilTeJIbHO HHXe'
rIeM 6egt'c,rosHas BepotrrHocrb Haxox<AeHIrflIicKCnaeNlofo). O.IeBli.lrro, reo.'rotn ucnoJ'Ib3yrorycJIoBHbteBepofrHocrrr Fia Bcex crztA l i t x n p o B e A e H a f lc B o H X p a 6 o r , A e ! ' r a f ls r o c o 3 H a r e r b t l o I l J l t H e r .
Ceq:r rIe)i{Ay ycJIoBi{brMlrrr 6esSrsrrsBHbt\IIr BepotrHocrttMi{
t l { e c r r , a H r . n r t f i c r o r oc B t t l l o x < H o B b r p a 3 i l T br e o p e \ { o r ? ,I I a 3 B a H H o fB
u{eHHHXa,xiuBrilefo B XVIII B. ri orr(pbrB[Iero ee, reope]Ioii Baiiec a . O s r i c c " q e J o B a Jnrs M e H e H r r eB e p o f l r H c c r r r n o r \ r e p ey B e , r H q e H u t
r i o , r n q e c r B a l i H r , p o p r r , r a u uO
u .c H o e H o e y p a B H c H H e E a i i e c a r M e e r
aTrx
P(A,B): P{BIA)P(A).
(2.7)
rrro coB\{ecrtratr
saB.rrlrBaer,
rb ,P (r1,B) roro,
Bepof,THoc
OHo 5,g1"
qro o6a co6brrrrflA u B npou3oriAyr,paBHaBepoqrHocrw
P (8 1,41
rlotBileHlrg co6lrtrilfl B nplr \:c,IIoBIrH,qto co6trrire I vx<e npoH3ot u J r o , y M H o x e s s o i i H a B e p o f i l F r o c r sP ( , 4 ) n o f l B . r e H r i r r c o 6 b r r l i r .
P ( B l A ) H a 3 b r B a e r c ryr c , r o B H o i rB e p o f l r H o c r b l o ,r a r i : i a r ( B b r p a l K a e r
BepoflTHocrb Tofo, qro nporr3otx,'Ioco6bITrre B, nprl ycnoBiil.I, qro
co6brrlle .4 yx<e npon3olriJro. Ec.niaco6brr[fl A u B cnl:aHu (u.rx
saeucuvsr), ro ror Qanr, uro co6brrr.ie.4 yxe nllori3orx.:to,foBoprir Har\r Heqro o npaBAono4o6uocru rroflBJreHriffco6Hruq B.
H a o 6 o p o r , T a K X i ec n p a B e A J ' t H Bpoa B e H c r B o
P(A,B): P(AIB)P(B).
f l p i r p a e H l r n a f l I r p a B b r eq a c r u , i l o . r - v u a € r {
P ( B l A )P ( A ) : P ( A l B )P ( B ) ,
riTo tr'lOititio nellenilcaTb
B BII.lc
P ( B1 . 4:)
P ( . . JI B ) P ( B )
P (A)
(2.8)
JI
3 r o o q e s l n o J l e 3 H o ec o o r H o [ r e H t r e ,T a K K a K r { H o r A a M b r 3 H a e M
ycJrcBHyro BepofrHocrr e oAHorl tpopve, Ho HHrepecyeMcs I{ Apyr o l i . H a n p z M e p , r r 3 B e c r r { o ,q r o p y A H b r en o r q q a c r o x a p a r i r e p u 3 y ;orcq Ha,luqtre:vIfeo\laflll.ITHbIX no,leii, oT,'ti{qHbIxoT HopMaJIbHbIx.
O i i n a x o u n r 6 o n l u e l H T e p e c y e [ I c a o 6 p a r u u M , a H M e H H o ,r { a K o B a
Sepogri{ocrb rofo, r{To HeKoropoe nor'Ie oKax(ercfl MI.{HepaJrrr3oBaH:rLrM. nptrqeM I]oc.TeAHeeo6-v-c.noe,TIeHo
Ha,'tnqI.IeMMalHI4rHoit agoN{a,,rrirH.
FIau npoure o(eHHrb yc.rroBHyroBepoflrHocrb p (arioua; : r r n / u u H e p a , r n : a l l l r n ) r r 6 e : y c . n o n H y r oB e p o f l T H o c r bp ( u l t u e p a , r n -rrili!lrr, r'rc^uA)lrrr II3)'I{eHLIgLi3BeCTHbIXpyAHbIX paI.{OHOB,
OAHaiio rpyi,Hee npr{\ro o[eHrrrb p
( N { r . i H e p a " r r H 3 a u r { u / a H o M a , ' rrxarK
r),
K . i r i . ? T o M o ) K e r n o r p e b o e a r b r i c c r e A o B a l { H rr e o M a f H u r H b l x a H o M a " ' l l r r i r . o r o p b l e , B o 3 I r o i K H o ,e u e H e 6 u " ' u t n p e 4 c r ( a 3 a H b I .
f i p e ; n o n o ; x u M , q r o M b r r i M e e M n r { e c o B M e c r r i M b rcxo 6 u r r n i 8 1 ,
B r , . . . , 8 , , , K o r o p b r e o 6 r ' c , r o s . l t r r e a r ccro 6 u r u e . 4 , r o r . l a B e p o f l T H o c r b
c c ) / t r t e c r B " r r e s rcr so d u r n s , 4 e c r r t l o I p o c r y c ] . M M a y c J o B H b r xB c p o qiaocrei-i P (AlB;), \'N{rro;fieHHbrx
Ha Bepoflrnocrll co6nrnft .B;,
) 4 ' t ' ' ' ' \
reo,rofnqecKoto AoKJIaAa LI Kaprbl peflroua
Onriaxo r.rccr'reAoBaHr{e
35% O6HaHHQopmaqnn o roM, qro OKOJIO
Aaer norroJrHrire.TrbHyto
iropoA s 6o,']rueM 6acceftne sBJlflIorcr MopcKI,IMII,
xesuii il,re,'roBblx
B ro Bpe\Irr xari B Mer-rb[re\{6acceliHe Ha Hx A,o"'Ircnpi{xoAl{Tcf
norirrr 800/e o6Ha>xeuuri Nr€a'roBbrX
[opog. Mu uorxev [ogToMy lto.cry.illlpoBarb )'c.rroBHytoBepoflrHocrb rofo, qro ecJIlI iicKoIIaeMblH
$ p a r v e H r r r p r r H e c e Hu : 6 a c c e i i s a B , o H f l n , ' r r e r c r r { o p c K H ML I c K o ilaeN{brM,B cooTBeTCrBrflrc n1)oqeHTHbr\{coorHollreHrreMMeJIOBbIX
Nrop!i{-iixo6saxerurrlr e 6acceilHe, T. e. ri.\"IeeTI\4opcKoenporlcxoiK4 e r { i r e ,r r r r r 4 . t H S r c c e f i H a 8 1 P ( A l B r ) : 0 , 3 5
r{ AJrr 6acceitsa Bz
P ({l82):0.80.
Ilcno;l:yr
3Tlr Beporrnocrn r{ Teopeil,ryEafieca, r{br tvrox{eM[oAcqrrrarb yc"'roBHyroBeponrHocrb roro, qro ucr<onaeutri:r QparueHr
r r p u H e c e Hl t s 6 a c c e i i u a B i , T . e . r o f o , q T o e f o
npotrcxo;.ri.I,eHrie
Mopci{oe, no Qopln,,re
P(BrI A) :
IO eCTb
P(A\:
' 0,'14'
>P ( A l B ) P ( B ) .
'Ec"rrr(2.9) rorcraBrrrbBMecroP(A)
u ypaBHeHHe
Eaiieca,B Qop'ue (2.8), ro Mbrno"ryyquM
6o.neeo6ureeypaBHeHrre
) Bi)P(Bt)
-P( |
P iB'I x':
(2.10)
pt,tl B1)p(B)
Z
llpocrori nprluep c .qB\:trrflB03Mo)KHbrMu
He3aBrrcuMbrNIr{
lcxo.r,aN{rr
nn,'IlocrprrpycI reopeMv Eafieca.
B pyc.ne noroKa s 3anaAHoM KaHsace 6un uafi4eu QparneHr
HAa MeSO3aBpOH
B , C I e U H a J I H CrTr o n a A O C H X n o p H e r { 3 B e C T H OBf O
,eoHToJrotl{u rro3BoHoqHbIX
c!te,'I uerecoo6p a3HbIM flocJlarb cr\..IeHqecKyl,o noJreByronapruro Ad'rflnolrcKa 6o;lee [oJIHoro ua6opa rrcKonaeMbrx ocrarKoB. I( coxa.neHlrlo, Mecro o6napyxeuua
)')Ke
uaftAesnoro SparrrreHra HeJrb3rr6tr,lo uAesrnsrar{Hposarl c no,ruofi
yBepeHHocrbro,Tari Ktri Hcr{onaeuoe 6u,ro safiAeuo Huxte cJlrirrHufl
AB)rx cyxux pycex. flnoulaAr ApeHa)xuoro 6accer?sa 6o.uee rpynHofo lroroKa oKoJIo lB yc,roouux eAHHltu, B To BpeMfl KaK [Jrou{aJ.u 6acceftua, ApeHupyeMofo Megburr.rMpycJroM, oKoJro l0 vc.itoBIibIXeAHHHU.Ha ocHose ToJ'tbKorattoft HHQoprr,raqug,MbI MorrTo BepoflTHoCTbrOrO, UrO
xeNl rrocTyJrr.rpoBarb,_
QparMeHT npr{rreceH tr3 xaxoro-,lu6o or,Horo_ApeHalKHoro 6accefiua, nponopqlioHaJrbHanr'rouaIrl eroro 6accefiHa ulu
32
( 0 , 3 5()0 , 6 4 +) ( 0 , 8 0 ) ( 0 , 3 6 )
(2.et
i=l
P(B1): LL : 9,64, p (Bz): A:
P(.4t n1)P(81)
P(A I rilP(R1)+ P( ,1| B r )P ( B r \
( 0 , 3 5()0 , 6 , 1 )
9,36.
Aga.nornqHo, BeporrrHocrb rofo, qro ricriolraerusriiQparrvreHTnpHFIeceHH3 Meub[rero 6accer?na, \{oxuo no.],cqurarb no Qopuyne
P(B,l A):
( o , B o()0 , 3 6 )
: 0,56.
( 0 , 3 5()0 , 6 4 +
) ( 0 , 8 0()0 , 3 6 )
K c,racmn Arq cryAeHToB, r{oropbre .r,o.rx{HbrlrccJreAoBarb n.lloilIa.4b, npexcraBnrercfl Hecr(o,rrxo 60;ree IIpaBnonoAo6HrrM, tlro
Qparueur IuopcKofo rrcriolrael,{ofo Nre3osaBpatrpriHeceH H3 ]ueHbuero 6acceftua, a He rr3 6onrurero. C:saxo pa3rnrrr.rfl B BeporrH o c r t x o q e H b M a , ' I b r ,r r , K o H e q H o ,: l t t B r r c E To r o 6 o c H o s a H H o c r LAI o nyur,eHuft,ucfroJrb3:"'eMtrx
.lJrr orleHt(il aepoxrnocrefi.
I.rtq roro .iro6H nepeiirn K caeAyrolreri reMe, MbrAoJrxHbr BepI{}rrbcfl n 6lrsovlraJ'rl,HoM\-pacnpei,e"'reur*o.Ha pvc. 2.2 rrpelcraB,{eHo BepoflTHocTHoepacilpeAeJieHire-fJfl Bcex Bo3MoxHbIx ql,{ceJl
B b I n a A e H H sr e p 6 o n r f p e u l e K n p l r r p e x 6 p o c a u n n x M o H e r b r .A s a " r o rttqHrIIi gKCIreprrMeH
f rvrci^nHo
oc)'ttlecrBrrrb nptr 6o.nlurerra r{Hcre
u c n n r a s H l i . H a p l r c . 2 . 7 , u a n p u u r e p , r p e ^ r c r a B J r e n bB
r eporrnocrr.r
noryr{eFir{fl3aAaHHofo r{rrc"ra<<}cnexoB>(rep6oe) B AecflTr.r6pocaH H f l x M o H e r b I ,a H a p u c . 2 . 8 - B e p o f l r H o c r H o ep a c n p e A e J r e H a eK, o Topoe onHcbrBaer pe3y,'rbrarbr oricreprrN{eHTa,cocrorruleto H3 50
6pocaHirfi MoHerbr. Bce sru BeposrHocrli 6sr,rn rroryqeHbr llg ra6,rnu 6trsouHaJ'rbuoropacnpeAeJ'reHrrrI{,Trr Moryr 6btrt gsrqacJIeHbI
I{3 6rtHounallHofo vpaBHeHLIrr.
B xaxAou Hs grfix 3KcI]epr,IMeHToB
Bbrr{flclrrflJll{cb
Bce Bo3Mo](H b i e q l I C J I af e p 6 o B , r i o r o p b r e M o x H o n o i i ) r q r r r b ,H a q u H a q c 0 A o 3 ,
10, 50. Hunaxae Apyrue nolr6uHar{uurep6oe H perueK He Moryr
3-201
33
0,20
F
o n{q
F
O-nrn
!O
0,05
45678910
q14crc
rep6co
p a c n p e . t e J e H l l e r I o K a 3 b l B a K ' i i e c B e p o r a r H o c r bn o . r t y q e H H f3l 8 . { a H H O t Oq l l c , l a r e p o o B l r p x A e c f l r r l 6 p o c a n a r x M o H e r b t
P s c .2 . 7 .f l t i c r p e r u o e
0,151-
I
I
"l
5 0,10
F
ol
Ii
LII:KAY ,U,B-\IM'II3MCPCHII'INIII,CC!'III NPOBOAHTbH3MEPCHH' B AOCTA.
grofo vrBeD}K-4eHIIt raKoBo. qro
ii!riilo Mevrrr{ofiuxa,re. Cne:crnlie
iiax<Aufr rrcxor B nefipellbrBiroii urxane nsuepbHnr? vHHr{aJreH u qro
tsepoflTHocTb noJryqeHlrfl KoHKpeTHofo ToqHofo pe3yrrbTaTa paBHa
Il
oi
o 005F
I
li\-r''IlO,
I
I
L
0.00
'1,
,.-. o ;r,c6c=
5D
noKa3,brBarouee
Puc. 2.8. ,Il,ucxpernoepacnperteJlenrie,
BepoflTHocrbno"lvqenrifl3aqlrc,larep608 rlpH 50 6D]ca]rr4rxMoHerbt
IaHHO]-O
BcrpeTrITbcfl. Tax xax rrbr o6fi3aTeJrbHo rrorvqaeM Karior?-"rH6o pe3yJrbTaT Ii3 neper{HCJIeHHbrxBbrrre, ro c)'MMa Bcex BepofiTHocTe}r E
K a x A o M 3 K c r e p r . r M e H rAe o J r x H a p a B H r r b c e 1 , 0 0 . 3 r o y l o o H o n p e l .
c r a B H T b ,n o , r a f a g n n o u l a A n n o A r n c r o f p e M M a M r {H a p n c . 2 . 7 u 2 . 8
p a B H b r M t r1 , 0 0 , x a x 3 T o c A e J r a H oH a r H c T C i p a M M e ,1 1 3 0 6 p a x i e H H o f i
ira puc. 2.2. flpu raKoM ycnoBrla yBefluqnBaloqeecff qrrc,'ro6pocaHHtl MoHerbr 6y4er coilpoBo)KIarbcfl To.lblio cyi*ieHrre:,r txnpltHbu
34
l C e 6 o , r c e H a r o M H H a l o q e f ir . l a A I I o J I o c .f n c r o r p a l t u a c r a H o B H T c t B
K y l o r r H e n p e p b l B H y l oK p l l B l I o . M o x s o n p e a c r a B u r b c e 6 e 3 K c n e p H MeHr, cocroqu{utl B 6eclioHeqHoMqlc,rie 6pocanriit MoHerbI' B penoJloc
3vJlbrare i(oroporo 6yaer [oryrlego 6ecxoseqsoe qilcro
decxoHeqnoMaJIoii unpIIHbI. TorAa rncrorpaMMa npeBparllTcq B
He[pepbIBHyI.oKpIlBy]o, II roptl3oHrarbHatl ocu 6yAel npeAcraBnsrb
cKopee HerIpepbrBHylo,qeN{ AucliperHylo nepeMeHHylo.
B eNcnepnrr,tente6pccaHtllt MoHerbI MbI HMeeM AeJIo c AHcriperHbn{!r rrcxoAaMr4,T. e. co cneqllQr.ruecroit xotr,I6usa(nefi rep'
6cs H peuex. Oasaro s 6o.ltuuHcrBe oKcnepl'IMeHToB,BcrperlanUCXoAbIHe ffBIqIOTCfl AHCKpeTilrrxcq Ha npaKTLIKe,BO3I\{O)KHbIe
Hbr\{a. O6uqHo r.rMeercs6ect<oHeqsltil t<ouruuyyM Bo3Mo}KHbIXI.lcBo3MoxHbIX
xo.toB, rioropble Moryr 6urs no.lyqeuu. MsoxecrBo
rlcxoAoB Mo>Ker 6url xoueqHblN{I{ Ha caMoM AedrleorpaHItqeHI{bIM,
pe3y,'Ibrar, xoropurl uox<er 6url
HO B npeAeJIaXgTOtOrltHOXieCTBa
irorryqeH, HeJrb3flnpeAcKa3aTbToqHo. B AaHsou c,lyqae lvlbl llMeeM
c,rvqafiHttN4LI [epeMeHHbIMti. llpeAno.noAe.rro c HerrpepbrBHbltur{
lipaq paKoBux i r { M , H a I I p I l M e p ,q T o I { 3 l v l e p r r c r c A
fi .lnHa 3aMOqHO|O
uu 6paxuonoAbr u ycrsHoB,rreHo,rITo oHa paBna 6 rtlnr. O4uaro
ucrio,'Irsya 6r.tHory.naputrfi MHKpocKotl,
ec"rlt npoBecrH r.r3MepeHrre,
KoM[aTo MoxHo nod'Iyq[Tb tr,'InHV6,2 Ml't, a [prr lIc[o,'Ib3oBaHI4I.I
- 6,23 MM, I!, HarioHerl, Ircno,'Ib3ys criaHlipylouliri eurextira r opa
p o H a u i i M r i i i p o c K o r r ,n o . n y v i r n r6 , 2 3 1 u u . H e n p e p b r B H a f l[ e p e M e u Fiar reoperrir{eci.:HMoiKer 6ecxoHe,{HonoApa3Ae;Inrtcs. 3ro flBntg,e-icr cJre.{crBrieMroro $axra, qro Bcerra N{o)KHogafi,ru paggocrb
ilc"rit{ 3To Tari, To ria;{ieTcE HeBo3Mo;KHbIM
onpeIeJIIlTb BepOgTiro,rrt H ocHoBe orHocrrreJbubrx qacror BcrpeqaeMocrlr. O4uaro
xori HeBo3\{o)KHolra6nioAarl [cxoAbr, Koropbre B roqHocrx coortserrrBi'ror 6,000...000 NrM,BrroJrHeLocrynHo rio!'ryqlrrb pqA H3Mepeuiiii, nonalalotrrr{x BHyrpb HeKoropofo }rHTepBaJIa,BKnroqa}oulero
sro 3HaqeHue. flpu rcM, riro nrlAHBuA]'aJrbHbIe
I,I3MeHeHHfl
B ToqI'ioCTi{He u-leHTLIqHbt.oHII AocTaTor{Ho6"rksxq u Mox{Ho crluTaTb
r{. npt{Haf"re}KaurtiMrio-:HoMy r{Jraccy. B rlrore paso6teu He[peirbrBHyIoIxKa,Iy Ha Auch:DerHbrecefNleHrbr,lr TofAa NroxHo noAcru'rrrb quc,rlo co6urlrfr,
norraBIxHX BHyrpb r{a}KAofo rrurepsa.na. Cy-{iaR rpaHrrllbr K,lracca, Nrbr vMeHbmHM qHcJro co6urgfi B HeM, H
cHrr3trN[orIeHr{HBepoqrHo:Teii nogsreHus co6urHg.
Ec,ru uu rrlree,trxeJ'ro c AucKperHblMlrco6urilqr4r, To olpeAer f i e M 3 H a r { e H r r rc a 6 c o n r o r s o r i T o q H o c r b t o .H e n p e p u e n b r e n e p e M e H ilbre, oAHaKo, rrsMepflrorcfl c fioMolr{bro HeKoropbrx Qusuuecxux
!r oueAyp, KoTopbre of p aHHqr.rBaror Tor{Hocrb r.rx H3MepeHHfl.
B i r o a r o p u u x l 3 M e p e H u q K ,c A e r ' r a H H b rH
x a o . q H o MH r o M N e o 6 g 3r
JD
OTpaxae K T e , B O 3 H l r K a l OM
Taflble OTXJOHeHUg
B,e " ' i i l 1 1 r i HKaO T O p b I X
e r K a K e c T e c r B e H H b rrer 3 i l l e H e H n o
f l 6 b e K T a , r a K A r r s \ { e H e H l t tB y c JIOBHflXnpoBeAeHi.IflI1311epeHllfi
il, KpoMe rofo, il3\,teHeHIIf, O6yCqerO II3l\{eJIOBJIeHHbIe
rrCC"TIeAOBare!-rff
AetreJIbHOCTbtO
, npOH3BOAfl
peHHfl. E4trricrneHuoe, Toqitoe, <<rrcrr{HHoe))sHzrqeHueHe Nro}Iier
6urs onpe4eJreHo;HHbIMrrc.roBaN{II,nalt ui5,rrcAaeM He[pepblBHoe
pacI]peAeJreHlreBo3Mo)KHbrx3HarreHaii. Tar'rre csoiicrsa I]pIIcyu]I
HenpepbrBHoficn-yqsfissii nepe:uteunoli.
, [ , l s I r n " r r c c r p a r { r I H H e i l p e p b r B H b r cx . t ' r ' q a r i i H u x B e , l r r q r r H , p a c cMoTprrM3aAaqy onpeAe"'IeHr.rg
rroKa3aTe,tltnpoHlrllaeMocrrr oop:, rI{oB Irs r(epHa cIiBax<r-iHbr.
Ilpouuqaeuoclb cnpeAe,rtflercflBpeMe}Ie}r,
rpe6yeltul,r Lrq ripoHr{KHoBerilifl3aAaHHoro i.,or'rHqecrBa(L}.niouJ.a
npu craHAaprHbrx ycnoBrrflx uepes o6paseu nopoAbr. J.onycrlrv,
qTo B pe3yJrbTaTeoAHofo orrpeleJrerir.{flnoJyrleHa npoHrrrraeMocrb,
paBHafl 0, 108 lrNu2. fleirnercg .:IlI gro uncd'Io<<ttcruuHori>>
npoHuuaeMocrblo npo6lt? Apyrrre oilpe-teJreHnsHa 3ror\r >xe o5pa:qe N{or y r A a r b n p o H r r l l a e M o c r bp, a B H y i o 0 , 0 9 3 r r 0 , 1 1 2 M r o r r . H a r i p o H r r qaeMoc'r'b,3arrHcbrBaeMyrc
npn6opa\rr.i B xo.1e irro6oro 3ricilepr.rMeHra, Br'rHserpflA yc,rroBrrri,roroplre BHyrpu nplr6opa seu:6e;ruo rr:l,reHqIOTCS
OTOAHO|O OI]peIe.:IeHIIflIi Apyfo\I\,: B pe3y,TbTaTelianpir3oB rroror(a u ero ryp6y!'reHTHocrHH He 3aBiicsr or ,f€r:icrnuli oleparopa. Hli oAHo u3 nonyrleHHblx 3HalreHlir'iHe.[tsg B3flTb B Kaqecrge a6cornrHorl tuepu ucrrrsHofr trpoHr.rqaeMocrr{. B
r{Tore
pa3nrqHble HcrorrH14KrrQnvxryaunrr riopoxrAaror HenpepbrBHyr,o
c;lyuaftuyto BeJrlrrruHy,Korop.vio r\rbrnoABepraeu olpo6oBaHllto, .teJ'IAff TIOBTOI]HbIC II3MCDCH]IS.
14sueHuunocrl, o6yc,loe.reHuan Heroqriocrbro HHcrpyMeHToB,
6 o n e e o q e B l i A H a ,K o r A a f e , , i a i o r c r n o B T o p H b i eH 3 N r e p e H r rH
ga eAirHL{tIHoM06 lrexre, T. e. acrblraHllt iloBToprrorct 6eg lrsNleHeHriir"
T a x y r o I i 3 M e H q H B o c r bH a 3 b r B a r o ro m n 6 N a r r r r o r ( c n e p r i M e H T aK. p o r , r c
3TO|O,
IZ3MeHqHBOCTb MOX(eT
xpOfBvIIflTbCfl
B IOCJIeAOB2T€r-lbHOCill
prJrripe3yJrbraroB 3KclleprJMeHroB,npoBoArr\rbrx Ha
uarr.lepeuirr:i
tr)flo6T,eKToe.O6HqHo rrMeHHogTa r.r3Merrr{HBocrbtr
u3yliaeMbrx
Ae
rrpeAcraBJrrer HayqHbrrlrlrilrepec. ,U,osontHo qacro o6a arrr rlrr a
H3lvleHqllBOCTUTaK IIepenYTaHbt IIJIII COB[{eUIeHb],IITO 3ticfiepI,IMCijTaTOp He MOX<eTOIip€!,€r-IiiTb, ilaiiafl qaCTL iisX,teHtILiBOCTH
BO3i{Ittiae T B C H . r r yp a : n l r u r r i i l l c ) K - 1 1 . y- c J r o B r r f f M r rr i r _ - r 1 L . i T 2 H r Ii l i , l i a r { a f f r B .-IgcTCfc.Tcl.crBIIctt oruttrioti ::f]tcqcntifl .
qro y Hac He 06pa3erl ncpoAbr, a sHaqilre,ur,Hoij
llpelnonoxrrtrr,
uepe: cnoji necAnnHbI KepH, B3trbrrt tz: crisa;;{iiHbr, npoxolfluleri
qaHLIKa. Mtt xorlrll ollpe/le,-rrrrb npoHgldaeuocrl, necqaHI.IKa, Ho He
Mo>KeM BBecrH KepH A-,riHori e 20 ycJr. el. B annapar A,'rr lr3r{epeHHt rrpoHlruaeMocTlt. Buecro sTofo MbI BbrpexeM Hs
r{epHa HecKoJrbKo r{a"'rbrx qacreri (HHrepea;loo) rr orpeAeJrirllt
npoHrruaeMOCTb KaIKAO|O I.I3 HI{X. Ha6,rI,OAaeUag lr3MeHqilBCCTb flBrITCfl
cJreAcTBHeM pa3JIHqHil KaK ilre)*iAy ilCnbrrl,eMbllt{n qacTfl}ru KepHa,
TaK 14 r\le)KAy ycJroBr4flMri 3;iclepnMenra.
Paspa6orria
Mero.(oB
.to
d
F
F
o
d
6
(s
r
0)
F
s
I
F
Meusue
A
i+
l l e r r p a , r g r - + o e3 u a L i e H k e
5onb'.t.tg
P r r c . 2 . 9 . f p a r p r r x I I J o r H o c r l t I I O p r t a " ' l b l t o r op a c n p e i c , r c H x n
HcroqHHKoB II3MellqHBocTlI - oAHa
oqeHKH Be,llrqHHbI orAerbHblx
gAXHCIiU]I,IX
CTATHCTIiKI,I.
3A,U,Aq
HS
Br,I6opKax,
u3MepeHHt, rIpoBoAHMbIe Ha 6oli,rurlx
llonropuue
OXaAaIOT BO3MO/KHCCTL'
BSflTbIX I43 eCTeCTBeHHbIXCOBOKyIIHOCTeU'
qacrb
6o'nlmas
paKrepH3oBarb pacnpeAe,'IeHIIe qacror. O6uqso
s n a q e u H r ? f p y l n H p y e T c f f o K o J I O H e K O T O p O f O U e H T p a J I b H O | Os l l a q e H 1 l f l , ,T r p U y A a J r e H H r ro r K o r o p o f o q a c r o r b l y 6 r t a a r o r . f p a Q u x , r p e 4 MaKcHMyNl LI Ha3bIBaercg
c r a B J r e H H b r f iH a p H c . 2 . 9 , u u e e r o A a g
qacro AeJlaercfl
HOpMaJrbHbrM paCnpeAeJIeHLIeM. B npu.noxeHuxx
qTo
HOprlaJlbHo,
pacnpeAeJleHbi
c,lyqat?Hste Berl.lI{HHbI
AonyuleHr.re,
u MHOTHe CTaTHCTI4qeCKHeKpnrepl.lll oCHoBaHbl Ha STOM AOilVIIeHHN.
Mex<AyrpaQuxolt HopManbuo3ar{JrloqeHHylo
O6uryrc rrJrorrraAb,
ro
pacIIpeAe,rreHr.if r.r ropIi3oHTaJIbHOI.{ OCbIO, MOX(HO CI{I-ITaTb paB-
nofi 1,00 (z.rru 100%). floerouy, licnorlb3yfl rpaQux, MoxHo BbIqrrcJrrirb BeposrHocrb coorBercrByloqero co6blrHff. t{nrarens yxe
3aMeri.rJr,HaBepHoe,cxoAcrBo oAHoBepIxHHHofiHenpeprtenoft xpHeor?, uso6paxensofi Ha pHC. 2.9, c rucrofpaMMol?, npeAcrasreHnofi
F r a p u c . 2 . 8 . O A s a r o n o c K o J l b K yB c n y q a e H e [ p e p b l B H o r op a c n p e .fe,rreHuflqHcr'ronoApa3Aeneunii no ropusoHranlHoft ocH MoxHo
cqllTarb 6ecroueqsuM, BepoflTnocrb nonyqeHllr KaKofo-.nu6o xonripeTHoro 3HaqeHHr paBHa HyJrlo. Btrlecro srofo Mbr paccMoTpI.tM
B e p o f l r n o c r b r o l B r e H u q a H a q e H a r lB r p e A e J l a x H e K o r o p o r o 3 a A a H Horo HHrepgara. 3ra Beporrnocrb paBHa nnoulaAl.I rIoA KpHBor?
qacror, 3aKflFOqeHHOfi
MelKAy 3aAaHHbIMLInpeAeJIaMH.EC;tn yra,.,auHsrfinpoMexyroK BeJrHK,To OCyqeCTB,'leHHe
co6Hruq B STOM
irpoMexyrKe npeAcraBJrflerct 6o.nee npaBAoroAo6Hutvt. EcaN as'iepBaJI
oqeub Ma,'r, To IroflBJIeHHeco6urHg MaJloBeposruo.
Burue 6H,'ru geeAeutt 6es onpeAe,'reHl.Iq
ABa Ba)KHbIxcraracrllqecKr.Ix IroHflTHf- <(coBoKyIIHOCTb>>
H <<BbI6OpKa)>.
COnOrynUOCt,
cocrorzr lr3 BIIoJIHeonpeAeneHHoro MuoxecrBa (.rtN6o KoHeqnoro,
6
ra60 6ecKoHer{Hofo)s,rrer{eHroB.Boo6ule 3.r.r.r9.rer{eitrbr r\,roliiuo
paccN{arpllBarb KaK rr3MepeHHr,BbIrroJrHeHHbIe
Ha o6texrax 3aAaHHoto Tr.rna.Btr6opr<a- oro IIoAMHo)KecrBo3reMeHroe, Bu6pauHnx
LI3 HerioroDoricosoxvnHocrtr.
flpnrue'ponr xoueqHofi coBoKyrrHocrn Moryr cJry)Knrb nce ue$rriH b r e c K B a x u n u , n p o 6 y p e H H b r es K a u g a c e s 1 9 6 3 r . , a n a 6 o p L c e BO3.MO)KHbrx
ur"raQon necqaHuKa TgHcnHn- npil Mepolr 6ecxoneqsoft reo.norn.{ecxolicoBoKynHocru. 3auernM, qro B [ocJreAHeMnpuM e p e c o B o K y n H o c r b B K ! ' r l o q a e Tg c e 6 s H e r o J I b K O O f D a H p r q e H H o e
quc"ro ucnuranail, Korophte 6lt.ltr.rcAe.naHbl,Ho raK)Ke
H Bce Bo3MoxrHbrepe3yJrbrarbr ucnurasufi. l4cnHraurrq, rioropbre 6unu 4eftcrBlire,llbHo ocyuecrBJleHbl, MoX{Ho paccMarpliBarb KaK ou6opxy
H3 coBoKynHocrn BCex roreHllua"rlbHo Bo3MolKHbIXHcnltragut?.
Ec.uu sa6,rrroAeHr.ir
c 3aAaHHbrMucsor?crsaNrrr cucreMarriqecKll
HCri"-ilOqanlcflr{3 nu6opxrr, ro rar{yrc nu6opxv Ha3bIBanr cMeul,eHrroii. fipegno!'rox{rrM, HanprrN{ep,qio sac rrHrepecyer rroprrcrocrb
r a H H o f o c , ' I o E n e c q a H i l ( a . E c . [ l t l r : n u 6 0 p K r i i l c K r ] o q r . { T bB c e p b I X "rrbreu pa:gpo6,reHHbrenopoAbr, TaK r{a-Krrx loptrcrocrb
rpyAHo
rr3I'reprrrb,ro pe3yJrbrar rr3MeHr.lrcr{.BepolrHo, noJryqeHHbI
ft u:H' r e p B a . rs H a . { e H u r l
n o p t i c r o c r r . r6 1 ' l e r y c e q e H c r r p a B a , q r o A a c r c M e _
rueirrie eu60pxi.r B cropoHy 60nee Hu3Krix auaveuur?,u [oroMy MhI
iroJrYrrrlr"loulr6oqHo SaHr{)KeHrryrcoqeHXy Ir3D{eHqr.rBocrr.t
nopHc-
o
a
{6
d
T
!
F
::
c)
I
(d^,
d : : f
j'lq
:+
:*o
Prc' 2.10. coornoueHtte MelKAy MepaMII ueurpa'lrHoit reH'qeHulili B acuMMerpllqpaCnpele,'IeHllr
HOM'IaCTOTHOM
U AJrfl rrpoBepr{urxnoTe3, ccpoplty'rHpoBaHxoLHbIX COBOi(VfrHOcrerl
Hbrx orHocllreJibHo STIIX COBOKynHOCTeI'{.
I{.rIH BbI'
Hau6O.nee oIIeBHAHaqXapaKTepHcrI{KaCOBoKyTIHOCTII
BHAbI
pa3r'IHqHbIe
Cyurecreyrcr
3HaqeHrle.
cpeAHee
ee
6opxa
Ho ToJIbKo HeKoTopbleI,I3 Hltx ricno,'Ib3yloTcfl
CpeAHero3HaqeHI-19'
C O O T B S T C T B yHeaTI { 6 O J I b H a 1 -qacrore.
1 p a K r r . r KA
e ,. l o a a - s H a r { e H p r e ,K S T O p O e
pacIIpeAeJIeHI'IH'
IIpllBeAeH.Hol{ Ha
n
Hanputuep,
ureii
pnc. 2.10, MOAa coorBercrByer HauBbrcuefi roqKe l<pnnofi qacror,
r i M e A H a H a- c p e 4 H r q r o q K a p a c n p e A e n e s n s . H a p u c . 2 . 1 0 n o x a 3aHO, qTo nor'toBHHan!'roulaAIt noA xpunofi pacnpe.!,eJleHllflHaxoA H T C TC I I p a B a o r M e A a a H b I ,a A p y r a f l n o J I O B U H a C , r e B a 'L p e n H e e
a
p
l
t
QveittuecKoe, i{oc
p
e
A
H
e
e
: r H a q e H l , r e a r o , I I H b I M Hc ' r o B a M l l ,
ropoe olpeAeJlteTcs KaK cyMMa Bcex pe3yJlbraroB ita6nnleHi'tli,
Je,rreHHaflHa Ax r{ucflo. B yc"looanx acllMMerput{Hblx Kpl'iBblx pacrpeAeIeH[qMeAI.iaHapacnoJlo]xeHaMexAycpeAHuM3HaqeHrIeMI'l
rro4ofi, a B Cfiyqae cHMMerpllqHbIXKpuBblx' IloAo0rlblx Hop]'{a!'IIr,uori, nce rplr Mepbl coBnaAalor.
Hexoropue cuMBoJIbITpaAlrquoHHo l{crloJlb3yio'icflB KaqecrBe
O6ltquO Ailrl 0603HaqeHllfl
xap ar(TepiIcTHtiIipI.IBbIXpaCDpeAer'leHI4s.
) ; t p a K T e p t t c r t t t (r e o p e r t t q e c l ( H Xp a c n p e a e " l e n u t i t t c n o . ' l l 3 y l o r c f f r p e qecxue 6yxeu, a rJrn nu6opouultx -,'IarllHcxlle. Tax, HafipllMep'
s n 6 o p o u u o e c p e A H e eo 6 o s s a q a e r c f l X , a r e o p e r l ' l q e c K o e c p e A H e e
p. OCHosUafl sa(aq.a O6UqsO 3aKJllO'
:Ha.reriHe eCeti COSOxyIIHOCTI4
qaercq B ToM, qro6st oIreHHTbHeKoropble napaMerpbl H3yqaeMoro
no ort6opxe
pacnpeAe,'Iesus.CrarncrLrKa, Koropyrc MbI BbItlHcJIfleM
ua sisrofi coBoKyIIHocrlI, HcI]o"lb3yercq KaK oueHKa rpe6Yeuoro
napaMerpa. flplttr.teHeuuefpeqecl(Ilx Il r'larHHcxllx 6yxa ilo.]'qeplillBaer pa3HIrII)' Mell(Ay [apaMerpaMH I{ coorBercrByloulHMH HM cra'
TOTjTII B C,IOe.
o6srrHo err6opxlr rr3B,rreKaiorcfl
rr3 coBoriynHocru HayAa.lv. oro
3 e a r l u r ' q r o B C e 3 , ' i e M e I I T bcIo B o K y r l H o c r LIII M e t o r p a B H b i eB o 3 M o ) K rrocrrr 6ut, BKJrroqeirHbrnru
e sH6opxy. Cnyuar?Has sbr6opxa 61r.re;
r i e c i l i e u { e H H o ilrr, n o M e p e B o 3 p a c r a H H f le e - o 6 : s e v a o u a 6 y A e r r o v I r e e o x u c b r B a r b p a c c M a r p H B a e M , v rcoo B o K y n H o c r b . K c o x a , r e n a r c ,
]l0ijlqeHire rrcrrrHHo c.uyvafiuoir nu6opxtr npaKTLIqeCKH
HeBbrrroJrHr.t_
r \ ' 1 0T, a K r ( a r i r p i r o n p o 6 0 n a u r r r f e o J I o r H q e c K I , IOX6 r e X r O s H e B C eH X
qacrlr -locr)'nHbr. llpo6u ii: r,'iy6auHtrx o6ter<roB
He r.iMeloT:raror?
)rie BC-l\'lOx(HOCrri
nonacrb n eur60pxy, xar< npo6rr
- n o , 1 o 6r.r3
H urroBepxHocrx
usrr o6uarxesuri. 3agaua onpo6oeaunr n
vifloerisx
B c c b t r s c J l o x { H a .B x o H u e s t o f i r , r a s H p a c c M a r p H B a } o r c rer r p r p e x : r , i .
B O 3 H l l r i a i o u i l rreI 3 p a 3 J r f i v u Re n 6 o p o g H b t x c x e t 4 , H r r p o B e . { , e Hcop a B H3Hire noc,rre-IHrrx.o4Hatio npx pe[IeHr{tr M}rortrx f eo,lOtHuecKHx
3 a i l a q a H a r r r 3 f i p y r o r c f lA a H H b r e c, o 6 p a H H u e 6 e : n p e 4 B a p H r e J r b H o f o
n H 6 0 p o u H o f o r r J r a H a f. p x n l t r o M V n p f i M e p o M f l B , r r r e r c r H H T e p l p e r i . l [ r r s n o r p e 6 e u u u x c r p y r r r y p f l o A a H H b r Mc K B a ] K H H .
CTATI,ICTI,I
KII
P a c n p e 4 e l e H r f l r { M e r o r p f i A x a p a K T e p u c r r r K ,H a r r p H M e p ,r a K r { e ,
x a t i c p e A H r r sr o r r K a , t r e p u p a : 6 p o c a I l N r e p b rc H r \ { M e r p r . I uO.r l r x a _
pi-!i'ifepl'lcrl{l'illila3bIBalorcff napaMerpaMH, ecr}I oHH onHcbrBa:or
c ^ o B o t i v n H o c r uI ,r c r a r t i c r l l [ i a N l r { ,e c J I I {O H I I o r H o c f r c q x n n 6 o p x a n t .
C r a r l i c r n x t r I I o l K H o H C n o , ' t t r 3 o B a rA
b, I I f l o t l e H t i t i n a p a N { e T p o B I I c -
TIICTI]KAMI.I.
38
39
rl
rfli
a p u Q l r e r u v e c K o e ' B b r q r r c J r e H H or reo
.IIMeer
..- !!tonrt
A a H H b r r rnan 6 o p x l r .
ABa B esrcuefi crerreHrl )KeJrareJrblrblx cnoficrna,
K'TOpbre
Ae,laroT ero 6onee no.rre3HbrM
AJIff orleHKr.r,
cpeAHefo HJrr4UeHTparbp a c n p e A e r r e r { i l r , , r e N , { , , r r o 6 ai ;.
orv*'
: :0: :p. ,o: ql _l i1b"r.xH r r n
uo,_
0
x a p a K r e p u c r ' r i : M e A l r a H ar r J r r .*i o l u . B o " - n aafpr ": y" ,. r "
ap":aee aprtrpverllrjeclioe tBd'IfleTcr HCCMeurerrHori
oqeHrofi HcrrHHoro
cperuefo 3riarrcHirfl coBoKyrrHocrr{.
Heo6xoAuu; ;il;;r",
rrro
cTaTIIcTII{ia- qTo HeCMeIUeHHafot_(eHr{it
cooTBeTC.l.BVIOUIefo
napa_
M e r p a . e c r r r e e c l ) e l H e e 3 H a q e H H eB
, 3flroe no Oo"riuiomy ua6opy.
a u 6 o p o r < ,p a B H o e r o u y n o p u u e r p l : .
Bo-_er.opr,rM
x ,o x { H o r r o r i a 3 a r b ,
'irro -r'rrfi clrM\'rerpr'rqHbrx
pacrrpeAe,reHliii,rtorooa'.r rrop*rrono.r,-,
cpe!Hee apltdluerr-vecxoe-xapaxrepa3yercfl
reuleurlrrer? "ryyqrrter.o
qelr ;rn6as
l]l_n:gr]rrr.nxfl K cpeAHelry :naveuiroo".ouonl,rrrocr',
"]pyrirE uectr{cureHnT
( r a x a a , r . ; a x M e , 1 n a H a ) ,u o c r . p o e H u a a
rxe nul6opre. X
Olrao^ npta: ,B H o o t r , r b H o
r o x , r y , q r o n u^6ro" Ipror avrHr b
nlre
u re,
cTp el:ol H
u M e r o T M e x b u y l o A ' _ c n e p c r r r cu, a '
n"6opoun*
rr, c; e19:arer b Ho, rB,,rflrolc, 6o,,r'ee
eQ $exrlio r_rr,r
r,rI r.
', npaKTfiKe feox,Mr.lqect{oro a*la,trusa
npuHfTO npoBoA?r.rbce_
purc oflpe.qe.lesarl Ha o,[HoM o6pasqe.
B ra6"r. Z.t-:irrirho
rrflrb
:Haqe't.ft coAeplr{aI{LifxpoMa, iro,ryueuHrtx
B pe3y,r'bTarecleKTpoI ' p a Q H q e c K o f o a H a J r H 3 ao 6 p a s q a
i " r a u u c r o . o c-irliiii""'
JraHila [eHcHJrb_
acra u3 rof o-BocroqHofo I(a H:aca.
7T*tre
:1:119i:
lo3p
v rvLA
,rrE
ap'eMeruqecr,oe ro 3TrIM
"ne
AaHHbIM.
flpyrar xaparirepucrrlxa pac[perer.reHl,_ Mepa
pas6poca or_
re'rrbHE'rxsuaqeuufi orHoorrenrrro cpeAlrero,
HJrLrAucrepclrs. HsBeCTlibIpa3"r'qHbre rlepbr sToro cnolicrnr,
I{o TOJIbrioABe u3 HHX
ur.tpoKo Hcno,'rb3),rorcs.OAua rrs Hrrx _
- r{Banparunri
c,n,a .4pvrar
xopeu"
;''f,,|.'}Jo".TffuJll",fl5#ilt
(rraH.r'aprHbrM
o r r i J I o H e H r r e u{.l r c n e p c H l o r { o x { H o
paccMarprrBarb
KaK cpe,{Hee 3HaqeHLIexBaAparoB
OrK,toHeHtrfiscex BO3N{,}I.HbIX
; r s a q e H U r cl n v q a f t s o f r s e J t " u t t H o ro ,
,,arunnofo cperHefo coBOK\'[-
co,lepxanuexpoMaB cJ,ra'rrax
lu1,:#
I J o r re p
CoJ.eD;iirc:le
ua 2'l
Cr.
205
l9i)
220
235
Cyrrrlra
CpelHee3HaqeHrre
40
l I l0
It10 15 :
222
r/r
Irocru, Koropas onpeAeJlnercsno Qoptrlyle
I
ot-
n
ltx,-p)'.
(2.11,1
niJ
i=l
coBopaeeHcrBoM o[peAersercq ]ICTI'IHHafl 'r'licnepcfls
cl'lMBo"IoM
l.ryn"oar"'o2. Bu6opoqHat All,cnepcHq o[peAerqercr
cnyuaiiuar esr6opra H3 coBofl Xt, ..., Xrsi. Ecnl, ua6.tr,oAeu1t
TO 52 flBrflercl aQQerpacnpeAeJIeHI'IeM'
KyrrHocrll C HOpManbHbIIlt
rHeHofi ouesxofi ailn a'.
cpeAHero 3HaqeHus KBaAparoB oritJ'IoilpHuuua HcItoJIb3oBaHI'Ifl
OqeetIAHoIl'MOixer IIoKa3aTbcOBCeM
He
seriHii MOXST oKa3arbcq
npocro
c f l , q r o u e l e c o o 6 p a 3 H e e o x a p a K T e p l { 3 o B a r Eu'3 M e H q n B o c r b
KaKcpeAHeeSHaqeHHeoTKJIoHeHlIfloTCpeAHefo'HonpocTaflnpoHy'IIP'
BepKa nOKa3biBaer,qTO TaKafl BeJIIILIIIHa BCefAa paBHa
T. e.
gritu
'
T 1( X , _ k ) : o .
(2.12t
n4
l=l
oT cpen,Hea6co,tlotrioe oTK"'IOHeHlle
Koneqno, Mo)KHOOUeHLTTb
(MD):
orx"'loHeuue
cpeA,Hee
raK Ha3btBaeMoe
ro, Lrd'rlr
MD :
I Slx,-xl
(2.13)
n IJ'
B e D r u r a . n l g b l e q e p r o r l x l { o 6 o s H a . I a p r a 6 c O n r o r H 9 e3 H a q e H I 4 e( T . e "
B 3 f l T o e6 e : s u a x a ) s a K " ' r o q e H g o fsi H H x s e , r t l q t r g t t . O A ,"ira""a,
H a K O M O ) K H OA , O K a 3 a T bq,T o 3 T a c T a T l l c T H K aM e H e e e Q S e x r u s n a '
14 HeIOHflTHO"
ueU ett6Opoqgaff AItcnepCLIfl.Xors grO HHTyIITHBHO
qTo
KoTopble
HMeeT
CBoI4CTBa,
Aucl]epcl.Ifl
Heo6xoAt.tltonoArIepKHyTb'
qeM Apyr[e Mepbl H3NleHqlinoneauoft,
6o,lee
HaMHO1O
ee
Ae,1aloT
BOCTI.{.
, IB a A p a T o B
T a r x a x . { u c n e p c t s s B J I q e T C gC p e A H r { M3 H a q e H l l e NK
orx.nouesuit or cpe!,Hero, ro ee pa3MepHocrb xapaKrepll3yercfi
n3MepflJrHcb HcxoAHbIesa6,'trcAexBaApaTaMu eAlrHurl, KOTOpT,TMH
no"{eBoro
coAep)Karb KpI'lcraJI"'lbI.
Mo}Ker
I{arpliMep,
Hul. flopoAa,
iurlara' bo.tlltuue ocu roropux i'lMelor cpeAHIoIo AJII{uy 13'2 un'I r
Mgorue He cql'lralor nJIouraAb uepoii AllcnepAucnepcnlo 2,0 tr,ltut2.
cHH AJTHH.B 6olrrnuscrBe [puMepoB' fAe MbI HMeeMAeJIo c AlIcnepcuefi, oHa HcltoJib3yercs B craIIAaprll3fipo-BaHHoM6espasltepHOM BrAe, r. e. B BLIAe,He 3aBHCflqeMor nu6paHabix eAI{H}III II3Mepenrit. Sror nonpoc 6yAer eu{e noApo6Ho paccMorpeu B AasHoft
rJIABC.
qro6u noJlyqllrb craracrnKy, Koropas xapaxrepu3y'
,[,.nn roro
cpeAHero 3Haer Ar.rcnepcvro,rllilr. pas6poc AaHHbrx oTHOcHTeJrbHo
4t
rreHlts H o6naAaer rori )Ke pa3MepHocrb]o, qro H I{cxoAHbIe AaHHbre, Mo)KHo BocrroJrb3oBarbctcraHAaprHblM orKJIoHeHHeM. Oso
onpeAe,'rflercfiriax xna4parHuft I(opeHb H3 Ancnepcun t{ o6osHa'IaeTcq clrMBoJrotr{
o, flBJrgroql{Mcf napaMerpoM coBoKynHocTI{;cooTBercrBylou1aq au6opouuan crarllcraKa o6osHarlaercg qepe3 s.
Ma.noe 3HaqeHite craHAaprHofo orKJroHeHLIfl yKa3blBaer, qro
ua6,rrcAeHrrrrxopouro rpy[rIt4pylorcfl oKoJIo IIeHrpaJIbHono3Haqeuns. Hao6opor, 6olluroe craHAaprHoe orKJIoHeHHe noKa3bIBaer,
.ITO Ha6rI,OAeHHfl
CpeAHefO3Haqerxr.rpoKopaCCeqHbIOTHOCnTe,IbHO
HHfl rr r{Melor cna6yo regAeHllr-{rcK ueHrpaJIIr3aIIH[. 3ro npov.nnrocrpupoBaHo Ha pvrc. 2.11, r4e uso6paxeubl ABe cIrMMerpIztIHbIe
pa3,'IUqHbIe CTaHAapTHbIeOTKpHBble paCnpeAeJIeHI'It,I'IMeIOII{I:le
KJIoHeHrIt.Kpunaa ,4 xapaxrepl{3yer HacblilleHne ueQrrrc (n npoqenrax) o6pasqoe KepHa H3 npoAyKrasHoft 3oHbr ceBepo-Bocroquoft Ox.naxonau. Kpueaa B npe4craBJrfler re >xe BeJruqr{Hbr AJrfl
ueQreuocHoii o6.nacrn 3anaAHofo Texaca. Cpe.qnee HacbruleHne
ue$run B grr{x AByx peruoHax pa3JrzqHo, Ho Hau6o.nruree pa3nriqlre MexAy KpHBbrMa3aKJlroqaercqB roM, qro AJIfl Texaca xapaKTepHa 3HaqIrreJIbHo 6o.nee BbrcoKafl H3MeHqHBocrbHacbrulenilfl.
,
Beclua rroJre3Hoeceoftcrso HopManbHofo pacnpeAe,rreuurI cocrour B ToM, qro IrJrolqaAb rIoA xpnaofi B npeAenax HeKoropofo
Hanpzlrlep,
3aAaHHoro HHTepBaJraMo)Ker 6Hrl ro.{Ho BbIrIHcJIeHa.
6o.nee 213 sa6nlr.:p,esuil (68,27|6) nonalalor B l4HrepBan c lreHrpoM B cpeAHeM 3Haqeunr.rLI AJII{HoII,paauoli AByM craHAaprnblrl
orx.nouesHsrtr.flpurvrepno 950/o scex Ha6rloAeHnfi 3aKJlloqaerct B
[HrepBane or -2 Ao -r2 craHAaprHb]x orKJIoHeHar?n 6oree 99%
coAepx*rrcrr B HurepBa,{e or -3 Ao +3 craHAaprHblx orr.noneHrtri.
3 r o n o K a s a H oH a p u c . 2 . 1 2 .
Pacnpe4e,reHae, yKa3bIBaIoqee creneHb HacblnleHur se'.1;rtrc
n o p o r , c e B e p o - B o c r o , r H o iO
i x r a x o u s l ( c n . p r r c . 2 . 1 1 , x p u n af l A ) ,
n M e e r c p e A H e e3 H a q e H r . r2e0 , l 0 l o n c r a H A a p r H o e o r K J I o H e n n e4 , 3 % .
HopMaJlbHo,To c,'teAyer
Ec"rn lpe4noJro)I(HTL',qro pacnpeAe,-IeHLre
0)KH,Iarb, qro oKo,ro 213 uccnelyeMblx o6pasuos 6yaer fiMeTb HacbrrueHrrcne{rrln or 16 ao 2401s.I4zyueHt{e HcxoAHbIxAaHHbtx [oKa3aJro, qro 1145 npo6 xaparrepl.reylorct HacbluleH[eM, Koropoe
cocraBJlfler oxo,ro 689b
HaxoAr.rrcrrB yKa3aHHbIx npeAeJlax, qro
B c e x A a g H b r x .T o " r r x o l 0 l o 6 p a s e u , T . e . o r ( o J l o6 f q , u M e e r H a c b r lr1eHueBHe HHrepBana2o (12-29olo).
Te, xro He riMeJr AeJIa co crarncruqecKur{ aHa!'rHsora,o6srqHo
e I C ! ' I e H H O T3OH a q e c T p y A o M p a 3 B L r B a I OHTH T y H T H B H OBeO C I p H H T I I q
orKJIoHeHHs.
Hr4g AucnepcHH rrJrr4craHAaprnoro
fengercrr Jm Ar.tcnepcufl, paBHar 10, 6olruroi,t w,nw,ua.nofi? LIro sHaqur crauAaprno^e orx.tionenrre 23? OxagHaaerefl, Alfl HHrepnperallrrn KaK AHcuepcnl{, TaK H craHAapruoro orKnoueHnfl r{e tpe6yercx [ptlltrcbrBarb Kax(AoMy r.r3 HHX q[creHHoro 3Har{eHrfl,,a rpe6yercx cpanHI'IBarb oAHy Ancttepculo c apyroti. Bu6opxa, uMelourar Hau6o,'rrulyro 4ucnepcHrc IlnH craHAapTHOeorKJIoHeHHe, xapaKrepr.r3yeTcfl
12
s00
400
s
Q:oo
t
o
o ?nn
U
s
l-
{nn
40
30
CO
50
o,/.
H a-csrulexr,te,
70
HacbluleHhe HerpP H c . 2 . 1 1 . 9 a c r o r u o e p a c n p e A e J I e H U en p o u e H T l l o r o c o . ( e p x a H H g
(A) u Texaca (B)
TbIO B HeQrRrtottt no,le O x . r a x o v s l
io,iu,i
r__]-___-1
-3
-2
I
0954
i
0997
-1
x
|
I
+1
+'l
+J
Pnc. 2.12. flroulaAn craHAaprHoro HopManbHoro pacnpe.lleJleHut' 3aKIIoqeHIIble
Ba"IoB, Kp arHblx craHAaprHoMy oTKJIoHeHHIO
npelen ax I.rHTep
6o,rtruulr pas6pocou Ha6,rroAaetrbix3HaqeHr.lfinpu
B C E I I 3 M C P C H U f l C A C . T I A H b IB O A H I ' I X U T C X X C
ySJIOBHII,qro
CAI4HHII.AX.
P a s e H c r e o ( 2 . 1 1 ) , x o r t l H . o n p e A e ! ' I f l e rA n c n e p c u r c , o 6 b l q H o H e
'tax Kal< coAepxllT n onepauHft
rrcnoirb3yeTcA AIrs,sst'{ucrelrttii,
t
L
-crox{eHHfl. Buecro eroft Qop'
r
r
y
M
H
O
)
K
e
H
I
r
f
l
t
L
BHqHTaHHs,
OqeHKI'IAHCnepcI'IH licro'rlb3yercq Apyfas
\ryJrbr AJrfl BbIqIICJIeHI.{fl
q
Qop uy.rra, Korop a LIMeer cneAylouuft BI.I.4,:
(2.r41
43
! r Y . - - Y , z . \ ) ' r r r r t ' e r M I I t u t l i a J l b H O e3 H A q e H i l e e p e . l l l B e e . \
. K O T O I ) O t ._u) \ , , t
n
"
./
\rx? -"
i-
\2
L)"1
r.
" r.:l
I
n ( n-
C noltoullro
;-l
n
Sr'.i
l
/
r2,15;
l)
HacroJlbHoil Bblqucr'rr.rreJ-rbltori
MariluHbr XX; u IX,r
MOIKHO IlOACril1TaTb
qTO
O;IHOBpeMeHHO,
IT03BOJIfeT
HbIC.
.[,.nn nuuucd'IeHr{qorreHoK AltcnepczII Ir crarIAaprHbIx orK,'roHeH r 4 r iB B e A e MH e r ( O T O p b nr ep o M e l K y T o q H H e
s e , ' r H q u u u ,x o r o p b r e q a c r o
6ya1'r IlcnoJrb3oBarbcflBo Mgoflrx npoqeAypax, rr3d'iaraeMbrxB noc,'reAl,roxlrrxf,'raBax. HeqeurpupoBaHHafl cyMMa KBaAparoB- 3To
rrpocro XX;2; qeurpupoBaHHarcyMrua KBaAparoB (SS) onpele,raercfl no (ropril,re
n
!,\'
h\1r
i-
i2.16.1
/ f\ , r|
i:l
Itl'Ilt,
qTo
a"'Ite6paHqectiLI
3t{BHBaJleHTHo,
n/n',
qq -
T,xi--l-(tl",l .
tt \{/
\ J:l
U
i:l
.,,: I ss:
tr-t
-
I lrl":^-rl,E,
I
( 2 . t 7)
l
O u e l r N y , i t , H c I e p c l r rBr b r q r i c , T f l ] onr y r e r , r A e J I e H r r so r o f i
n-1, r. e.
I
ti
\U
n ( n _ t )f,ix?-/$='
L
?:,
Be,rlI'IqHHbI Ha
:
(!"')"]
",J']
(2.r8)
Be,ruqnHa n-i,
x o r o p a f l c o A e p l K r . r r c fil( a r i n Q o p u y , r i e ( 2 . 1 4 ) ,
raK ri n Sopu5,,re (2. l5), rpe6yer HeKoroporo rro.flcHeHnfl.
!,acnepc u s o n p e , q e J r f l e T crrira K c p e A H e e s H a q e H n e r i B a A p a T o Bo r x , r o n e n r r f t
or cpeAHefo. Og,Haxo, lrMer AedroJruurb c nu6opxor?, MbI He 3HaeM
CpeAHefO 3HaqeHr{rrCOBOr(ynHOCrH
HCTHHHOfO
F, HO MO}KeM OrIeHHTb ero c noMorrlbroau6opouHofo cpeAHero X, xoropoe Bblqr4crrrxBa^qparbrorxaoHeHar?oT Hero.
ercfl Tar(, qt'o6br MrrHIrMr.r3rrpoBarb
lluaqe roBopn, onepauafl F :
L
X ",,
n
,,;t:
14uunu c.'roBaN,irr,
yllerrb[]UTb
qHcJIoTpe6yeMbrx olepaUuft Ha qHcr'ron. Ha BbrqucJlrrre!'rblroii
Mau l r H e Q o p M y J r a ( 2 . 1 5 ) M o x e r 6 u r r H c u o n b 3 o B a H aA J r f l o A H o B p e MeHHO|OHaXOXAeHUflCpeAHetOH Ar.rcllepcfitl,r{TO IIO3BOT'rfleT
H36exarr Heo6xoAuMocrrrABax{AbrncnoJrb3oBalboAHrr tr re iKe .xaH-
ui -Q - -
cpeAllero oqeHKa
BO3MOXHbI.\. B cltrr,v 3Tcfo cBoficTBa BbIoOpOrIHOro
I
i
c
t
l
o
"
l
b
3
O
B
a
r
b
e
c
.
q
l
t
$ o o u 1 ' . ' r y ( 2 . 1I ) .
3
l
H
t
{
;
'
i
{
e
H
a
'
AfiCIIepctlll 61"rer
^ 1 a e r 3 H a q e H H eX , A . r q
-.1-5t (.f', -,f
n /^J'
olreH1' tlB.lrerctl cl'teu{eHHoll
i_l
t1
fiofr J..']n,3-:
1' r a
r{To6blycrpaHllrb cMeureHlle'
)'l (.Yr-pi'. .L[,.nrroro
nlJ
; - l
B QopMyre Arfl BbI6oPoqo6pa3oM oueHl{y AI'Icnepr
a
K
I
'
i
l
u
}-Be,{HqiiBag
!'l bi ncIItr.l b3)'e \'I B Ii aqL'CTB e 3H a \IeH aTe'''I9
u{)fi ru:nepcrrti n-1,
CIlLI-
feo'
Buqltc;reut'te 3Tttx Bertl{{lIH Mo}I{Ho rloiia3arb Ha npllMepe
Cd'IaHXtiMtiqeCIillX Aai{HItrlX nC COAep){(aHIiIO XpOMa B IJIIIHIICTbIX
!IToIlax, rrpliBe]eHHblx B re6,'L 2.1' flepenucaB 3ry ra6"Iuuy raK,
2
'
2
'
r
a
6
n
'
n
o
.
r
l
y
r
{
H
M
x
e
a
g
p
a
r
o
n
,
c
r
o
.
r
y
6
e
u
6ur oHa co-tepxia,IIa
npI{6JIIl3lrpaclpeAeJIeHH
!,orri'crtaai qro corep)I{aHIIfl xpoN{a
IrTO
OKO!'IO
AByX
O)KIIAaTb'
3elioH)', MOIKHO
TC,iibHOIIO HOpN'la,rlbH(lx1\'
A
H
a
Ipts
r
h
.
1
9
8
2
4
6
n
p
e
A
e
"
r
a
x
B
p
a
c
[
o
r
'
i
o
;
i
{
e
H
o
rpereri ssaqeHrrit
t:r6"rrruul noria3bIBaeT, qro rpH 3HaqeHllfl ll3 rlgrl'I' r' e' 600/0, Aeft, J I B I I T C " T I L HNOO I ] A A A I O TB 3 T O T H H T C P B A J ] '
3arrerrrlt, qTO np11 BbiqllcJIeHIlHCyMM KBalpaToB reox]{MlIqec]{IIx -].aHiIbI.\ no']B,,IflIoTCf qllCJIa' coAep}Kaql,re ceMb 3HaI{oB. 3Ta
T a 6;ru ua 2.2
Buurrc,neuue
oc#ffi"fgil:rrn
AncnePcrfi
42025
65025
38025
48400
205
25;
195
220
235
<( 9t(
!-ti:1,110
I
2Xi2:218 700
( x X ; z : I 2 3 21 0 0 ;
1232100
2280;
S S : 2 4 8 7 0 0- - - :
,,AA
-'
-* s2570:
A-
s:570:23,88.
45
Ta6.nu\^ 2.3
Co4eprxanne
xpoMa,HnKerss r,a:aa!.as
B cJraHrlax
Kan:aca.rir
0
i
205
255
195
220
235
130
i65
100
180
ztll
200
115
qnt
o
o
r
fi
I
t
ts
s
Cylnru
cP.,tnu.
il10
222
675
t.tJ
935
187
o
I
3HaqeHHq
TEHACHIII{fl K BO3HIZKHOBEHI{IO B NPOqCCCC BbIiIIICJIEHHfl OqCHb 6OJIb[I].{X. qI]CCJI NPHBOAHT HHOTAA K BO3HHKHOBCHIIIO SATPYAUCHATi N
9IJlvI,
npHcnocooJ'IeHHbIX
A,rlfl pa6oTbr c qrjcJ'raMlr,
coAeplKaurr\IIr
rr{aro 3Haqaqux uzQp. 3ro Tar{x{e rp}tBo.lrrr K Bo3HlrKHOBeHr.lIo
TpyAHocrefi ilpu BbrBoAeJ,aHHbrx,ec.-rrrio.trr
Scprr,lara HeAocTaToq_
HO IIIHPOKIT ,1!-1fl TO|O,
I]T06bI
BMEUTATb qIICJIA,
KOTOPb]C AOJIXHbI
6urr saneqaraHbr.
n n g 6 o r s i l r u u c r s a r e o J r o f r r q e c n u x , c c . D e r o s a H r ' r i. \ a p a K r e p H o ,
r{To Ha iia)KAoM rr3yr{aeMoMO6rexre H3Mepqer.cs
60,nee o4Hori'nepeueHuofi. B Naqecrse npr4MepoB]\ro)KHo npriBecrr.r pe3y,,rbrarbl
usuepeHtfi Kor'I'reKUII'tKOpaJ't!10B,
nocd'IeAoBare,lluocut npo6
ii3.
prAa cKBa)KriHHJrrr)Ke onpereJreHHffnapaMerpoB nopo,u,B xo.rrJier{qaa o6pa:i1oB necqaHnxa. Taxue raHHbre o6brrrno
i,anrrcusarcrcq,
B BHAe raSrnllrr nopflAKa nxm,
r!.e /? - qricJro ua6nrc4eulrfi,.
a mQHCr'IO
r3]'qaeMblx repeMeHHbrxT
. ax, Harrprrr{ep, fror"rHbre
aHar'lII3bI'II3 KoTopblx I't3BrrterleHbl
AaHHbIera6n. 2.1, cogep>xar i 7
nepeMeHHbrx.B ra6,'r. 2.3 npe4craB.,reHbrro"rrbr{o rDu rr3 H}rx.
a H M - e H Hcoo . r e p ) K a H H fHf H r i e J r f ,B a H a - ] r u H x p o M a . . [ " r a x a x 4 o r o
cro,r6ua MoNiHo noAcquTarb cooTBeTcrByFolllrecyMMLI l,t oqeHlirr,
c p e A H e e3 H a q e H H eH C r a H A a p r H o eo T K , r r o H e H r j e .
o A n a x o p a 3 r ' r r r q H b rnee p e M e H H b r e
Moryr He 6urr He3aBrrclrML,rMH,.Mex{Ay J{u\{rr Mox{eT cyilIecTBoBaTbHeKoT.opaa
Qoprr.layc"rroB_
Hoii cBfl3ri. Baxuo, qro Mbr B cocrorrHr.rriorreHnrb npxpoAy H
ct..Jry
STIIX yc"rroBHrtxcggseil, Tar{ r{e xax 6uuro Ba)KHOOnpeAeJrHTb
yc_
.IIoBHbIeBepofiTHoCTHnofBJIeHHg,qHcI{peTHu,rco6urali
ConnaconaHHoeH3MeHeHfie
AByx nepeMeHHbtx
BstcHcrHrer'rbHbrertpqrreaypbr, Hcrro!'rb3yeMbre
AJ19 noJryqegHfi
o u e H K H A H C n e p c H HO 4 n o i i n e p e u e n H o f i , M O ) K H o p a c u H p H r b
AJrfi
BbIrrHcJIeHHfl
Mepbl ssa[I{Hori H3MeHgHBOCTr.t
napsi nepenne""r,"^
46
HOpMaJrbt r a c . 2 . 13 . c c a l v r e c r s o e B e p o f r H o c r n o e p a c n p - e A e J l e H uAeB y x H e 3 a B H C H M b I X
I i b i \ c J ' l Y q a i l H t l xB e l l l l g t ' I H x. 1 u x 2 H o p M a l l b H o p a c n p e A e " ' I e H b t
f i O B a p r r a q H e i if,l B . [ s e T c qx a p a K T e p H c r n r o i i
3 r a r u e p a , r r a 3 r r t B a e M aK
coBMecTHo|oII3N,IeHeHlIf'{.B-vx[epeMeHHb]XI]ooTHoIIIeHI,IFoKHx
Ha
o6uteuv cpei.ile\1\' 3HaqeHHIo.3To coorHoIIIeHl'le noI{a3aHo
p
a
c
n
p
e
a
e
J
l
e
Hnfl
n l r c . 2 . " 1 3 , ' r , l e n a o 6 p a l K e H b rs O p r , r n n o B e p x H o c r e f t
pacHopMaJIbHoro
I':pIlBbIMI'I
b"po"'r""cteit, nopox,l.ei{HbIX AByMfl
fl
rrpe,4,eJeHII
'
fl_vcrl xt u xz rrMeror Kpr.rBbrepacnpejleJl€Hut BepofirHocTe[I,
a n a , l o r l u n l t e I i s o 6 p a x e H H b I MY a p u c . 2 . 1 2 . T o q g o r a K x e , K a K
A l i c f i e p c l r f x a p a K T e p u 3 y e r O a e 6 p o c s n a q e H r l i i o r H O C a r e J I b H IOI e H T na;rsnbit roqxH, KaK 3ro rloKa3aHo Ha pnc' 2.12, xoeapnall,E ffB'
JrffeTcrruepOfi pa:6pOca siiaqeHttil pacnpeAe,'IeHHq OTHoChTSJIbHO
o6qero cperHero.
orleHKri KOBapHarIUrrMbr cHoBa BBeAeMBeJIH!,.na eHulrc.rreHr.rfl
3ra geflHqllHa Ha3bIBaeTCq
quny, aHa,Iorur{HJiIO
cyMMe I(Ba,4,paTOB.
(SP) u onpenpol'r3BeAeHuit
el'{emauHLix
u-uipupoeasHoii'cv,rluor't
Jr,e"'Itlercflno cPoPui'.ne
-qPjr:
2(X,, -X llX rr- X ut,
(2.1e)
i-l
- f-e sHaqesue k'fi'
rAe X;i - l-e gHaqenue i -ii neperteHHol't,a Xrn
c)':vllilallpou3BeAeHHft IIeHTpHpoBaHneDeMeHHoil.CuNleon SP,,,
3anlturert
sto BbIpa)KeHHen $opue,
ft-il
nepeMeHHbIX.
nuix i-li n
:
yAo6sot? AJI9 BbIqlICreHllfl
: f*,,*,,- +E* r,;
sPr,
",,.
i=l
i=l
(2.20)
i=l
47
BenHqasa 2(X,iXtn)
Ha3blBaercs HeqeHrpupoeauHofi cytr,tnaoftcrueIuaHHbtx npor.r3BeAeHHfi. Css:tt' BeJIlltIHHbI SP;a c cyuntofi iiBaApa'
TOB MO)KHO,'refKo yCTaHOBHTb,eC,'rHBbl6parb i:ft.
TorAa noJryqaeM
F
L)
I
z\;;.\;;-n
51X t i
lJ
i:l
1
Ta6,rr.rua2.4
xpoMoM(Xt) n nnxenem(Xz)
Y/
A2
n
n
sPi.r
lcJreHhe olIeHKH KoBapnaqHfi MexAy
fl
-
v
''tt
*,,i1:ssj
It tF.r?,-/F
J
\kt
rn,n
L r:l
(2.21)
130
165
i00
26650
42 075
l9 500
29 700
34 075
42 025
65025
38025
48400
50225
IJO
l6 900
27 225
10000
1 82 2 5
2t 025
;=l
XXr:675
Ecnu lru BblqucJrHMcJ-\r\rbr c\IerrraHHbrxnponsne.4euuti li c y M MbI KBaAparoB A,'rf BCex Bo3xroit{Hbtxtor,t6rruaqrrii narurrx rpex
fiepeMeHgbrxr.is ra6,r. 2.3, ro [o.ryquM c"'reAyloil{yrcra6.rruuy nopa4xa 3X3:
sPr,2:152
000-
2X22:93 375
(ilr0) (675)
: 2150.
2150
covt2: ---- :537 '5.
t
Cr
Ni
SSc.
SPnr-c,
SPv c.
AIIC[epcI{l[
ecrb rarixe Bce Heo6xoAlIMbIeAaHHbIeAJIfl BbIqI'lCJleHntl
,Y: (Hrrrierq) no $opuyne 2.12. Hurarenb lllo)Ker ronblrarbcr BbIrrnc,'rHTb3To 3HaqeHae, 3arroJIHi4ara6,'tuqy nopfl,4Ka 2y2, npuae,4eHHyloHfi)Ke.
eD_
SPc.-.';i
SSsi
SPv-Nr
SPr.i-v
SSv
.Ilerxo 3aMeTIiTL,,qTo Het(oTopbten3 Be,'tlrril.iH BcTpeqalorct R
erori ra6,rurle ABaxiAbr: HanprrNlep,cyMl\{a npou:lBeAeHar'ia,rn naHaAH', ri HHr{eJlgraKag )Ke, KaK H CyMMa [porr3BeJ,eHr]i,I,,'If HnKeJrf H BaHaAr.rs.o6o6utarr 3Tor Qaxr, MoxiHo lranHcarb sP;a:
:SPri.
3ro paaencrBo 6yler HaMu r{croJlb3oBaHoB c"rleA}'roul}tx
fr'IaBax.
floAo6uo roMy Kar( Mbl rrprr Bbrr{ncJIeHH}rAllcnepc}lr Aelrvnn
B e J r H q H Hsys s a / z - 1 , B b r q H c r - ] I lO
MI { e H K yf . i O B a p H a U I IrI a
r ,r i x e p a 3 A e n l i B B e , ' i l l q f i H ys P n a l l - l :
sP in
COV;;,: n-l
n-ttiJ
- ' i i\ x,,1
:
fI -r,,",,
",,
n
L,=l
g
l:l
H
r=l
: ^*iL' H.x,ix,,i ",,i",,j
r
J
/Q .)tr
I
II
X p o n a( X 1 )
Hrrxe.,ru(X2)
570
l t 3 7, l t
I
I
urr.
u
sz2
LIro6u 3aKoHrrHTba[ailr43 feoxl,rMHqecxux AaHHbIX, npriBeqeHHbix B ra6n. 2.3, ocTaeTcfl BbIqucJ'rHTb
TpH Be,'tfi.
Aorro,IHilTe,rIbHo
rulHr,r.3ro oqeHxa KoeapHaqr.riirJrfi xpoMa H BaHaLHfl (covrs),
H u K e . r r frl r B a H a A H f l ( c o v 2 3 ) t r A l t c l e p c r i r o B a H a A h r r ( s 3 2 ) . C . r r e a y r
npoueAypaNl, rlcrror'rb3oBaHHbrM
npH nocrpoeHl]r.rra6,'r. 2.4, euruuc,'ilire BerHrilruy (cov13).
H a p u c . 2 . 1 4 r r p u s e A e n aA r . r a f p a M M ac o B M e c r H o r op a c f l p e A e n e HIIfl .{BYX ilEPEMCHHbIX, I{OTOPb]C TCCHO CBfl3AHbI }I HMCIOT
AOBOJIb-
T e n e p l , B o 3 B p a u a s c b r i f e o x r r M r r q e c r { r i MA a r I H b I M ,i l p u B e A e H HblM B ra6t. 2.3, MoxHo Bbtqirc.iurrt'oueHrci xonapuaqufr AJrrr BCex
T p e x s n e M e H r o e . o 6 o s H a q a t r c o A e p ) K a H H rx p o M a L r H i l K e J r f c o o r uepee X1 H X2, Ir{o)KHoBbIrlHCd'I}tTb
BeJIItqHHbI,[pHBeBeTCTBeHHO
A e H H b r eB r a 6 J r . 2 . 4 . M w 3 H a e M r e n e p b A u c n e p c H n X 1 ( x p o u a ) H
oIIeHKy KoBapHarInI{Me)KAy Xt vr Xz (xpolrtoru u uuxe.leu). V sac
Ho Bblcor{oegHaqeHpteKoBapfiaqi.ri{.PacnpeAe,,ieHrzfl
AByx l]epefireHHbt\, n3o6pax{eHHble
H a p r r c . 2 . 1 5 , n l r e n r r e x i e A r z c n e p c H Hq, r o B
n p u B e A e H H b rH
ea puc. 2.14, uo He 3aBr.rcflT
oAHo or Apyroro, o qeM
orHocriT€r'rbHo
Hrr3Koe
3HarreHHe
KoBapr.rarIHa.
99llnerenrcrByeT
H H r e p n p e r a u H f l 3 n a r r e H u t io q e H o K x o s a p [ a q u r t A o n x H a r r p o B o AIlTbct'far{HM Nie 06pa30M, KaK Lr ArrcIjepckir, Ho np]r 3ToM cr'reAyer noMHI{Tb,qro paccMarpr.rBaeMble
3uaqeHlrrr He cJIr{IuKoMcoAepxaTeJlbHbl, TaK r{aK OHLISaBHCSTOT enI.tHIiUU3MeoeHIlg.
48
4-201
-
,'=l
i=l
t-l
4g
cBtl3u MexAy repeMeHHbIMI{P
Anq oqeHril creneHn ssaaluHoft
xoaQQuIrHeHT
n" ri"ra"urefi or eAVHr';r\Ir3MepeHI'Ir'I{cnor'Ib3yercr
KoBapHaorHoueHl'Ie
co6oli
npeAcraBrqer
r, roroputi
Koppe.rrflul.lH
orKiroHe-'
ux
craHAaprublx
npoI43BeAeHI'Io
K
tt"'ti ,c"y* nepeNIeHHbIx
Hl t t i :
(2.23)
r t n : c o vt n l \ s f ) '
I
5
I
i
*J
4
-lI
3
_l
')
I
i
I
0
Psc, 2.14. ,[,uarpauua
p a c c e x H x t r I B - Y X n e p e M e H H b l xc B L ' I C o K u r xa o : $ ( l n l n e u r o u
K O B a pi l a I I 1 1 H
TG'
Tax xax xoa$@uuueHT KOpp€,'IflIIHIIflBJIfleTcfloTHOIleHHeM,
paBMoixer
lioBapualrufl
arona
flpu
6espasn'repHat'
3Ta BeJ-lHqI4ua
pacnpousne4eu[a cTaHAapTHbIx OTKJiOHenAli_
Hflrbcf Bed'ruirHHe
, o H e M o ) K e r I I p e B b l [ I a T be e ' f l o e r O c M a T p u B a e M b l xn e p e M e H g b l x H
rry xot${_rlrIHeHT KOppenqqr{HrrplIH}IMaer sHaqeHLIflB I'lHrepBane'
K ro p p e ! ' I f l I I I { Hp a n e n + 1 , 3 r o '
+t. Ec.rru--xoeQ$uqileH
oi -t,co
1,'tia3brBaeT
Ha npflMyIO .nnuefiHyto cBs3b Mex(Ay AByMtl fiepeMegs u r n r u .E c n H x e x o e Q Q n q r l e H TK o p p e , l f l l l u l rp a B e n - l , a t o v K a 3 b l Baer Ha ro, qro oAHa nepeMeHHag I'i3MeHtleTctlB npoTIIBoiIoJIOX{-.
no orHo[IeHIiIo K apyror?. Mex4y ABVNITvnoiroI,r HarrpaBd'IeHIlH
c,'IyqarMLIHaxoAnrcr cnel{Tp MeHee cllJIbHbIxxpafiuuun
l"rqHyrbrM[
css3eir, BK,'rrcqalouruitcny'tafi, paBeHcrBa xoarlQzqueHra Koppensut.trr HV,Irc, qro yKa3bIBaer Ha no"lHoe oTcyrcrBl'le rlo6ofo rIIna.
r u Helisr,ix gaBI,IctiMocrel?.
Ha pac. 2.16,a uao6paxeua crryalJ'Hfl'' KorAa cI'IJIbHagKoppe"'rflrrufl \{e)KAy nepeMeHHblMltor{eBHAua i.r xoeQQHqueHr Koppens-Xr6
tI
r0T'
t
i'
I
I
I
i
r = 0,98
o
r=054
l.
r = O JA
Xz
a
e
a.
o
r = -0,90
2
3
Pnc.2.15.,[,uarpauuapaccetH'ufl
4
..b
A1
o
r
aByx nepeMeHl{blx c HII3KIIM xoadQnuuentoM
BapHaullH
Ko-
X,
x1
r He onpeAe,teHo
a
r = 0,00
Prrc.2.16.ToqequueAlrafpaMMbr,
r.r,rJrncrpripyrcufie
pa3nnqnbre
Kopr<oecpQuuueHrbr
penquHr.rMexAy AByMsnepeMeHHbrMI.i
bt
I { H r . rn o q r i l p a B e H + 1 , 0 0 . M e s e e f l B H a q r i o p p e J r f l r { t r ful s o 6 p a x e u a
'ira puc. 2.16,6. B erou cJryqaexoeQ$r.rquenr
K o p p e J r n r l I l rp a B e H
ro,'rbxo +0,54. llonoxeuue roqeK Ha piic. 2.16,a onpeAeJreno no
t a 6 . n u u e c , r y u a r ' l n u r xq r . r c e J rr , n o 3 r o M y 3 H a q e H H f4l o y i n e p e r t r e H H b r x
coBceM He HMeroTcBff3u lpyf c Ap-vroM, o qeM cBLIAeTe,'rbcTByeT
xoa$$rrur'reHr r(oppe"{flqrru,6,lrrsrrHrix ur',rro. OrpuqareJrbuafl r{opp e J r r u r r o H H a f3l a B r r c u M o c r bc x o : Q Q r l u r r e H r o u r { o p p e J r f f u r { up, a B sulr --0,90, ltso6pa>xeHa Ha pr.rc. 2.16, e, xoropnii rrJrJrlocrpHpyer
ror c,t\'.Ia11,r{ofAa oAHa nepeN{eHHarr yMeHbrxaercq, B To BpeMq
KaK Ap\,faq yBedrrrqr.rBaercr,14urepeculrri npe4e,rlnuft c,ryvari
n p e A c r a B r ' i e HH a p r , r c .2 . 1 6 ,d : o A H a n e p e r u e H H a fr 4 H B a p l r a H r ar,. € .
ee 3HaqeHrrfl He u3N,reHflrorct.llonnrra
Bbrquc.TrlirbxoaQ$rqueur
K o p p e , ' r f l r { r rIrrrp r i B o n H rx u e o 6 x o A u r l o c r n A e J r e H V fHl a H y J r b ;B 3 T o M
c,rrlrqsg rio:;rFrDituuegrnoppe,rfltlrrr.rHe orrpeAeJreH. B npr.lMepe,
u s o 6 p a ; x e H H o MH a p u c . 2 . 1 6 , e , o r { e B r . i , r , H8a3 a u M H a s 3 a B i r c n M o c r b
Iv{e>KAy
IB}'x,trr nepeMeHHbruH.Ha6,rnAeHrrfl Xr w Xz pacnoJrox{eHbi
Ha orip\';.i{Hocril,noSro\{y coorHorxeHue N.Ie}KAy
jlB-VNrflnepeMeHHbr_
MH MO)KHOnpe.:lcraBuTbB BrrAe
X":l
a'-fr,
B npe.lIo,!o]xeHIrH, qTo qeHTpoM Oiip\,)t{HocTu flB!'rfleTcfl HaqaJIo
KoopArrHar. Pa4rrlrc oKpyxrrocrH paBeH a. O;1Haxo ec,rrHBbrqlrcJr[Tb
K o p p e , [ u t r n M e l K . l , vx 1 r 7 x 2 , o H a o r { a x e r c a p a n H o r i H v I r o . 3 r o
ilporrcxoitr.rrrroroN,ry,uro xoe$$HqrreHT KOppelrfiuHrrecrt Mepa ,'rr.rH e r i H o t ' r3 a B H c L r M o c r r 4 . . r u e x { A y , [ B ] r M
r rqe p e M e H H b r M H
a, y r i a 3 a H H o e
COOrHoiUeHHe
HeJIHHeiiHo.CyulecreyeT MHOfo BO3\.,IO)KHbrx
HeJrfiFreiiHbrxcoorHotueHur?,xoroprre N,loryr Bo3HuKHyrb Melr{Ay AByMfl
IIepeMeHIrbIMH.B noAo6uoii curyaqurl r<oa$QuureHr r\oppe,rqiI14H
HeJrb3rrcqHTarb y,[,oB,'IerBoprrreJrbHorl
uepoii creneHrr raKr.rx 3aBr4_
Clttr,tOCreft.
Ha npaxrnKe Bbl6opocuuri xoeQSIlqlleHr Koppe,rrfiur{nr Bbrqucrrrrercrrno QopMyJre
'rr: ,-ft- *,u-+
(,1",,.)',u)
,**,,
{,*
,*"'r')
lIJl pH l n
IE , 4
16,9
r3 , 6
il,4
7R
ri 4
1 5 ,l
ln q
a7
74
6,3
.[,era,rluo sTor Bolpoc 6y.4er paccN{orpeH B c.lcAyloulnx fJIaBax'
r.
Be"rllIqI'iHbI
a sn,ecb r\'{blocTaHoBIIMCgI{a npolleA}'/peBbIr{lIc,'IeHI'Ifi
llpn 6uo;rofnqecKux Llcc,'Ie!,oBaHI'lflxo6bIqHo Ha6.nnAaercq
cHJrbHafl rioppe"tlflIlltfl ceoficre B npe,4,eJIaxoagofi 6uo.noruqecxoii
rp\'IInbI opraHLI3MOB,raK KaK pe3yJIbTaTbIII3MepeHI'IfforAeJIbHbIX
x a p a K r e p I I C T L I IBi 3 r I a q l l r e J l b n o i ic r e n e n u 3 a B l c q r o r o 6 u u x p a e r u e p o Bo c o 6 r r . T a x , u a n p u M e p , B r a 6 n . 2 . 5 n p I ' l B e A e H bpIe 3 y , t b r a r b l
H3MepeHnff.4JInHbIII ttrxpLIHbIpat(oBHH 6paxrlono4 poAa Compo'
SiIA.
K A X J ' I C T X O} / C T A I I O B i l T I , , I , I M C C T C f f C H J I b I ] A f l C B ' 3 b M E ) K A Y S T H M H
XAPAI{TCPIICTIII(AMI-I, O qEM CBIIACTC!'IbCTBYCT BbIqUC,,'ICHHOE
ABYT,l'
KoppeJrruuH.
3Har{eHue
nu6opouHoroxoa$Qlit1}reHra
oueHKr.ixoaS$rzqueura KoppeJrflrIr{?{
MexAy
I.'rs snquc.rreHrrfi
coorBercrByrolrueKBaAcror6u.al'rrruslrepeunfinoAcqr.rraeM
irB\/r\,rq
parbr n cMeuaHHL,re
npou3BeAeHuq.
3ro cAeJraHo
s ra6n. 2.6, rAe
X r _ . I J I I I H A , X Z - I I I H P I J H AK
. O O $ Q U U U C HK
T O P P C f l q I I I , I HP, A B H b I f i
0,99, ora:uBaercfl orleHb Bbrcor{r{M,lrro noATBepxAaer noAo3peHne
B roM, qro nr,reercq nprMas cBq3b MeMAy AJrHHofiu tuHpl.rnofipaKoBuHbr.Cro.nl cu,rrbHble3aBucrlMocrlt BcrpeqarcTcq He Bcerd,a: B
r l . e i i c r B r r r e l b H o c r tB
r ecbMao6trqsu saAaqH, B Koropblx rpe6yercf
g_rrpeAeJrHrb,
cyxlecrBver JrH xorb
xaxaR-nu6y4t
Kopperrruus.
K arouy Bofrpoclr Mbr eule BepHeMcs.
Haoep,eHHas
Koppelcurfl
(2.24)
Tax xax ,r r.r3Meprer.nuHefiuoe
coorHoureHne
Me)r{AyAByMenepeMeHHbrMH,
MO)|(HO
OnpeAenHTb
xapaKTeprz3ylo_
^rlprMyroJrr.rHHro,
rrlyro 3aBHcHMocrb
Mex{AyHr.rMu.
3ro saxHHfi aonpoc-crarucrHqeCKOrO KOppe,'IflIIAOHHOIOU perpeCCHOHHOfO aHaJIHgA, sBntIOUIefOCt
ocHonort6o.luuruscrBaMeroAoB annpoKcl{MaUuu noBepxHocrefi.
52
Ta6"rIIua 25
Pasueprr paKoBIrH6Paxnono.q
poaa ComPosita, r'ru
Hexoropne Koppe.rflur4r.r
MOKAy [epeMenH[,rMlr
He orpaxaror
cooTHollleHl,ill
rraexAv HI]MH, Ho oHI-,I I,IHAyIIIIpoBaHbI
onepaIlI-IflMI,I
vnu npeo6paeonanuRur.r,
KoropbrM 6u.tpr [oABeprrryrbr nepeMeHHste. ,[,ne He3aBr.rcnMbre
cnyuafinue BeJrr{rrriHbr
o6srqiro r.rMercTHyKopper'rqqaro.
OAnaxo HeKoropbreonepaqr.rnHaA nepeMeH"'reByFo
Hbrlvtrrr\{ofyr np}rBecrr.rI( KoppeJIflIlI,ILt,
orJrHqHofior HyJIg, xorrr
He cyulecrByeTHuKaKoro,rugefiuoro coorHorfieHr.rfl.
XexAy Hr.rMH
\-yilIecrByrotqile Koppeilfl\utr Moryr 6urt ueNrexeHbr
r.rJlr.r
4axe o6P AXICHbI TAK'IMI{
O N C PA U H ' I M I - I .
53
Ta6nnua 2.6,
Burqrc;eH.re
cyMMxBaAparoB,
cMeruanHux
nponsne4enrii
r xoarpSuqnenra
xoppensqrnrroAaHHbrM
ra6n.Z,d
T a 6.rrlr ta 2.7
nJlfxte,
-ll,,nusu (s crrr) ocefi o6PaaqoaraJlbKlt, co6panHofi Ha
Ocu nePeuuc.leru n nopc,[,Ke nsmepeuufi
xl
\,2
338,56
285,6 I
184,96
I 2 9 ,9 6
6 0 ,8 4
3 9 ,6 9
rB , 4
16,9
13,6
1t,4
7rB
6,3
283,36
2 5 5 t, 9
148,24
l i 0 ,5 8
57,72
3 3 ,3 9
l(
2 3 7, 1 6
228,01
l i8,81
9 4 ,0 9
54,76
28,09
|
r0 , I
a7
C
d
e
f
X X , z : 1 6 3 96 o
g
h
i
\Y.-7,.1
sp;r:(888,48)-
(74'4)(63'8)
: g 7 , 3 7 .C o V 1 2y_{ :
rn,nr.
s s t : ( 1 0 3 e , 6 2 rr-' n ' : r " : 1 1 7 , 0 6s .s r : ( 7 6 0 , 9 2 f)T_ l 1
"
t,':
a
b
I17,06
rJ:
:23,41.
s,:Vr{T:4,84. s22:€jl:
: 82,51.
ro,so.
s,:7T6So:+,00.
'' ':
i
Cyuurr
CperHue
t9.47
:
'
[lTJGrd o'eer
Ilpe,1lo"'ioxuiM, qro o6pasuH fa,rbKn
c,ryqafiHo Bbr6aparorc_qc
raJrerr'oro n'rfx{a H r{3MepsrcTcfiTpir
oproroHaJrb'bie oc' Ha riax-
;il;;,;;; ff ";fr;
ff#"ii'
I'*
:::,.::."y9I,,;.til;'
ilb,\
y*
npe4nprn
"i'l'l;
*, d,." ;;;' ;; ;';" #;
:i
"e p
"i:,1:'y?*g:o:a
l;frfun""u
R
I
t2
5
l1
l3
li
q
9
98
AR
Ta6;rsqa 2.8
o6pasqonraJrbK[,co6paunofiHanrq)Ke
, - ,(nl.rurr(n cm) ocefr
(a nau6o.nuuas
ocb,b - nporvrexyrottHag
ocb,c - ralrueturual ocu)
t ;; ;; ;;;' ;;;, ;; ;;, TT#
:uao6opor
:y :'| _66yaer
"' iiruerrlauru,u
" rpeM.
pasuepu ro BCcM
2.2
npuaele'r,r 3aMepbr,
cAeJraH*breHa Ko,rJreKrrr{u.
-nepeMeHHbiMrz.
H IiOppeJIsIIHr{ Me}KAy
!auHure rariiKe
n p e A c r a B n e H bB
r B H A ec K a J r f l p H b r x
4liarpauna Ha prc. 2.17. Olnaxo
ec.Ilr{ relepb oclr nrr6paru B cooTBeTcisuu
c cofJrarrreHrreM
_ ro.
orrpeAeJleH'p sau60,rruras ocb raJrbKHA, HalrMe'blrraf - c;.
cpeAHqq-b,
ro raKoe^ynopflAoqeHnenpuBeAer
K H3MepeHHroKoppe,raqafi (ra6,r. 2.8). Oio bcoOenHo-xoporo
Br.tAHoua cxa,up'orl:
.uuarpaMMe(puc. 2.17), raK KaK raKoe olpeAeJleHae
npHBoAHrr(
cMerIIeHArOBCex roqeK B npeAenax
ceKropa Ar.rafpaMMbrc yfnoMl
45'. B c6ny sroro Bcerla. AoJrxHa
cyqecrBoBarb noJro)KnTeJrbHarr,
Koppentl{Hs MexAy Jrn5ofi napofi oceft,
unw MexAy orgorueHr.reM}fi
54
_
_l lu6r.
rar'lbKll,
8
LByx oceii H rperbeir ocbro (HanpHMep, Melr(Ay bla B orHoueHI{H K
c).
HasereHHr-re iioppeJrrirIHH,rptrrruHflroulrJe HalI6oJrbrrlee6ecno- 3TO J'IOXHbreOTpUUaTeJrbHbre
KOricTBO,
KoppeJ'Itqnu, IioTopble IIoflB!'tflroTcfiB 3aMKHyTbrxMHOXeCTBaXAaHHr,tx.JaMKHyToe MHo)Kec r B o I a H H L , I X- 3 T O T a K O e M H O X e C T B OB, X O T O p O M C y M M a B C e X
IIepcl,4eHrrbrx,
r43\{epeHHbIXHa rrH,{HBrrAyaJrbHbrxnpeAcTaBr.rTeJIsx
M H o i r i e c r B a ,p a B r r a 1 , 0 0 l r . r r u 1 0 0 % , q r o o 3 H a q a e T ,q T o 3 r r r I l e p e MeHHbre[pencTaB"rrflrorco6or? olpeAeJreHHbrelponopuH]t oT ueJlof o . T a K K a r { c y M M a r r e p e M e H H b l xe c r b Q n x c u p o e a u u o € 9 r 4 c J r o T
, o
; J^y";;ff ;;' ;;; ffi ii'i' ;'iJ"T;
li "?.10
:::: :; *:r:: y,'
.6"jiu:n9
tu,,';
-::
n
;;;;;;;;; - ;": ,i'
- J''#:i"J
l;
lI#:J" y.{.
f:j,:l_"::_"
orrb ue pr, ; ;
:i":'I : ":
e
7
5
l6
L2
l0
l3
16
14
8
9
i6
l3
3
6
l5
9
l3
l0
109
94
q4
10,9
rrt:0,279 rr.s:-0,021 rr,g--0,349
Koppe"rarrrl.r
a
A
u
e
h
j
i
Cyuuu
cpeAune
8
i16
T2
l3
lf)
e
8
l0
t2
l4
I
l3
l4
l6
lt
o
15
I
l3
l0
t34
98
13,4
9,8
Koppeaauuur oo:0,597ra":0,499 roc:0,467
a)
I
K
8
l3
J
I
I
69
6,9
OD
ae
aa
N
,
;
6n
J
aC
.J
i
.'l
I
I
.c,
itoc
o
Oo
J
a4
all
oD
fr.J.C
.L
ae
n - n n",
I
0 cl 1
o -i
ef
j
.d.t 9
aU
of
co
of
:l
:- ll
0 c sJ
0ct 2
I
I
I
0
j
a
!
Coo oa
f.
h ea oo,e
a
Ccs a
Pnc.2.l7.
luarpaulra
nepeMeHHofi Mox(eT JIHIIIb npI'{BeCrH K cO'
VBe,tHqeHr4eAoJtl oAHoii
[epeMeHHbIX'
Apyfsx
AOJIU
noaure""to
'
B I{OropOM II3MepeHIIt He nPeACtaSnq'
B OritpttroNl N{HO)KeCTBe,
,'lv HeliHo HesaBIlcIIl\{bIXnepeMeHHbIX'
AB)'X
rcrcr B nit. .e npOnOpqUfi
KOTOpafl He3HaqIIMO O',I'IHqaeTCtl
I<Oppe,lflllHq,
c:,'uleCrBOBaTb
6\,-ter
lrtlo)KecrBo AaHHblx 3aMliuyrb [peo6pa'
oi Hvaq. Ec,rtt orxpuroe
3 O B a ; i i e ) , rr r 3 M e p e H I I i i B n p O n O p q u I . I , T O t I O s B s T C t ! , a B H O 3 H a q I I M b l e
( ) l . p r r u a T e . i b r { b l eK O p p e J I f l I l r I I i ,x O T t I l c x o A H b l e n a H H b I e n p e I , c T a B I q , 1 1 L ( ) 6 o i i c o B e p t x e H H o I I e - l a B I i c l I M L l en e p e M e H H b I e . B c r e q l l a , r r b H o M
( ' r v r t J c 3 i i \ r t i i l ) T o l i T i l 6 . l l l u L I f a H l l b l x , l J I s r p e x n e p e M e H H b l xI i o p p e J'rfilli:lI rlex(Ay 3axlKIIy',rbIi\'lHnepeMeHHbIM]I oilpeAe,'It]orctl To,'IbKo
qepe3 !.ircficpcllll B cooTBercrBIIII co c"rier]1rrculuMcooTHoueHHeM
'
. . o z- - ( s , r {
srz)
(2.25\
L,2
ZJlJ'
o
-l'ariirt'-
Ocs
a
0cu b
pacceflHur ,c,nuuocerl (s_cu) o6paerloB
raJrbKr.t,
oro6paHHI,IX HA |ATCqHOM
II,,],XC:
,_rcroA,He,{axrue
co6par_r,^..T1-yjlolt6_s3MepeHHr_p,accopT'poBaH6r
sro qptrBe,ro K cMenle*Hro Bcex roqeK
no ocqM a, b, c,
inx"
auaronaa;;i;;;rl;;5,".",
E3alr\rFir,ie riol)pe.riflrtru npric)'urr
,rroSr,rNr feo.'loiHq.ecKIiM
A a i l l i L r N { , i { o T o p b t e r { a H e c e u b r r r a T p e ) ' r o , ' r b l t b r eI U a r p a M N ' r b r , t t a n p l l r ! { el ) , A r r a i p a M M b r n e c q a r r r . r n- r , i r i l H a- i l 3 B e c T H f l K t r " I i l T p e - \ o a 3 H b l e
ailafpar,l\rbr. 3ru o6paTrrbre cool'ilourelrIifl nporrcre{iaroT 143 Tofo
Sailra, rtro rro Mepe yBe"llqeHr.rfl rrponopqrrii oA,Hor? cocraBJtsroUleri ripoilopqlirr AB),x Ap!'f irx cocTaBrflror(rrx
-Io,r)r(rrrJr )-MeHbL L IA T b C ' .
P l r c . 2 . 1 B- a r o r p e ] ' f o J r b H a r A u a f p a M \ , r a , x ! r o p u . 4H a r p r r silHfli4piiT - f.rrLlHa- cocTaB,'rgrclIIrrxrioMtroHe}lT oca.lorjHbrx Iopilbrx nopo.1. HaUecenutre Ha prrc)'HrieroqKrJ npeICTaB,'rflroT
ocaloqHbre ,'ilrr0..rofilqecKrrenponoputrrr n S-rpyroeo\,r}rHrepBa,reco,rreBoto
q,teHa Xlqrrcosa nepMcr<oir
Q o p r u a U u n B e , r , t i l . i H r r o n aB c K B a x H H e ,
npo6ypeHuoii Ha repprrroprrtr L{enrpa.nruoro KaHsaca. Konrlo:uuhil 6bl"rrr Bbrquc"rreHbI
no pe3yJ'rbraraMT-, HerlTpoHHofo,nJioTHocrH o r o I J t r l i y c r l { q e c K o r ox a p o r a ) I { a , i l c n o J I b 3 y e N t o t or ] r t t I l 3 M e p e H I t f l
I I e r F o q l r i u r J e c K I r xc B o r i c r B I r H T e p B a , ' i aE. r , l , r a n p o 6 y p e H a r { o H T p o " r t b tlafl cl(Bl.;KIlHa .1"'1floilpe^le.rteHHfl IIoreHI{uar'rbHbrxBo3Mo)KHocreft
pa3I!1CX{eHU
p aqA n O a r i T i { B H bO
r XT X O I O B .
B T a 6 " l . 2 . 9 n p u n e , q e H bKr o M 1 1 0 3 H r l r ]l r0r g H . r e p s a , ' r o BH, a H e c e H Hbl.\ Ha pric. 2.18. B uefi rar{}Ke [peACTaB!,reHbr
A ] . r c f i e p c r r r rr p e x
MI'lH€plr,,!OrltqCCKilX TiOMnOHeHT U r{OppeJIflq}IU,
BbIriltC,{eHHbre
Ha
O C I I N B C3 T H X ! I i t . f l Q p C H I ? . 3 a M e T H M , I I T O
KoBapIIauHII He o6fl3aTeJIbHbl f.Ilfl Bbrql.rc,IreHr{fl r(oppe,'rflt{Hr?,
KaK 3rO 6trno
nperlonpeAe,,IeHo
/ I l r c i l c p r ' r iM
f u rr eQQexroM 3aMr(HyrocrH.
I i l h : i 3 r i j l a H r r b r ec r l o c T o g H H b r M cay i l { M a N { t H
r a H 6 o J , I epea c l l p o clplHeHbr B reoJofrrI{, 6br,ro npeAuprrHflTo
Mrrofo IlonbrTor{ rrpr{_
NA'IL
A H['14ApL4T
Prc.
.fjj
'l'ouxll
v"urtLq ^ar
KaKroMIIo3EIrI{oH'
KoMnosErraoH,?.t1"10ffi
cHcreMa.
#"il"i;::l:li5_
l*:HruAprrr-c.iraHer{
xaparrepn3yror cpelHue
;;;;;
Be,tnfiHrroltoscxofi $opuauua fn.p"ij,
,.sreqeHHbrx 'rq crnqvr,-':"Yl^.1-"-p-%
fiafl
gopuaur.r
a (nepur), r.rs
i,reueH'
ui ;; ;.',i#;,i ;" ii. ; i,J;#"ffi,jiffuff ";
tHrepnanou l,b
rrl
C[IbIC.] CTATIICT}IqECKIIM
CBfl3flM
I\{C}KAY HIIMII.
I(OX
U JITiNX
t i l r ; r . l 1 ] n p l i a o l x r H e K o r o p o eq u c . r o c n e q r r a , t b u t r x
crartrllo:
c,Tilqecrilrx
r{prrreplreB,nprrroAHbrx L,r, TaKux IaHHbrx, gefiec
IbJ
H a n l l c a , ' IK H H r y , n o c B f l q e H H y r on p o 6 , r e M e
3 a M K H y T o c T r rI (. c o x a , r e nrrru, npe.lJlafaeMbrecrarticTriqecKae
npoqeAypbr He yHr.rBepcaJrbHH
o/
Ta6as11a 2.9
Jlrto,nornqecxnfi cocran (c rouxocrurc no byo) r,E-uerponux rr'repBaJroB
a nepmcrofi Sopyaqnn Beaasnrrora s (errpa"rrHbnr Kansice; oqeHKuocnoBanu
na nerponpaQHqecKllxtl3Mepenurx rto pe3ynbraraM xapora]r:r cKBaxftH
d
D
75
65
l5
u
IU
5
f
g
h
i
i
Cyurru
Cpe4aue
.[,ucnepcuu
Crau4aprHne orKrogeHut
-
60
290
29
832,22
28,25
20
30
80
25
u
5
bl)
60
5
l0
90
l0
25
284
28
l 0 0 r ,n
31.64
oo
90
85
(
45
r5
430
43
962,22
3l,02
\ 7c3,47
l!q1.lt_ (832,22+e62.22_
2.28.8s.31.02
l7B9.E5
9 6 2 , 2 -2 ( 8 3 2 , 2+2 1 0 0 1l l, )
2 . 2 8 , 2 53 r , 6 4
E 3 2 , 2-2 ( 9 6 2 , 2 2+ 1 0 0 1 , n \
2.3t,02.3t,64
-R7r
1l
I 7 8 76, 6
[19, 1] rr e Hacrorillee BpeMs Her B[o,rrHe y,aoB,rerBopnreJrbHoro
r\{eTOAaBbrqucJreHrifcr]JrbtcBr3efi rraex4y rrepeMeHHbIMrZ
B 3al{r{Hy-
Tb]X MHO}KCCTBAX
.IIAHHbIX.
N POBEPKA TTIIIOTE3b I O HOPMAJIb HOM PACN P EAEJI
EH I,III
llperx,r,e .{er\a t'poAo!'rxr.rrb usJroxeHHe, Bo3Bparr.rMcq
Her\.{Hofo.
Ha3a/l' Ii pacnpere,'ieH[flM gacTor H' B r]acrHocr]I,
K HopManbHoMy
pacfipeAeJresrrc' Ec.nu BMecro rofo qro6br paccr{arpr.rBarr
osr60pIiy ro,rbr(o rrs luecrH 3rraqeHHr?,npeAcraBJreHHbrxB-ra6"u.
2.'c, is[repHTb AdrrHHbr
paKoBHHOqeHb 6o"ultuofi KOrrJrexuHItComposita, ro
MbI yBlrill4M, rlTo qacToTHag AaarpaMMa 6yaer BbIfJIflAeTb
aHaJrO-2.
rrrqHo rpaQury, uso6paxeHHoMy Ha puc.
lg. CpeAHe:li, 3HaqeHHI' AJIHHbr,B if,aHH.M c"'ryqaepaBHoMy 14,2 vm, 6lae"
coorsercr.
BOBaTr,Haw6oilbutaq qacTora, a nocrenegso yMeHbrIIapilIHMCrIt4
yBer'Iur{HBarouruMCfl
3HaqeH}rrM 6yayr orBeqarb yMeHbIxarcrtli{ect
rracrorbr' flpv6nnaureJrbHo.
aee ipeiu paKoEHH.[OfiaAaror B rrpeAeJIbIHHrepna.na (p-s, p*s) c Uenrpo]v B roql,ie yt:14,2, rpnqeM
orIeHKa craHAaprHofo orKJroHeuux npu6nu3HrerbHo
DaBHa 4S ttv.
Dd
3HaqeHsfig;tuttutoco6eirpoAa Compo'
I'unorernqecxoepacflpeAeJIeHHe
sLta
Tenepr paccN{orpIIM u3N'lepeHlrtllxllpHHLI, Iioropble 6lt;rtr cAe.naHu
npr] ucCJIeAoBaIIuII3Toii o,{eHb 6o.rrr,ruoli IioJiJIeKrt.llHCompositA.
P a c i r p e " e , l e H l i es r o r o n o r { a 3 a r e . l f l n o $ o p t ' t e H a r l o \ l l ] H a e r p a c n p e '
AeXeHlle .l.,TIlHbI,IIo efo cpe.{Hee 3llaqeHlie }I cTaHIapTHoe OTK"IOI { e H r r eB 3 r O M C , r y q a e I i H b I e .o H o M O X e r B b I f J I f A e T b , I { a r i p H M e p '
f l o j r o 6 i i o r p a c p H x v ,I I 3 o 6 p a l l i e H H o M yH a p \ c . 2 . 2 0 , c o c p e I H I r M 3 H a '
qcHrietr,r
3,6 uu.
i0,3 rravrrr craHAaprIJbIMorK.rloHeHHeM
i\Lox{er\{dr}r Mbi crraBHr{BarbABa pacIIpeAe!'IeH]Itnpyr c ,[p]'.or\,{?H3\repeHHfl [poBeJIeHbrB OIHI]X I;l rex x{e eI[HHIIax, qro
o6rerqaer npo6,lerrny cpaBHeHHflpacnpeAe,'IeHIIiiAJIIIHbI It unpHN{ox{Ho11306pa3arbB oAHoM H roM
slr. O6a 3rrr pacrlpeAe.rreHrirr
)Ke r'raC[lTa6e,A pesy"rlbTaTerlefo nOIyqi.IM pHC.2.21.
I ( o n e u u o , c p a B H e r { H e6 u , r o 6 u t t p o u 1 e ,e c J r r {6 b r o 6 a p a c n p e , r . e J I e H r r t r , M e , ' i Ho l r r r r H T o T ) K e u e H T p , T . e . p a B H b r ec p e . 4 H H e3 H a q e sttq. Mu \,rolKeMu,eHrpr.rpoBarbHx rro orHouerruio K o6ueMy cpeAHeMV 3HlqeHl{IO, BbtqHTarInojlxoAfrl{ee qrlc"{o H3 Bcex 3HaqeHIIIi
coBoK\'rrHOarH
( n , r u n p H 6 a B J l f l gH e K o T o p o e q n c , { o K 3 H a r { e H H f l M
Ap]'roii coBor(ynHocrrr) raxlli,r o6pasorra,qro6u cpeAHrre 06eHx coBoi(\'nHocreii cosna,rn. Buecro srof o BbrqreM coorBercrBvrouee
cpejr.Hec3Har{eHIJeI.{3 Kax(Aofo Ha6r}oA'eHHf B xa>r4orYtII3 AByx
c o B c r i y i i r - r o c r e i f?l .o r y r { } r M H o B b r e3 H a q e H H q . 3 r o n p e o 6 p a 3 o B a H a e
cnBttfaer KalKAoe H3 pactrpeAeJreHHftBAorb ropH3oHTa!'rbHoriocn
AO "iex nop, noKa I{x rleHrpbr He coBilaAyT co sHaqeHueu 0, ln.nfIoulx\,tcfl cpe,qHHMA"ls o6oux npeo6pa3oBaHHbrx pacnpeAeJ'reur-rfi,
I t s o 6 o a N e u H b r xH a p u c . 2 . 2 2 .
5 p a c c M o r p e u H o Mn p n M e p e M b r c B f l 3 a H b r p a 3 r r e p H o c r b o p e 3y"lbraroB u:uepeuHft, Bbrpa)KeHHofis r\arirruMerpax. flpir erou
HIII(aKnx npo6,reu He BosHuKaer, ecJII{ usr 6yAerracpaBHnBarL,pac.
npe.lereHlrq ,EJri{HbrH rxapHHbr, Ho ecJrrr Mbr 3axorr.tM cpaBHHBarb
rrll DSCnPeAeJIeHH
c sp a c n p e A e , r e H H f l M H
X ,a p a K T e p H 3 y r o [ l l r M M
rr ac.
EA
UY
Ta6,ruua 2.10
tlc craH.qaprnoro
3HaqeHEs KyMyJtflrIrBHofi tpyuxqun pacnpeAeJl-eH
lropManbHoro PacuPe4e;renun [15]
-16
cTaH.[aPTH5le
OTK,IOHlEHHg
oT CpelHero
3taqeHHq
I +ro
10
15
*L l^J fpi pnH rH^a , r z , f
2s
-3, 0
3(
qecrioe
pacnp
ercre-ioru
3,::.
E r r e ?,r-9,
s r r r v".f.lrorerl
cHrrfi-rurrprrHsr
contposita
oiooef
: . ,?
_ari
.2t,{aarpavna pacnpeAeneu&,
sLHya're
H
-T:'
;.4;;;?;
;:,,T;:r',**
-.,
I
.-'9R
-)7
-,)
A
_,
I
DQ
to
ol
_9ll
q
-l
-l
R
-r7
-1 ,6
t(
-j
.l
12
-1 ,2
-t
10
-
iqr,n
P_uc. 2.22. pacnpele.neuas
HMero
r Hy.
n."oJ'".'pfi
,,.iu:f 3i:ffi:-#i.ral{;l4
prHoe
orK,,IoHeHue,paBHoe
cy paxo'r,H' ro HaM 3TO
cn€r:r.Tb
He yAacrca. clrulectByer
xoe-nu6oAorrorHrre,,rb:":r,rrl Ka;t;6puJoiu"ru,
Koropoe nosBo,rrer
cAerarb HarIH paclpeAeaeHis
oJlru"aorrlaMrr ot eAHHr.rq
peulrt? Olno as raxax up.uu*u,i-#
rr3Me-
Ha3brBaerc'r., ona aq;efi: .
o;;;, JiJr.".T:lff iu"fH?X'
1q1-1,
Hl
no'* r Joi"?"..39ru
no
HyneBoe
cpe^r'ee
"':""""fffi
sesnrls;;;;;;;lhT#T.ffi
:[r'i,:liT*ii;*llr.";
3HaseHrt pacnpeAerrellir
as -dA;;;
-n-rli"",ua1ltopewtrq
;;';".',i.il:H""*'rl:"n
tr AeneHHs
pu'"o.'"
naup,noe
o,nnon.n,e
X;mX[#;:uJ::";1
pacioBafl nepeMeH'aq
60
I
(l
4
0 ,0 0 1
0,0019
0 ,0 0 2 6
0, 0 0 3 5
0, 0047
0,0062
0 ,0082
0 ,0 1 0 7
0,0139
c,0179
0,0228
0,0287
0,0359
0,0446
0 ,0 5 4 8
0, 0668
0 ,0808
0,0968
0 ,I 1 5 1
0,1357
0,ll-87
Kyrr yJriqrHsHaq BeporTluocTb
0,1841
0 , 2 1l 9
0,2420
a,2743
0, 3085
0 ,3 4 4 6
0,3821
0,4207
0,4602
0, 5000
0,5000
0,5398
0, 5793
0 ,6 1 7 9
0 ,6ii54
0,6915
0,7257
0 ,7 5 8 0
0 , ;'B8l
0 ,8 15 9
C,8113
C T aH A a p r H b r e
OTK,TOHEHHq Kyny.nsrHglidt BePOqTor cpe,lHero
t{ocTb
3H aqe llilt
-;-l
I
;1,3
-j-i,4
:l7
-r1,6
-l-l
{l
A
q
-r9 0
:o 1
oo
roD
'q
I
*2,6
_L9 7
--:..q
oci
-3.(i
0,8613
0,8849
0,9032
0,9192
0 ,9332
0,9452
0,9554
0 , 9 6 11
0,9713
0,9773
0 ,9 8 21
0 , 9 8 6r
0,9893
tr,99i8
t),9938
{J,9953
0,9965
0,9974
0 ,9 9 8 7
0 , 9 9 81
pu^
sgaqeHfiri
Arlrr'hrlr *"p"*i"iloo.;fi.;;'b',;;:!
srraqe'rri
i[i:,.2:?9j_.--Pu.npuou4u"""
posita
;;;"*1""t:luuu^_oco6eiipoti Ciii'ii'.
MatbHylo eoprrry
I
Craxga0rnrte
Kyl ya,qrHs. l l oT&'roil€Htr,i
H A r B e p o t T - ll dr cpeAHero
ll
HOCTb
3HaqeHtrt
ll
relteer
Zi : (X; - zL
X)) t lr.
o.
atunarpr"vt
Hop-
(2.26)
Tenepr, KaK 3To noKa3aHo
puc. 2.23, HaurlrripuBbrer{acror
p a 3 . ' u r L l r r b rcxo B o K y n H o c r e r p
i o g a Composila HAeHrr.iqHbr.
Xaparrep l i c T l l i i t l C T a H A a p ' I H O f OH O p I ' 1 3 r - I b L i O fpOa C f l p e . : ( e , r e H I I qO q e t t b X O p O mo lr3BecrHlt, a ta6lnr{bl
[noi]iaAefi, orpaHuqeHHbrx yxa3ariHbil\{lt
cerl{eHraMx
M
o
}
K
H
o H a f r r r . r n c q r r i B o B C e x - v . r e 6 H r r K a xn o
lpuBoii,
cTaTICTrlr\e. HalontHritvl, qTO nJlox-(aAil Bbipa)KarcTcfi npr\to qepe3
Bepoltrlrocrrr. tr4crio,rrayn cor(pauleHHyro ra6.tuuv
(Hatpilrrep,
ra6t.
. 2 . 1 0 ) , u o > r < u os a - r t r n n r o 6 , v r c e e r r o R r H o c r t , c B f l s a H H y r oc o
c . r i y u a f r H o tni u 6 o p x o f i u s H o p u a , r i H o r i c b e o x y r r H o c r r r s, H a q e H r r ri i o r o p o r l p a c n o , T o ) K e H bBr r r e K o r o p o M3 a A a H H o M u H T e p B a , , r eO. r s a i i c
AJlfl 3rofo Hy)KHO3HaTb AtrcnepctrrocoBoriyrrHocTlr.
;laBafiTe cAe,rraeMHepea!'tbHoeIlpellno,'ro)tieHtle,
qToMbt It(:cIeAoBa,lIl BCrocoBor(yrlHocTbpola Composita. 3ro 3HaqfiT, qTo i!{bl
3 H a c j t c p e A H e e3 H a r l e H r r e
, aBHoe14,2 lttlt, u ux
A J I H He e g r e M e H T o B p
c r a H A a p r H o e o r r ( r ' r o H e H u ep,a B H o e 4 , 2 u r t .
Ka,<osa BepoflTHocrb
I l o t B . I i e H u r rn p n c l ! { a f i H o i v r
nrr6ope o6pasua, lreuoueio 3 lru?
Ar'Iff Ilo"IIl,geHliflorBera Ha 3ToT BOnpOCnpr,tBej,e\{3 r.lrvlx eAliHLII{alu craHAaprHofoorr(.iroHe}rrrfl
I { 3 a r e M o d b a r n r , t c sx r a 6 , r . 2 . 1 0 :
2 : (3,0-14,2)14,7
:
6l
Beporruocrb [oJ'ryqeHHrrnpeAcraBHreJrfl coBoKynHocrr,r p(
Composita, AIruHa Koropofo MeHbrrre- 2,4 cran4apruux orKJro
.HHfi, ecrt xyMyJrflrr.rBuaflBepoflrHocrb B eroii roqxe:
no Haur
ra6;t. 2.10 HafiAeu 3HaqeHHe0,0082, r(oropoe e geficrn[re,,rbHoc
oqeHb va,ro. Tenepb BbiqtrcJrriMBepoqrHocrb rrosBJreHtrrrnpeAcra
BHre":lt, .l,IIHHaKOTOpOfO
npeBblrxaeT20 rUu.
CHosa rpe6yeul'lo seru,riiHv npeo6pasyent B
soDi{a.rbH.vro
Qopuy:
craux,aprHV
_ 14,2)
: 1,2.
z : (2a,0
14,7
T a n r r a r : c v M M a p H a r ri l , , r o u t a j r bn o 4 x p r r a o r i H o p N { a r , r b u o rpoa c r r p e Ae,reHr.rspaBHa 1,00, ro BepoflrHocrb noJryqeHr.rfl
BeJrHqHHbr
,x, paB_
sori rr"lil 6o.nlrueri 1,2 craH4aprHux crxncueHarl, r. e. 6o.urruel't,
qehr cperHee, paBHa pasrrocru 1,00 n riyMv,rrfrlrBfloft
Oeporrlroctli
rrorrrvseHursHaqenur?,He npeBocxoAflrqux 1,2. L4laqe roBops,
P ( x > - 1 , 2 ): 1 , 0- P ( x I 1 , 2 ) .
T a 6 " l . 2 . 1 0 . l a e r H a ) , 1r i v M y J r f l T u B H b B
r ee p o f l r H o c r r .B
r l,{orb /.to 1,2,
[ - r B b r q r l r a e \ , r a fBl e p o f i r H o c r b p a B H a 0 , 8 8 4 9 . f l o e r o t r v B e p o f l r H o c r b
'1,0000
n o r B , l e H i l r o c o 6 e r l C o t r r p o s { . t a! ; ' r r l H H € €2 0 n a l r p a n H a
_
0 " 8 8 1 9 : - 0 , 1 1 5 1 , H . r r r H e r . { H o f r { r6,o{ . n t t u e o , I s o r ?4 e c a r o i r . T e n e D l
t s l r r r r r r a J l i {B\ 1e p o f i ' H o c T u c , r y u a i ? l l c r o n l r 6 o p a c o m p o s i t a ,
l,,rrrita
xoropofi :ionaAaern rrurepei,r or l5 ao 20 lru:
"4"-Iff l)
Xi:li
z : ( 1 5 , 0- 1 4 , 21) 4 ,x7 0 , 2 ,
,qas 20 r,i:i
z : (20,0_ 14,2)
f4,7x 1,2,
P ( x < r , 2 ): 0 , 8 8 4 9 ,
P (x -< 0,2) : 0,5793,
P(0,2-< x -< 1,2): 0,3056,
T' e. ilprrrriepHoo.{,Harperb o6pasu,oo norraAaeTn sa4aaHuli rrHTe0EAT.
I{eHrpallnaq
rtpeAe,rbHaqreopeMa
B aioi,l ''pr]repe npeAfioJrara,rrocb,
qro nu6opxa 6u.na c4e.naua
Ir3 HopMa,'rbHopacnpe4e,reuuoli coBoKyrrHocrn. K coxaJreHgro, MH
o6H"ruo He 3HaeM, xaxoft Brrr rrNlee'r pacllpeAeJreHHe,u IrHofAa
qro oHo 3HaqIITeJIbHoorr'Irlqaercfl
n_oAo3peBaeN{'
oT HopManbHofo.
HE eroro He cJreAyer, qro HopMaJ'rbHoe
paclpeAenesng 6ecno;regHO, TAK
KAK
HMCCT MCCTO 3AMCqATCJIbHAg IIEHTPAJIbHAE
IPCAENb.
Har r,eopeMa. osa yrBep)KAaeT, qro ec.rrlr au60pxlt
Ii3B,rleqerrbl
c,ryuarino lta ,rrc6oft coBoKynHocrtr,TO CpeAHrre,Bbrqr.rcJtreHHbIe
!,Jtfl
STHX AaHHbrx, a trMeHHontr6opouHbre cpeAHlie, flBJltroTcg c,lryqaii'62
Btr6oprta1
2
Bur6opna
*+
oo
o-
"----"-------a
Bur6oPra3o+-+
co
Atr
X
l-^ooo
z
X3
83flrble Ha!'Aaqy u3 coBoxynlrocrn
qePuc. 2.24. TPlr nlt6oPxu u3 nrrtl sa6,rrc.uessfi,
3Haqe'trr rn6opox o6osHaqeuut
Cp;;il.c U-o6pa:ttltn PacflPere'reHueM'
oes X
K HOp'
paCnpeAer'IeHI.IeKOTOpbIX CTpeMI'ITCfl
HbIMU BeJIHql'IHaMI'I'
O6beMa BbI6OpKH'
ManbHOMynpu yne.ttr'rtleHI'rH
Teopen{a raxercq Ha nepBblii B3r"itA
[peAenbHafl
[eurpallnafl
rlonflrb' floqeMy cpeAHIIe BbI6opoK
rpyAHo
He Bnorne noHRruod;
p a c n p e A e ' l e H H l oe' c n n o 6 p a 3 '
A o , r r x H b rn o A q l l H s r b c a n o p u a n s H o M y
rllna'
Irs conoxyn'ocrli -coBeplileHHoApyrolo;;;-'6;;"
3Ta
ToM' llro
B
y6e4urbcfl
""6punot
no3Bor'laer
OAuaxo Mo!.eJII.lpoBaHI{e
q
r
o
n
p
o
l
{
3
Bo'
M
b
I
reopeMa Ha caMoM Aexe BepHa.flpe4nonoxHM'
ornxqlloe
coBepueHno
HMenuleft
.qilt,i eu6opKy Il3 coeoxynHocrll,
B I ' { A a 'K a K 3 T o I I o '
o r H o p M a J- I b H o f op a c n p e A e J l e n u sU - o 6 p a s u o r o
qa
JIbHblx s a 6,n13.u.e'
crb rrgAriBr.rAya
Z'.i+. bo.,,'u a s
;;, ;;5' ;;
iii.
pacnpeAer'Ielliltl'
KpaeB
Hs
AByx
nuir s nu6oprie 6yaer ilonyrleHa
ycpeA'
3naqeHufl
eTII
KorAa
conoxyllHocrH.
Koropbre coAep)Kar nltx
Htriorcq c IIeJIbIo HaxoxAeHufl cpeAuefo apnQueriluecl{oro' 6oJIb'
IIJI]C 3HAI]CHI]fl
IIOIAIIIAIOTCfl
HH3KHMI'I
3HAqCHUflMII'
B PESYJIbTATC
n o . r r v q a e r c rc p e A H e e ,6 . r u s x o e K q e n T p y p a c n p e J . e . [ e H H sT' o n l x o e
o.reHl peAKrrx o6croflTe,'rbcrBax,KotAa Bce c.liyuaiiHo BbIOpaHHbIe
sa6;rrc,tesufl OKa)KVrCs6.[r.rsxlrN.{,.nn6o K BbICOKHM3HaqeHl'ltlM!
cpeAilero MbI nonytJHM
.,'tu6o x caMbIM Hl.tstttl,t, npI{ BbIqHcJIeHI.Iu
3HaqeHHe,Koropoe CI{JIbHO
OTIHqaeTcqoT qeHTpanbHofo'
3auetuu, uio ori6opoqHble cpeAHI'Ie3HaqeHI'Isl(nacrepu3ylorctl
(co6uparcrcn n nyuxu)- n6,r[su IrenTpanbnoro 3HaqeHI{qrunorerll'
r{ecKoro pacnpeae.rreHHeHa puc. 2.24. Ecnn sTor sKcnep}IMeHT
noBTopurb rbrcflqy pa3 H 6o.rtture, To oKaxerctl, llro ou6opouHue
.paln"e 6yAyr p"uanonu.atbcfl HanoAo6ue xopouro l.I3BecrHoli xo'
nopr',raJlbnoiiKpHBoft. llo cyuecrBy' re xe caMble
"roxoaoo6p-asLoft63,'
F
>,--,*M
-,^^^r^.rrHnaDTHofiouu6roft'OuootlHcblBaer[3MeHrIItBocrb'Ko'
ox'Aarb or cpeAHHx nu6opor< rpn noBropHoM
:I:.:;
;;;;
iutJyru
.ri"rn""-;
Crau4apruasorns6au6opet'tsroft xe conoxynnocrr'r'
!-ia paBHa
i/,^ uba*, FmL
t^
s":J/71i,
{ i . ' lt l . / ;: 8 i i B a " l e H T H O
t9 o7t
se: o {ln.
I-lei;rpa.,tlnaa xpex,eilLHaq reopeMa Il03Bo,'iler cQopn,lynupoL i , u . r .i tr r3 ' r I I C T l l q e c l . ; l l xep u T e p H I I ,o c H o B a H H b l eH a x a p a l { T e p I I c T I I K a x
UX .!,ax(e B Tex cJr,vqaflx,KOf-14
rioplra.lr,uoli xpunoft, H npu.\,{eHflTb
: o B o r i ) ' r r H o c r bI,I 3 t i o r o p o t i n : q r a e b t 6 o p K a , H e p a c 1 r p e A e J I e HHao p ,1rnoHo. flpe4no,lo>riiiM, qro IIar'leoHTo,'Iof, xoroprtfi 3a-HI'IMaJIctl
COmpositA, nanten oqeHb 6O.nguVrc
I{g,'t!'Iext11tn
rrcc.neAoBaHLIeM
IlJIllry'IloKpbITyIo6paxltono,lauu'I'lcronaeMbleBblf"rtIAtraHa!'lofrrr{Ho COmpOSitA,ItO tro pa3N{epaMOqeHb Be,rIHKIl,CpeJ.Hsfl.{,,rlllHa
r e c r r H o 6 p a s u o n c o c r a B , ' I t l e rl l p I I : , { e p H o3 0 , 0 r ' r u . H a n o u u r i r ' 1 , u t o
ilIL,I<<3HaeM>)'qTocpe!.HeeIIcTaHAapTHoeoTKJIoHeHIiflcoBoKytl.
Hocru Compqsi\t coorBercrBeuuo paBHbI npaMepHo 142 tt 4,7 uuM o x n o J r r . Ic q u T a r b , q r o H o B a t a l t 6 o p x a 6 p a x u o n o 4 6 H n a H s s r e qeHa H3 eroft cosoriynuocru?
Mu naoxeu onpe,{e"ry}irbpa3Hocrb Me}l(Ay cpeAHI.rM3HaqeHI'IeM
narueri Hoeoft eu6opxtr II cpeAHuM 3Har{eH[eM coBoKy[Hocrn. 3ty
KOTOpyIOMbI
pa3Hocrb 3areM MO)KHOCpaBHIITbC n3MeHquBOCTbIO,
5lr xorerr r.rMerbA,'rfi cpeAHlix snaqeHltti nlt6opox, c.nyuaftHo nsB J ' r e q e r r H r ci x s a A a s H o f t c o B o K y [ H o c r v . 3 r a L I 3 M e H q H B o c r3ba A a e r ,cr craunaprHofi ourr6xoii u ffBJlflercq Qyurirlaefi KaK Aucnepclll'l
- ' o B o K v n H o c r rT
. ra, K u o 6 r e u a u s r 6 o p x r .
Cpaeueune MexAy pa3Hocrbro cpeAHIIx H craHAaprnoft otttH6xotl ltorxuo ocyqecrBnrb no cJrer,yroulefi Qopitty.ne
|h* rlm* W^-
Pric 2 25. Pacnpe.re,resrre
cpe.(rrero. l ; 1 . n r 6 o J r , i l t o f o q u c J r a n l r 6 o p o r o 6 r . e v a n ,
33rrrLl.\Ha)"(aq1'li: coeoxl'nnocreii,c p a c I ] p e ; ] e J € H r r e i l ro, r , r r r r q a r c u { f i M C H
Or HOpMa!'IbHofo.
UeHTpaJhHat
YBeIIJc eH! tr
H3 KOlOp6lx
trpe.(enb$afl TeopeMa n03BonreT yrBepxAarb, qro pacnpe,ae,re"""
f no ,,"pe
n cTpe\lliTcl K HOpMarbHovy. 4 - pacnpeAeteHffq
rcxoaglrx
sosoxl.neocre?,
n e a r s r e ; r 6 o p r c a ; 6 - e - p a c n p e t r e l _ e H n c, [ a r s n u 6 o p o n
o6rerra n:2
(6), tr:4
(8, u n-25 (el l22l
pe3yJrbrarbr 6r'ly'r noJryqeHbr,ecJrH Haqarb rroqrt'l c .rrro6oro
4py_
roro
l ,K , H a n p f i u e p , u s o
- -6r o
- -a' x e H o H a
^ I r c x o A H o f op a c f l p e A e , r r e H r . rKf a
p u c . 2 . 2 5 , B 3 q r o M l r 3 K H r 4 f r il I . J l . f l a n u s a
iZZl.''
T a x x a r p a c n p e A e J r e u u en l r 6 o p o q H b r x c p e A H r z x c r p e M r . r r c r
K
HopManbHoMy' To efo Mo)KHo onllcarb ro,ilbr{o
crarrcruxaAByMfl
M H- C p . A H A Mr r ; l , H c r r e p c l l e f K
i.ax reopernvecxoe, TaK H 3M[rrptq e c K o e u c c J l e x o B a H H rr r o K a s b r B a r o rq, r o
cpeAHee3'aqeHue sH6op o q H b r xc p e A H t r xp a B H o c p e ] H e M y c o B o K y r r H o c r Hr ,.
e. f;^:St.
cn e p c u s n u 6 o p o u u o i r c p e 4 H e l i p a n H a A l c n e p c u u c o B o K y r r H o c r[ u
uA
, eleuuofi sa o6relr aur6opxu,un" ,1* :a2
ln. CraHlaprHoe orK,,roHeH u e n u 6 o p o q H b r xc p e A H u x e c r b l < s a A p a r g b l r lK o p e H b r . r 3
3roro qflcila v Ha3brBaercr craHAaprHoit ourn6xon o[euNn cpeAHeto,
I,TJII{
64
o
.\'-p
c/t
:_
X-Pt
01/
',
(2.28)
ln
3ail,reruu, qro npoBepfleMafl crarucrur{a BbMIIcJIgercfl TaKIIM
. 1 6 p a s o n aq,r o o H a s r o q H o c r t t o K B a B a , ' t e H T H ar i p H T e p u r c ,I i c n o , ' t b :rl/eMoNrvAJrfl cralr.q,aprr.r3arrur.r
nepeneHHofi (cu. ypanueuue 2.26).
I ll)oBepfleMascrarrrcruxa Z Hoprr.raJrbHo
pacnpeAeJreHaco cpeAHilM
l l { a q e H H e Mp, a B H b I MH y J l F OI,I C T a H A a p r H b I M
O T K J I O H e H H epMa,B H b l M
ir.I'ttHirlle,ec,ru nu6opoqgoe cpeAHee Aericrenrertgo 6tr.rro noJlyqeIio ,{Jittrrrnorerri,{ecKcii coBoKyrrHocrlt. Ecnu Z xpaftHe BeJIITKo'ro
illtl BIlpaBe 3aKJltoqilTb,rITo HaIIla nst6opxa ne 6ltna r3f'Ta rr3 3TOH
conoxfttuocru. (Doplra,rnuoe peuleHae, oAHaKo, rpe6yer, qro6lt lrlt
npoBe!'cTaHoBrr.rincoorBercrByloqylo npolreAypy AJ'InBbIqIlcJIeHI'Ifl
l)fieMoir crarr.rcrlrKII.
5-201
Bep{q,T_O
oHa
BO3HIII(aeT
fleosbrfi uaf B crarlrcrnqecxofinpoaepKerrrnores- $oprray.nu- r , r . p ; . , o T I l c D ! - i t i ' ] t . 1 , 3 H a t r l v i c \ / l . n e J l e
poAa' Hao6opor' ecrll
l l , I n l . , " ' ; 1 , . , i , ,, e, i : i e o t u i l 6 l . o i i r r c p B o f o
poBr(airollxoAruleriranoresu o6 ucc.ne4yeuor?
nepeuesnor?.
O6uqO fl t l " ' ) i : 1 B - l O - , , , t , ' , " i l l r l o i c 3 ; 1 I l l ) l l H l l \ 1 a ( ' ' l CT
C
O
tsCptl]aeTC
O
t
l
'
i,:.
Ho raKaf rnrrore3aHa3brBaercrr
Hy,reooft,o6osHaqaercflHo v, B
ilalt:eMy llPllNiePy' rlpOIi"IJliO'rT'ililp):eNl
i
i
l
i
o
:
l
l
l
i
l
i
{
a
n
C
b
cyxlHocrrr,r-iBJlfiercs
runore:or?o6 orcyrcrBHripa3rnqnt. Hanpri,',, ,;.,.1a.
rITo AaHHafl ett6opxa B3flTa H3 coBc)Mep, Moli(Ho irpeAfio/'ro)KnTl!,
Kyrrllocrrr, nvenuqeir 3aAaHHoe cpeAHee 3HarreHr.le.
Hy.tesal rfirrore3a Bbrpaxaercq B Sopue
He : !.1,r: !-ro,
(2.30)
I-It : pLr*Lro,
T. e.. r{To cpeAHee3}raqeHHecoBoriyrrHocTrr,
}r3 Noropofi 6H,[a ssgra
B b r 6 o p K a ,H e p a B H o 3 a A a H H o M y3 H a q e t r r r r cp r o .T e n e p u p a c c M o r p r . i N i
J r p o u e A " V p br irp o B e p r i r if i l r o r e 3 i r p r r 3 a A a i r H o My p o B H e s H a q n r { o c r H .
Ec.[u Aee rr3yrraeMne coBoKynHocrr oKaxyrcr pa3J*iqHbrMu, cJIeAyer cAe,[arb BbIBoA,qro ircKolae\4bie ocrarrilr 6u,tri B3flTbI He Ir.j
coBoKyrrriocrfi poAa compositg, a- vz coBoriyilrrocrrr Her{oroporo.
Apyfofo poAa.
( a r < i o r i l x o f r l t o r e 3 a c $ o p r t v , r l r p o B a H a ,M o x i H o H a o c H o B a H L I r I
-XPIITCPI]fl
IIPi]rI'ITb
CE IIJI}I
OTBEPIHYTb.
I n n o r e : r r a K > x e M o ) r r e r 6 u r s i r c r r i s H b f ; r r " r u . n o i l * r o r i .3 r o ' l r p r i e o AI4T K loMy, r{To Bo3Htlriaer trerbrpe xolt6lrHar{uu Bo3Mo){(HLl.x
ucX O A O Bi,l B e l i s K O T O p r , l x n p i r B o J f i K I t p a B I r r . r b H O M B
y b t B O A ya
,
3ro r,ro;r<HorrpolJJl,TiocrpHpoBarb
ABe - r{ ucrrpaB}rJrbuor,ry.
cneAyIorrrnl.fo6oasoM:
frinorc:a
lunorcsa npurrrrMaerct
t-r r p a B r . r b H opee u e u u e
i
fzncre:a orBepraerct
I
Oruu6xa nepBofo poAa
neBepHa
or,,o,,uBroporo
poAa
I Ipaeu.rr,uoepeuer{rre
T o , r l x o n p H H a r L I enpanunluofi rrJrrr orr{,'roHeHHeHenpaBr{JlbHofi.
runoTe3bI Mo)KHOCqllraTb Bepr{brMpeileHileu. Ec,rn Hyd'reBatrH66
i
(2.29\
KOTOpaffO3HaqaeT,qTo cpeAHee 3Har{eHuepl H3yrlaeMor?cosoxvnH o c r u , u s r ; o r o p o i i r6 u n a n s s r a n u 6 o p x a , p a B H o 3 a A a H H o N { cy p e A HeMy3HaqeHHro.
B HaruenanpriMepe Mr,t Aol)r(HEr 6yaeu
npeAnoloxrlTb, 1116
c p e A H e e3 H a q e H u ec c B o x y n H o c r r , u B r i o r o p o f i d H , r r r s s s r l r 6 p a x l i o noAbI' rlaroAt{Iu}iecfl Ha nJIllre, coBnaAaer co cpeAI{HIu3HaqeHHeNI
c o B o K y r r H o c r tpr o A a C o t r p o s i l a .
C$oprrry,rripoBaBHyr,ieByioriirroresy, Mbr Aod,rlKHbryi{asarb n
a,'rbrepriarr.rnyli I{ei.i. llolxoAsu{as aJrbrepHarr.rBaB erori crlrl,itlalr Moxcr 6utl cnervnuefi:
HAITCTO CTATTICTIIqECKOIO
:
!,uC.ielJHI)'le nOHflTIIF
fz note:a
Ir nJIIITbI:lro
.r n'iiirbl+po
B..ci;:rDlritJlbllofru
I oaoou a rJrirlr nptrtll,lre; r i a r c o D o r <nt )r i o c r t . l
|
ll
llpann.rsuoeperxettue
Oruu6na I;epBcroPoAa
|
I
ocoSl c nJllirLl tl'i npl'luannr>I<ar ccaonlnHot'rll
Ouru6xa Bropofo PoAa
Iipanirir'uoe peu;eltlle
CO- ' . , C C i , < < i - [I l r l I ] T b l ) ) O T H O C I I T C t t ' K O ] l e r l ] l O ' K C p e A H C ] ' { y 3 H a r i i - ' l i l l i O
c Ir'iil{TbI'
JOii\. jittocTrr, 1( rio.l opoit I]pilHzt,]l,ijetrii.,T oc06rl, co5p.l]llibie
L-rci}:''f}locrb
crir'i ttcrlillect{llx npoueiiypax
i3 pacnpo,:rpatteHHIix
r- rl liil3blp
o
A
a
o
5
o
:
J
I
.
I
a
r
i
l
l
e
T
C
t
i
.
{
e
p
€
3
rrore.,rel{H'l orull6Kir lrcpBoto
Rael'cflypoBHe\{3Haq}l}.locTII;3Tvl]epofll.IiCClb'lroil{Ho:..:i:i].bAo
qro6bl Mirllul\,lllilllpoBiiTb BepoFTgpHl{cHeHurr ripgTepur.
A,rg roro
pO;li.l' 3ailillilelll HJi.'ieByiC fllItOO
1
)
O
f
O
8
1
O
L
t
I
l
i
6
l
(
1
1
itOC'fr, ItO:IRJlCIIttfl
,re:i). ijl)rr ycJroBrrri, rrTO OHa 61.'.ier o'i'ri"roHefl . Ei,'!il f flllo'i'l3a oT' l ' 0 B c l l o t t T I I o c l ' b n c t i i J . i : : H l l : i c u l l a . i l i l l ; ' r c r i l c f o 1 ; ( l ' r 1 3l l i l t 3 I . : , ' t o H r i c -cff i .
t'o"'
t i i i i r ) , ' r - i J , T 0 f . { a I i i i K B e p o E l l l o c T b 1 i o : ' i B ; 1 e H I ' I foi 1 g r l 6 . i i i I i l ? l l o t o
I t : t B L t C i' 1
l l, T[1i ](aK oHil 3ajiaeTCu sapaHee. EC;rtt, OAHaI(O. lipllTglllli
( r . e . U 5 , ' , ' : : , 3 ' - qI l i l l O r ! C n l ) i r B O . 1 r r 1 r { O T I ( . I I O H e } t r t I O} l y . r I C : l O i i r U n O r e : u t
C.ieBepOuTliOClb
T O n O f l B , ' l - q e lC f l H e l i C T O p a t
le3i
riprrlutvaercli),
J r s l b o r r r i r 6 r i yB r O p o r o p o A a . 3 r r B e p o t l l l o c r l p , o o o 6 t t : e f c g c p t '
a pllBeHCifi cpe.lliux
i r e u . i i l a ' c r H a . ' I : i r i l tol t6 p a 3 o N I e, c i l l t r I 4 I I O T e 3O
: j l I l / , ' i ) l i l e l C t l , l , l b I A e " r I a C XB
4 b I B O AO ' i ' O \ { , L I T O A B e I i 3 y t I a e i ' t i j e i ' C ? 0 l i Y I l l l O C li { i l N { e l O T p a 3 J ' i I l r { H b l e C i l e j l . H : ' i C3 H n q e H I I t i l I _ B 3 l ) O t r l l C l ' l b
'loro, rtro
ripriHgro ogn6orlHoe peueHle, paBHa a. C ;1p1'roii tlloriln Cl-tq.1i11it'
1.)OHl,lrC'llttt 116 Ue OTBepraeTCu' yTBep)li,iellHe O TOI'1,
jlllr. ., uoBrlli) ,.lIoc'i eii coBllil.l.aloT, Moxie'f oI(a3aTbctl "[o)i(ll;ri\{ c Hoi i : r r , . r . ' r i r c i iB e l ) o z T H o c T b i o B .
ilce c'ia'rgct'lqe1rKue i{ptiTep}rlt CCHoBaHbI Ha ilpeAllo.iiol{ieiiIIH,
' , f ( ) I l \ ' , ' t c u a f l f u ; i o ' fc 3 a t t a , r b r e p i l i l i t i B : t t ( I I e r l B 3 : i l lu l i o l l c K . T i c q a l o r
-rJ)-\,' .ilp)'fil li BNlecre o6pa:yrc;t' 1io'rlHoe x'Il{o}KecrBo co6lirritl. Tar
:'ilt'; ll)',rIcBUrl fIl.tio'ie3:l 3aIII.lCblBl:i.ii-]t1B flBHCx,IB!1Ae, TO il"tlbTcpl{3illi-r:l -lo"rilr{lta 6r,lrb AoBoJibHo o6lleii. Ec,rli Ho orBepfaerc:1, To MbI
'lilin
a C l r i , r tr O 3 a A i l F r F r O eC O O ' r ' l t O t H
e y . r l c B O i il i l u eL I e e , O I I U C b l B a e X l O H
ll() i c3oir, llc IlbIito,TIt;!ercfl. Do.rlee rofo, I'lcrllHlloe coorrio[IeHHe B
-, ioM c,rI)'q;lc co!,eplKrircfl B o6rIIHpH0l,l MHo)KecrBe a,lr,TepHarl'IB'
3:itirtoqer{Hbrx B o6uef{ a.rrb'lcpHarrrBe. /vlbl He Mo)KeM oillr€,u,€Jll{Tb'
iilil(oe Ii3 coorltoueHrrri ucrr.{HHo; Mlrl I\{o)KeM ToJIbKo ycrzlHoBllrb'
KaKoe H3 coorHotuegufi ge BIrtIIoJIHrercq. HHorAa ts MareMarl'lqecl(oii cralrrc'rnKe npaMeHeHue crarucruqecKlix
KpI{TepI{eB no3BoJlfl-
5*
o/
X1?ti"'i"'%T".i#'i'#;
Hgrepecve-r-31'JJ#1""X;*1{,"1:v,'':r*":"'ff
0/o
3AH, or p aHHqen-
eT IOBOpHTb
o6 <<onpoBeplKeHr.iu
Hy/'reBoi',{
r}rrroTe3br>>
npoTrrBaJIbrepHartrBbro Heycnexe onpoBepx{eHHe.
Heycnex onpoBep)Kenr.Ifi, Kp rrr uuecxa."_::':::;;;;;";,
I{OTOPOMY
COOTBCTCTBYCT HCII38ECTHAfl
BEPOflTHOCTb IIPHHfTHfl
ouru6oquoro pe[reHris, He cJry)Kr]T3r{BrrBa,leHror,r
npuHflTlrfl rulloTCSST.
CTATIiCTHIiCCKHC
IiPITTCPIIH
B HCKOTOPOI,I
CMbIC,ICHC ]lTO|YT
c K a 3 a T b H a M , q T O U \ { e H H Ol t t e e T M € C T Oa, T O J t b t ( ot l o r Y T c K a 3 a T b ,
qefo HeT.
. . B o : n p a q a f l c b K ^ H ) - , ' r e s oriiil n o r c 3 c t r u . i t b r e p H a r r j B eo, n p e I e J , l e H H o i i Q o p u y " r a u a ( 2 . 2 9 ) n ( 2 . 3 0 ) , n p e - l n o . r j o x l r N rq, r o r , r b r c o q , r H
y p O P e H _3bH a q L t M O C T(l rt . c . B e p o r r H o c r r , o r L r i t 6 x u t r e p B o f o p o A a )
a:0,05 noAxoAflu,\uNr
.lJlfl Ha[Jrrx ue.rreii.i.iirrnrr crloBa]tH, ]rbi Aon y c K a e M B o 3 M o ) K H o c r tl p r . i 6 n n : H r e , / r r , H 5o p a z u a 1 0 0 n c n u r a , H l i r ?
o r u H 6 o q n oo r B e p r H y r b n p o B e p E e M y i of l i n o r e 3 y B c , 1 )q a e , K o f A a o H a
BepHa.
llpe,r.no"roixilNl,qro Auclrepcuf coBoKvnHocrli, 'to otHorIeHlrlo K
t t o r o p o f r B e A e r c r r r p o B e p K a ,H a M H 3 8 e c r H a . I l a n e o H r o " r r o ro n p e . l e qro Ar]cilepcHfl suaqeuilfi A,tilHbr .1";tfl coBoKyIIHocrH oco6efi
vrlr.IJi,
p o y a C o n t p o s i t a p s . F . u a2 2 , 1 ( H a n o u H n n , q r o c r a H A a l l r r { o eo r K , r r o H e H I 4 e6 u n o 4 , 7 ) . T e n e p r M o ) K H or p o p u a , l o H os a r r u c a r b c r a r i l u r i r r i e cxaii rparepuii c,re;yrouulr o6pasora:
1 ) n y c r l r r p o B e p r e M a qr u n o r e 3 a r { a J b r e p r i i t r t . t B ar { } r e } o r B l { A
Ho: Pt: &0,
Ht: Wt+poi
2 ) n p u H r l u a e My p o B e u b s n a r ; r l M o c r u :a : 0 , 0 5 ;
3) onuHc,rneM crarlrcrriqecxuli xpHreprrt:i:
7 -_
L
x-Fo
-_=:.
ol/
l t tn
(2.31)
Ec,ru asr6opKa B3flTa HayAaqy ns Hopr'rarrrbuofi
coeorylrHocrn c
ttssecruoii 4zcnepcaeli, ro crarr.rcrnqecxHri xpurepuil Z 6yler pacn p e A e n e Hu o p M a ! ' r b H oc o c p e A H H r ,3, rH a q e H t r e Mp, a B H b r MH y d ' i r oH, A I C nepcueii, panuoli eAriHrue. Mu npzunrur corJrarreHrre o roi{, rrro
n p n 6 , r n s u r e d r b H oo A u H p a 3 l r a 2 0 u c n l r r a H u i l l A o n y c K a e r c r r o u u 6oqgoe orKJroHenr.le
rnlrore3br o paBeucrBe c-peAnr.rx,
B To BpeMffKaK
o u a B e p H a . V l u a w n c , ' r o B a M r i ,M b r n p i t l r u t r a e M 5 f l e - u u r Z y p o B e H b
pr.rcKarrJrlrBepoflrHocrl ouriz6KrrnepBofo poAa paBH)'ro0,05. OnpeHOpMa,lbHoropacnlle.r.e.reHuqo6AeJrI{MA,'rfl CraHAapTLr3OBaHHOfO
,'IacTb,3aKrloqaloulyio 5% nJIolr1aAlIno4 xpunorl HopMa,'lbHoropacf l p e A e n e n l r f l .3 r a o 6 l a c r b H a 3 b t B a e r c rr i p n r u ' J e c x o i i .E c , r l r e t r q u c ,{eHuoesHaqenue crarucrarrecKoro Kpurepilr nonaraer B ery o6JracTb, Mbr BbrllyNiAeHbroTKJIoHfirbHyJIeBylo runoTe3y.
T a r < r a r a J l b r e p H a r r . i B a - l p o c r o o a H o i r 3 H e p r B e H c r B ,T o r a , r i o resa 6yAer orKJIoHeHa,ecJIr{ sHaqeHue KpnrepHfl cJrurxKo}I Be,'rr4Ko
r{Jrn cJr}[rrKoMMaJIO.3rO SHaqI.Ir,qTo cyuecTByloT rpr.i Bo3MoxHble
c n r y a r l H l r : l - r :1l - t o ; P r l p o H n a p r < p 0 . B A a H H o N {c n y q a e H a c H e
68
rr.Tror{
*, vraLr 2,b
pacnpeAerleHut'
HopMa'rrb'oro
lllli-'^r'rt"q
o6pasorl: MbI
^''
pe"o*nLpol^arb.-caeAyloul'I'lM
MoIKH;CiasaHuoe
l",,orr
(illKJafl
lluA
":"f"tff J.t.""?"#
,",I*",pu1Tr:::ll*'""J#T"?i,13i,Tt;f
reoper11:::'L,:;;#";;;ilr;;;.-"e."'1
Arlcrepcur HopManbHo
l:i;;:il;$";ii";;;;-vn1oc-rr
rax}rienporo Mbr3HaeM
u3Becrl{a'
Bpa3'
3ZlKr'lIoe€HbI
J c o 6 e i l ' p a 3 M e p b lK o r o p b l x
i1"nr"o" .ol"p,tun'*
o
C
o
6
e
r
l npi{xoAnrcn Ha
( n . l n'tpta"i'*
p"ttp'
paBt":.:l:1"
r r r r q n b r xn p e A e n a x
AJIHH-Y'
Hr"'terculuii
u
'rt"'po"I'13
::,i:,tr""''
rrlrepBrr
li3B!'leqeHbl
"
b'n"non"Hunu) ' Ec"itt oco6u
Hyro ,tB).\{ cTaHAap'IHb'*'
no!'I\IqenHn
BeponrHol'rrb
e'ioii coeoK,vnHocrr'rt""r';;;ttt
96!1::*'
p a c f l p e J ' e " l c ] I l l t l1 ) : l B H a
x
p
r
l
a
o
i
i
i
l
H
r
e
p
B
a
r
e
KpIinu6opNrz ,rArnno*
nol coorBercrBylonlcl'1"t:]-":--::':l:i
rrJloluaAIl," 3aKJIIoqeHHofi
oqeHb
iu 06flacru,- coorBercrB)'toueti
eori. Ecru noi6opr:.^n"s'riuHe flBJltl3Haq[T' -qro gaura er't6opra
rtaroti BepoflTltocrnt,
npoaepleilor:l rflIloTe"o
yKa3aHHOii
"o
ercr nu6oproil Hs iouo*yn"o.r_r,r,
HeKoropan RIrorl'e
oli:^:.,r{Meerctr
.,or?,xoropylo MbI J;fi;;&'
o6II3
l{p^Irrn-q'ecroii
uoi6op'*y
H3Bileoo
oltpeAeJIeHHu"u"po"'"ocrb
o6r'13crH'
r<putuuecxoii
nn95?I:"oit
,rracrlr coBoKynHocrn, paBHaq
poAa Composita' HanllIUeM:
Boenpauran.o,.'ilf'*tpy
l) Ho : !i n,lllrbl : 14,2 t'ttvt;
H t : Ft nrl'trbl t' 14,2 xtttt',
2) a : 0,05;
30'0'14,2 : 8 , 2 '
3l t: *n
oTBepraeTcpeAHI,IX
Msr yNe 3HaeM'qTo |IlnoTesa-opaBeHcTBe
'rlu6o cluluBeJII{Ko'
innufioM
cfl, ecrll{ nl,6opouuoe";ffi;;;6o
Kpllrep'lo' rpeAcraBi"* *uno. 3rb npraeoi'r K ABycropouneMy
Koropan no corrlao6nacrb'
u- pi"'.''z.ia.'Kp""udtxaq
;;;;;;;
pacnpeAe50/snnouaAH HopMaJIbHoro
Ilennlo AoJIx{Ha
"o,l.p*rio
Prrc. 2.26. Kpnoan HopMaJlbHoro
pacnpeAeJeHr-rn
c AByMtt3auTpll\ r r B a H H b l M l t X p U r u U e C x n l t l tO 6 , l a '
craMH,
oxBarbrBaroullrMl.I 5 %
nroqaAn nog, rpueofi
J l e H l I r I ,p a c I I a I a e T C . S
H a . ( B e r r a c T I . rI ,] p H q e Mt i a ) i . . I a . qt i : i H r i x c o l e p .
)KHT 2,54f0 o6ur,eri Ir,'IouaAIi. Ec,'rrr i;,tqlrcJ{iHIrca
:Jr*i,retrie n no-
IIaA:leT B JleB)/IOilO"TIOBIIH)',
TO MbI ,:le,rite:,rtsbtBC.q,,
triO BLrSOIli(a tjt_
BJeqc':i n:-; coiloH\rIt'oc].il, t{tlcrcuicii
t \ , 1 e t { L i I I ecep . ; l u i e : r u t i i i a H } 1 e ,
qett jlatlliirfl coBoriyrrHocrr,.
liao6oi_ror, ec,tlr oito Ito11aIaet.B Iii):i_
B y I c l l o . l o B I I I r v , T O c p e ; r , I I C ee l r 5 o y t c i , r ; r o l i
c o l o i i ' ' i i , , . c . . , , ( i o , r o u r e .: r c v
cl)eAgee sa.qannofi coBoxyirHoclu. v:t ra6.,r.
2.i0 Inbr rraxojlllr,' ,,,o
np'lt6.utslt:'entilo 2,50fs tr,rlotrla;ii riojr. xllrso;i
Hlt..io-lirrcs (,,Teilil 0.f
- nycTble c{BaR}1H61
nPOr:133
- n pOAt,iHrhBll5le
cKBe}'1 z llhl
n pOrHO3
H;
!
I
I
I
\1
I
\
I
3 H a u e H f i n Z ,p a B H o r o
g Z , b o l s ( 1 0 0 %_ Z , S 6 l o : S Z , S %l)
.-^1,9, u
cripaBaor 3HaqeHrla
1,9.
BH.ircleuuoe
sHaqcrrrre
f
Kprrrep'rrB,2"npe_
IthIIIIaer 1,9, Hs r{eto Mi,I Ae,laerr IlrjroA, rlro
cpe"qHle 3Harrerl.tg
AByx coBoKynuocrer.iHe paBHbr il{e)i{.llycodoii, ,r ion;ieN,l,ra ri.i{o_
IiaeMbIXocrarlioB Ha nJlure rc,ri)riHa nfilHarre)riarb
I{ poAjr, or,!HqHoMy or poaa Composita.
Heo6xoAHno orMeruTb re AorryrqeHrzr,(oropure
r€.-j;icl.clt li*r
r r c r o , ' r L , 3 0 B i l r { ryr ri i{ a 3 a H H o r ox i ) i i r e p H r r . I ( p u r e p l i r i
z oc}roBaH Ui
i ipeAIIOJIO>KeHLrqx:
6 p a x i r o n o A r i 3 B . r e q e n ac . r y u a r i u r , r u o 6 p a s o l , r ;
l l coBoKynHocrb
^=9rila
zJ
AvlrriHocrarr{oB compostta pacnpe:i-eneHaHOpl\{a,rbHo;
^ ^ _ 3 ) r r r c n e p c t . { f ;l t n r { H o c r a r r { o B C o m p o s i l a t r 3 B e c r H a u p a B H a
22.1 vy.
l,cJ'Ir{B rlacrHol\f np'r,tepe xaxoe_"rtr6oH3 yKa3aHHhrx
npeA,,ono>t<eHtriitBr'Iflercfl Heo6ocHogaIII{brM,
pe3yJIbrarbl, 11o.rlrqgi1g6re
c nl)}IMeHeHrrei'Iz-XpUrepv.fl, MOfVT [.xaearic,q coMHr.ITe,]bHrruH.
TOlla
c J l e A y e r . o 6 p a r l l r t c a x A p 1 ' r o f i i l p . o q e A y p ei l p u u f l r x q p e u r e u n r i ,
^6
ocHOgaHHO
ri Ha npe^qIroJIox(eHII
fl X, 0,'ree'orBeqarou.(r]xcJryqaIo.
3naqruocrr
lloe'i1e qeM npoAoritiarb flepeqeHbcrarr.rcrr.qecKHX
Kpr.ir.epreB,
IioJ'Ie3HocAeJraTbHecKo"TblioKoMNreHTapHeB
orHoc[T,e,{bHoeoroopa
}'POBH'I 3}IAqIiMOCTII. BO MIIOfI.{X CTATIiCTIIqECI{IiX
PYXOBOACTBAX,
B qacrlloc'ii'l rex, Ko'ioJlLIe Iiacalorcfl Ro'tlpocorl ceJILcKoro
rio:l_rrricrBo Ilritl Iipol"Ibll-u'rieHlIoi'o KoIITI]o'-'Ifl IiariciyiBa, Il rrpri,!Ieilax
II _\'npa)KHeHiiflx o6r,rqHo uciloJrb3yrorcs
)'poBI{a sHaqfi140crfl or""',-n
ABarrtarir- icz:0,0b,y H!'rrroArr{ r{ .rbrcflr{c (2.- C,00l-). 1tarr"rro,,o,
qro nolo6ttarr nl)aKTI,rI{a\,10fd'ra6lt
nol,to.rt o60cnoeail qe"recooop a 3 H o c l r r 1 a r ( o f o r s r 6 0 p a , o , r l H a r i o3 1O l r e r a r .
onpere,leHile ypo'-
III 3llaqHllOCTIi IlaxoAHTCrr rie/IliKOM B KOMIIeTeI]qliH
UCCd'teAOBaT€r_
ir,t, oti AoJl;iieH peulurb, xaxoi:i pIcK npH orK,'IoHeHriII
ucrilauoti iri_
IOTe3br rIBdIreTC,IAOnycTI{MLrM.
B r e o " ' r o l r i r . rl t t t l i a c r o
rilreerr iledTo c o6c.loare;rrciaatiir 6o;rrruolf ueonpeAe!'IeHI{OCTH,II KaTiiercq Maro peaJIbHbIM, qro
r\,1brMor{eM IIO3BO,tUrl Ce6e cAer'rarb oruil6ry ,roJrbKo B oAHoM
CflVqae Ir3
TblcflqH rrJru Aa)i{e B oAHOM C!'ryqae }13
ABaAUJrlr. Ecnu err60rrr
oqeHb crecHlzreJlbHble ypoBHI'l 3Haql{Mocrtt, Mbr yBflAllu,
uro uy,',c70
;
I
o-4
crarncrl{qecKoroKplrreput c KpHTIlqecxotl--o6lacrlto'
2.27. PacnpeAe,leutle
''.,,'pin."ti"ur.ii
T)vc.
otti.loueHueffinore3bI o ror{, tlro pa3BeAKa6espesymrarHa:
o6JlaCrl 4'rr
6-rpllTHqeclias
o 6 r a c t r a n f f y p o B l l g 3 H a q U f , I O , C ^i loI - 0 ' 0 5
.J-ripurHqec(aq
q a t T a s c c r u 6 y p e r r l { q ; -2 n 2 ' - c o o r B e r c r B e H H o
t t - . 1 ) . 1 A I. x . t ' - c o c r B e r c t i " i i t t o " p " a * u "
^H
Beponrrra"lat
tr
6orruat
'l-.i,,i.;t"r";:i;rresrto
o-uo*n
,i *.io,"
;i";;,;:
"".ni"it'o6rt;
6,vAe1{ Hy}K'llarbct Bo
luyio rr4ijoTe3y Mbr FIIIKo|jla Iie oTBcprHc.n't,u
K
o
ropble IIe lllleeM Bo3i , i e 6 o , T l u : e i l u S o n r , u r e i " to 6 ' l e r t e i a H l l L I X '
ypoBHI'I SHarIHMocKpoMHble
6o'ree
Bot6tipan
r,1o)I(Iiocrr't[o,rtyt11115.
BepotrHocrb noxorfl
.rn, ttoo*no 6r'icrpee lpurlrir K 3aK!'IloqeHI{Io'
B
sltcoxotl
orleHb
oKa3arbct
MoiKer
BLrECiil,l
,,r'o;to ourit6oquite
i r'D i i B H c H H r Ic o c r i l H A a p r { l \ { l I , I l p f i H t i r b l } l i l B A p y f l l x o 6 ' { a c r f l x '
et|tQerr or npI{Hflrrla pa3r}iqFia plc. 2.27 npouuliocl'llllpoBaH
o rHiioTeTu'qecKoro cTaTI4rreKoToijof
,,r,r, yp'outtcli :',t,iiil.icc'f'r A,'IrI
flpeAcraeL{ila
ct.ltqecKofo Kpfirelrrirr B ]lporHo3e uerfreuocHOCrrl.
nei)eMeHKoJ'IllqccTBeHHbIe
cc(je, uro ro;,iiiatru:.t FrarrrJla Hel(oTopble
ueJIb
6ypeunu'
npI,I
npl{opHTe'ibI
orlpeler'1lliTb
rn,ie, II03BO,rtlcilIiie
rioropot'o -- t SeAttrlct{ B IlpaBurbHocrll npofilo3a npoAyKrnBHocrI{
, , r , , , ' r , < u l r . l ( i , r . r l e i H i i . qn p l r m e H r . e r c r a r r i c T i l q e c x t t i i t i l l t l r e p l l l ' I K 3 r H M
.iej)cr'reHHblM c rle,'ibn peiIIi'l'lb, npoAoJ]ilial'b 6vpeuite cKRa]KUHbI
c:oc'Iollr B Ton{' qro
;t,ilii .rjyri[te oc iaBH'rb ee. FiV,reeafl lllro]'e3a
o6r'eNroe;
6
c
c
t
'
e
p
c
n
e
rltisHblx
oOpariir,r n:ttirtri 1{3 coeoxl'nilocrH
,r,qbTellHal
l i.tDii cocloHT B TOM, tlTo oHlt Il3ttTbI 113 COBOK,VilHocTH
r;e ,) ..:: l : "'I L:t\ i, ll oll!Iil !rBHstx o5.},elirog.
i . r - ' , , ; l 1. . r . . r a a i r i o a r j i l p l { H f i T b ) 1 1 ) o t s e I I b3 H i l r { H r ' l o c r l ' I ' H e n p H n l e p
z'-J,i,t5, ti itaHec'ui eio Hll pacyttoK iaK' KLiK 3To cAeraHo Ha
,io or{eHb rreMH6rrie npofgo3rrr Or(ax(yrctl- 9T"IIIIqanL11u1tlc. 2.27,&,
iiiCl o'r rre11epcneKTuaHofi Hyncnoii cOBoKynHoCrlt. Ilc,'ill )Ke OKazlic'lcft, !i'ro ot{l{ oTJII4rlubl oT Hee, To 3TO IIOqTII HaBepHfKa AacT
()trii)Lrrile npri 6ypeUur.r. KOluiliarll.ln nO,IyqHr oqeIIb BbICoKOe orHOrUt)FIne.i{rtq ,.rl,icflaycnexoB, tto llpu 3roM nponycTl{r Mgofo o6lerf ()ll, IioIopr,re uor,ri, 6r,t oxl:a'llctl
ilpo;1yKTllBllbINlII' B urore xor'tu ocraBHr MHOIo
rirililj,l 61,ter peAKo 6ypnrl,
pe.[,Ko ourr6arlctl
i i c 3 e p B ya p o B H e o r K p b r T b r M L r .
Ten-epi npeAcraBtiM Ha pt{c. 2.27,e raroii ypoBeHb 3HaquMocrI'I'
tto* o:b,40.'TorAa
MHorIte npofHosHble yrlacrKfl rlpllAercs 6yprrl'
7l
oAHaKo.BepoflrHocrb orpHqareJrbHofo }rcxoAa 6yAer 3Hasr{reJrbHo
BbIIIJC. fIONATAqCS
HA 9TO NPABI,IJIO NPUH'TTq
PClxEHHfl,
KOMTIAHAF
6 y . n e r v a c r o 6 y p r r r b , q a c r o o u u 6 a u c i l , H o r . rH a M i r o r o
veulrue ued
Ta ocraHercg rreorxDtrtorl.
B H e O r n H o r l n p o u u u r , n e H H o c r r rp a c c M a r p H B a l o r c r n o c r , I e A c T B l r f l
no,'ryugHHqorplrrlareJlbHofo pe3y"rblara I'prr 6ypeHliu,
ec,rH Hefrrr
c y q e c r B y e r ( o r u u 6 r a B T o p o r o p o , r a ) , 3 r r a q l r r e , , r b r jror a u r e , q e M
noc.rreACTBirfl
rro"ryqeHriq no!'ro)firire,rrbHof
o pe3:f.rrb]
arA rprr 6ypeuuu
l r y c r b r x c K B a l K H i {( O r u n 6 r < af l e p B o f o p o r a ] . h p i r u r r u a
irofo cocroirr B TO\{, Uro $riHauconrrfivcnex o.lrrofo'6clntiuoio
o T K D b r r r . rqf ia i.rro xlox{er^IIoKpblrb croHr'rocrb necfiTI{oB rilil
fa)rie coreH Irycrr,rx
r:KBa)tiatr.OqeHxa Bel)osTHocrr.r
)/cflexa n rr.:(l;:irrrofi nporruiu,o"iirlocrrl CllI;\ rrpu 6ypeHnH N,rerolol,{<<g'xori iror,,u'
puuuu ,,p"_
M e i r H o 1 0 0 7 t .E c n n 6 a : t r u c K B a x H H b r6 r , r " r t il r p o 6 v p e i r r , ,H a
oc.ioBe
i l p H M e H e H I i fcl r a r H c r u q e c K l r x K p u r e D u e B ,T o 3 T a o I I e H K a
c
o
o
r
Bercrj . r o B 3 . 16au
i ' p o e u r o 3 H a q u M o c r an p u u e p H o a : 0 , g 0 .
3 r o , n e p o n r H o , x p a i i H t t f i c , r y v a l : i ,i r o o r r r o K a 3 r r r B a e r ,r r r . o v l ) o _
FieHb3Haqll\,tocrlr c,rle,IyeTeltduparl B coo't.BercrBuuc KoHKperHbtutr o6crosre,rrbcrBaN,rH,rrprl Koropbrx ucrro,lb3yercq xpr.rrepnr?.
3HaqeHIit ypoBHq a ocFIoDi,lBaIorcflHa
oueHKe roc,'IercrB].rfi, xoroprte
tso3HUKHyr,ecJrHcreJra'rr ouu6xy repBofo po1zr. 3r.u IIoc,reAcrBr.rfl
\{oryr 6nro ocqsire\{brMrr}r ilpfiBec'rH ri ilOrepe
reHef, BpeMeHn H
;1axe >KH3Her?,
fi"qn oHH MOf)'r 6srrr seccs3aeMbrMll H Ilpr{BO4rrrb
Il )'uep6y npo$eccaoHanlHotl penl,1oott" HJrri r'rgqHori oplocra.
Jlrfl Toro q ro6rt coxpaHHTb rilrre,r,'IeKT),'aJIbHyio
qecrHocrb, Ilcc,[e-loBare./ib iioJllieH IIpIIHIIMaTbpeilleHr.{qHa rpaHr{qe o6,racru pucK a l c o o l B e r c r B l r r o u { u u o 6 p a s o r , re m 6 r r p a r s y p o B e H b 3 H a q [ N t o c r u .
t t l , t u o p y p o B l t f l 3 H a r l H N 4 o C nr H
o c J l e n l ) o B e l e H 1 4 f i p o B e p K r rK p H r e p l J r ,
riofAa pe3yr'ibrarbr yxe H3BecrHbr,
- 3TO 6ecCrirAHoe ucxaxegne
rpaxron. flo,ryueuuue raKHM o6pasou 3Har{eHprflypoarieli Moryr
orpaxiarb JIIIIIIb xeJIaHHe I.ICcJIeAoBaTett[rpHHtrb r.L'rHorKJroHlITb
fllrlore3y, a He ^qarb 6ecnpncrpacrHyro oueHKlr rlMerouefocfl pr{cKa.
I.KP I,TTEP
I' IZ
l , . l n r o r o q r o 6 t r n p u M e H H T bo n a c a n n u r r iB r , r u l ex l l a , r e p a i i , H y ; x _
Ho BbtnoJ'IHttrbptA yc,lonuii, Kot'opbre pe.lKo ocyqecina,rau Ha
r r p a r { T l r K eM
. s r o 6 s r . r u o H e s H a e r { r . r c r u H H b r :xg a q e u u f i I ] a p a M e r p o B
r r 3 y q a e N r o r op a c f i p e A e r ' I e r r u tT, a K r { a l { H e M o } K e x ,ul 3 y r r a r b e c e i i c o _
BoK)'ilHocrr-rpop,a Composila, n rcHo, ql.o 3ro HeJrb3ffcAe,rrarb.
Tan raK p Lt a Hen3BecrHbt,.r.or'ryq[Iee, qro Mox<HocAe,rarb,_
3To oueHlirb HX no au6opxe. Or,Haxo raKHe orleHrirr Aorr).,cr{aror
HeKorop)Irc crefleHb Heo]lpeAerrieHHottrH,
rtooroMy peueHlrfl, npuHfiM a e M b t eH a I 1 I xo c H o B e ,H e J l b 3 fcl r r r { T a . f T
boqHbtMlI.
H e o n p e l e . a e H H o c r bB
, o s H H K a r o u l y l oK a K c f l e A c r B 1 e n p u M e H e H H ,
ol{eHot(, locrpoeHHbIx no ou6opKe, N{o)t(Hoyrrecrb, ecJlt lcrror,Ib3oBarb pacljpere,reHl.rec 60.nee ruaponoir o6"racrlio 3HaveHrlri,rreM y
72
Crrrc'
Pnc.2'28'/-pacnPeAeleuse
ACHTA
I
E
I
!l
c 6l
oFl
Fol
si:l
o6l
:l
Vre.fiwe
0
t
pacnpeAer'1e"]lL.^"uttoto
eHun.Hop)1a.nbHofopacnpeAe,T
-!1To.:'
Otio lioxo)l{eHa
Crln'nellra'
,-pacnpeAeJleflHeu
rurra Ha3blBaercfl
Tnnuqsas
eur6oprilt.
s:qroir
HopNrarbHoe, ruJ,i""i ;--;6;;*a
@opua
pnc'
Ha
"o
-7?.8,:.
ripuBat ororo pacrp.o"ntn'i"-ltao6parreua
IillltnoiiN{etigeTcgB3aBI.IclIMocTlloTI{}iclarra6,rioleuuii'Kor.a.a
I'i'."i"'"ro"ioLerr"it e asl6opxe 6ecKoHeuuo'ro /-pac;lpe'l'e"leutie
CoBnaAaeT C HOPMaJ'ILHbIM'
Crenenuceo6oAtt
crarucrl'lqecliolo KpllreArq roro qto6tI noAcqnTarb3HaqeHl{fl
o
l
t
e
H
f i r b n a p a t v l e r p b tr r 3 ) ' q a e n o n r r 6 o p o q H b r MA a H , H b r r r
p,,rl"v*no
peIilHTb
HcB03]1o)l{Hbllvl
noii coeoxyltHocrlr. I'lHtyu"aeuo Ka]KerctI
npur{eI
{
c
o
B
o
K
)
'
'
I
i
H
O
C
I
i
l
c p a 3 y . u . n es a A a q r : o u e u H r l n a p a M e r p b l
6e: xaxot:t-"tu6o
aut6opt<y
:xe
ry
lI
oluy
IIcno,llsl'a
Hurb IiprlrepHll'
i( Hi\'leotrlerioMneHcaut4n,cBfl3allHoii c leynparHbIM o6peqenHeM
gTHM
Be"iIIIqHHa..
BBOJ.'ITCt
c
cBtt3_II
B
nuOopl: ua6nro1ell,fi.
\'10)l{Hoonpef'eKoropyrc
qllc,'IoNl
cso6oIlt,
"!"n
CreneHeii
ua3bluae\1afl
qIICroM ua6;rroAenllti e eul60pxe I1 qHC"[Hrb Iiali pa3Hocrb Me]Kn]r
rlo est6opouHltLt
'o\r rapaN{erpots, notopoi" rpe6yercl olreHrirb
I4HnnK cnonavH, qllcJlo CreneHeiicso6oAnt npeBbl[Jer
I
H
C
,
'
I
O
M
g
a
A
O
I
I
e
H
I
'
i
B
a
e
M
b
lnXa p a M e T p O E
g
a
6
,
r
N
r
A
e
n
U
t
i
"t o
n rJ'I.a
r nnen,ol r,C
o
6
o
s
H
a
q
a
rcicq f peqec
e
o
6
o
A
l
t
c
r
e
n
e
H
e
t
i
9
n
c
.
n
a
p a c r r p e A e r , r e H. r . l ' I
q[c,'I4.
cxol'r'6yreofi v, eto BcetAa UeJIbIe[oJIOXI.ITe!'IbHbIe
B l < a . { e c r n en p H M e p a p a c c M o r p l . r Mp u c . 2 . 2 9 , H a I i o r o p o M n p e , 4 '
B b r q H c r e H I i sc p e A H e r o u . t , u c n e p c H un u 6 o p x u . c p e a H e e
c.faBr.relro
Pnc. 2.29. flpegcrasleuue B BuAeAI-IarpaMvbl MeToAaBbrqHc!'IeHHff
cpeAHero
H .&Hcnepclrn
no llsrti Ha6aoAeuuql\4.
cpe.nsee
tro BceMua6lpae'
F
HH9M:IHCne
""."o.r"u"."
pcur-no
D a 3 H o c T H} l e ) l ( I y H a o r l o n € H H T M HH c p e A H H M .K o r a a q e r u p e p a a Irocm HaR,u.enbt, ntTat
pa3H'ocTb r3BecrHa
//),--.1
r?\/
\y
\\
\\
\\
\\
(,
lit
Ta6nuqa 2.ll
t r ( p l r r n , , e c x u e3 H a q e H fqi l-xpurepul rrplr v creneHqx cBo6oAbI
I i 3 a A a r r r i o M ypoBtlesuauun'rocrlIl7l
I-poeirrr
XIloarouy
t ntlf r:
Xu: 5X__ (Xr * Xz i Xz * Xq).
0.5
rrNreercflTo,rIbKorrerbrpe He3aBficr.rMbrx
]rcroqHrrKa Huc]cp_
3,0t3
opbrM sHqucnner i ri Ar.rcnepcr n.
^,]-g^t9 I
\ coir(aJtcr{tilo,
]loHqTr.Iec.Iefleiiefi ceo6o,1rr peAxo
!:'i8
paccMarpuB".o ,,pn,.,,,,rbr
]:,,9]-{._Y_.ta.rrbue
l,ra3rriqsr rrr{ce.ucrefl
eHeri cao50,1l,r,accoi{uiipoBbltirr,rx p,,rrrn
urrorNl' crarrlcT'qc:,r'r r{r{
KpriTeplrfiM! ilo Mepe Hx rlorBnellri'I" g
Texcre.
Ta6,rrr.rr{r,r
l-pacnpe4e,reuHn
1u apy."*-eu6opouur,rx pacxpe.lc_
ricno,rriynrce roqHo rarirr4'>i<e
oopa:oM, KaK u ra6nrrqr,r
:]lllt'"r)
K
y M y " I f i r I ' l B ' o r oc r a H A a p r r { o f o H o i l M a " r b r , o r o
p a c l p e A e , r e H ' i n ;o r . n : . rrue cocrorJT ,'IrittIb B
ToM, r{To A,,rf Iiei,ox<,(eFraarpe6yel,rofi
nelto_
flTHocrlr e ra6,'ruqe f-pacnpeAe,leuut
HaAo 3Harb ABa q[cra: a_
3aAaHHr'rfi )'iloBeHb 3Haq',]iocTrr (nepoaruocrr
ouru6xr.r nepBoro
po'a ) rr qricdro crenerieii cao6o,1i,r'r,. 'Ta6.r.
2. 1I a;nr;;r.o".,..njr. _
u_(eHHbrM
BapualrroNr ra6.rrrqrr :Ha.rclirri
/_pr."p;;;;;;l;;,;
0o.rcr:
[orpo6nUe ra6,rlrqlr MOX{HOlrarlrH
BO MHOrr]-\ pyr{oBoAc.rts
ax
;:o
Mare[.rarr.rqecxoiicrau:ciurce.
cfl B TOM'
pflA o6pasi10e llecqa*rlixa reHc,ria,',pe3y,IlbraT.rri
alra_
"qrl3oB Koropbrx npHBeAeHbre ra6.{. 2.1.2r.us'* ,; ;,";;6;rHocrr.r,
u u e n u e f i c p e ; r H i , o rnc o ' r c r o c r b 6 o n e e t B % .
E;";;r*";;j'o6pr:qsr 6u,ru 83srbr HayAaqy rr3
HopMarrbHofi".*;;y;;;;r;,"
Bbiqlic:_
.naral-rpHrepuri:
.l :-+ _ J
X-Pn
se
f-uo
tfil-n
2,0t5
.943
, B{]i;
,860
,833
,+/ll
cKoMrioHrer{crecoAepx{rircre riu're
vort,.pu'isbj". itrir'"npur-
Tar<nasbrsra*otl.1_lprirepr.irr,
KoropbreocHoBaubr
Ha pacnpe..re_
JreHHr{
Crrro4enra, noJre3nrjAno npoubprar.,
r[noTe3br o ToM, riro
AaI{Har nu6opxa B3flra ri3 coBor{JrnHocrrr
c 3aIaHHL,rMrr
_xapari.rep,crrrKaMHlrJraxe /rJr, frpoBel;xrr
i'lroresu o6 orlllopo,qiio.r.r,
anr,,
alr6opox. flpo6,renauraxbro iuna paccnaarpr{Barorcfl
Kypcax B MareMar'qecKyrocrarucrilxy rr rBJrrroTcfl eo neo4ulir
OCHOBHbTM'{
B
3KCICPHMCHTAJIbHbIX HAYKAX A E
O'6TAtr''
KOHTPOJI' KAI{CCTBA NPOAyKrtxv.
Ilycru, Hanpr.rMep,
rirr, Tanore3y, 3aK,rrrc
qarcuryio^T{T:_o lpoBep
qro
6 , 3 fi
2.9':i)
2,3r3
,886
o6l,qc}rxercq
B,-Haqa/'rbHlrrx
riypcz,\
cKopee oHo rrpeAcTaB,IrreTc'riaK
_cTaTHcTIit*:,
o t r e B r r A H orel p o r i s B o . r r b H oqeu c J r o ,
u u n p i n n c pn - r .
ornuquoe o6uee
I l 3 " r r o x i e H i IseT O f o B o l r p o c a K a I {
A CplrsHuecxoM
, Ii ri B crarHCTitricTa
I
,441)
, 41 5 ;
,397
, ',l-t
333
I,B12
l,796
| ,782
t ,771
1,7fil
I ,7l,lj
1,746
|,740
i ,363
I .356
I ,3i;0
I , ll.l5
'),1
I
I
,JLJ/
Q',l2
1
, '31 {3) q0
I ,31):'
t)\,
i20
t,lJ+
| ,72\l
i ;2,'
1. 3 t 3
1, 3 2 1
1,3i9
l,3i.s
j.316
I,3L5
1,314
1.313
1,31I
I ,310
l ,303
1, 2 9 6
I ,2ti!)
I
9i?
;91
. 71 7
, 7t 4
,7tl
,708
,706
I t\.)
,7 0 1
,699
,697
6q4
, 6 7|
,658
t2,ia(;
4, 3 0 3
3 ,t E 2
2,776
2 , J 71
,
747
2, 3 6 5
2,306
2,262
t ,rt.q
2,201
2,17\)
2,16t)
2,14;'t
2,l3l
2 ,1 2 0
2,110
2 ,i 0 1
2 , {'rg.!
: ('t86
2 ,('E{.)
, (\74
2, 0 6 9
2,a64
2,060
2, 0 5 6
2,452
2,048
2,a45
2,012
2,A21
2,000
I,980
I ,!ic,i-r
3 1, 8 2 1
6,96ir
4,541
:1.365
3,1,13
2 ,9 9 8
2,896
, krl
2,764
2 , 71 8
2.681
2 ,$ 5 0
2,62.1
q
i,{.,.)
2 , 1 ;S
f
2,L€t7
o
i(o
2,539
')
EDQ
2 . l t1 B
2,508
2, 5 0 0
2,492
2,48-o
'
(2.32)
6 3, 6 5 7
9 ,r]2ii
5 ,8,1
I
4 ,60,1
4,032
3,747
3,499
3,355
3,250
3 ,1 6 9
3 ,1 0 5
3, 0 5 5
3,012
2.977
, Q77
9 091
2,898
2,878
2, . 3 6 1
2,84r.)
2,831
2.819
2,8A7
,
7A7
2,787
9 L1q
9 774
2,473
2,467
2,462
2,457
2, 7 7 1
2,763
2.756
2,750
2,7A4
2,660
2,617
2,576
o
lqa
2,390
2,358
2,326
3 l r l , 3l 0
22,327
i0,215
I,tto
5 ,8 9 3
5,208
4,785
4,501
4 9q7
4,144
4,025
3,930
3,852
3,787
3,733
3,686
3,646
3,610
3,579
? (-.o
3,527
3,505
3,485
3,467
3,450
3,435
3,421
3, 4 0 8
3, 3 9 6
3,385
3,307
2,232
3 ,i 6 0
3 ,C 9 0
- s- o u e l l r r a c r u l H A a p r H o f o O T K J I o H e H L I f i ;s c - c ] l l H . r : l l ) i l l l r f l | i i t ; i i l r i l l 0 I I p e A e " i i c l i l t t cl p e 4 H e i o 3 H a q e H H f l . 3 a l , t e t l t N t , , t t o
'.i,r iii)ilicirriii coBliirj.eer
c xpiil'epucxl (2.3i), ucK,rIoqafl To, irrn
r l . ' r ' l t i o{ ) r l c i l l t l
b critHllspru}'trl ouur6xy no dropuy,re s.,:s/1/n, a Hc
,, ' ,i'i;11-,i';.1sc!W,
rilK Kai( rrcri.iHlrafl Ar{cnepcrirl coBoKynrrocrtr }reri rl(,C
flla.
apn$nreruuecKoe,
Bbrqr.rcrreHHoe
no Aarirri,rMBbr_
:l:.-T.-"p.Alg:
oopKr.r;p0_frinorerr4qecKoecpeA'ee, paBHoe
lBToi- r_u^"no
'7,l
3iirqH\i(JcTiI, ct. qb
( i - i ( )ji'). r a J l b HM
obr
n p o B e p f l e Mt H n o r e 3 y
Hs : pll -< p0
rj r , r i \ i l i ( ) i H e c T B e
a!--IbTepHaTllB
Hr:lrrlpo.
T a6nuaa 2.12
Pely,ruraru H3MepeHI'lt nopflcrocru Aecsrl{
o 6 p a r u o n n e c r l a H f i K o BT e n c l l l n n e H c u J r b B a H c K o r o
Bo3pacra, BnaAHHa Durxopn, Bafiomlrsr
0l
02
03
01
05
00
07
08
09
tn
t"::'::"+:
:tilu,1t"\1?"4i!ffi
3Haqel{rlirpi:11':'#'ili;,1-#"'f
aqesotot"t"HHoe,3H
^',oueHuI"rpacnpele"Ietlffi;'i#'.1"^;: il05,
p
tuot'
p
H
o
)K
"b
Jr
H
to
np
KprrrepIIR ao
' l_ g"iln
';p'li;;;il';;;
q ";';:.;;;oni
Jl,,
l.
981e"
ir-rrrrvre"J
l"it:T
#:"""1'
BI'IA'
I 'L'IIf
xe BI{A'
>i(e
ror ..1t
ror
" l..l.o
"' ox,HocropoHHero'npnt"p"o
;eT
".o
lrMeer
"ii,tt'
"i.r:'
"'"u
crarHcrll
HIIe
l)',' oi'F,,:+;$;:i3ffi
li:""':i''.1'.;!i{.:,:3;
cC":i;;;;5;;H'ipiiitp"ii
n\
r l ) 'qae:
qae:
UIJro r"*.rrrt\.[l€M
qTO II u rrl'L+"'-'
l3
t1
1i
23
2i
29
t8
27
20
o{
C y u u a2 1 3
21,3
CPeanee
s , : 3 0 , 4 6 ,s : 5 , 5 2 , s " : 0 , 5 7
r o N I ' r { T o c p e A H e e3 H a l l p o a e p n e v a f l r l t l l o r e 3 a 3 a K r l o r { a e r c f lB
qeHl{enopHcrocrllCoBoKynHocrH'I'I3xoropoii6lt'ra,s:traosl6opsHaqeHH]o lB%' &lHoxecreo
Ka, MeHb[Ie H'rll paBHo :a-lauuouy qTo
u S y I { a e M a ' {C o B o K y n H o c T b
T
o
M
,
B
3aKJIruqaeTCfl
aJIbTepHaT}IB
1B0/o'
ilpeBocxoAsurvn
nopllcrocrb,
r.rMeercper.HloFo
/ nO ra6'rr' 2'11 rpes
U
a
u
"
H
t
t
q
, [ I , , r no , 1 , e l e , ] l e l j l l f K p l l r l l q e c K o r O
q
u
c
r
a
:
y
p
o
B
e
H
b
:
J
l
t
a
q
l
l
\
l
o
c
T l i4l q l z c J l oc r e r e H e H
6 y e r c q 3 : i - r . a r br c a
tlro .JIIH napaB ,iriruonn IIpHMepe npernorarelercu'
;;;;;";.
- t p ' e 6 y ' e r t oo u e H l 4 r b ( o u e u x o l i ! ' i l n 6
M e r p ( l t ) I I : l B e c i e H ,a i p y r o r " n
uinotipo'ino" craHAaprHoe,orxlolreHue)'
flBJlflercff lle'iitlt{tiHatl i'd
roDlicrocrll'
B b r 6 o p K e ,c o A e P l K a r r t e i li e c a r r n s r l e p e u r t i i
n;;;;;y
c
B
o
o
o
'
l
t
l
'
c o o T B e T C I B V i oATe B f l T l 'cj T e n e H e l i
B ToM cJIVqae' KofAa
Hy"leean fl{nore3a orBepfaerctt ro"lbKo
lB0/o' Il nosroMy IIo'
cpeAHrfl IloDticroc'rb cyutecineuHo lpe:-blIrIaer
Tod'IbKooqeHb
ctlllrilrb
l{o)KHo
o6'nacrl
naAaloulltMH B I{pl'l'lHrl'ecxyio
Ha pllc' 2'30' Ta[
o
K
a
3
a
H
o
3
T
o
K
a
I
(
K
p
u
T
e
p
u
u
'
6o.nrune :illarleHllfl
raK xaK ero Kpurrlqen o ; i - n p n i " " p t t i ' tu i t : b i e i r e r c s o . l n o c r o p o H H I i M '
o
A
u
ofi cropoHbl o6'lacru
c
r
o
J
l
b
K
o
cKag o6reicrb pacnoJloxei{a
l) llo: Pr-< l8o/0,
Hr:Fr) 180/o;
2) a : 0,05;
e tr re_'2- 1 , 8 - - 1 8 j 9 : l , B g .
u
5'52Vlllo
ra6'nnqHoe'coorBer1'89 nf::-"futt
3
H
a
q
e
l
l
l
i
e
ypoBHIo-3HaqliMoBlrqlrc,reuHoe
ciooorot
t';;;;;;
r
e
B
n
r
r
i
s
%
u
o
u
r
3 H a q u T 'q r o M b I
"
3
i
c
i
crBvrouree
a"\brepHarnBy'
c r ' , r . e . n o r a . l a e t " ' n p i t " " o e ci";:::t^{,'
x y r o - o 6 n a c r rnp"noto
'
;y;;;fi
it3 Koro,'loII)KHbIorKrlolll.rb
'i;"
;;'-o6pu'oo' nol'1-t191"i "duorynnott,'6o'rrnue 180/o'
.**i,'lloqalouryrocfl B
i;;;;'
ntt"u""itlu
ro
qeu
poii 6bt.'rrturun"ut"u'
'1'83'
911:;;;*tnot" qro eut6opouuoe
Ecrn 6sroo,u"tntntiu"--u"no'iuu"-/
np"rionararb'
;;;;;;n'r'
yrBepxnan"n'iii;
se 6sr.rooo,
j'ii ' s'"t^r,M' qro *it np" 3roMHe
6o.rtule'
cr)efHce
.'{il.;"i:fl.J'r:l*;
:;e5p";i;
;'i;i; * ".n.".s
e,r;V* ;;i"l'J,
HeB
[t]"
I"
1i
iii ii,'il il ill; ;:i"";:,#"-:-^:t$i",.
*";i';i:";''
r{efo HeT' Ho He
o i r u u o r y r n n n " u ' o " ' " ' t r qe rnoo ' o p ou; t' ! : :"Mt peoc"rton' o t t b l o '
xe
i l ( )r B o J I f l I o yr c r a H o B H r b '
6u'rrl no'nvqeHbrfecflrb Ao'
nno*'oi
C rp1'rori
B trecqaHlIKax
",,4'n9y13.1e
sHaqegltir nopt'lcrocru
u o . ' I I I t t r c ' : i b l l b l x" t i e p e H r r i f
'rli cpeAHIle
A"lo;xtto
2'i3'
-B
ra6n'
"i'crt.rrtir, ,,oropo,"'''if;;;o"";
a"
o*uu"e or rir e'lblryutefis
6orro,..u,,r'ut'J;il;""1t11i
\'r DLr
.rrB
tp"o"te c :alrnnuru Bst6o,,0,.puu"i'Ju"ilrelr6opounot
t'.te
ir,
-i,,'r
cJr\.qae npo'
coBoKynHociu' e '11'HHo\1
'nuutnn'"t
l ) ( r , tt i i , t\ l c f e ] t H I I \ l
ert'f ;
{JCl)t'tl.,i t'u,,,rr",o' IIMeIoilIaq c"le!'ytoullt:i
Hs:!t1 :Pz'
B T o r ' l ' r t r o c P e A H e e3 H a '
1 - l r , r , n e p t i e r t alfLl I n o r e 3 a 3 a K J I i o q a e r c t
eu6oPtra,PaBHo
'ielrr!(: t'oiloltvrlHoc'r
lt, I'{3 xoropoii
ltP:.1o 8 3 f l r a B T O p a f lB b I '
"]1t1
I13-,xoTOpoll
cl)e.liie)l\' :iHaqeHIiH)coBOl(yilHOCTil'
fllrlore3bl
Sirpxa. triHolt<.ecreoaJlbrepHarllB tJIfl
H y ' .g r * l t z
He paBtITO CpeAHHe 3HaqeHHfl {-Byx coBOKyfiHOCleu
oH
) ' ' fB e l ) i l i . f l i e r ,
nycrb
3HaqLIto!ll:--l
Hsr.cuosa ro, lonriit 3aAarb-ypoBeHb
KpI'rrepHH
crarlrcrHqecKl'rrl
;il.;^';;;.;"10't
(":o,roi'
Teneps
I{NleeT e,reAyIOUIHHBI'rA:
t = J,83
/D
Puc. 2.30. Pacnpe,lenesueCrlnaexra
c reBttrbro crenegflMHcso6oAbl
7: (Tr-x)/s,,
(2.33)
77
T a x x a r r a 6 r l i q H b l e 3 H a q e H i i qA B y c r o p o H n e f o K p l ' r r e p [ s c 1 B c r e IIeHt{N{llcBo6oAbI, cooTBercrByloul[e l0 0/s-IlotuyypoBHIO 3HaqIIMOc r u ( 5 % H a K a l K A o M K o H I I e p a c i l p e A e J l e H u s ) ,p a B H b I - 2 , 7 0 v
3HaqeHue He lrorraAaer B KpurllqecKylo 062, 10, ro Bbrrlr.rc,'reHFroe
,rracrb i.r Hyd'reByrofiltrore3y He,lrb3rrorKJIoHHTb. (HanouHuu, qro
r(pr4rliqecKrlfl06racrb oxBarbrBaer 10% nr'IoqaALI noA Kpl'{Bofi
l-pacnpeAe,reHua). OrcrcAa cJleAyer, IIro Her ocHoBaHI'IiiltpeArloJrafarb, IIT0 ABe Iz3yqaeMble Bbl60pKI4 B3urbl U3 COBOKynHOCTeU'
H M e l o u { r r xp a 3 H b r ec p e A H H e3 H a q e H I i f l .
A,rs roro qro6bl npLIMeHtIrb3Tor Kpllrepafi, ueo6xoAllx'loBbInoJi6bITb
iilrrb cdrreAylouueycJioBrrrr.Bo-repnltx, o6e nu6opr<14AO,'IX{HbI
Iror'i){el{br Ha oc}loBaH,Hullpou,eAypbl cni,tlsfiHofo BbI6opzl. Bo-ero-
Ta6nuua 2.13
nopltcrocrnAecrrr{
_ Pesy,ntrarrrfi3MepeHHq
o6parqon [ecqaH[KoB Tenc,lnn neHcurbBaHcxoro
Bo3pacra, dacceriu pexu Vuu.q, Bafiouusr
Florrep o6Dasua
flopacrocrs, o[
pbl;r,, 3HeqeHHtl C,Iyqai1HblX Be,'IIltiHH B COBOKyIHOCTflX'H3 I{OTOpblx
HoprleJIbHblN{
Slt.rtu ugn,terictii-.r t;t ti.topxLt, .i.cJitt(Hbt otiucbtBarbct
pac]lj]ele,leH]ieh{. B-TpeTbllx, Ai.icilepcuu 3rl'lx coBoKynHoc-LeiLAOJI)KnepDofo ycd'IoBLIq B bo,'IbulllHcrtse
Hbr 6birb paBHLr. BunolHcslte
oAuaxo efo HeBblllo,rHefeo,'rorr{qecKHx 3aAaq [paBepl]]b'rpyAHo.
HIle B Cr"ryqae, ecJII{ Bbl6opKLt I{Meror cl.lJ'lbHoe H c14cTeN,l:!.1I]qecl(oe
c i r r € r J - l € H i 4(€r a r r n T o M c J r y q a e , K o f A a L I s M e p e H U t ln o p n c r o c r l r I p o BOAflTCfl TC"ribt{OB 06pa3r,ax, 83flrbIX H3 npoAyl(TIlBHbl}l :'}oH rlJlu
ireqlrrHrrrx noJreii), Moltter ttsHTbct{ cepbe3IIbIM HcroqHIlKoM ollII{o l{ol)x.{a,rIbHocrr pa...:ipe[eJ€5ox. KoHc,Jlro, itlloBeili(\, ar,rot"rbr
rrriri 3Haqerririi rilrU:rr:lKa IlJyqaeltoii eonoxyllHocr]{ Mo]Klio npoBe.3itr, o,lUeKO OAIIO ',i'O,'rbKO
OlIi.4OHeHHe01' HOpl{a,'IbHOCTI,I
lleAKO rlpLiij0;in'r' K Ir3MeHeHHiO pe3yr'IbTaTOB, B OCO0eHHOCTUec'l!l r:Ul6OpO.tr a r i c o B o K y l i H o c r b i l o c T a T o r i F l o B e r l l K a . T p e r r ' e y c J I o B H e- p a B e H C T Bax{Ho, TaK KaK Iioqrll
tso Irlcitepcuir ,l.eyx col]oKyIIHocreli -oqeHb
KplrTeptll{ ocHoBaHbI Ha npcAno,'Io]Kelll{iI o paBCe CTa',irrcTfiqecKlie
s e H C i B e g r r c n e p c a i i c p a B F i r r B a e r r l l , l xc o B o l ( y r l H o c r e i i . K c u i i c ' r u i o , a r o
lipH6,raN<euHlte
i,-puiepI4II
npej,no,lo}I{eHrre d'lefKo IlpoBeptlercfi.
i i p r { M e r i r \ , r b r ,e c J ' l HI r p I 4 c p a B H e H r i l I B y x e u 6 o p o r o K l x ( € T r ' ; i , t t T o o F I t l
3Haqtitio pa3,'tHqaloTcg.oHu npHBo;lffTcrl B 6oIbruliHcTBC BBoiiHbrx
KypccB, BK,qro!tati re, KoTopble nepeqHcJieHbl B cllllcKe ,'IIITepaTVDbI.
Cynaua 189
Cpe4Hee18,9
s,:28,21,-s:4,82
r'r1e Sc - {lueHKa Cl,aHAap'rHofo crK,'roHeHrrs pa3riocTri MCX{A} _T1
II X2, Ito,IIlrreHHas no llByx,r o5.be:lHHeHsbrr,r B;r60pKii[,r. 3TV c)ut]H..
tiy se lric))iiiio BbirllicJIriTb Iro qiojrlry,le
"e
_
Jp
-r,'
|
-i---,
-1-
*nr_ _r
n,
3 4 e c r , . 9 ,-. o 6 b e A r r H e n [ r a foi r l e n x , i c r a H A a p r l l o r o o r K . q o H e r r r i ,i]r,a i r AeHIIa fl r{o}16nHa r{Iler:lAByx tsbr5 op oriHbrx Luc jiepcfi r:r:
.:-(nr--l)sr2-i-(rr-l)srz
nrtr72-2
,o.r,
\z'')'ri
'
fAe HHAeKCbT
COOTBeTCTByIOT
Bbr6opKaM r.i3 6acccfiHoB Erifxoplr fi
V H H A F u e e p . l l p o q e c c o S b e . l t i H e H l r r. I B V x B b r 6 o p o Ki i p i i B o l r r r t { , t o [o,'t]tflTe.rrbHbnvl
cTeneH-rrM
cBoSoAL,I,
TaK Kat{ Tpe6yeTct olleHliTb .j.iB;l
napal'rerpa or2 11oz2. Lluc,ro creneHeii cBoSonLi nberovry Arfl l-i{l)irrepilJl 3r{BHBar're}rrHocrH,
3aj.iar[rofo rf opivlli;ioii (2.32), €c.rrr \.:,.]
:n1!n2-L
F e n n c i c r l . r i Hp a 3 J l u q { e \ { e } K A yA B y , \ , r rc l ) e A H i t r , r i.. i: i . j
ql.lMblI{ Ii p H AecflTl.IIIp oqeriTi]oN{ yp oBFre3FIarlHlvlocf U?
'sP- , _
L:
I(opp e.rinqnoHHr,rfiKpr{repnft
Buure r,{br BBe,furKoooQI.IIIHeHrKoppenflIraH KaK craHAaprH3ocBfl3r.{Mex(Ay AByMfl nepeMeHHbi14!r,
Ho He
BaHHyrouepy "nnuer:iHor.i
eroro KoeQsullaccMorpe.lr.rBonpoc o cTarlicrlllIecKoii sHaqLiMocTI.I
r{i.{eHra.KoecpSuuueHr Bbr6opoqHotlKoppeJitrl\Hwr sBJrrercfl oueHr(ori [apaMerpa p, Koropbni orpa)Kaer cBfl3b Me)KAy AByMff nepeMeHHbrMuccBoKyrlHocrlr. flpeAno!'Iarafl, qTo o6e nepeMeHHbleHophlar'rbHopacnpeAereHbl H Ha6JIIOIeHI.IfcnyqafiHo BbI6paHLI lI3 HeKO'iOpor'rcoBor,yllHocTll,IlfbI Mo>I(eMocyqecTBHTb rlpoBepKy 3Haqu-
9 ( 3 0 , 4 6+) 9 ( 2 3 , 2 t ) _ 4 8 3 , 0 3
-: ! " )' 6
u rR
' ^.
ro+lo-2
lB
sp:5,18;
21,3- r8,9
2.4
5 ,r 8t / r/ r o+ v l o
1,03.
MOCTH T,
79
Rt
,A
_-
F.KPHTEPI{R
f l p o n e p n e u a f l r a [ o r e 3 a 1 4a " r b r e p H a r H B ar a x o B b r :
Hs:p:0,
H1:pt'\,
T. e. MbI MOllieM OnpeAe,rllTb,3HaqIiMO,lll
Ol,luqaeTct
OT H)'"'lf BbI-
6 o p o u H u r r iK o s S S s u t I e H r l i o p p e , { a u u r i .F I y J e B a f l l i r r t o r e 3 a y c r a H a B e e 3 a B H C H MlbI l q r o r t 0 6 o e H e H y " I e B O e
. / t I 4 B a e Tq,T O . ( B e n e p e M e H H b i H
3Har{eH[e r Bo3HlrK,']oIrpocro LI3-3a c"]]:qaliHblx Q;lroxrl'aulrrl npi{
c , ' r l q a i i H o Me r r 6 o p e . / - x p r t r c p r r f is H l t l l i t l o ( l J I / ' J a . ] l i e t c n n o Q o p My,'Ie
t
t:-
rli n-2
r2.35)
I l-:F
r . In M e e r ( n - 2 \
creneueri cso6oAut.
B K z r q e c l n e r p H M e p a ^ \ , { o } K F Inop c B e p i l r b 3 } i : i t i l } t o c r b B b r t l i i c . I I e H H b r x B b r u e H i l o c H o B e J a H H b r x t a 6 n . 2 . 8 . t \ o 3 { } 4 , i 1 I { r i e H l o BK o l l p e , ' I f l ;lpiit\iH f il":lbKll C f aIII'IH, I!O'iOpt,le \'lbi il3Nl€lllla'Ill :'1eX(J,y 3i'--je)4il.r1
lioi,lle,[tltlt]ll MeiI{Ay ocflJ'IeqHoro Ir,'Iii;K?1.flepemil xo:tprltrUucHl
Mrr a 1r b (r,a:0,597 ) BLl.IIlc.']eH no Jectlr]I Ilapz!]l ll3MepcHHii.
llpoaepxelt ar{ cr zliircrliKa Bbtqr.ic,{flerctl it o rpopity,re (2. 35 ) :
_ ,) r r ,
_ r,csS
t : o ,? e 7 yJL =L
Tffi___ffi2:_,,.
K p n r u u e c x o e 3 ! I a q e H l t e/ c B c r c n e H f l M l 'cI B o 6 o A t ru 1 0 0 / s - i i b l \)1' l l o B s e M 3 n a q r l M o c r t ii l i i B I I o 1 , 8 6 0 . F I a n o \ { H M I , q l c I i p l l r c p u i l l B l c r o 6o"ttlue ii!'IH ryleHblileHy,'tt'
pouur.iri rt r Mox(eT 6ltrb sHa'IHTe!'IbHo
T}iIIOTE3b] PACNAIAETC'q HA
TA.K qTO HAlllA O6,'IACTb OTKJ'IOI-ICHHfl
qacTI'I. Tar tiar [poBepfleMafl c'raT]'lcrlllia roBepxHlolo I.i HLI>I<HIOIO
B BepxHlolo KpLITIII{eCKVIO06"1acTb, },ibl AOJ}KHbi 3aKJI}OraAlcl
q l r r b , q r o I r a c a N , l o MI e , ' I e c ) r q e c r B l r e r x o p l l € r ' i i , i l l l f l \ ' 1 e ; l ( - 1 \ - l ' l l l l l a rurrruaq6o,'Iruleii fl cpejll{eii oceri nn'I>xuori ra,lrxtt.
!,nn .lnyx .rpyflrx troppe"latluli NI]{oxecrBa raHHblx' ttplrBe-]eHHbrx B raO,r. 2.8, ro":0,499 n rbc:0,'167. CooreercreeilHo
,
r-+
v t0-2
0,499
1rr1--g,aggz
I , 4 1I
0,866
r . ,-r-^'
''
0.467
li to- 2 - t ' 3 2 r : 1 . 4 9 ' 1 .
0 ,8 8 4
1/1- o,+vz
, I M b l B I I A I 1 Mq, l C
K p z r i l u e c r O e s H a q e H l { eO C T a e T c rf le M ) K e C a M b l M L
H
e
o
r
r
l
l
q
a
e
Tcf 3HaqltMo oT
K
o
p
p
e
,
r
q
u
H
i
i
Hlr oAHa Ii3 3THx AByx
'Hyng.
no.illtocrblo He6st;lli
ec,'1I{
fiepeMeHHb]e
cJIoBaMH,
.[,pyruun
saeHcriNaHApyf or Apyra, ro Ha6,rrc4aeMbler<oeQQuqHeHrblKoppeCJIyqaIiHonpu c.rryuar?Hounu6ope AecfTI{ O6pa:Bo3HrIK/lL{
Jrtrr\ur4
K p u r e p n H r n s n p o B e p K u f n r r o r e 3 b r o p a B e H c r B eA u c l t e p c t t f to c H O B a H bH
r a T a t { H a 3 b r B a e M o nFa- p a c n p e A e J r e H r .@
r Hr r u r e p a .3 r o r e o '
i ) e r i . r q e c K opea c n p e A e , ' r e H ro4reH o u e H l s F : s t 2 l s z 2a n y x e u 6 o p o t t H b l x
- l u c n e p c l r r i . 1 , 1 no H 6 o p o K , 8 3 q T b r x r i 3 H o p M a i r b H b r xc o B o K Y n i i o c T c r ' i
tITo IicTaHHbIe.lucnepclll,I paBHbL
npll _vcJIoBHll,
B n o , r u e e c r e c r B e H l l o ,q r o B b r 6 o p o q r { b r el u c r r e p c r i n B c ; i } ' q a e ,
HC[o,!b3yeMoe t.irn irx Bbtr{]lcr'reHrit.
iior.la riHC"to Ha6"'IroAeHHr?,
B J.oBoJrbHo
[IIIpo)1a.iio,Ii3llellfiIo'lcfl oT ucnbrTaHHflK rrc,IrbrTaHIfio
il3MeHfeTcfl c ri3lio\r Atrafla3oge. llogroNry Br.rA,F-pacnpeaeJreHHg
\ r e H C H I \i le o 6 r , e u a a s t 6 o p x t t . 3 r o c H o B a 3 a i c 'l il i J . : i t l e T) . { u T b t B i r T L ,
3aBilcllr
c T e l r e H r iC B O 6 o A b rH, O B A a H H O MC r ' r ! 9 3 €F - p a C n p e l C , ' r e l l i l C
o T . i B \ ' r i s u a q e g u r i \ l , K a ) d l l o e H 3 I i o T o p b l xc o o T B e r c T l - l v epT; 6 1 ' r i i I t 3
-lBi'-\ oqcr{o}. Jxcnepcnji ,F-orsoureHHrr.TaK Kati /j-crarucrifia flB. l 5 i e T C qO T H O T U C I { i t eIM
B y X n O J I O ) l i l i T e J b i l b r Xq i t c e , { , T o g c H o , l i T o c J r y - : ; 2 . i ' , i 1 sB
n e i l I i q t - r H aF H e u o x ; e r I r p u H I i M a r b o r p t i L ( : i T e . I i b H l , r .' \l l t a q e ,,,,;l
nrrrr.
E^ -,.
L!,r1r
-, ,R^^,.,.
o!ruvl-,r\u
lled'lH1(a,
'l'O
iipA
!CJIOBI'lH
paBellalTBa
l{LT!{iiHi,lX
61':er 6;ti:orrioLUctrHir
:;uer.icrriiii
cperHee 3HaqeHrie
-lrrcnepcrrir
x o x'i':rri
1.0.
Iiax F-pacnpeAe,'IeHHe onllcblBaer iloBeIeFMe orliorueHl.lli
l r , r 6 o p u , ; i r L , r r . i r r c r l c p c a i i , r i o , r S , u e l r u b r xr t o e l r 6 c p r i a : ' l i r . l o . t i r o i i i r r o f i '
r i i € c c B C K ) ' r l H o c T l r ,T o e f o M o x { H o H C I j o , ' I b 3 o t s a " IJbl n n p o B e p r i i i r H : ' o T ( '; b l o p a B c H c T B eA l c n e p c H H .
\!.c;rtuo npc.lIIo,roN(i.lTb, rITo 4ee eor60pxH ts3iITL,tIr.J coBoliViltrocle;r, xapaxrepi.i3yrorquXcfl paBI{brN{rr.lrrcrlepcrr,rvri.floc"te DLlrrrrc.
"-tclrirfl lk-oTHoIIleHLrq Mo}liHo onpe.I.e.iilTb Bepofirrccl'rr nc"iIYqeHnfl
:iHa'-icr.rl,iff,6o,tr,[telo HJ'Iii paBI-totc BbtqIicreHHoM\, ;],rifl -lBl'-i c.ny.r r.r,l.l 'H; ,b,,l,.x, - , , , < ^ , . , , . ,, , .
{ O B O K } I I ] l O Cf i]. l , C J I i l 3 T O
D b I 0 o l l o K l l 3 O A H O I JH O p i v i a J I b r I O iC
J H a q e H r r e o r - i e r H e n p a R ; I o n o J , 0 6 r ' I b l MT, o N r L r B b i H \ ' ; x . l e H b r c q i u a r b ,
ilro Brrr6opKII r.r3BJIeqenbrIr3 pa3JIIzrIHbix coBori),ngocrer'r, ii-\reioulrrx
llep a BHbre IrrcIIepcHLi.
ll-^
-,^t^9.-^^.
.1Ba oTi,]t .r1lo0otrnapbt orleHoKAacIIepcul,IMo]xHo BbtrtliclTltTb
H o u e H t i q s 1 / s 2H S 2 f S 1€, c . r l l :nr p r i H q T b ,q T O 6 6 , - 1 b u a f lo r I e H K aB c e r ] a
6 r ' - I e r I ) a c n o J l a r a r b c f lB r r H C J I u r e l t e3, T o o r H o r u e H l t eB c e t . q a 6 y . q e l
6o,risrue 1,0 rr crar[crarrecKrre KpfirepHr.{nptrHH\{aror 6o,ree npocrolj nnr. B eroM cJryqae AocraroqHo I{crIoJrb3oBarbroJIr,Ko o,itHoI eo T e 3 b rH a c z M o M . { € r ' r €
c T o p o H H f i eh p H T e p u l r ,H a d r r b T e p H a T H B Hf ibi n
fiBittlorcfl yrBepxleHlreM o roM, rITo a6corlorHoe pa3Jllique Mexi.x,y
.:.ByNrrBbt6opoqHblMHAllcnepcuglvrn6o,rl[le, qe]r ]tox<Ho 6lr,ro 6lr
c ) r { r r . t a T bB c J r y q a e ,e c " ' i a 6 n r H c T H H H b I3eH a q e H l s 4 n c n e p c u l i c p a n HfiBaeMbrxcoBoKy[HocTerl6br,'Ix paBHbI.TarrrqHrrr.i rpaQlrx xptraori
F-pacnpe.ledrreHusc 3arrrrpuxoBaHHor?KpkrnqecKofi o6nacruo, u,nn
o6,'racrbto orKr'roHeHnflrrpoBepreMor? runoresH, lrso6paxeu Ha
pnc.2.31.
IIOB IAJIbKH.
B r a q e c r s e 3 J l e M e H r a p H o r on p r l M e p a n p u M e H e u r r . F - p a c n p e A e paccMorpl.IM4ne nu6opxi.i pe3ynbraroB ir3Mepeuafi nopacro"'reHr.rfl
80
6-201
8l
_v_
Puc. 2.31. Tunuqsoe F-pacnpege,reuue
c c)r:i0 H !2:25 creleHtM' cso6o,lu
Ii 3aurprrxoBaHHoiiKpr.rrrrrrecKoii
o6,taclblo, cocraBJlqroqerli
59b n,rouralu noA
KDI,IBOiI
c r a t ' i r c r t t q e c K l l 3 K B r B a . [ e H T H r , t M I t .E c u r u o g H o K a S b r B a t o r c r p a B H b I MH H ecJitr alr6opxn 6bt,rn usereqetitr 6ea c.Meu{eltirl l{r !13\'trleMbIv
coBor(\'IIHocreii, r'o x,n,l \{o}r{eM ci;oroilgo neperi;ri ri ncro.tb3oBaHfi lu creAyrcIriHx cTa'irJcll]qecKHx KiirrTeplleB.
il xa.recree npr.iMepapaccNrorpiiMrer(yro 3aAaq,v.C61r:rur,r
c I I ej ' i l H I b A a , c o 6 I r p r e M b l e c y q a c T r i o B 3 e M , l I I , i l o K p b t l i . ' i : i t r i l o f o qaCTiiqi{ll lll)l/'lIi, Ha3l,IBae]\ible ,!liilipOa'i€i iii:)ilI JlbIai4II, CO"l.Cl);^I{aT
i
CIII
c-t
tiilt-'IriitllMIi.
.',t-+
TCCqAHTIKOB TEHCJIHI],
HYX(HO
BbI'ICH}ITb,
OAI4I]AKOBA ,rI{
AIlC-
ricpcHfl Ha AByx cpaBHHBaeMbrx[norqaAqx. c 3TOi.irleJrbroBH6e_
p e x { . v p c B e i r F3, H a q r r N r o c r n5 0 f 0 . T a x u u 0 6 p a s o M , n p r r H r r r u eH e B e p Hoi'r t'Hjrcre3bl o rol{, rITo rlopnCTocrp{pa3,.IaqHL,r,
B To BpeMfl rixK
t)IlII o/]tHar{oBbr,^6yAernpoHcxorHrb D cpel}te;ri oj{iilI pa3 }ra AB:rrI{aIrr ricxo.r.oB.orleHxu 4ucnepcufi gnyi sr,r6opoK N{ox(Ho BL,rqticiio cpopl'ry,re (2.i5). Toiaa coorlercrnytou,ee rr-u F-orHourc"nrrL'Bbrqr.tcrTflercfl
Iuie
rro $opuy,ne
F : sf lsz2,
f A C s r l - 6 o n t u r a q n u 6 o p o v n a l A H c n e p c r . i rI, s r 2- M e H b l r a t
p o q H t r f iJ . i i c n e p c l i r .
ilo errru AaHHbrMrpe6yerca npoBepr.rrbflrrrore3y
(2.36)
nu6o-
fl6io12:622
nporHB r\{HoiKecTBa
aJrbTeprrarl{B
Hri612*o22.
Hy.rienar rHrore3a yrBep)KAeer, qro u;VqaeM're coBol{)/nHocrg
H r , r e r o Tp a B I I b r e I I I c n e p c I i t . r ; M H o ) K c c T B o a J I b T e p H a T i l B , v C T a H a B J r r . i BaeT, qTo 3TO He raN. creneHri ctsoooAbi \i1 tl \l2, oTBcgaiou{tre 3ToM y K p H T e p H I O ,C O O T B e T C T B e H HpO
aBHbr n1-l
u nz-| . I(pHrH,recKoe
3 H a q e H l . t e^ F c v 1 : 9 n 1 z : 9 c r e n e u l l t t t c e o 6 o A o t i . r y p o B H e M 3 l { t j t l l r (o:0,05)
raocrn 5|e
MolKHo uafiru
no ra6;r. 2.14. ero 3HarreHlre
p a o u o3 , 1 8 .
3Haqeuize
F, nurulrcreuuoeflo Qopuy,re (2.36), rorraAaer B
oAHy H3 AB)'x o6,'iacrefi.E,c,ruBbrrrrrc,reHHoe
3HaqeHIre
.F npenuruaer 3,18, ro HyJreBagrnrrore3aorBepraercs H MbI npuxoAlzMK ga-
rlTo Aucnepcnl,I[opHcTocT]r MOXHOC[{HTaTbHeoAriHaKOKJIIOTIeHlrro,
B L { M I .BI A B y x r p y n n a x . E c . n l t B b r q u c . r i e H H o3eH a r r e H n eu e u r , r u e 3 , 1 8 ,
To Mbr lre MoiKeM yrBeplr(Aarb, qro Ar.rcnepcuu pa3'rfirrHri. B Kar{ecTBenprrMepa BbrrrHcrHMArlcnepcrlio rroprrcrocifi ,isyri coBoKyri,trocTefi necrIaHHKoBTesc,ryun H npoBepr{M npeAnono}Kelrue o paB c H c r B e4 u c n e p c r z i in p u 5 0 / -su o N {y p o B H e3 H a q H M o c r L I .
B 6 o a s r u u H c r B en p a K T I I q e c K l r x3 a A a q N r b r0 6 b r r r H oH e 3 r { a e MH C 'rHHHbrxsHa,{eufiii IIapaMerpoB coBoKyrr]rocrH]t Mo)KeM drHurb tro
au6opxe BbrrrHcJIHrbHx oueHKIr. flpu cpanneHHrr AByx au6opox
cHsr{aJra ueJlecoo,6pa3HoycraHoBHTb, fiBJ'rfnrcg Jr}r }rx Ailcnepcl.tH
82
T
" ^p,b. I
l ' l)l^3^M, e
OTIe!'lblllrlX'j'ili{illt
qaCTIilI
IiNIeIO'l lill(li.eilbI
o r 0 . l j . 4 o 3 , 0 r t l ( \ I ; o r i H n o r r l . { i t I o i ' l a r x o c , l t e p } ' i t r : i H r , . \ r li ti \ . r ; i r . r I I :
B i ) r " r . j \ ; " T b T al lTye! ' r K z r H r r q e c K lIrr.xl n e p x e u i r i i , f l b l , t c B b t xl u l . r i i r : i c ; 1I ,l a t{iicrlrriu Hlc'ioJirrr(o r.{a,'rbr,rrTo }'IolyT
trei]]i'] l,rilKIlol,reTeopHToB.
B
3
u
e
r
u
e
H
n
o
r
{
5it'rt rio
c o c f o r . F l u aI i e o f p r a } r i l q e n H oBep e u f , H o . i i e r K o
r ' f l 1 1 p a t I Hl . r l r r K p l i c T : t . I J I H 3 a i l o f , T o r r ( i l K ) ] ' cct l l e f o ) { , T z r ( K a K c , ' r y ) r i a
i [ r n . - l b l i i l .c y u t e c r a y e r f ] . r n o r e 3 a ,r i r o i r c p e M e u u B a H f i ea r u o c o e p u
l i l K p c q a c T i i u r rnr o n a A 2 } o T B c H e f f i 3 B o : l J V x a ,
u r y T r r , I { o I o p b r N , l lM
ripr.rBoj1tT
K p a B H C N { e p r r ol if oi H u e H r p r r r H r rM r . r K p o q a c T } iBr 1c H e i ' i H a
: e r t i r o i i n o B e p x H o c r u . E c , ' I i i a ' r a r r i l l o r e s r r c o o r B e r c r B \ i e ' rl'e i ' , : r n H Te,'IbiiocTl{,To BbtBoAri il3 IIee ilNicicT 3trr-.rcHtie.1,'rflilieic}ia:j:1HIlfl
Iroc.rcjlcrBrrii rrcnr,iriiHlifi fi,IeLrHofocfryx<rrrin l'rr,toc{re1le.iIo:r'ror,Iy
6lr"ru co6paribrIBe nrr6ofi';1 npsS crre.a B cneroBbrx IIoKfoBax
K o l i r l ) o . l ( ' . H L ' ll l a c '
^f r r: r...r.r.r-:.t.u. .n-r.r. r. r r r l s r l.n. r. ri l .r.r.l.:.r.,. . , . -] -^ lrn. l. r.t-t-t .r.rl rJ l h l l o \ l
rr,TasH.rIir Ii c iiovoudblc
3"rrer{TpiiqccKofo r<,laccrrcprrnaTrtpil olipt,tc-
B Hei"{ qacri{r]. KouueHrp:lt(lt,q \i!r{ito;urJrrr rrrlcr,'roco.xepx<aun:'lct.[
. i a c r r t UB T i l J O l , c{ l i e r y n p } i D e ! e i l zsl r a 6 " ' 1 . 2 . 1 5 l.' t c l x l o . , I i r l l r r : r T : : T r ,
o 6 c n u 6 o p x r { I r 3 B , r e q e H F I } , i x} ir3u lo A n o l " rn i o i i ) J i e r ' o t s { , K y n } l o c r }r rl
i r p r i i l c j i l r - r r r rp c 3 1 ' . ' r rl , fi r . r r i C , r L r T r n : r ixr t r o - lf B e p ) ] ( : r e i r i i rror " r ] to r p o nci,.ir{eri
rlo r-1crr o5 a.r:.rclc(;epuoiio-riiopo;r.uoc'l
ir?
f l p e l i i o ; t a r a r , i { T o r s r 6 o p i ; l r 6 r ' r . { r rn 3 r r r L r 6 c r c i t c r t l c H l l r rr t r I T o
H O l , ] t a ' I I b i I O l , l ; ra U * O " U
i l i i i -i i i ) e . ' l . C J e l l l l e N I i l X p O T I a C T r I lt{l O . ' ] t i l i ; 1 q 6 ' 1 g O
l r a B C e r \ {I I p o T f l } r i c I { H r {c } { e i - o B b i i i r o . r e r i , i l p o E e p r . r l { c t H i r r a " r I af i t i t [ ) T e 3 y o p i t B e I I c r B e i l , i l c n c p c l t i j n o I a ] i t n t . r 6 o p r a t t . I ' I c i t o . T r , 3 ) , r.i l - , c p i r 1 - .r.,- ( 2.3S), 3 Anritire]{ H),.iieByroriri-rore3\' n a "rrbrel)irilruB\':
flo: ot2 :
H1 '. 612*
622,
ozr.
-f:ri,rIr.1
ti.ilcrrcpcllil Iic cll.tblr{) oi','Il,IqatcTCrl,To c,1e:l\rloiuttit itl3t Iif.;cIlelivilhr - nf oBepKa flrllo'Ie3br o ilaircll:l Be cpe.ltlrJ: :el ,tcluiii.
( 2 . 3 6 ) , s r . l r . i i i r c l , I c o o r B e r , - ' i B \ , i i l r r ( i . ' . cl r ' r , i i ) JIr iro;ir-,:l'fl xDineputi
pll I T I1B1,'
i
:r1.t,.) - i1| i oTe-t\.r II 2.rlb1"€
H6:!t1 :p2,
H1: pqS
p2.
TaKrrrr II\'!'reBatl rtrlrore3a coorBeTcrByeT npe.4nonolrieHr{n: }rer
i l l i i ( i t r i i I X o c t t o e a t r n i r c L r H T a T b ,r i r o o J , H a o 6 n a c r t
LrMeer 6orr,uree
cl)elHee, qeu Ipyfat.
flcuo, qro ypoBcHr, 3HaqHMocrrl,coolBer-crn r r o u l n i i 3 r o M y K p x r e p H l o , H e r , r o ; ' r { e r6 u r u g m u e , q e M y p o B e H L ' s H z rti.
83
Kpurnuecxue 3HarreHlc F-pacnpe4e,neHrdgc v1 u v2 cr€rreHgMll
v' "g l
6
7
8
I
t0
il
l2
t3
14
l:)
i6
l7
IE
l9
20
2l
22
23
oA
2'o
26
27
oa
29
30
40
60
€
[t7l
t
I
lvr
I
I
2
3
4
T a6nsua 2.14a
cso6oAHr 50/6-xurnypoBHeM3naqrMocrfl (o:0,05)
r
|
2
|
3
i
+
|
b
l 6 l , 4 5 1 9 9 , 5 0 2 1 5 , 7|
2 2 4 , 5 8 2 3 0 l,6
1 8 , 5 1 1 9 , 0 0 1 9 l, 6
t9,25
1 9, 3 0
qte
9,01
1 0 ,l 3
I,t2
9,55
6q4
7, 7 1
6,26
6,59
6, 3 9
6,61
5,05
5,41
5 ,r 9
5,79
5,99
4, 3 9
5 ,'7t
14
4,76
+, D,t
,+,12
L
5 ,5 9
3,97
4,35
tr ao
3 ,8 4
3, 6 9
4,46
4,07
5,12
3, 8 6
o,o,i
3,48
4,26
4, 9 6
3, 3 3
4 ,1 0
3,71
3,48
4, 8 1
3, 9 8
3,59
3, 3 6
3,20
4,75
3,89
3,49
3,26
3,11
4,67
3,81
3,41
3 ,1 B
3, 0 3
4, 6 0
3,31
3 ,i I
2,96
3,7+
4,54
2, 9 0
3,29
3,06
3,68
4,49
2,85
3,24
3,01
3,63
4,45
3,20
2,81
2, 9 6
3,59
441
2, 9 3
2,77
3,55
3 ,1 6
.r'71
4,38
2, 9 C
3 ,l 3
3,52
,'71
4,35
2,87
3 ,l 0
3,49
4,32
2,68
3. 0 7
J,t/
2,84
,2q
4, 3 0
2, tj6
3, 0 5
3,44
4,28
2,64
3.42
3 ,C 3
2,80
4,26
3,01
2,73
2,62
3 ,+ 0
A,J
tqa
2. 6 0
3,39
2,i6
Qa1
, 71
4,23
2,59
2,98
.) trj
ct ia
4,21
3,35
2,9t
, 71'
1,20
2 ,i ) o
3,34
2,9it
4 lR
9 7(l
2,55
3,33
2,93
.) (?
900
4,t7
3,32
2,69
a o?
4, 0 8
2,|i:t
2,?,+ 2,61
.) e.a
t(?
4, 0 0
3 ,l 5
2,76
., 1(
I 9a)
3,92
3,07
2,68
3, 8 4
2,21
3, 0 0
2,37
2,60
|
6
|
?
|
233,99 236,77
1 9 , 3 3 1 9, 3 5
8,89
8, 9 4
6,09
6 ,1 6
4,88
4, 9 5
4.21
4,28
3,79
3, 8 7
3,50
3,58
3,29
200
3,l4
3,01
3,09
2,91
3, 0 0
9q)
2, 8 3
2,76
2,85
2,79
2 , 7i
2,74
2, 6 6
2,70
2,61
2,58
2,66
2,63
2,51
o (t
2, 6 0
9LA
2,57
2,46
,4J
2,53
2,42
2,51
9LA
2,4()
q ,4a
2,39
o .iA
2,37
2,36
2,4i
2,13
2,35
9L'
t??
2,34
99{
tt(
,17
2,l8
2,10
2,09
t ol
quMocTll, Ecnonb3oBaHHbrrlripu rrpoBepKe riirToTe3rrro paBeucTBe
AHCIIepcnfi. Ec.nu AucnepCI.IHr.r cpeAHi{e oKa}K}rrcs Hepa3,,rrqr.rMbrM L I ,T . e . H y n e B a g r H n o T e 3 aH e M o X e T S U r r O i x n o H e H aH a o c H o B a HHI{ Bbl6opoqHblx AaHHbix, To HeT r{ cTarrrcrr.rqecKrirxocHoBaHHji
cqriTaTb, I{To cpeAHr.reKoHrIeHTpau[Ii MzKpoqacTrrll Ha AByx H3yqaeMbrx nJrorl{aArx cooTBeTcTByloT pa3JII.IqHbrMcoBoKynHocTflM.
C apyrofi cropoHbI, ecJrr.rxorfl 6u oAuu H3 AByx KpirrepueB npHBoHy/'reBofirtrrroTe3br,To Bollpoc o6 arr,{oc$epuoL',l
AHT K oTKJroHeHI,M
MO)KHOnOCTaBIITbtrOA COMHeHI.ie.
EO,'IeerOfO, eCJIir
oAHOpO.:lHocTH
rr{rrore3br o paBeHcrBe
KpHrepHri (2.36) rpIrBeAer K orKJroHeHr.rlo
AHcrrepcrrri,ro r{ rpHMeHeHaeKprirepuq (2.33) B Harlleii saAaqe Tepfler cMbrcn. flpa6ru3HTeJIbHbIe KpHrepHrr, aHaJrofriqHbreonr4caH-
240,54 2 41, 8 8 243,91 2 4 5 , 9 5 2 4 8 , 0 1 2 4 9, 0 5 2 5 0 , 1 0
19,38 19,40 19,41 19,43 19,45 19,45 19,46
RR(
B,8i
8,79
8, 6 2
8,74
8,66
8, 6 4
8,70
tr, 17
6, 0 0
5,96
5,91
5, 8 6
5, 8 0
6, 0 4
AAa
L74
L99
4,56
4,53
4,50
4, 6 8
4,62
4 ,l 0
4,06
3,Bl
4,00
3,94
3, 8 7
3,84
4 ,1 5
3,68
3, 6 4
3 ,3 8
3,51
3,44
3,41
3,73
2
t
o
Q NA
3,39
3, 3 5
3, 2 8
3,22
o,lD
3,08
,QL
QOa
3 ,l B
3 ,1 4
3,07
3,01
2,90
2, 8 6
9q9
Qn7
I Ol
3, 0 2
2,77
2,70
2,84
2 , 74
c)tr.7
.t 10
oo(
97'
2,90
2,85
2, 6 5
2 , 6r
q Aa
rR<
2,80
2,75
2,69
2,54
2,51
2,62
g A9
o'71
,17
2,67
2,46
2,48
2,60
2,53
o(a
,7i
2,65
2, 6 0
2,35
2,31
2,46
2,39
c) t(
., A4
9tq
2,59
2,54
2,48
2,33
2,40
t(o
,4q
2,54
2
,
3
5
2
,
2
4
2,t9
2
,
4
2
2
,
2
8
() A<
D !(
I
lq
2,49
2,38
2,31
2,23
a l(
t (l
9t7
t tq
2,46
2,41
2,tl
2,34
,L9
t92
, t9.
2, 3 8
2,t6
2,ll
2,07
2,31
o e(
91'
I 99,
2,39
2,20
2,08
2,0+
2,45
q Ao
o
a
o
o
c
)
(
I
lR
2,37
2,10
2,01
2, 0 5
t02
I r(
2,31
2,30
2,47
2,03
2,40
I,98
q
Q.,
,97
,37
2,20
2,13
2,05
2,01
l,96
()<
,
taA
2,30
2,03
2 ,1 8
2,tl
I ,04
,98
o a4
2,28
2,24
2,09
2,01
2,16
I ,92
,96
,r7
Dao
,,,
o(
tqq
2,t5
2,07
I ,90
q
l
I9r^
o er
o
r
e
2,20
2, 0 6
| ,97
I ,88
, 9l
919
ol
9ra
2,ts
2,04
l ,96
I ,87
,
9
'
,,R
lq4
2,tB
2 ,l 0
2,03
1, 9 0
1, 8 5
,91
2,21
lRq
2,16
2,09
i,93
2,01
I,84
,19,
o9
l7q
2,t2
2, 0 8
2,00
I ,84
1,74
lq9
2,0+
1,99
2,l0
| ,75
| ,70
I ,65
,84
9i,
l,96
l,91
1, 8 3
I,66
I,61
I ,55
l
(
9
lqi
I ,88
I ,83
| ,57
1,75
1, 4 0
,67
2 3 8, 8 8
1q e7
Hor,{vB pa6ore frcurepa I4J, npuueHriMbrAJrrrrpoBepKr{fHllore3br
o paBeHcTBecpeAHnx B ycJroBr.rflxHepaBeHcTBaAnc[epcrirl, Ho oHLt
M a J I Or r O M O f a r OnTp u p e u e H r z HA a H H o r is a A a q H .
.tIUCNEPCIIOHHbI U AHAJII,I3
J-In nrrv
rrnn
t r r L r paccMaTpHBanH To"rrbKo MeToAbr cpaBHeHr.rff
]ltsyx Bbroopor{,TofAa KaK cyxlecTByer exle prrA 3aAaq, KacarculHxllpe4no.no)Kr{M, Hanp}rMep, qro noJryqeHo
cfl fpyll[ Ha6,'iroAeHr.rfi.
nflTb o6pa3(oB recIIaHHKa c KaJrbrlirroBbrMUeMeHToM.I(axAufi raa
HUX 06,'raAaeTCBOI.IMH
flI.rTorofr{qecKHMr.r
OCO6eHHOCTflMH:
B OAHOM
6pocaerca B f,'Ia3a efo KpyrrHo3epHucrocrb,Apyfoft xapaKrepr.r3y-
84
ND
Ta6;rnua 2.146
K p u r u . r e c x u e 3 H a q e H i l q, F - p a c n p e 4 e , r e H H fcl g q H \ r 2 c r e n e r r r M r {
ypoBHeM3HaqnMoct-t(a:0,025)
csodonu rr 2.50/e-Huru
-l
I
2
a
4
5
6
7
B
I
t0
l1
r2
l3
l4
lo
t6
ta
1B
19
2A
2l
22
ta
o(
26
27
2B
29
an
40
60
120
647,79
39,51
t 7, 4 4
799,50
3 9, 0 0
16,04
19 9'
10,65
10,01
8,43
8,81
7,26
8
,07
6 ,5 4
'7 r-'7
6,06
'7 ql
5,71
6,94
5 ,4 6
6,72
5, 2 6
6,55
5,l0
6,41
4,97
6,30
4, 8 6
6 ,20
4,77
6,t2
4.69
6 ,0,1
4,62
5 ,98
4, 5 6
4,51
5,92
5,87
4,46
5,83
5,79
5,?5
5,69
5,66
5,63
5 , 6i
5,59
9 3 7 ,I I
39,33
14,73
9,20
6, 9 8
5:,82
5,12
4, 6 5
4,32
3 ,8 3
3, 7 3
3, 6 0
3,50
3,41
_?
,31
3,2d
? ,rt
3,Ii'
Q
4 1,'
I'
ll ,0!)
3, 0r-r
3,c2
,i ,3li
+ . ,l:)
tr.32
4,29
', trc
947
,{ o:
c)
oi
4.24
,a9
4."
2,9(r
2,38
2,,87
2.74
2,63
o,Di
4,20
4,iN
5,42
5.29
u ,1 5
5,02
3.93
3 ,S 0
3.69
rl
, {,ii)
c1c1-I ft:tJIIrriileM f ,iil;iltici ii.i
? r:')
2.11
Lracrlili, TpL'iilii
c.i[]50
01tic;ie3Hit]t :t t...:,
l . l l t x o r r r y o r n e . l e " , r i r l b ,o : l n n a r i o t s b .r1 u r J t { u _ {c o A e p ) K e H I r fri{ a p 6 o ,
r r a T a . A , ' r f l l ) c l x e r { 1 13f lT o i i 3 a I a q H M O } l i H o t i c r r 0 t b 3 o B r T b O ; i l i r r i r - j
c l z l T l l t r l l ( l e c K H X N i e lo ! o B , I I i i . ( b l l l i l e l T t i,it . f l l c n e p c l t o H r i L t l t i . l i i l ' t J j li C
i l,{.
B o 6 u l e r r B r i , 1 e 3 ' r o T j \ i e ' j ' o . io c t j L ) i l l i t r t r a p a 3 J e , t e I I f i H o 6 i 4 i : t i . i l i c i l e p c u r r I r 3 y q a c ] ' l o i i c o B o t i y i l ] r o c r l l t r a x o ] , r i l o ] I e H T b r ,c o o r B e r c ' 1r \ : ] o Iilite iic;orrrlr.tKa[,r H3Nler!qilBocrr], a IIplrl{eIIfler,rble Kp]ireftl]t no*?ili)" 1 l T 0 . i l t O B p e M e H H OI t 3 Y q I I T b p a l ! ' i l r q r r f i ( : r r i B C p e , I I r i t X 3 t r z t r r ( , H i r : t X .
TilK Ir B ,lficnepcllux.
3ncneplrnaeHTaflbHbrfr IroAxo.r, K 3Toir 3aAarie 3aKJlror{aeicfl rr
r p 0 6 " { c i r i { i r o 6 p a 3 t l o B H a 6 o J r e e 1 \ { e J r K r - iqea c r i l r r o n p e ! e J r e } r ' ! i r ( . o r e p l K i t r r l l r l x a p 6 o H a r a B K a r { A o i r i l 3 } t } i x n y t e ] l B 3 B e u l H i l a } t H r iI o c , r e
86
e I
s
l0
L2
l5
20
9 8 4 , 8 7 9 3 3 l, 0
9 5 6 , 6 r i 9 6 3, 2 8 9 6 8, 6 3 9 7 6 , 7|
3 9 , 3 9 3 9, 4 0
39,45
39,37
3 9 , 4 1 3 9, 4 3
t 4, 1 7
t4,17
14,42 1 4 , 3 4 t4,25
t4,54
RR4
8,66
[],56
B,S0
8,75
8, 9 8
6,43
0,33
6, 6 8
6 ,6 2
6,52
6,76
trqa
5,t7
5, 4 6
o,.t/
5, 6 0
4,47
4,57
4,82
4,67
4,76
4, 9 0
4 ,1 0
4,00
4,36
4,30
4,20
4,43
.J,I /
3,67
4,03
3,!16
3,87
4 ,l 0
2'/O
3,52
3,42
3, 7 8
3,62
3 ,8i,
3,23
3,59
3,43
3,33
3,53
3,66
a ta
3,47
3,44
3,51
D,.t/
3,28
et(
t q-r
3,31
3, 0 5
3, 3 9
3 ,1 5
.)1
2
901
2,84
3, 0 5
3,29
3,lir
2.i6
3,t2
2,86
3,20
3,06
2,96
? l9
9qO
t90
9TO
2, 6 8
3, 0 5
tet
979
,qq
2,62
3,06
2, 9 8
o o?
9X7
2,67
3,01
2, 5 6
,R'
9 7c'
, (:,
2,51
2,96
2, 8 8
tql
2,57
2,46
2,8.1
2,77
2,68
o
(
o
It9
2,87
2,80
2,64
2,73
2,84
2,76
2,39
2,50
2,70
2,60
9Rl
2,67
2,i)7
2, 3 6
q79
q
O RA
A1
92e
2,70
2,64
o 7:,
2, 0 8
2,61
2,41
2,51
2,30
, 1..
tao
2, 6 5
2,59
2,39
2,2i1
q o(
, il
2,63
2,36
2,57
2,47
c) ?l
<) tr
I F,O
a oe
2,61
2,5r,.
.) '19
t rl
2,67
2,59
2,53
2,t3
2,57
2,65
2,5t
z,,L I
2,41
2,24
9q.e
,4q
,ro
2,39
2 ,t B
2,a7
loa
2,41
2,33
2,27
2,17
2, 0 6
g ct9
23A
2,16
I ,9+
2,05
| ,82
9 lo
2,11
2,05
I,94
I,83
1,71
ao7 ,L
3 9, 4 6
14,12
B,5l
6,28
5,12
4,41
3,95
3,61
3,37
3,t7
3, 0 2
tqq
i00l,4
rig,46
1.L,08
d, 4 6
0,23
5, 0 7
4, 3 6
3,89
1i,56
3 , 3i
:i,12
2, 9 6
..r
R4
2,79
2,70
2,63
2, 5 6
2,50
2,45
2,41
2,37
2,73
:t,64
2,57
2, 5 0
2,44
2,39
2,35
o?a
,,J
2,3A
2,24
,17
o ot
,
9t)
2,19
2,17
2,15
2,14
2 , 0i
I ,88
1'7{:r
I,61
i)
Q l
911
2,18
,17
2,13
2,ll
2, 0 9
2,47
I ,91
l,B2
I ,69
o6pa6orxu KLIcr'Ioroii.KaxAaa Me,'tI{arirracrb Ha3brBaercfi noBTopeHrie&r.IIenr, r{oropyrc Mbr rrpecJre,u,yeM,
pa36}iBafl nepBoHaqaJrbHbrrl Kycoli Ha qacrH, - onpeAc!,reHl{e
H3MeHqHBocrIl,BbI3BaHHoft
IIorpell]HOCT'IMHB3BeU]UBaHHfi.OueAU4UO, r{TO eC"IH Il3MeHrl}tBOCTb
Me)KAy iloBropHbrMrronpeAeJreHHflMH
Arq OAHOTOO6pa3ua BeJrHKa
no cpaBI{eIIHroc pa3"rr[qr.rflMrr
N'{e)KAyo6pa3uaM[, TO IrOCdrreAHHe
rpyAHo o6Hapyx{krb.
flpeano;roxr{M, qro Mbr pa36rrJrn r-rcxo.qHbrri
o6paseq Ha rrJecrb
qacTefi }{ co6rrpaeMcr [poaHaJrH3HpoBaTbKa)KAyr,oH3 Hlrx. Ha6.tro-llaeMbrer.r3MeHeHrrfl
Bo3FIprKaroT
no pgAy [pHqHH: I{3-3a KoJre6aUlrir
c o c ' r a B a B H y T p H H c x o a H o r o o 6 p a 3 t l a , n 3 - 3 a H e 6 p e ) K H o c T lBr l t o n y -leHHr.r
noBTopHbrxHa6JrroAeHHfi(ocrarxH oAHoro rpaBreHiifl Mofyr
87
Ta6rnqa 2.14n
Kpuuruecxue 3HaqeH[s F-pacnpege.reHrgc !r ]r vz cr€n€HrMrf
cBo6oAbr r
I0/6-Hnlr ypoBHeM BHaq[Mocru (a:0,01)
I{gcro
crenetreil
cBo 6oAbr
!2
I
2
3
4
5
6
i
8
9
l0
lt
12
l3
l4
t;
t6
t7
l8
i9
20
21
22
IO
24
25
26
27
28
29
30
40
60
120
oo
, 2 4 9 9 9 , 5 5 4 0 3 , 4 5624,6 5 7 6 3 , 6 5859,0
9 8 , 5 0 9 9 , 0 0 9 9 , l 7 9 9, 2 5 9 9 , 3 0 9 9 , 3 3
3 4 , 1 2 3 0 , 8 2 2 9 , 1 6 2 8, 7 1 28,24 2 7, 9 1
2l,20 18,00 16,69 15,98 15,52 15,21
1 6 , 2 6 t 3 , 2 7 i 2 , 0 6 1 1 , 3 9 1 0 , 9 7 1 0, 6 7
8,75 8,47
l0,92 9,78 I,l5
l.t,/i)
7, 4 6
7,19
12,25 9 , 5 s B,'llr 7,85
6, 6 3
6,37
8,65 7.59 7,cl
I i,26
6, 0 6
5 ,B 0
i0,56 8,02 6,9e 6,42
5 , 6 1 ij,39
1 0 , 0 4 7, 5 6 6 , 5 i ; 5 , 9 9
5, 3 2
5, 0 7
9,65 7 9 1
6,22 5,67
5 , 0 6 , +, 8 2
9 , 3 3 6 ,93
5,95 5,41
4,86 1,62
9,07 6,70
5,74 5,21
4,69 4,46
6 , 5r
5 , 5 6 5,04
8 ,8 6
4, 5 6
4,32
8,63 6,36 l>,42 I ,89
t41
1,2A
E,53 6,23 5,29 4,77
4 , 3 4 4 ,1 0
5,18 1,67
8,,10 6,ll
+ , 2 ; - ) 4, 0 1
I ,09
4,58
8 , 2 9 6 , 0t
417
3 ,S 4
4.50
5, 9 3
5 , 0i
B,l8
3,87
4 ,i 0
4,94 4,43
B , 1 0 5 ,8 5
4 , 0 4 3 .B i
B,02 5,78 4,87 +,6t
- 1, 3 1
3,99 3,76
7, 9 5
5,72 AR'
3, 9 4 3, 7 1
7, 8 8
5,66 +,761 4,26
Lr?
3,90 3,67
7, 8 2
5,61
3 , 8 5 3 ,6c?
7, 7 7
5 , 5 7 4 ,611 ,1 lu
7 ;.)
4 t4
3,82 3,59
5,5r3 4 , 6 4
, 1, l l
3,7E 3,56
7 , 6 8 5, 4 9
4,60
3,75 3.53
4 ,07
7, 6 4
5,45 4,5i
3,50
4 ,04
7 , 6 0 5 , 1 2 i 4 ,i't4
4,02 3,70 3,47
7 , 5 6 5 , 3 9I 4 , ! . 1
3,83 3,51 3,29
7, 3 1 5 , t B I 4 . 3 1
3 , 8 5 3, 3 4 3 , t 2
7 , 0 8 4 , e 8| 4 , 1 3
3 , 4 8 3 , 1 7 2, 9 6
4,791 3,95
6 ,8 5
3 , 3 2 3 , 4 2 2, 8 0
6 , 6 3 4 , 6 1| 3 , 7 8
I
z s , +l i s s r ,
9 9 . 3 6I 9 9 , 3 7
2 7 , 6 7i 2 7 , 1 9
1 4 , 9 S :l + , 8 0
10,46Ii0,29
8 , 2 6| . q l,0
6 , 9 9i 0 . 8 4
6 ,r 8i 1 1 , 0 3
5 , 6 1j 5 , 4 7
5 , 2 0{ 5 . 0 6
4 , 8 ! iJ ' + , i 4
1 , 6 4: 4 , 5 0
4 , 4 4i 4 . 3 0
4,28i 1,14
4 , 1 4i 1 , 0 0
4 , 0 3| 3 , 8 9
3 , e 3| 3 , 7 e
3,81i 3,71
3 , 7 7t 3 , 6 3
3 , 7 Ci 3 , ; ' 6
3,611 3,51
3 , I r 9I
3,15
3 , 5 0:
3 , 4 6i
3 ,- ? 6
3,32
3,5.113.'11
3,421
3 , 3 9i
3,36;
3 , 3 3i
3.29
3,26
3,23
3,20
3 ; 3 0i 3 , 1 7|
3 , t 2 1 : , 9 eI
2 . 9 5I ! . 8 2|
2.7e1 2,661
2 , 6 4 1 2 , 5 1|
tl
6url npoublTbl 6oJlee rrl,arer'tt'Ho,qeM ocrarKli Apyroro), I'13-3ali3([OBropHHe o6pa3ubl Mofyr co.]epMeHeHHrycr'IoBHfiB3BeUII{BaHI.lfl
KOJIItqeCTBa BJIafll JIH6O Ha pe3y"IbTaTbl B3BelllH111aTb pa3nlirlHbIe
Hyd'leBoH ToqK}l
n
o
B
JrIl.IflTb 3aBHCHMOCTb no,tox(eHl4g
BaHItfl MOX{eT
B TeqeHl{e x:Hs' vr T. A.) Il 6"'Iabl
H a B e c a x o r I I 3 M e H e H I i f t r e M n e p a T y p-roHKI'Ix
Apyflrx
roAapfl BJtHeHy.to
6oaee
Qaxropoe. Kou6tlHal{ug
I',I3MeHqHBOCTH
iIpHBOAHT K BO3HI4KHOBeHHT
BCeX 3TI.{X I.{CTOqHHKOB
TaK Ha3bIBaeMOIi 3KCnepHMeHraJIbHOti O1UH6K14l{,ill] II3MeHqHBoCrH,
TOJIbKOpa3JIHqHflMI'r MeXAy 06pa3UaMI'I.
He yqHTbrBaeMoli
-!,.trn
rOrO qTO6bI H36eX(aTb BO3MOXHOCTHnOflBJIeHI,IqcIzCTeMaTIIqSCKOTIOTUH6KUB CTaTHCTIIqeCKOMaHaJILI3e, IIOBIOpHbIe Ha6,'Irc88
6 0 5 5 , 8 6 1 0 6 , 3 6 1 5 ,73
6022,it
99.3!
99,40 99,42 99,43
2 7, 2 3
2 7. 3 5
2 7, 0 1
26,87
1 1, L r 6
11,55 t4,37
tl ,2(J
479
l ( ). 1 6
10,05
9
,89
'/'/q
;qF
[, . 7.]
. r . 9i
: .35
+.!1
I .63
I ,39
4.ill
7, E 7
6,02
5,[Jl
i,26
Ll5
54
4, 3 0
4,10
3,9r
3.i:!
j.78
- ?, 6 9
3,0u
3,52
3,80
3,69
3,59
J,+ll
o.o/
3.1i)
3.35
3,30
3,26
3, 3 1
3,26
3,21
Q ti
3 ,r 3
3,09
3, 0 6
3,C3
3, 0 n
2, 9 8
2, 8 0
2,63
2,47
2,32
3.ls
3 .r 2
3, (i!)
3,07
2,89
')
i''
2,56
)
41,
6,47
5,67
5,1I
3 , 5r
3,43
.J,r /
4,,10
4,16
3,96
3 ,B 0
3.67
3,55
3,46
7, 5 6
6,31
5,52
4, 9 6
1,56
Aqf,
4,01
3,82
3,66
3,52
J,ol
3,31
o j It)
3,30
3,23
3,t7
3,12
3, 0 7
3, 0 3
2,S9
2, 9 6
3 ,l 5
3,09
3,03
2, 9 0
2,87
I
2,66
2,50
2,34
2,tB
4,10
3,86
3,66
3,37
3,26
Q02
9R4
441
J,+l
J,O/
902
6208,7
99,45
2 6, 6 9
14,02
9,55
7, 4 4
6,16
ir, 36
1, 8 1
?qR
2,93
2,89
2,85
2,81
2,78
7tr,
2,73
2,70
9qo
c) 2(
2,19
2,04
3, 0 8
3,00
2.9+
9 ea.
2,83
2,78
2.74
2,70
2, 6 6
2,63
2,60
2,57
2.37
2,20
2,03
I ,88
6234,6
99,46
2 6, 6 0
13,93
q47
6260,6
qq 4?
26,50
13,84
9,38
/.ol
7q2
6.07
5,28
5,99
5,20
4,65
4 ,2r,t
3,94
3,70
+, iJ
4, 3 3
4.02
3, 7 8
3, s!)
3,43
3,29
3 ,1 8
3 .Oil
3. 0 t )
3,5r
3,35
3,21
3 ,l 0
3, 0 0
,a,
949
2,84
2,66
2 ,E 0
,
,
q
2,67
2,62
2,58
2,54
2,50
2,4i
'7;
2,70
2,66
DA9
2,5"9
2,55
2,52
9Iq
947
9ra
2,12
I ,95
| ,79
'7a
'io
9LL
2,41
2,39
2,20
2, 0 3
I ,86
I ,70
6url oro6paHtr HayAaqy. 3ro rax }ra3brBaeMat
AeHi'rfl.j,c'rrx{Hbr
p aiiXor\1ll3aurf.Ha6 Jtn LeHHir. Heo6xo.x,r{
Nfocrrr 3rori rpoqeAyp br cTaHer oqeBHAHor?,
ecJIH r.rNreeTcfl
HeKOTOpbrr?
Qarrop, rioropr,ili Henpel r r r r B H or J 3 M e H f i e T CBf lO B p e M q 3 K C I l e p r r M e H r aH, a I ] p H M e p n p o A o n xiaFouleecflBbrcbrxaHllenpo6, orK[Aarou{lrx cBoe}i oqepelrr B3BeuI[B a l r l r r . E c " r u e s s e c n T bB c e [ r e c T b n p 0 6 , r r o J l y q e H H b lH
x 3 0 6 p a 3 r l aI ,
a 3 a r e r l B C e n p o 6 b r , r r o J r y q e H H b r ie3 o 6 p a 3 \ a 2 n r . , q , .T
, o rrprrnoc . ' r e . I H e : ,813 B e r r r H B a H l rM
r .or r y T 6 s r r l 3 a p e f H c T p l l p o B a H b 6r 6 n l u n e
BecoBblenoTepI.{JIIIIIb no Tori rlpxqnHe, rJTonpo6br Bbrcbrxa,'rH
B TeqeHrie 6o,tree [poAo"'r]KHTeJrbHofo
IIepuola BpeMeHI.r.oArrH ris cno. 0 6 0 B p e u e H r r r 3 T o f i 3 a l a q r r- n o c J r e ^ t o B a t e J I b Hl tayrM e p a [ l r rK a ) K 89
T a 6 , ' r n u a2 . 1 6
Ta6nnua 2.15
KonqeHrprquaMfiKpoqacrurl
n ra,noiisoAe,ndr/r
A u r a D K T : | K a ,n = l 6
3,7
2,0
lpeHuauIHq, n-18
0,6
I 'o
IL
,T A,
0,2
3,2
1,7
3q
l4
L'
4q
C o a e p x r a r * l e x a p d o u a r u o r o q e M c H T aB l t s l H o 6 p a 3 l l a x
n r - c l i S H l l l i o ,% ( ' r I c . l a e c x o 6 l i a x o 6 0 s H a q a F r
nopl,rixoauii rioudp npo6ul E npoqecce aua,rtlra)
,1
Aq
3,7
7,8
I,9
2,0
I,6
on
I 'D
9A
ll
1,.)
lc)
9'
2A
0,8
1,8
3,5
1'
,r,oii noBropHoir rtpoqeJ.]'pbtH Bbr6op arrlx HoMepoBB nporiri.i.,t rrHa,lll3a IIO Ta6,'Iliqe C/'IyqatiHbIXqncerr1.l[eiiCraUrenbHo, eC,'I6npoqecr:
n p o r e K a e r I r o s T a i r H oT
, O UeJleCOO6pasH
l r op r 4 r r r ] c a r b
H a v A a ! i i .H o M e pa KillKi{oMy o6pa3qy Ha iiax{AoM rxare. Tof-la pa3,Tr.{;Hbie
ltcrorrHHKr] oufi6oK nepeMeruHBiiloTcfllltn coBNleluaroTcflJ,"trt BCex tro-
I{orrcD o6D:3ua
I'lolep ro
gTanHoil
n pc6;t
r2,5(28)
l 4 , 3 (1 6 )
8,7(20)
1I , 4 (2 9 )
e,5(27)
1 6 1, 1 ( 0 1 )
18 , 7 ( 0 4 )
14,3(ls)
20,2(14)
17,6(0i)
l9,3(05)
l6,l(2s)
1 9 , 2 (ll)
r8 , 7 ( 0 8 )
2I , 3 ( o s )
r 6 , 5 (1 7 )
17,3(26)
22,4(t5)
Il),rj(21)
2 0 , 31( 2 )
2 2 , 5 ( 3 0 ) 2,,l,ij(06)
1 i , 6 (1 8 )
l7,0(24)
1 8 , 4 ( 0 3 ) ?0,2(22)
1 8, 4( 1 2 )
l 5 , 9 (l 3 )
1 9 ,l ( 1 0 )
le,0(02)
5 e u , - ! l c . r t i l { x K B a A p a r o B ,K o r o p L , l l lcl o r e p x { l l r B b i 6 o p o q n b l eo q e H K I l
3aJ , u c [ c ; ) { i i l i tH 3 H a q e H l 4 lJ' ic - x p u l e p u n . C o o r e e r c r B y l o u , a g H a u l e } : t
jlaqe '! :3,tirtu,attpllBeAeHaH!l)lie:
Hctoq sHx lr3MenquBocrl
BTOPHbI}^ I-IP06, A HE KOHUCIITPI{PYIOTC'I B HECKOJIbKIIX I.I3 iIII.\.
Ilpoeepr<y rtrrrore3br 3KBr.rBadrreHTHocra
r]r{rri odpa3r{oB l,{o}r(Ho
npc3ecrrr c rroMoilrbio nIorleil.ypbr, Ha3brBaelroir orHoqlar{Top}rbrM
A u c u c D C u o H H I r laMH a , ' I l I 3 o i i ,n t ) i i K o r o p o M I I p c B e p t i e M a ;r t i t i o r e . l J I r
a,rIbT: pHaTIIBa It nietoT CJIe;lyloljiu fi BIIA:
Ha: Vt:
llr :
: tt4 :
tr13
plb;
Hs: rro KpafiHeii Mepe oAHo cpeAHee 3HarieHizeordrrr.rr{Ho
or ocraJrbHbIX.
nponepr{r.r 3Toii rrrrrore.-?brrDe6yercrr Briiro,!tteHrie itexo.to,
!,nl
pLix yc"rloBllri, a atreHii{-):a) Ka)KAoe MHO)KeCTBO
n O B r O p F I b i xn p 0 6
llacc\iaTl)trBaeTCs riai! J"'ilqaiiHafl Biri6opKa il3 cooTBei.j'fB\:louleii
coBoK)/IHOCTH;6) K:i,ri.lar HcxoAH:ir{ coBo]{ynHocrb xapiiFi.fepli3yeTct HopMartbHbrM prclll)ei.eJlcHtreM; E) B:C ticxoJ,tibte ccIai,.\:jiHocTH r.rMeForpaBHbre Aricirellciiir.
!,_auHsre^,'r.,,ra paccl,{alpr,rBaeMoir HaMLr 3a,raqj.{ ni)rrBe:IeHr,r
n r a 6 . r . 2 . 1 6 . B o . ( H o Q a x ' i o p H o M. u r c [ e p c u o H H o ] var H a , r u 3 e o 6 u r a _ q
Aticnepclrfl pasSriBaercrrHa .qBecocraB,lrrrout,tre:
rtircfiepclrroBHyTpa
riax{Aoro N,lHo)riecTBzt
noRropHbrx np06 (nuyrpuou6oporlHVro ArrcIlepcl,rn) H Alicnepcfito Mex(Ay cpaBr{HBaeMbr\,1r.r
o6pa3r{aMH (Me)KB b r 6 o p o q H y r oA r r c l e p c r r l o ) . B M a r e M a r u r { e c x o f ic r a r h c r f i K e p a s p a 6 o r a H a $ o p r . l a " n l r s o B a t { H i ri rt p o r l e A y p a A t r c n e p c r r o H H o r oa 1 a r 1 3 a "
K o r o p a s n p l i B e A e H aB l a 6 r l l l u e A N O V A ( A p a l y s i s o f V : i r i a n s e ) .
flocleAHriri coAep)iar riepeqeHb rrcrorrHlrrioBHSNteHqHBocrH,
croJr6 e q l i c n p a n , ' I e H H b rcxy M M K B a A p a r o B ,c o o r B e r c r B y r o u l u Xp a 3 . { l q H b r M
rtcToqHrrKaM,qucJro cTeilelreii cBo'6oAbr.I,,ls Ka)K,lOr?H3 HkX, cror90
MS 1/r,lsw
Mexiay ntt6opxalru
BHyrpu su6opor
O6rttaq ll3i\{cnquBocrb
O 6 u L a n I i 3 N { e H q u B o c rnbo B c e M H a 6 J l i o . l e H I ' r f l(rn' Io B C e M: ; c B . I o p '
(FcpHurr itlo6ax{ L{ fio BceM o6pasUalr) SSr xapaKrep143yercfl
M\'.toii
;j {1.r,,',',
xt,--r
ssz: Tl
Tl
''
i
'!J ;.i
.\
a u
j:r
i:|
ir.37)
l:I
l:l
l j l e F , - l - a n o e r o p H a f l[ p o 6 a B j - M 0 6 p a 3 ( e .
ll)oB : e o i i i r o i r c Y M M en e p B a t l y K a s b l B a e r 'r i ' l o c y N I M l l p o B a H ' i e
np06'
iloArrr:t1riio xa)K lol\{y cr6r6uy, coAepx(aueNIy l? IIOBTOpHLI:':
a 3aTet{ cliJIaAbIBAIOTCttItOJIyqelll{bIe pC3\'!'IbT:-iTblBCeX m. CTOISII.OB.
O 6 u r c e L s i c , ' I o u a 6 . n l o ! . e H l 1 t 1A r p a e r t c q H c . r y yl l o B T o p H l l x I I p o : 3 B b i flot-''ierittlj'l
5 o p x e , ) : r , l H o ) l i e H H o M yH a q t t c , t i o n u 6 o p o x ' r ' e . ' V : n t r l '
u.n'eHe rrpaBor? qacrH BbrpaxeHr.ifl (2.37) r{a3bIBaercfl nolrl)i'?oqq ' l e l l b l i 4 l ' ' l e r c ' l c uH B , { p y l u x
THaJIOI I b t l L ( i 1 . X 4 e T H Mq, T O T a K I I e ) I i e
fL{'-rHbrr:c)'}iMax,
c v v uy, xa p aKrep r43Jirouytocfl MexBrt 60 p oqHo ri II3 l{eHql.lllrjcrblo,
]lirxollflr llo cJleAyloueii sopuyle:
tn
ssA: T'! nI
KJ
;-
I
tn
\Ad
-+(I E,,,,
12rtftfl12
(Il x,,
/
'
(2.38)
i=l i=l
9l
rAe cyMMrzpoBaHue,rnpoBoAr.tTcr
no BceM noBropHbrM ilp0,6a11 B
K a l K A o Mo 6 p a 3 q e
u 3 a r e M K a x A a , H 3 n o J r y q e H H b r xc y M M
tZ
: l{ t , ,
B O 3 B O A H T C g B J { B A Apar
P A It no,'ryqesuuui pe3y.rrbrar
Ae,trrrcs Ha qrrc,,ro
nonropeuHl'r n e xaxAori au6opxe;
Aa,'reeno,rryqeHHbre
pe3yrbrarbr
cyNrMHpyrorct iro BceMnu6opralr H, HaKoHerI,
BblqnTaerc,
fiorpa_
e o q H H r .ql r e u .
B e ' r n q n s a ' x a p a K T e p u 3 y r o q a r ro r o p o r i [ c r o q H r r K ] r 3 N r e H q f i B o c r u ,
---.
HMCCT BI],4
L'l
q q , . .-
t,2
_l
t1
E (Tlx,,)
M
;-l
\.(d
rtlutl
I
;-!
Ja\{erit}r, uro nepelrri rr.leH.
qacru 3.lccl iaxoit xie,
^npaoori
K a K i r l e p n l l i r u l e u ( t o p i r r y n a t ( 2- B
. 8 7 ) A , , r aS S r , a n o c i r e , t n i i n . , . r a n
c_nepBblMrr.rrelio.r,,i
Soprrl;;rrr (2 Bg) A,rs S.Sr
:.
:T"ll^1:l
SSly,
Mo)xHc-r
ssr,{ac,rrtrl nO 4Op'ray,re
S.!rr': SSr-SSa.
TT^^-^.".
r rutrulYl]
Q.4at
9 I , I c " u oc r e n e n e f i c n o 6 o A u r r o B C e M
A a H g b r Mp a B H o , V - 1 . L l u c , r o
crenei:eri cso6oAH AJrrr BeJrurqnsuSS.4 paBlro
,ir_l
raK KaK Mbr
o I I e H [ B a e M e e r o c p e A H r r N r3 ] i a q e H f i f l M K a ) K A o r o ,
b6pasuu. pas_
Hocrb MelKAy or'MH r{Hc,rax,{u
crenerer:i cno6ogur puuni ur'any a"aneHeir ceo6o.lsr .]rq Be.lrlqannrSS6..
C {enr'io lrdrJllocrpar-(Hrr
3Toro N,reroAaAacnepcuoH'oro aHaJrH3a rpoBeAeM Bbrqr.rcrreHnq
no AaHHbrMr.76L 2.10.
- - - ' -t{cno.rliiyr
qop'--'--'""r
u r y n y ( 2 . 3 7 ) a n q S S 7 , r o n } l e " n nS S r : g g g , Z g .
Aaree Mhr MOX<eM
n o A c q H T a T bB e J l n q a H ys S . r n o c p e A H n M3 H a _
qenLIflM Arrs.ilnrr o6!1uo".
I4cnonrsyr Qopnay",ry
npocyu_
-e (2.d8f,
'xna4p21
MripyeM cHaqaaa BCe ntrb cr.o"r6rlos,-soieeaeM
nsrtl,_
p_orA.nr{Mpesyrrbrarbr Ha 6 }r gbrqre\,{ norrpanou_
:::.:":^..yrXojl
q
J
r
e
H
.
9
T
o
Hb:ir
nacr Hatr{ uexnut6opounyro cyMMy KBaioaroB
SSr : 237.42.
H a xorieq, Bbrr{r,rrarr Sf
qr_ SS 1, rroJr}ruaetr BHyrpHn ar6op ounyrtr
c y r l M y K B a A p a r o BS S r : l 4l 6^ , J T .
O6rrleeq'cro creneueri cno6oAlr paBHo ly'_1,
unu 2g. Tax xax
MbI OIIEHHBAENI MC)KBbI6OPOVUYTO ],I3MC}II{HBOCTb
IIO
N'TH
}I3MCPCHII.
arr. (r. e- no cpeAHfiMsHaqeHHs,M
rrflrn cro;l6qon), ;;;;;;;
crere_
Heii ceo6o.4br.,r.rrr
S-SapaBHoffi-y, r. e.4. pusli.jcii fi;;; crerre_
HCIi
CEO6OAbI AOJi}KHA COOTBCTCTBOBATb
OCTA'KY
CYMM
KBAJIPATOB
pa:Hocrbqr.rcerr
creneseftcno6o4r,rpae-
;;;; ;.;;;;.""& #;,"";
t "n'2Fir::.pl BbIrIIicJIeHHbIe
"1,n".r.""oi;;Irc''paBJIeHHbre
:i" iv-IIL'
J,*.j.ri, nrttt
l3t1u"-";Pj1
na
zo' r enepb
!2"!:I:
cy*rvsr
KBaAparoB
SSz, SSA u SSu Hy)KHotrirl.nuro Ha
coorBercrByroq}tC,'Ia
q}tc,'Ia
U { I l e IiM
u{re
IiM
CreneUeti
creneueti
CeO6OAH.
ceo6oalr.
E
De3vJrATrrp
pe3ytbTaTe
r t r L r rlo,'ry"iaeI{
n^r,rrr-r.,^r,
Mbr
uapu,o,,sro nBlr
nercrnpocro
?:::I:
f ::j:,f
:1.1
.{"
a3BaH
lreM
A
pyfrrM H
rJ:::,
e x x (:t.^ry
e n e . i l a _.
uu
H).
92
ttt
388'79: q3
:
13
N_ I
29
O u e u x auexeu 6opouuofi.qucnepcuu
sse
237'42
^/tq.b9,JD.
m_l:--4-:
LlrreHKanHyrpHnu6opouHoii
AHcnepcru
otnz
t2
t'f
l-/ Ll
O I I e s x a o6qeri ALIcrepcHH
:
sSu..
t46,37
--:
\-m
25
C l u r u o c r l [ p o B e A e H H o f oA u c r r e p c i l o H H o r oa H a , t l i 3 a , ' i y q [ e l r o r c H r i r b , p a c c M o r p e Br o r n p e A e J l u n r i c . r t y u a t l r, o r A a B C eI l o B r o p l t b l e
n p c - , 5 r ,nr . l e H T r q H b r .T o r . r a c p e A H H e3 H a q e H r r . cs r o n 6 U o s 6 y f y r r a I { r r x , I r)ri i e , K a K c p e A H H en o B c e M c r o n 6 l 1 a n n ,H o r ( e H I ( aA E C n e p c u H ,
Bbrrl[cv'reuHaaIIo BCeMga6nrcAeuull,t, 6yAer coBilaJ,aTbc oueHnoll,
Bbrqiicd'rerlHofi
rorlxo Ha ocHoBaHr.rr{
AaHlrbrx o.lHoro clo,r6qa. tr4Hutl \ r r rc . r l o B a N I IM
1 ,e p a o u l r 6 x u o 6 p a r n r c t B g \ ' , r r b .B s r o l r c " { y ! I , , r H e I
A H c i t e p c l i n ,B o 3 H r r r i a l o u 1 er ri i: - : : t p a s , r r t u t z i\i{ c r , l i J } I' t o B T o p t t h i M }n!p o 6 a l u r . T a x o i l H e n p a B J , o r o l o 6 H l t i 'p
r e 3 ) r r ' i b r a r f o . 1 N ( e F Ir t a B e c r i t H a
r{brc.rrb,Liro nepBoHarrarbHbleo6pasqu Ha ca\'to-\t A€"rI€pzt3,r'i11'iHbI
u iiro ria)riroe \4HolKecrRc'noBTopHbIx npo6 6r,t.rtoIt3tsJIeqeHoLi3
pa3.rrHrtHbtx
coBoKynHocTerr,ilMeloulHx HyJIeBbreJilcnel)crlll.
Den,
rrnrnouLrr.rri
npr.rMepfB.rlflercfl MeHee 3r(crpe\{a!'Ibgltrt. Boirrr.Icr'Iff3HaqeHrleF-xprrrepun, NIbrrro,ryqaeM c,reJ,yrouleeKpHTHqec r { o e 3 H a q e H u e .B u 6 p a B K p l l r l . l q e c K y t oo 6 , 1 a c r b , c o o r B e T c r B y l o u l y r c
3 a L a H H C M yy p O B H r O3 H a q n M O C TII]r 3 a A a H H O M yq l l c J l y C T e [ e H e icl B O 6 o l u , \ ' r o ) K H or e n e p b n p u H r r b l r . r r uo r B e p r H ) r r b n p o B e p r e M y l o r t a I]ore3y:
F : M S e l ( n 4 S *:)
O l H o $ a n r o p u u l i r l u c n e p c H o u H t l iat H a r , l h 3I I p H M e H q e l c f lB ' r e x
c " r r ] - q a s xK
, o f A a r p e 6 l ' e r c n n p o B e p l l T br r r l l o r e 3 y o r o M , q r o l - t e K o r o p a r i i H a S o p c o t s o K ) ' I I H o c r e f ni ,p e a c r a B , ' I e H H b tnxt t 6 o p x a u t l , c o c r o t t r
rr3 uJ,eHrr.rqsuxo6rerroe. OrrHzti(oA.rIr ero npoBeAeHut{rpe6l'ercr,
qro6u Mbr MofJrrl c,ryuariHoeu6parl loBrop]rbre lpo6r,r BHvrpH
n u 6 o p o x I t n p o B e c r u r r x a H a , r t u 3n c " r y u a f i u o i i n o c r e . l o s a r e r ' t b H { J c r r . r .
ofpaHHB Hexoroptrx cl{Tyarrnlx aro Mo}rier oKa3arbcq cHJlbHbrM
q e H r r e MI r M o ) K e r I I p l l B e c r ] l K H e l I o r H o u e H H o M a
y H a . r l I r 3 yn, p i r l i o r o p o \ r r e p r r e T C fcl ! ' i l l l I I K o MM H O f Or i H Q O p u a q u uo 6 u : r ' t e u q l j e o c r l i .H a n p i r u e p , i r p e A n o l r o l K H Mq, r o H e K O r O p a fIli 3 M e p H r e J I b H anf lp o q e l y p a
n p u B o r r r r r i 3 a B b r r r e i r r r r cr t l c n e p c H I , t . I ' I c n o " r r : v q o r u o Q a N r o p n l ' r o
llOle,rlb, Mbt He MO),KeMOUeHllTb Be/'ll'lrlHHy BO3HilXalOuIeti nO grOit
i l p t r r r n H e I l 3 M e H q H B o c T r . rT, a K r i a K o H a B x o L H T B c ) ' M M y K B a l l ) : l r o B
B M e c r e c u 3 M e H l r u B o c r b r o , B o 3 H l i K a r c u r e i i o r ' l p y r n x I r p H t I L r H .O r , H a aHa,'tII3 MolKer Aarb Bo3xo 6o,ree KponorJIHBbII? crarucruqecxnti
Mol,t{HocTb BbIAeJIl]Tb 3Ty H3MeHqHBOCTL'l.l OIIeHUTb ee.
93
oy x {; a xroli li r,lli,x,i.rc n r p cu o HHurri a Ha,'ru3
"4,
i { . ; e i , . ' i e u p r . 4 S o n c c c , r r o l r i l r b r xr i l l r l e p i r e B , n o . i p o 6 u o o n H C a H , i b l - ' 1 ) r i ) i i i i ( i e O , i { l l i l i } L _ I i O i { l , l J I l e p C i . l t ) i l l i C - r . , 1 _ i\: } i I i . l l i . : l ) ' l l l i . i i : i } i l l p O B a H i i i t . - 1 l i f , ' i l c l j j . r \ r c I r ' f i ll.l p e K p : t c i l H e
oIIlrcatIrrfl Hct{o1'opr,r;i cxel!1, Becblla ilO.'le3i1t,l)i Iiilli iCaJ.riOfi{(lCCIiti-\jicC,,ie.iOijllititii,\^, C0.tiCl)it{iiTCfl ti
T a6 nnua 2.17
Ilponuqaer'rocrsc,ny,rafiHoorodpaunux o6pa:qoe necqaHltKoB Ceirr-IInreP
(urrar lln.rnHoiic),usmepeHHaq
B pa3ruqHbrxHarIpaB,'reHHfix,MKM2
HanpanreHux
r i r r r r i r xI - p r r r b Q u ' r cf 1a3 l r i i i 1 . , a r , r 6 c i i l a ,l p e i i 6 l r r " l a [ 2 C ] . 3 . r r e c r
I{bI
0fpaHHtiilllCtl
pzlCCxiOi peHIIeM
v-tI4IUrrOiHOfO
r i p t l i \ { e p a l r c o o r R e r c r e } ' m u l e i i c r r r r c r r l r t { - . c r i o itrr p o u . e . t ) ' p r , tO. p ' i o B H K C I u i er e c q a I r H l ( t z C e H r - l l u r e p l p e A C T a B , r e F r bor q e H b q r . r c r ' r , ] M i i
o p r o l i r a p q u r a M r r , K o r o p b r e p a c f i p o c r p a H e r r bB
r B e p x o l : b r r xp . i " ' i . i r c 'far
cucrrlrir.
r a x 3 e p H a3 T u x n o p o n x o p o t u o o x a l a H i n r i o ' l ' c o p r i t p o saHbr, To cHrr Heo6srxiroeeHHooJrropo.lHbr lro cBoeN{y crpoerrrirc
B cnR..'ruc irrrl,r He$uuue Mecropox{Aerrriq,npuypoqeHgble Ii recrlaFruriar{,nprr 4o6r,r.re ueQrlt ltyrel"I orriaqKH Be.[,yr ce6fl TaK, ]iat'
:"to)KllOB 'lOI{HOCTII
npe.\CK:i:3:lTb
C IIOMOIqbIO
TeOpeTIlrleCI{LIX
I;Ol.C, r e i r l t r n o B e . i c H H f lx, o r f l I t o c , ' j e I H I r en o c t p o e H b rI I a o c H o B er . t A e - J H 3arirtrr 1'c"roerili. Orx,roncgufl roBejteHHr{ Nro,eJrlr or AericrBHTc,xbH o c r r i N { o f J , Ty K a 3 a r b s a o u r i S o q n o c r r n o n ) ' u l e n r r f i B c r p y K i v i r ( ,
r{oJ.e.1tr.
i{eOo,rr,ruol:iHeQrnuor? pafiou B rclKHo\r I4,t,tunoirce ttpeAC]i,tB'
coElrii;r.c
"rzcrcrr HAea,'il,Honpncnoco6.,reHHbIi{L,'rr r.rccJreAoBaHIifl
H l r r B n c B e . r e H u u\ 4 o - ( e r ' t H
i r p e a r b u o f o H e Q T r r r i n i oM e c i o p o x i A e H u , i .
- . - ^ r , - . , ^ . . , 1a p e H A o B a , l c E ] ' o J I b K O O X H O I i K O [ ' l | i a i I l { e l 1 T
, II.iaT e J r b H o x p a H n B [ r e l " r A o r { \ ' M e t ' t r i l r { r i o , T o n a H H b r e o - { , 0 6 b t q eI I e ( F r r , ] r r
3 T O f O N , i e C r O p O ) ! i j ( e H i ior K a 3 a J I H C b A O C T y 1 1 1 1 1 , 1Ay"nl l r r r C C r T e J , O B a l i l r r .
O1uar<o, npelKAe rreM BbrIio,rHHTb ricqepilbrBaloxdlrfi aHa,rIIr3 iroBc.ieH r r r i r r e c T o p o ) K A e H r r f i ,q e . I i e c o o 6 p a s H o r r p o B e p l r r b H a n p r . { M e p e B b r [e]rno[,rar)"iofo
xecqaHuKa rrt)e,q[o,1or{eHrle 06 oAHopoAHocTI.I cto
C B OI i C T B .
tr4:rt',tuo;xecrBr cI{BaxirrH, npo6ypeHHbrx B fipouecce pasp:rCrorxrJ, .lcciilb 6u;ilt nu6paFibr cryqar:ruunr o6pasol"I .q!'rfl trpoBeAerlrr"i
a H a , ' i r r 3 r i .B r a x r l o i i n p o 6 e F r a y A a q y 6 b r n e n c e q e H I x y 6 n o p o , r , i , r
c 6 ' b c x l o i l 1 6 c l l 3 T t K I I l t 0 6 p i r 3 o M , I t ' I 0 5 b t B e p r t t K a , t l b l i 3 . qo l ) l i e l i r , , i rlurr r)pcdri coxpalrr!'racr. C rovoulblo coo'fBercrBylouefo
nplt6opa
6lr,rrr cler'raHrr
ABIix(eHHfl {r.tiloi;4a
ABa u3nlepeHHrr cKopocrn
c K B o 3 r - ,B b r c e l r e H H b l eI { ) ' 6 L I : B B e p r u r ( a l t b H o } r } I a n p a B , t e t } r i r l n o o i H o II B l'Opi:i.rOIlTaJIbllO\'1,
IlapliJIJIed'lbHOCJIOIiC'IOIUeHIilii K C.TIOIICTOCTII
r rH l t r l a e M o c r b o 6 p a : c l u . ] I c n o r s : v : i g T r i I . i 3 n { c p e I I I r f lI,r L , r q r . r c , ' r r r r 'pt o
u a B l ( s a . r , p i l r H b r xl { [ K p o M e r p a x .
n - ^ . , , , .. ,
3uoH€IIIiri rrpoHHr{aeMocTIlIIpuBe]cHIrl
AtsaAUi1lb tsbrqucJIetrHbrX
rioJlyrirrrb
B ra6.ri. 2.17. l7o 3'frrilr ABr j'.r{arlr 3r{r.rrcFurrrMrpe6yercr
r trpoHHuaeMoo T B e T l r a B o r I I l o c : 1 4 M c i o T c a" q i l 3 H a q r M b r e p a 3 , ' I L r r r u rB
B r.r3yqaexloM paiioue
crlr, 3aBrrcflruue or no,'iolKeHr.rff o6pasua
( r . e . o r p r c l r o , ' r o ) r ( e H I . i tc r ( B a ) r ( r r u ) u , r r r o r n r i 6 p a H H b t x H a n p a u . q e Trt'
tzrrrl r'fnr
nriinrr
anaH
lr.ana nao
r'nnr-
tr.iritrsueueuus?
3ry sh4au1,Mo)KHopeur.irb c troMorr.lbr,o
4eyxQaxropHoroAHcflepcnoHHof
o aHalr4sa.Paccuorpnu ABa rraBHblx I4cror{HHKa
v3,94
fopu:outrrrroe
AOnO.rrEil'ie.lbur,f (l
I ,037
0,963
o,842
t,t2I
I ,043
BeprirKarbfioe
| ,124
0,9,r0
0,921
|,202
l ,028
0,928
I ,108
0, 8 2 1
0,797
0,949
fopIlsoHTarbHoe
0,943
1, 1 6 5
0 ,8 0 3
n 749
I,004
MeriqiiBocrH: oLHH, Bo3Hur(aloulnfixar cr'i€.{crBltepa3Jlllqtzt4MexAy
lp06atvllr, r.r gpyroir, BosHirKaroulvfr.rr-3a pas,ruutifi HanpaeneHuft
jtilrr ri3NlepeHrrflxrrpoHlrr{aeMocTrr.TperHii rrcrorrHr.rKil3I\{eHqKBocrlr - ccraroK, Li,'II4AllcnepcHa omil6t(ll, coorBercrBy]oxlafl AHcnepc n x B H y r p u n o B r o p H b r x[ p o 6 B o A H o Q a K r o p H o Ma r ] e , ' I [ 3 e .B 3 r o M
ilpriMepe IIpoBepfl]oTcflABe frrnoTe3br:
Ho:Ltt:p2:...:pr0'
I/6 llt,aeor:propus.
Ccorsercreyroulre arbrepl{arirBHbrc filrore3Ll 3aKr'Iioqatorcf
B T o , \ { ,q ' r o r r o N { e H b r x e rt l\ { ( ' r e o J } l A c K B r ) t i l i i l l } r \ i e e l H e p a B H o eo c nilOHaClle.lHee II qTO EejlTriliadrbHbTe lI fOpli3Cllril"IbHLie
3ra
t
oqe}lb
ll [i]lor\ilil]l :ie1.'\"11'ie
uzleN,locTl{ HeoniiHaKoBLt.
npo5"le l'.a
Ta'IbHLIM
p a c c i \ { o r i l e r { H ) . .3l oa i l a q y r . r s y q e H H lc o r e p a i a H r l i r . . : p 6 o u a r o B c l i o r l o u { i , l c o , i r r o r p a x r o p H o r oA r r c r e p c l r o H H o r oa H a J I l i 3 a ,H o c o A H I I M
o ro 6 p a : i l L r i i i r i o r r e H r 4 eBM\ ,:r e c l or o l o q r o 6 r t x i ) o r r 3 B e c r i r . r 3 N r e p e H H
IIax Ha ocHoBaH14ucnyuaiiuoro nH6opa, i\'1brnpoBe,la il3'\,iepeHLIfi
p N 3 H C r or i r r a . l l o c . r e A r i l r e N . r o x < HHoa 3 B a r b s c p $ e N r a u H : 3 T ' o r T e p rlriii osr{aqae'r, qro qHcJra,I]opoxij{eHHr.reol1}rrn{ sr!Qenrolt, MofyT
riryHgalteHra,rrbHoorJILIqarbctt or qlrce,'I, rlopo)KAeHHL.rxx,pyfllM.
J.a)r{eB cJryqae ec,'ru liclroJlb3.viorcf oAH}r ii Te )Ke npo6r,r. Tar xarc
ri3Mcl--cHrrfl
i1 B\{ecTo 3Tofo pa:,,.le"'IeFre BIro!'rHepaHAoMH3rrpoBaHbi,
H L r B C O O r B e r c r B n zC B O 3 I e f i C T B r . i eHMa H H X p a s J r n q H r , reXr p Q e m o n ,
pa3,rr}ITo naHllbte Mox{Ho IIpoaHanH3HpoBaTbc rleJlbro BbrflBJIeHIrfl
q | l i n a l i M c r ' K A ye t p s e n r a l ' i l t , T a K H N [ e i K A yo 6 p a : t l a M r r . T a x n i v r o 6 1 r a 3 O h {l t, 3 M e H q H B O C TBbO, 3 H H K [ r a fxf 3 - 3 a p a : , r a . i l . r i rn e Q $ e x r a x , u e
BO3FIIIl(iUeii
IIO ApyfllX,l npUCoilrrzrAarbc I{sMeHqHBOCTbIO,
J,O,TIKFra
r[iHir]t, n ]to)KeT 6brTb oTAe,'leHa ]la ocllt)BaHHll cra'r]icTuqecKoii
rrf oqeAypbr
! , r n o 6 o c u o B a H H o r oi r p r 4 M e H e I I t 4gra y x Q a r < r o p H o r oa H a r l i 3 a H e cJi,o,r.ttlt0 BbilloJIHeHHecJIeAyrcu{Hx rlerbtpex ocHoBHbtx Itor'io)Keuirii: a) Ka)r{j1aflKoM6r.IHaql{rloQqreKTan o6texra t{n,'Iflercs cJIy. u ,. . n o i i n u 6 o p x o r i , s : n r o t i I I 3 p a s , ' r i { q u b r xc o B o K y i r H o c r e i i 6
; ) xeirH
3
)
r
q
a
e
M
l - lcco B o '
B
C
e
B
)
H
o
p
M
a
,
'
i
b
H
a
;
c
o
B
o
K
y
n
H
o
c
T
b
H
C
X
O
A
H
a
g
AaR
Ya'
--
KynIrocTH HMeIOT I
ffii:1?X?;
?;ffffffi""';e:
;*iy*1fi"#;;^;1,;;{"il?
llocneAHee AoTy_rr{e1Te
,BJrrrercfi yrBep)r(rer{ireM
roro,
O6 p a s 4 u r
2
1'#',T: :oo"-', """opi.u, Herrp'BoAr*
x 6o,rru
err
il!l:;:#:
E_c,i,,'oii'ra;';;,;yrT,'#i"ilr'otj,1
ji1,,:!,:;!i1:i:,*{l;f
tl
o
;;'
oo
i
:"l?.:iY5..fi
oio"
",
i
u.
J;
9
:r
*l#+J#x.
T:::
F- o6paseq), ro MofrH- 6;
",,,.p
e
a
fo.rHaKo
: Hu
; 6,;:llff;i"
.-.cx.,,.
n sroir nnoc;gy.
*ii
qro n:arnro1efio,.,i.,*;
;;;',
;, roHx
I'J';-ru;i,:'#"
;iernorrc
:il,'"J'#:lixil"
rIP
-.Id
ixenrre o ;".;, J"#;;:::.i "'- l-tl-"]r aHHn npo6. Omn6o,{Hoe
BH,,i o
: d ;',i;ili""- J;"iiffi.
1:l
"'
aHar rii a 6e:noarop.n,,'i
:;?lri?,,
no eopr,r)-/re
(2.871,
jjl_"" " "i.,il"#"fi
pop*yri 1r.lts;.Be,rH,{rrHa
Jrrcrcncl.vrvori
"$i.J;ffi::;:::;
SSu .qsKB,rjrparoB
n" ,$6[niur,
.AnVX6a
r rr',,jre IIpHBO-1ilTCfl
CXeMa
'- ,','n
(, )l x,r''
,' N ,,8,i
E
t7
,'l
I
sc,-Sl
.km
r=l
r".;
,2)
^ti
,=,
),
t2.4tt
j..:1._"I]oe no,ToxHrerrbHoeq IrcJro.
ourr6xa .yrrot- n*11ii;;
s"' :is'-
Tax xar Be,rr{qaHaSSa
s*
no Qoprr.ryne
3u"o1"1c.8
(ss,
+' ss').
(2.42)
rs,raerc^o,ii"''
s H aqegafi
q e g a f i rro
..{B1rr
{ B \ / Y ccper,ua:
DeJ,Hax
o o
o6pasuaM
6pasilaM B
Bn
nnpno""-,,-...-_^_locrL'Io
p e . q e r u _ ,, , u * iuAoo' nf oo.c: Q
r Lc' Ipoe r < r at,o
paBeHCrB
,ru*
.S{,"o,ta*I"t"qrn
",,
r l|
o l|
.l
.l
x2
i::""i&&X],li::
n"p"*nonu.reM,
^'^?o, nn
d*ey o,in
uno,.i.;
y:
: .*,y'
?n':
l:
";'
of o u cc're,qoBare,'rn 1i"
5er: r.r
";:ili?f,'
X opot..
9l]x
;r,o
r|Qe
xron 0,,,,
-r.p#ll ; ;; " ".,t." ;; ; ;"^i,'*u":,r^lea
of.,iI r
-
3
.l.l.l=l'
.l
.l
qro
r,
ol
x1
;
.l ;lz'
. l l BRl l "
.l "] o
i4
|
i
x.
x^
x^
x,
Puc. 2.32. Cxeuu cyunltpoBaHnr B AucnepcuouHoM aHaJllr3e:
a - o , l H o o a n r o p H b l n , E I { c n e p c { o H H b l - af tH a J H 3 ; c y M M H p o B a H l l ea J I f l H a x o x a c s f f s a b l o o p o q H o r o
- , u , o y x $ a x r o p H i b l f i A n c t r e p c H b l f ta H a . t r x 3 :
c p e ! , H e f o n p o H 3 B o A H r c qc e e - p x y a n a : , n o c r o l 6 r { i v : 6
npox3Boanrcs Kax no crpoKaM' lax
cyrlvrpoBaHire arq saxoxaeinfl Bhl6opocuHxr;fffilil-
B r , I 6 p a a u e x o r o p u f i y p o B e H b s H a q l l M o c r HA ' r i R o 6 e u x r l l n o r e 3 '
npoueAypy-c IIeJIbIOHC3Ty CTaTI'ICTUqeCXyrc
MO;{iHOI{CnO,lIb3OBaTb
n
p
o
H
l
'
l u a e M o c r l ]B
' onpocst, Ha
[
o
2
.
1
7
c J I e A o B a H I . IAf la H H b I x r a 6 n .
- I]MeK)rcr JIII
Koropble Aaer orBer sror Kp[repHii, c,reAylox{ue: a
3HaquMblepa3Iuqfi'IBnpoHHIlaeMocTIIBnpeAeJIaXHeQTeHocHoro
p a r i o u a ? 6 - n u e r c r c f f l n 3 H a q H M b r ep a 3 , r I I I q H fB n p o H L I [ a e M o c T H
' no BeprHKanrtr11ropusoHram?
tax, uro6ut ona
npoqeaY-P-Y^
MbxHo ttstueunro o.u,HoQar<ropHylo
,
'lneHu
MSe
U UOeHil nOttble
HaxoAIITb AOnOr'IHIITe,'II
, nO3BO"'IfljIa
, n D a s o q u u t f iq . t e H , 4 4 S " ,a 3 a r e M n e p e x o A l l , l a 6 u K H a x o ) K A e H u I o
, . a ' " y * s H a q e H u i iF . O 6 p a u r e H u eK p u c . 2 . 3 2 n o M o f a e T I I O H f r b , I { a K L I e
pei Hs\aeHeUllflAOJISHbI 6Hrb sHeCeubI. Vqtlrlteas nOJIyqeHHble
.
3yJrbTaTbi, KaKI,te 6lt sl,t XOTer'1flAaTb peKOMeHAalI11I]OTHOCI'ITeJIbHO
qenecoo6pa3HocrH I'IctIor'lb3oBaHI'ltl3Tux MeroAoB AJIfl rIpoBepKH
: Irloleleli ga,rexu?
)
a H a J I H 3- o A H H l t : u a l t 6 o l e e p a c n p o c r p a H e H 4ncnepcuoHuufi
xaK
Hbtx crarucruqecKHx MeroAoe, oco'6euHo B TaKHX o6,lacrlx,
tt 6nO.nOrAqeCKI'Ie
I(OHTpO,'lbKaqeCTBa U:Ae;lUft B 11pOMb11IL'IeHHOCTII
no
e n c n e p u n t e H r u t . C , t I e . r o e a r e J I b H o ,H y 7 1 i l i b tn p o r p a M M b l a , ' r q 3 B M
c,ro)KcreneHll
.llto6oii
aHaJIIt3y
rpaKTilqecKtt
AilcnepcuoHHoNl)'
-*:fll ;"..T
'""i,f;:;:"#":::?,:P;
&ii?:;1".}'fff "i l;;"J
i,';t1
l"f"{; ;;;; U #:;:
"*-*:"!lg,l,li#::*]iit"}':':'i:rff
;:f,:i1,,:3lJ:'3ffiXX'1"::,:*Lii{1utJ';i'5;,,.,,;;""HilT;
"
y: t tu n""-i.;
uo0a
ut' srlt.x IlcroqHaKoB
H3I,reHqHBocrr.l.odo:HaqeHilq ;-;;;:'_::'*,^
D r t v ) v t c J l v _ t l a eT a K H e
u o $ a xxr
r oop
p uu
oo
Mr , x l l c f l e
)Ke, K
;;;;
aK Ii B o
oo
r -l",",,tJ"oy,,
:: :
qI{c..i
g
o'rlbKo
".,]J"""t#it
ox{:Q exro
",,.e. r "; " ""Xl?X
i l"lljl:- : ;il61
-t.n.pi
",'nlu;oli'#
::_'j1.,@
- o".ro*'
I,1cr,oqHIr<
A3MCHqLTBocTIJ
t u^y r l l r a
I
i
Mex.ly n116opxauli
me)riny e()Sexraulr
UuJlt6Ka
O6rlrag ir3MeHrrHBocrb
KBaA
D ar o B
SSo
SSa
SS"
DJr
4,.
\pureprii
Pa3,'lucut ilelKjty
6- . .
n purepai:i 3Ha 9tr:{OaTjI
pa3J,IUqH, MeXAV
96
gHc.ro cren e H e r ' ic B o 6 o'4't
m-l
n-1
(m-1) (n--t)
l/l
Bbt6opKaut
3OrbeKTM
au
CDc,qirHfi
KBaIpaT
MSn
MSu
,44s"
lr- - " r.
" ". "
3qa.reHus
1'-KJ] !I TCDHfi
MStlMS"u
MSelMS,6
HOCTI,I'
12-xpnrepnfi
TecHo cBq3aHHoe CHOpeu1eoArropacnpeAeneHue,
PaocuorpHIr,t
Ecnu eH6opr<ao6r,elra n B3flTarr3 HopMa,'IlHoii cogorvla.qbFrbrM.
p H cTaHAapTHoe oTKITOHe'
KynHocru'lluerculeii cpeAHee3HaqeHIIe
npeo6pasooarn
Hr{eo, To Ka}KAoeua6lIoAesI.ten est6opre r\{ox(Ho
(2.l6) :
no Qopr',IY.ne
(2.43)
Z: (X _p)/o.
c MareMarl'IT a x a s B e r H t { H H ar a K } K e p a c n p e A e n e H aH o p M a J I b H o
q,ecKHMolinAaHneM 0 n rlrinepineri, paeuoii 1. Eclrr sua\eitutr Z
7-2Al
97
T a 6 . ' r n q a2 . 1 8
Bo3BecrHB r{BaApar Ir cJIo}KIrrb,ro cyMl{a 6yaer npeAcraBJlflrbHoByIo crarucrHKy, r{ol'opyro Mbr 06osHaqar\.{
222, r. e.
BHaqeHrrr12-pacnpeAeleHun
Kpnrnuecxne
c v creneHffMtl csoSoAr,t n p l l 3 a A a H H o My p o B H e 3 H a q H M O C T IIIl 7 ]
Vpoeess gnaqsllocrH 0, o/o
n
222:F/-\'t-t'\'
TJ\
i-t
a
(2.44\
P' Y-,6
I
I
2
To oHa
Tax rar 3Ta crarlrcrirKa crporlrcfl no BbI6opotIHbIM.qaHI{bIM,
H 3 M e H s e r c go r a u 6 o p x u x n u 6 o p x e . E c , r a B 3 f i T b B c e B o 3 t l o i K H b l e
n u 6 o p x u o 6 ' b e M a n H 3 H o p M a n r s o l i c o B o K ) r I I H o c r IIII H a H e c r t i c o '
orBercrBylourfie ur{ 3uarreHufl222 s,a rpa$ux, ro oHII Syayr noAquueHu 12-pacfipeAerer{[to. Pacnpe.le,'ieHrley2 sanucut or riuc,'Ia creneseri cBoooAbr,Koropoe cBfl3aHo c o6reuou coorBercrBYlouiux BbI6 o p o r < . T ' r { n u . r H a s K p H B a f l 1 2 - p a c n p e g e , ' r e H r . 1r rf sl o 6 p a x r e H a H a
plic. 2.33, a 3HarleHrrg12-pacnpe,le,'reHtrfl
creAd'Igpa3,'Ifir{HbIxq14ce,r]
n e s e i i c e o S o r r , sur y p o e H e i t 3 H a r { u M o c r r rn p a B e J , e H ssr r a 5 , ' I . 2 . 1 8 .
Orlrerlnr, qro KprrBafl 12-pacnpe4e,.'IeHIrfl,TaK )Ke KaK I{ KpIIBaf
F-pacnpe:e.rreHrrfl,BbrxoArrr u3 Haqa,rraKoopAHHar II, rrpoxoAfl qepe3 [o,{oxri]Telrbubre 3HaqeHilq, crpeMiircl r 6ecrogeqsocru. fIoApaccMorpeHo B KHI'Ire,rlu [23] .
po6Ho 12-pacnpeg,eJleHue
Pacrpelenevue y2 IrMeer 6o.nruroe sHaqeHlle B rlpatirl{I(e, TaK
KaK ero Mox(Ho IIc[o,Tb3oBarb A,'Ifl llpoBepKII fHrlore3, coAep;Ka'
TaK LI nopfl.IKoBble AaHHbIe.!,o cnx nop
uIHx KaK HON{HHaJrbHbre,
MbI paccMarptiBa,'tu ro,ilbKo MeroAbl I.IccJleAotsaHIlfl
l.aHHbIx, npe.I,craBrsroullx co6oii pe3yr'IbrarbI H3MepeHHr gHaqeHttii nepeMeHuux. Tenepb )Ke MbI o6parl.IilIcfl I( HeKoropblM NIeroAaM HsyqeHfifi
AaHHbrx rroAclrera, HaIIpHMep raKI]u, KaK r{l.icdroMopcKlIx exeii ga
eAI.IHAqyn,'IOXIaAIIMOpCKOIO
AHa, Il"llI qrcro Kpl{cTa,'LtoBIL'Iarfio'
pacnoilo)KeliHbrx
Ha llepeceqeHlruur,ru$a, Hi-lll 9IIC,{o 3epeH
KJIa3a,
saAausori rpaHyJloMerpuuecxor?
Q p a x q u u n p a s . r p o 6 , r e H i I o MI I e c qaHLiKe.
O6qeli:secrHafl 3aAaqa crarucruqecKoro aHa[ru3a 3aK,'lloqaerc f l B c p a B H e H E as s t 6 o p o q H o f o p a c l p e A e , { e H n f lc H e K o r o p s i M3 a p a Hee 3aAaHHr,rL{cTaHAapTHbIMpaCIIpeAerresueu. Tax, craTI'IcTI'Iqe'
c K H e K p r r T e p L I uM o x ( H o n p I I M e H l l T bA J I s n p o B e p l ( H f x n o r e 3 b l , 3 a '
H3 coKJlloqarcIIleircgs 'IoM, qTo HMeloulllecfl AaHHble I,l3B,'IeqeHbI
Bo3Mo}KHo,
C 3apaHee II3BecrHblM pacnpeAe,''IeHl.rel'{,
BOKynHOCTH
LI!'ilI JIOTHOpMa,'IbHbIN{.
HOpMaJrbHbrM
!,,r4 rOrO qrO6SI y6eg,urlca e
He npoTllBopeqHTAetcTBi'Ire,''IbHOCTI{,
TOM, qTO 3TO npeArloJIO)KeHIre
HaAo cpaBHIirb nu6opouHoe u reoperuqecKoe pacllpe.{,eJleHIlfi.
B 6onlurugcrBe cdryqaeBreo,'Iof BaAaer coorBercrBylo[rile K,rlaccbl
pa3MepoB qacrHil u 3arer{ npoBepfler, cor.rlacyeTcflJIII pacilpeie,'Ie'
CKOTIIeHI'IflX
rpaBUs, V:It4 H&
Hr.Iepa3MepoB riacTHII B eCTeCTBeHHbIX
B b r x o A eH 3 K a M H e A p o 6 u l x u c H e K o r o p b l M s a A a H H b I I I r e o p e r l l q e '
B . O 6 e H x p a c c M o r p e H H b l x3 a A a q a x r p e 6 y e r cKuM pac[peAeJIeHLIeM
cfl ycraHoBrirb ccorBeTCTBIieN{e)KAy.
QOpMOI AByx pac[leAeJIeHHIr'
o]Ho u3 Koropblx [o"IyrleHo no nut6opxe, a lpYfoe ,lu6o sapaHee
98
J
A
o
7
I
I
l0
1l
12
t3
1L
l(
l6
tl
IB
l9
20
2l
22
23
tA
25
27
28
29
30
40
50
60
70
80
90
r00
1-64
3-22
4-64
5-99
7-29
8-56
9-80
l l-03
t2-24
l2
AA
l4-63
l5-81
l6-98
l8-15
l9-31
20-47
2l-61
22-76
23-90
2c-04
26-17
27-30
28-43
29-55
30-68
31-79
32-91
34-03
35-14
JO-Zll
47-27
58-16
6B-97
79-71
90-41
l0l -05
I I 1-67
2-71
4-61
6-25
7-78
9-24
l0-64
r2-02
l3-36
l4-68
l5-99
t7-28
Id_DD
l9-B I
21-C6
22-31
23-54
24-77
25-99
,7_r0
28-41
29-62
30-81
32-01
33-20
34-38
35-56
JO-
/+
37-92
39-09
40-26
5l-81
oJ-l
/
74-40
85-53
96-58
LVI-Ot
11 8 - 5 0
3-84
5-99
. 7-81
9-:49
I t-07
l2-59
I4-07
l6-92
l8-31
l9-68
21-03
OO
QA
23-68
25-00
26-30
27-59
28-87
30-14
3l-41
32-67
33-92
35-17
36-42
J / -Ci-)
3B-89
40-l I
41 - 3 1
42-56
43-77
55-76
.67-50
79-08
90-53
I 0 l- 8 8
Il3-15
l2+-3+
trno
/-Ja
9-35
I l-14
12-.83
14-45
16-01
t7-53
l9-02
20-48
21-92
qQ
cA
24-74
26-12
27-49
2B-85
30-19
Q|
tra
32-85
6+-l
DA
OO
27-01
29- t .t
-?c-53
32-00
33-11
34-81
36-19
I
35-48
36-78
38-08
39-36
40-65
4l-92
43-19
44-46
t(
6-63
9-21
I l-34
r 3-28
l5-09
16-81
l8-48
20-09
2t-67
23-21
24-i2
1a
46-98
59-31
7t - 4 2
83-30
95-02
108-63
ll3-14
r:9-56
38-93
40-29
41-61
42-98
44-31
4V)-64
46-96
48-28
49-59
50-89
63-63
76-15
B8-38
i00-43
l l2-33
124-12
l 35-B I
-il3BCf
THO, .nH6o npeAIIo!'Iafaercr{ IlMeloul11t{ onpeAe,leHHutrlTtril.
l p e o y e T c f l B B e p o f T H o c T H b rT
x e p M u H a x n o J i y { ] l 1 ] ' bo r B e T H aB o n p o c :
I I O X i H OJ l r r A B a y K a 3 a H H b r xp a c n p e A e , ' r e H r o
. rrfH
l e c T HK o A r r o \ { yr r r n l ' ?
A i r a " ' r o f u r r H a f3l a A a r l a B 0 3 H H K , ' I ai l p r r o n p o 6 o e a H i . r uB g a , ' I L r B e
- 1 / a i i r y o r e p ( l r r a r O l o p u g a ) , r 4 e 6 s r , r o n p o B e A e H o4 8 H : l r e p e H n i i
c o J l e H o c r nn o B e p x H o c r H b r xB o . u , ( r a 6 , r . 2 . l g ) . l l p e 4 e a p r . r r e . r r , H r t i t
qTo
ts1.13\'ilr'lbHbli{
aHar'iti3 orlix AaHHbtx IIo3Bo.rtIeTnpeAno,'to}KI,lTb,
3HaqeHur coAep)KaHr.rr:i
co"rn n ntr6opxc c r{eKot'opoir n.[ou{aAIr
p a c n p e A e J . ' I e HHboI p M a J i u r o . E c " r r r 9 T a r r i r r o r e 3 a B e p H a , T o H 3 H e e
x
t:
il
7.
99
Ta6"'rHqa 2.19
Hsrrrepenunco,'reHocrr.r
BoA B 3ad'rHBe
Vafiryorep, urrar @"roptl.qa
Puc. 2.33.7,2-pacupeJ,eureHr.re
npH Aecflril
crerreHrx ceo6o.lL'Ic aaurrplrxoeauHori
ripuruuecrori o6.racrtrc, otpaHHrrHBalo.,.^s
(o/
lI(eH C% n.roula.tH no.1 Kpr.lBoll
Colesocrr, rrxr/r
46
37
62
59
40
ir3
58
49
60
56
58
46
47
i2
51
60
46
36
34
51
60
47
40
40
35
49
48
39
36
47
59
42
61
67
53
48
50
43
41
49
46
63
53
40
50
78
48
42
c"reAyeT,qro IrpoHCxoAflTcBo6o]Hoe nepel,leullBallHc u 06)'teil \Ie)liJ.y oTKpbrrbrMH],ropcKriMrrBolar,{rr H npecHoti eo.foir, Brel(iliou{eiI
B 3ar'ruB.C .lp1 rori cropoHbr, ecru 6br c)xlecrBoBa,'I KaKoii-,rltt6ouexaHll3M, rloTopbil:rcTpelrrx,'tcfl6lr pas,r.e,ruTbcod'IeHyloli Iipec]l)'[o
B O A y B 3 a , ' r H B eT, O p a C n p e . l e " r r e H Hceo l e f ) r ( a H I r r r c o , ' I r i I ] o l B o , r I H r T O
nod'iyqI{rb nper6u ero o6Hapy;61.11b.
3To J,a,'ro6br B03N,rou{Hocrb
CTaBr'ieHue
O UrlpKyr'IttqHllBO.qbIIl npeAcKa3aTbTun paclpeAer'IeHllfl
!,oHFrbro
x c a ! , K o B .c n o v o t q l r c c o o r B e r c r B y l o q e f o K p r l r e p l l f c o f " r l a c H f l v o l K H o I r p o B e p l l r b ,H a c K o , ' l b K ox o p o l x o n l t 6 o p o u H o e p l c n p e J , e JleHHe COf'llaCyeTCfl C HOp M ar'lbHliM.
qro coBoKynHocrb onpeAe'retlHi't co,teitoctu, rts.
flpeAno,roxuu,
KoroporiB3ffTa
Hama Bbl6opKa, xapaKTepl{3yercfl Hop'\,{aJIbHbIM
paCrnpe;Ie'rleHVeM
C H e l I 3 B e C T H b l MC p e J , H H I { 3 H a r l e H l 4 e l dL t I { A H C n e p 3Toli rrIIore3e, I(oHeqHo, 9B!'iflercq trPelcueit a2. A,rlrepHaruBofi
IO,'lOlI{eHIle, rITO 3TO pacnpeAer'IeHue He Cord'laCyeTcflC HOpMaJIbHLI\I
3 a K O I { O M .3 g a q e g u e c r a r H C T L I q e c K o f o K p I l r e p l , l f l M o x { H o B b l q l l c , l l i r L , ,
rryTeM noIpa3Ae"'IellHs 06JIacrH OnpeIeJIeHHfl CTaIIAapTHOfO HOpf l a. H e K o T o p o e q u c , r o o r p e 3 K o B . B e p o l r M a r ' r b H o f o p a c n p e A e d ' I e H i 1 -H
HOCTb rOrO, rITO OAHO C,'IyqaiiHOe Ha6,'IioAeHue, I'l3Bd'leqeHHCeIJ3
c T a H . q a p T H o f o H o p M a , ' l b H o r o p a c n p e A e " I l e H r l f l ,I I O I ] a A a e r B 0 A I I H I l 3
oTpe3KoB, paBHa ILIIOqaAi.I nO.I, KpHBol'I B npe!,e,'lax orpe3lia- I'lcIioJrb3yfi 3TI,I BepOflTHOCTI{,MO}KHO Bblrincr'luTb o}ltulaeNloe qilcilo
Ha6rroAeHHir e Kax(AoM orpe3Ke. ONI'rAaevue qacrorbl B Kalli.lo\t
oTpesKe 3areM cpaBHIlBalorcf c coorBercTBylollIiMu Bbl6opoql'lbll'lll
qacToTaMi-i. Ec.[H eru qHcr'Ia 3HaqllTe"lbHo orK,r]oHflIoTcfl oT oi'liHqTo6bl Bbl6opKa 6bLrIz'lH3BreqeHa Tl3
AaeMblX, TO Ma,'loBepofTrlo,
14cnoJb3yfl 12-pacnpelelreHlle. Mo1I{Ho
HopMa,'rbHoii conoxyluocru.
u <<Ma'rloBeponpltgarr BepoflTHocTHbIfi cMblc,rl c,qoBaM <<3Haql4Mblii>>
'THbIfi>>.
Vra:ausrtii
ilryJIe
crarIIcrLIqecKHfi
o
lsl
\ui-Ei)'
X - : l dr , - r.le o; 100
BbIql'lcr'lffercfl rlo
KptrrepHil
-
L:i
'
qHciro Ha6.IllcAellrlirn i -r,r l(,lacce, Fi -
{lop-
(2.45)
oil{fi!,aeMoe rIIlc'rIG
t
,l
g eroM K,'iacce.llpe:no,raraercfl, riro ltlleercn k pazHa6"'IloJ,eHI.tri
K
J
r
a
c
c o B( u , r u u H r e p B a J ' r o B ) .
JrrqHblx
B e r o r i 3 a . 1 a q e3 H a q e H r . rcer a r l r c r l r q e c K o r o r { p I I T e p u t B b I q I i c J g ercfl c IOMOIIIbIOnOApa3Ae,reHua06"'IacTLI onpeIeJIeHI.Ifl Ha6JIIO.lacMbrx 3Har{eHririHa rreKoTopoeqr]c,''iooTpe3KoB,HanpHMeil qeTblpe, Ho TaK, qTo6br IrM cooTBeTcTBoBaJH
paBHbren,'roxlaAi.InoJ, Hop\,ra,'tbHot?
KpHBoti, KoTopbtM,c,IIeAoBaTe,lbHo,
oTBeqaloTpaBHble BeiloflTHocTri noIIa,I,aHaflB coorBercreyrcur,ur?HHTepBa,'LfpaHitqaulI
3rHX IrHTepBa,rOB
C,O O r B e r c r B y r o q u xp a B H b r MB e p o q T H o c T s M6,y I , y T
- o o ; - 0 , 6 7 ; 0 , 0 ; + 0 , 6 7 u o o . E c " r u H a [ r r i r r , a H H b rcer a H r a p r ] . r 3 o B a H b l ,T O M O i K H OO l K r { A a T b ,U r O n p l r 6 , r f i 3 H T e J l b HO
o J,}Ia qerBepTb
3Frar{eHr.rir
noira.rlaer B KaxAbrii u3 rrHrepBaroB. .[,a.tee ro.]cqrrrbrBaercq quc,ro npo6, nonaAaroulilx e xax;1i'rr? r.r33TIx lilirepBa/'IoB,
HaxOALITCfl pa3HOC'tb
N{e}KAy ONilJJ,aelvlbIMH II pea.rlbHL'l\II,I qllc,l]aMI],
a pe3y,'rbTar Bo3BoAr.rrcrrB KBaApar. I(naApaT pa3HocTr.rtre,rrrTcrr
Ha oxr.rAaeMoe rrHCdrIo
rona,xaHHri B J,aHHbrrluHTepBa,l. flo"rryueul r b r e 3 H a q e H l r f cl y M M u p y r o r c f lr r o B C e \ r q e T b r p e Mu H r e p B a J r a l { .E c J l H
c y M M a n p e B b r u a e T K p r , r T H r r e c K o3et - t a q e H u eT, o H \ r . r t e B a qr t i i { o T e 3 a
o r K J ' t o H f l e r c qu A e r a e r c f l B b r B o A ,t I T o p a c n p e A e ! ' r e H u3eH a r l e H I I i ci o JeHOCTTT
He COfJIaCyeTCq
C HopMa,'tbHbrlr.
p
u
c
.
H
a
2
.
3
3
n
p
e
A
c
r
a
BJieH
r i l n l r q H b n in p u M e p 7 " 2 - p a c n p e - l e J e H [ q .
_
C,re4yer orNIerLITb,r{To efo xouxper'Huri BHA 3aBtrclr or q11c,'ra
c r e n e H e r ?c e o 6 o A s r .O A s a N o q u c J r o c r e n e H e r ic s o 6 o n t r B H a u e f i 3 a -faqe He 3aBHCr.rT
Or qr.rcd'ra
Ha6,'rroAeHHii,
Xar 3TO 6brJr0B npeJblAyr u u x K p r i r e p u t x . B a r o M c / r y q a e < < B b r 6 o p K -u > 3
>r o q e r b r p e r . i a r e f o p H H , C p a B H u B a e M b rce c o o T B e T c T B y r o x l r z M
K rarT e f o p l r f l M r cl T a H . l a p T H o f o . H o p M a J r b u o f op a c l p e A e r e H l r q . B H a u e M n p i r M e p e q u c . [ o c r e _
neHer?cso6o.u,stpaBHo_
-rrHCry xareropuii 6es rpex, H;iH B HatrleM
n p H M e p e- e A H H r . r q eM. o r n o r e p s n u : e e c r e n e H a c e o 6 o l l r f r o r o M y ,
qTO AJIfl
HC}I3BCCTHbIX IIAPAMCTPOB
P IT O2 ACilOJib3OBA,'iU IIX OIICH-
xu X u s2 coorsercrBeHHo, a eu{e o,qHy cre[eHt cso6oAsr sa cqer
T o f o , r r r o c y M M a q a c r o r n o I l H T e p B a , r a Mp a B H a e l l l l u q e . K p u r u u e _
c K o e 3 H a r r e H n e1 2 - p a c n p e r . l g / ' r e H r rcfol ,o r B e r c r B y r o q e e l 0 ! / e - i r o u y
y p o B H r . o3 H a r r u M o c r r .(io : 0 , 1 0 ) u o l u o f i c r e n e H H c B o 6 o . r , b rp, a B u o 2 , 7 1 ( c n r .r a 6 , r . 2 l 8 ) .
K a r a . B c , r y q a e , F - p a c n p e , l e r e u r i s ,3 H a q e H r { f 1
l 2-pacnpele"reuHbtx c!'Iyqat?HblxBerriqtrH He r.tMenr uegTpa B HyrileI{ BcIoAv tIoJIoi l { l l r e " r t b u b IT. a x x a r o r K J I o H e H I t o
f l i , t i H i l a e M L Iqxa c r o r o r i t a 5 . ' r r , t : a e r0l
T a 6r naa 2.20
Vafiryorep
B 3aJutBe
C r a u 4 a p r n s o n a H H b l e 3 H a q e H u c coJreuocrr.r
Hovep o6.
pa3qa
I
2
3
4
5
6
T
E
9
10
1l
t2
13
11
lir
t6
17
l8
19
20
o1
22
23
,4
B u 6 o D o qn , u e
3HaCetrjHg
46,00
37,00
62,00
59,00
40,00
5 3 ,0 0
58,00
49,00
60,00
5 6, 0 0
58,00
46,00
4 7, 0 0
5 2, 0 0
5l ,00
6 0, 0 0
4 6, 0 0
36,00
3 4, 0 0
51,00
60,00
4 7, 0 0
4 0, 0 0
40,00
C r a s , na p r u
30BaHllbie
CraxaaprH30BaHHble
3HaqeHItq
3HaqeHllq
-0 ,38
te(
l,31
I ,02
-l,03
0 ,3 7
0,91
-0 ,06
I,l3
0 ,7 0
n ot
-0 ,38
_fi
,7
0,27
0 ,l 6
1,13
-0 ,38
-1,46
-l
6R
0,l6
1, 1 3
-l ,03
-l ,03
35,00
4 9, 0 0
4 8, 0 0
39,00
36,00
4 7, 0 0
59,00
42,OO
6t,00
67,00
53,00
48,00
50,00
43,00
44,00
49,00
46,00
63,00
53,00
40,00
50,00
78,00
48,00
42,00
25
26
27
28
29
30
3l
JZ
JJ
QI
35
JO
QA
38
39
40
A1
42
43
44
46
47
48
-1 ,57
-0 ,06
_o 17
-l,l{
-l ,46
-0,27
l,02
-0 ,81
I
Kareropttg or -0.67 ao 0'0
Ao -0,67
l,B8
0, 3 7
-0,17
0, 0 5
-0,71
-0,60
-0 ,06
-0, 38
I ,45
0, 3 7
-1,03
0, 0 5
3,07
-0,17
-0,8 i
KBAAPAT,
TO
_n 17
-C, iJii
14
O5uee t{ttc,1oHa6JrcAeHI'iiri
O6uree qHc,rio Ha6,'IIoAeHtrft
Kareropur
K a r e r o p H qo r 0 , 0 a o + 0 , 6 7
0,37
0, 2 7
0,16
0 ,1 6
or *0,67 Ao x
I,13
I ,02
r,24
I ,88
I ,45
3,07
1, 3 4
1,02
0,91
I,13
0,70
0,91
0,37
0 ,0 5
0,37
0,05
t la
l r ru
O6u{ee .Iac,to H a 6 r l o A e H u t i 1 3
3HAqCHIIff
J I A C T b O T K , I I O H E H I , I fT
l IINOTC3bI DACNOJIO)KEHA CIIDABA.
B saueu npr.rMepeo6,ra'crl Ha6Jrio.u,aeMbtx
3HaqeHnfi Ao,lxHa
6 r t r r p a : 6 n r a I r a q e r b l p e s a c r r l c p a B H b t M HB e p o t r H o c r t M u . E c , ' t i l
3HaqeHlit co,'IeHocrr.IpacnpeAeJreHblHopMa"'ibHo,To npu6rH3[Te,1bH o 1 2 H o p l l a J r r r 3 o B a H H b3l xH a q e H u t iA o J - t ) K Hnoo i l a c r b B K a x A y I o H 3
qerbrpex Karefopuri. llo nlr6opxe BbrqHcJrfleM
AeiicrBHreJrbHoequcro Ha6.[]oAeHr.rii(qacror troIraAaHI{s),coAepxauIHxcfl B Kax{Aoi:ta3
gTrrx fpYnn. Tar KaK fpynn Bcefo qerblpe, To oxllAaeMble 3HarlecraHAaprn3a'
H r { s q r r c , r a H a 6 " ' I I o A e H Hpi ia o H r , t 1 2 . l l e p n u f i
q H r r r , a H H b r xn o Q o p M y , l e ( 2 . 2 6 ) , r o B r o p q e M o t i 3 A e c b :
(2.46)
Zi : (Xi- X)/r.
npu onpo6oBaHuHB 3aJIuBe
Br,r6opraAaHHbIx,IIoJIyqeHHbIX
cpe!,neroX:49,54 n oIIeHKycraHAaprVaiirl'orep, nMeer oL(eHXy
H o p M a J I H 3 a t l n fH
l a6.4toJ,eHlliI
Z; : (Xy- 49,54)19,27.
-0,17
-0,27
-0,\7
-0,60
-0,06
-0,38
-0, 17
-0,38
-c ,Oij
-0,39
-0,t7
-0 ,:is
8
O6nreequcnoHa6"rloAeunfi
MbIX B KA)KAOI? KATCTOPI,IN BO3BOAI,ITC'I B
102
Kareropns s1 -o
o1
cTarHcrrrr{ecKofoKpl4Tepr.rg
He Mofyr 6urr orpuu,areJlbHblMli.c,reAoBare,lbHo, 12-t<prrrepuftBcefAa qBrflercfl oAHocropoHHLIM,II 06-
H o f o o r K J o H e H i i , qs : 9 , 2 7 . l l o a r o n y
ocyuecrB.lfercf Ilo Qopvy.ne
T a 6 ; rn a a 2 . 2 1
C r a H g , a p r u s o n a H H b l e3 H a q e H f i t lc o J e H o c r t l r c r p y n n l t p o B a H H H e
p a c n p e A e n e H H t lr a K i l M o 0 p a 3 o M '
.[Jtg Fp
' oBepKu rltnore3bl o HopMarbHoM
qro KaxAofi rpynne coorBercTByeT neponrnocrr 0,25
l ra6.{. 2.20. B ta6n'
C r a u 4 a p r u 3 o B a H H b l e 3 H a I I e H I ' { f l n p u B e , u , e H bB
qerblpe
2.21 npHneleHbr pe3yr'rbrarbr pa36r4eHrifl Bceii Bbl6opKri ..Ha
riaTef6-pgri. EC.lu-BbI6opKy MOIKHO Cq1lrarb Ia3B.IeqeHHOit ltS uOp'
varrtHOii COBOKyIIHOCTH,TO Cr'IeAyeT OlKI4LaTb 1tp66,riH31Te"']bHO
l2 Ua6.rrrcAeuuit sa KarefOpIIFO. Blt.It{Cntlq 3HaqeHIIs l{pllrepilfl X2'
nO"IyrI HN'IC"rIeAylon 14en po M Cx{yTOriHbIe pe3ydlbTarbl :
( 1 4 - 1 2 ) 2 \ ( 8- i 2 ) ' : r
( 1 3 - 1 2 )2 '
,
7,":
t2
a
( 1 3- 1 2 ) :
_
|' 1 2 t 2
--
o
22-:
,,
-
1,E3.
2,71 1016-uoro
Buquc.ressoe3HaqeHue
X2MenbneKpurllqecKoro
IpoBIifl sHaquMocrt4
ri oAHoticrereHll cBo6oAbI.Iloarouy Her ocHoeanllli cql'ITarb, tITo paclpeAe,'IeHl'Ie 3HaqeHnii cor'I€Hocru B fioBepxHOpI{a"IIbHOro
HOCTHbTx Bo.u,ax cyulecrBeHHo
OTKJOHfleTCg oT
3aKOHa.
He
npoBepurb rlllrore3y
y 2 Ilo3Bortter
crarnctura
Koueuuo,
To,lbKo o HopMa"'tL,HoMp acnpeAed'leHllIl. Mu t'roxelr npHMeHurb STor
x p t r r e p u i r . [ , J 1 f lr r p o B e p i i l t r 1 4 n c r e 3 L l o J I I o 6 o \ { . x p y r o \ { 3 a l < o i l e p a c -
103
[ t p € J e , { € H I I f lH
' a n p l {N l e p ' T aK o M , K a K J I o l H o p M a r ' I b H b, l 3f iK C I I o H e H I I I I arrblrbtri H r. A. flpu erou npoqe;lypa [poBepKH He lr3MeHqercfl,
r0
XOTg ti]IC,TO CTCNCHCIi CBO6O.1bI B KA>KAOM CTYqAC 3ABHC]iT OT III4CJIA
:
oueHitBaeMr,rx
napaMerpoB.KoxpaH [7] noipo6r{o paccMarpxBaer
3TH BOnpocbr.
o
r0
J I O f H O P M A Jt I H O E p A C n P E A E JETHU E
H APyr[E nPEO6PA3OBAHIIq
rllCTOfpaMNIa,
IlOKa3brBaIOUlafl KoHUeHTpaqltlO
MeAH
B OCalloq-
H O \ ' {D \ : C , r eH a I O X O H e .H a u e l i n p e A c r a B , r r e Haoc r r M M e r p H q H opea c |rpe.le,teHile,THIILITIHOe
A,rtfl MHOfax Apyfax feor'rofllqecKl.{xnepeEc.nu sa6.rrloAeHl.{fl,
rrpeAcraBr'reHHbre
Ha pr4c. 2.34 u 2.35, npeo6pasonarr n .norapzQMltqecKyr,oQoprury (r-. e. nlrecro rrepeMeHu u x X l r c r l o J r b 3 y r o r cn
q e p e M e H n u eY ; : l o g X ; , r o M b r y 6 e 4 a l r c a , u r o
t4x pac-npeAeJreHLifl craHyr
npu6,,ilrszre.ltHo
HopMa!'rbHL,rMr.t
( p u c . 2 . 3 6 v 2 . 3 7 ) . T a x n e n e p e M e H H b r er r a 3 b r B a r o r c rJ r o r H o p M a , ' r b Kat(
OHI1I r{aCTo
BcTper]aroTCfl
B reoJjofHH,
L
a
l'lrlrlllrltlllrlrlll
o
>10r'rc
100 200 300 400 500 6c0 70q 800 900 1000
t ' lp o g g n r i ' r e x o c r b
noJlu , rsrc 6apperei
Prrc 2 . 3 , 1 . f r r c r o r p a M M a p a c n p e a e , ' l e H u qn p o l y l i r l l B H o c r n - H e $ r e H o c i t b l x n o ' ' j i i i ' o r '
Kpblrblx n ,Il,eueepcrou 6accetlHes 1969 r'
35
s
30
^ t(
{d'"
6on
fil
T :ZYtln
r.r
I(t'i-F)z
t
"z:
.
10
120 't40 160 180 200 220 24
Cu,r/r
TO J'tofHop-
Mar'rbHoepacnpeAeJreHfieB BbtctrrerlcrcneHI,I Balt(Ho. O4uaxo ec,rrt
o f p a H Hq r i T b c r rp a c c M o T p e H r . r enNp{e o 6 p a e o n a H H b r xn e p e M e H Hxb r Yi ,
a H e c a t r r i x X 1 , T o c s o r i c r e a r ' r o r H o p M a a b H o rpoa c n p e A e J r e H r iM
g olKt { o n p o c r o o x a p a K T e p u s o B a r cbc t r n x o f t H a H o p M a r r b H o pe a c n p e A e ,reHIre.
C p e r H e e r r A r { c n e p c r n , l o r a p u s r a u q e c K un p e o 6 p a s o e a H H o ini e p e u e H H o r i Y i H a x o A r r r C fol 6 b r q H b r M
cnoco6oM:
(9
n_l
O , l u : r r i o B r e p N r r r H a xr i c x o A H o ! ' H
r e n p e o 6 p a : o e a u H o rnepeueuHoft
.i
X;
104
o
on
J1s
MCHFIb].X.
I aK
rF
J00
)I
o
q
o
t:
,\'lHorre feo,'Iofr.tqecxt4enepeMeHltr,teoqeBHrHo He IrorqilHrrorcff
H O p r , r a J b H o Mp) ra c n p e / i e J r e H H FEoc. n H , u a n p r . r M e p H
, a H e c r r .H
r a rpatpux o6'leubr Heqlrflr{brxrroJierl (puc. 2.34), ro no.tryueHHoepacnpeAeJIeHre 6yaer s ntrcrlefi creneHr.racHNlMerpuqsur,r.Eo,rturrrHcrBo
r t o r e i i l r a J r b rr r o p a 3 M e p y , H o u M e e r c q y 6 u s a r c u q a q f l o c d t e A o B a r e , r b u o . c r l 6 o l e e K p l , n H b r xn o , t e r t , H e M H o f o p e A K H x r H t a H T o B ,K o r o p b r e
3 r J a q H T e , l b Hnop e B o c x o A f l TA p y r H e n o o 6 r e u y . f e o x u n r u q e c K r . r e n e pe\reHHbre,rroABepfHyrue onpo60naHrrroB Ilpollecce feoxlrMr.rqecKoI ' o I I C C ' : I e A o B a H HHf a
i ' I I p i l M e p 'T a K I I e ' K a K K o H I I e H T p a I { 1 4
f l J I e H aB
ce
r,raTepr.ra,le
rrr'ril KoHrleHrpauHfl r4oJ.a, o6Hapy>xeu_
PacTriTe.rrbHo\r
l r a r B n p o 6 a x r p y H r o B b r x B o A , T a K X { e r t o , l q r H f l r o r c f la c a M M e r p u q HbrIr llaclrpere,'reHHstB
r . p a c n p e , l e ! ' i e H H f lpxa 3 M e p o B3 e p e H B o c a A r i a x r ; l r i o B b t p a l K e H aa c I . I M M e T p X fUl , r \ e J l a f lc, l r c T e M ax . n a c c l t s u x a _
c fal 3 r o M $ a x r e [ 2 1 ] . r r a p H c . 2 . 3 5 n p e j r , c r a B r ' r e L r , r r i.r- r . ' H o B b r B a e rH
HbrNlil.
F
i
6
r
lia
F
F
200
!c
2.35. fncrorp:rr{rr
C o ; 1 € D } t { a t t u rM e ; l l t B o c a r l o t l H b l x n o p o . l a x H a n " ' I o u { a . l i l
Hauceu n lOxoue [291
cpel.liec Y cooreercrByer I{opH:lc_
n-fi creIleHLIII3 npot43BeAesvilXi
l:ct't:
n/
t' TIX,,
(2.48)
x o r o p r r i r r r e 3 b r B a e r c f rl e o M e r p l r q e c K u Mc p e A H v M , G M . C l t M e o n f I
a H a . l o r H q e H) , t o l s K o o H o 3 H a q a e r ' r l r o S J I e M e H T byl K a 3 a H H o f o
Bcr'le.(3a HuM psAa nepeMHoxalorcr, a He cKJlaAblBalorcfl.fI rax)l(e HMeer npeAe,lbl, aHad'IotriqHbte
reM, Koropble Hcrlo,{b3ylorcflnp}l
3 H a K e c y M M l r p o B a H n s> . t r 4 s o r A a g r a n p e A e J I b I e, c J I I t o H l I o q e B I I A -
t05
l-
,ru
f
o ,oo
o
2s0
r
Y
^^l
o
rf
L
*.
urf
(t
o.o^r
r0
):
';I
o
t
q
O
aaqn
o.,""
,!
\o
s
J
'
noolofnrru"o'.oro"l
r"," J3ffju,e;r00000
I
q
Pac 2.36. fxcrorpaMr{a pacflf
Macura6
QreHocHnx no'reit, O r .
KpLIrbIx ff.ff;i'.X Jf "#J:i,itT' f nHe
. l c r a p u 0 u "'
u.recrufi. B3qro x: xap6yxf
AaBroKa, .U.eBllca
i-
s20
.i = l,30to
s = 0,4123
n=158
d_
F
a10
5
t-
I
o
ra"o
aa
aa
,t,
c
oj
aa
a
a f :.%.20
30
40
50
60
[ 1. n o u 1 a g r , r b r c . a K P o B
xyno;r3ule 'rlync co'rflHblMu
Puc. 2.38.O6teuut He$rnuux garexefi, cBt3aHHblx
ure,ll$e (Mex''rxancruii sa,run). flo ceirc'
3uaHe Ha BHeuHeM*ont"na"tirouou
Mltr{ecKI.tM AaHHbIM
1,6 1,9 2,0
.1,4
(coAepHaH e Cu,
Pnc' 2'37' fumorparttratooto*ft111n*15-"""3:'ooq''x
flpe:crasaeHa a .roraplsMlrvecxov
uacura6e
nopoaaxHa n'roulara
[29]
I{bI, onvcr(arorcfl.Tax,,t
r:e .y,:2, Xr:3,
Xe:4, paBHo
i : r ",.
fIXr-2X3X 1:21.
noraplis-\'-rrr,ecKrr
ripeo.6pa:onasHor:i
neperreuHori
Hag----4]orrprrrn
brBaer crr reoMer it uqecrrcii :I rrcnepcireri irc nu,,
na.terrr ira
si.:s?:T'"r(#)
(2.491
Ha nparruKe, rioHeqHo,
npou{enpeo6pa:oearbHaurr sa6nn,l,eHas,
83rB r.tx.norapl.rrfivtul,
H 3are\r Bbrqrlcrtrrbr.i_\cpelgee
II AncnepcHto. Ec.nurpe6yerca__:1111
reo.lrerpHqecKoe
cpeluee H Aprcrepcrrro'To Hai10B3srb aHrilJrofaprrsr,rr,r
or y u s2i.40 ia*-nip nonu
106
V t r p a 6 O r a e M C A a H H b I l . l ua n p e O 6 p a 3 o B a H H OBM[ A e , B C eC T a T I ' { C T I r nepeMeHHbIM'
K O6bIKHOBeHHbIM
qecKHe [porleAypbr, npHMeHrreN{bre
nepeMeHHblx'
npr{foAHbI tt r^Jrfl..norapaQltruecnlt npeo6pa3o-BaHHblx
q
r
o
,
r
o
r
a
p
n
Q
u
t
l
q
e
c
K
o
e
n
p
e
o
6
p
a
3
o
B
a
H H et t e p e M e H .[,o6as]rta eilIe,
Hbrx rioJre3Ho,ecJIH rpe6yercr cTa6lrJllr3npoBaTbAucnepcurc Il TeM
ca\{blr\1npllBecrll [epeMeHHyIOC aCIIMMerplIllbIM paC[peAeJIeHxeM
x 6olee i"*r.tp"oecKo,My er.^y. Ha pnc.-2.38 rpeAcraBJleuuo6'sKynOnOM Ha
c COJISHbIM
eNrbr 3aJ'relKerlUeQrU, aCcOqllHpOBaHHblx
3rr'r
Jlyusuauu'
ue,'rroa
i]JrorraALI BHe[IHero KoHraHeHrarbHofo
o 6 r e u s r s a . n e x e f i H a H e c e H bHI a o c l i o p A H H a r r p a Q I t K a ; H a o c t i a 6 c qlicc orJrolKeHblnJIOx{aAucrpyKryp' B KOTOpbIXpacnoJloxeHbl 3a'
Je)Kr.r.B o6utelt c,{yqae r.rMeeTcflIOIOXUTeJIbHaq cBt3b }IexAy
r. e. 6o;ree {Pyunue crpyKrypbl o6uqso
fByMs nepeMeHHbronir;
coAeplKar- 6o.nee KpynIIbIe 3a,'lexu. OAuaxo pa3Mep saJIelKlI raK'
l.Ke yBerr.lr{lrBaercqIIo Mepe yBen1lqeHHspa3MepoB crpyKTyp' HJII{'
rtpyfHMr.l cJIoBaMu, sa6nrcAaeltas AHcIIepcEq rIponopIlHoHaJIbHa
cpeAHeMy.
107
1000
100
o
q
O
atn
rct
I
q
01
o,ot
o,t
1----io
ltnot\aAr, ro,.
loo
"tX.ooo
Pac. 2.39. Iaaur,re prrc.
2.3g, flpe.qcraB,[eHHbre
B ,,rorapHO]r'qecKoM
lracrura6e
rr_oMof
"#J11lT:;;:^":r{aKnpeo6pa:oeaHrie.
aer cKoppeKrupo_
_
3ro ,rerno 'B,..rer6
"rrf o6ren 3,r.r€rir,
,,u p,,.._.ii56. go..o
xaK
1eM'x.''o'.,
p,i,1,''o
1.i {:{f;*l,l;ffil.l;ryi#*ru;l
norapu*nta f,trtinepc*la
no.'up"q^r;"" oo-ua'os sa,rexeri
noqru noctoqHHori
ocraercfi
JJrfl u
B!Cv e^ x
Js iH1adqqeeH
HrIII lorapuQlloB
crpyxryp.
pa3MepoB
Xaparrepucru,r,l,,...::llopN{a.rrbHoro
p:lcrrpe;te,,reurrr
paccNrorpe-
t-ull.:o"i
', spuii'"o
l2li n,*;;;;;,u;;lio,,
ill,;.YftRX{1"j,
,,o".
gi,".""
:loqori
.";:;;;:.;,ii*;1
,"jl;o#jJ,"&"."
ru u;:l.m
(rrrxcuponaHuori
:r ffi-i."ti
ae,rliqr,"o,
y:l.t' " nn".,i.
r-."1er q;i;K;!:a
q,,;- ;' iT#;.''il#.:i'j, :.f,:|ff
c
Kdr
atr
bI
"1"
B
aFo i
u1-"
1o"''
ffii;:1" :'i; o1;,'
" .:^ -l:-ll.p.'i".;n, i,.,"ti;
a M \ ' . r r b r u n , r H I { a r u B H b t . 6 o ; r u r u l r H c rco, o
r y , u a i r H b rB
x o3\tyueurrii, neleMHo)KeHHbIXBMeCTe,AaIOT rrpoMe)KyrorrHoe3Har{eHrrenpor.r3BeAeHttfl, 6rusxoe K reoMerpl.iqecKoMycpeAHeMy. B pe,lxux c!'ryqarx
n p u c , r y u a i i u o l r n u 6 o p e B C e B o 3 M y u I e H t r fM
l oryr oKa3arbcfl oqeHb
I{ Irx npor.r3BeAerrire
Nra,rrbrMI{,
6y,ter 6.[Hslio Hi'.trc. Tax xre peAKo
Bce Bo3rvtyqeHrrfiMofyr oxa3arbcfl 6o.urunuu, H rrx [pou3BeAeHrre
6,v.ler 3xcrpeMa,rrbso6o.rluur,t 3HaqeHHeM.Pe:_v,llrarol.t MHorr.rx
c,ryqatigux pear'rn3arIHli6y.rer pacitpeAeJIeHt,te,
Koropoe HaqI4HaT O c B o e f o M a K c H M y M aI,r 3 a r e M C I I y C K a e r c f l B H y , ' I eH B O 3 p a c T a e A
e r c f l B H H 3 ,A o c r x r a f l a r { c r p e M a r b n o 6 o n l u u x s u a q e u x i r .
Elro,rorn qacro ccr,r,rarorcflHa <<3aKoHrrponopr{rloHanrHoroeQnepeMeHHofis reqeHue
clexra>>,cocrosultui B ToM, trro Lr3MeHeHr.re
n p o q e c c a e c r - b c J r J :aqr l Ha s s e r l r q r r H a , r r p o n o p u l r o H a J r b H Ia.f{lc x o A H o . a n p u n a e p ,B e p o r r H o c r b r r 3 M e H e M y 3 H a q e H u r og r o i i n e p e m e n H o r i H
H f i f l p a 3 M e p a x o , r o u a i i n u x p o 6 o n B o B p e M e H H o inr p o v e x y r o K n p o r r o p u n o H a i l b H ap a 3 ^ \ , r e pxyo , ' r o u r r i iB n p e J . [ r e c r s l ' n q n r r o r p e 3 o K B l ) e l'teHn. 6orrruile r(o,'IoHI.rlr
crpeMflTCr pa,cixlrprrTbcs (u;ru yMeHbruurrca) s 6o,'Iuurer?crererlr, qe\,r Ma,[bre Kor'roHIIH.BosN{oxHo,
HeQrrHure Mecropox{AeHr.IQ
r o p u a p o s a , r H C br a K t r N I x e o 6 p a s o l r ,
TaK r{To B TeqeHHeMufpaqllrr }'f,reBoAopoAoe6o,'IrulHe cKotr,'IeHrrfl
crpeMlr!'rncb )'Benfiqr.rrbcfl c rrponopll.HoHa'lbHo 6onrrueli cKop o c r b l o , q e M 3 T o n p o r r c x o A r J l o c M a r ' r b l M ac K o [ r e H l i q M u . T a x n e
paCnpeAeJIeHI'1!O.
npoqeccrr rrolqrJHflIOTCsJTO|HOpMaJIbHOMy
rr ^srr,/rur
^ - ^ - ,rr,
, IJUJruulI(HO,
MeHee 3HaKOMbIC <<reOpAeilApO6"leHttR>>,
i t o r o p a f l [ p e A c K a 3 a J r a3 a p a H e e l r o 6 r q c H l r , ' r a , ' r o r H o p M a , ' r b H p
oa
ec npeAer'reHueAJrg pa3MepoB rlacrtr,t, Koropbie ga6,rrcAarcrcfl B ecTecTBeHHbrx
ocaAKax u B LI3Me.rIbqeHHoNI
IlIaTepIIaJIe,npolr3Bo,tt{Mov
\ { e r h H r r r { a r { nr r . 4 p o 6 r n r a u u . l l p e r n o J r o > r ( H Mq, r o B 3 f f T H a 6 o p u a c r r i u o ] r H a K o B o r o p a 3 M e p a H 3 a r e M K a > K A a f lr r 3 H r r x p a 3 A e d ' I e l r a
c , l y u a i i u n l t o 6 p a : o u . B o 6 q e r r c r ) ' q a e B p e s y J r b r a r eo A H H l . r s o 6 ,troMKoBrax<roii ucxog,uofi qacrurlbr 61'eer 6o.nrure, apyroir - MeHrrue. Ec,ru 3areM riaxAuli ti3 srr{x o6.ronrxos cHoBa pas4po6rrru
c.,t1:v311ttot*t
o6pasotut,To It3 r{a,rtbtx x}:cKoB rIo,'I)'qarcfl eule MeHblxue, B To BperlrflKaK riax{.qbrfi6o,rlurori o6,nouox 4acr cHoea 6o,rltLlnrlrrr yestmnir KycKr4.Ec,rn eror lipoqecc rroBropflTb cHoBa tr
cHoBa, To B pe3)'.[brare [oJ]yrrltM oqeHb 6ontruoe q[c,rro oqeHb Maq a c r n r l r { H e M H o r o < < u : 6 p a u H u t x )3>e p e H , p a 3 M e p b r K o r o p b l x
"qbrx
5,ru:trr K lrcxo,lHbrMpa3MepaNrqacrr.rq.[p1 rnrra c,'IoBa[{a,'IorHopN I a . r l L r H Opea C I I p e A e . 4 e H H er { a C r O u a 6 , r l O ; a e r c n n p l l
u3yqeHHII
j:+,:t3;;"$!;iTF,:""#ff#:;,:l
l^:;I*.*u,1,:*i:
BpeA
Krr
x c.:i
y,{anx
rr[,{eTbor,r{H H Tor
ru',:.;:[.;l*T;'
'"oan'nr*o,
I iif".,;J,|ft
::f iyb
",X*::
sHaK, rr ,o.,ij
glicrpe}ra.r'bHbre
]re
ni *' "J'i'luo'o*o'ooop,* o"'''i i,i. nopffit'#: r?:: r:H::n oo'
J l o f H o p - v a r ' r b-H opea c n p e - l e . t e H r r e
o6.crosre"rr.tuu i.r,
",
108
lrox
b,r1,
uariur,re ;;r?.,"i.,.j,j!^" r;:t :ff
,,i.":;i;
O C AI K O B .
IpyrNe npeo6paronaHun
, [ , r a n o , r y v e u u R n p u 6 , r r r 3 u r e . [ b t { oH o p M a , r b H o r op a c n p e A e , ' r e H H f
i n p o } { 3 B e c r [ r a K x e r ] e x o r o p b r eA p y f a e
r { o ) K H oH a A n e p e \ , r e u n o fX
; r o e o 6 p a s o o a H l l f f ,K o r o p s r e n p e o 6 p a 3 y o r A l r c i l e p c u r or i 6 o n e e n p u 109
eMneMoMyBHry unn
Aaryr HeKoropbre,.rpyrse
rre3Hbre
crarncraqec6rie110_
pesy!r:13]br'xoii
o"r^ .-*."o-o6
rrrxartre
HcxoaHoii
Ii3MepeHHr,
""r".o';. qyBcrBoBaTt
Ho Mr,rl"ir_"i
ce6s cso6oAHull[r
-cio
:"'f#f;; ""J,ffilT'i, Fmf : "ry'un",i 1J.- 11*ocnery"""'J pa3rH'Ir
b*;.'nH"'#1,T.'i
I AriflH
"ilil::J
il:fff J#.","""0,1
ii""1'1::
xapaKr"py.:l:r_^
npeoopisoain"o,*
r{eHHb_rx
nupu_
ofu.to
en""i"oani'*nepe*n6n,o,* Kinlo;;,"H:fi:{";;#3ffi31"uo'"
" ".
o roM' qro6u
npeo6pasonanirn
tcrloJlb3yelrbre
ue
6ttnu nr..orf"
n
p
p
oa
,,..* ;'g;#'i. " uu.*ornio'i:; J HHilTJJ#.?","
l:lT;i.i
6o,1,
Hanpr Mep,qHcrro r po.
, u.'"'iii# T,l"#.XX; ;i :#: ;:T ; f,1.-..9
u,;;;;"'";l:";:i:].iltr"if,j..t;:.
$fi..T',;[,f;^y:.y''noa
npaBecru".";1i..,';#il',"T,,"Jriffi
i?#l;hru;*"i:
Hux xBaAparuuftro,peHu,
,. .-."iu*"ioe3HaqeHHe
X;_saMeHflercfi
l',: VT. Oro np_eo6p
Ha
a3oB
aHr{e
;;;;;." A'cnepcuu6o.nee
HbIM}lu np[seAer
o.qHop
or xBocranyaccoHoBc'ofo pacrpeAerreHr.rr.
X191lrt1e""fr-an""noro
Ec.nz'ua6r.auilor.,rruu"na"-".'ili.o"rru
x,.irl""ru, uu"
y;#W'*"#
v4o6uee
np.oopurouu*"u
y,:
)HHoB Tex c'IytIaflx,KofAa
nanoroporuna6,rrcAeuns
paBHbIHy,rilo.
Po6auco' f2sl pe-KoMeH^yer
Hcrrorb3'BarbcreneruHoe
pa3oBaHHe,
npeo6Hanoar,aep
J i_=1x;2-,'yi:'ij_"
raree, nplr BbrflBJreHHJr
nerpo$u:rzvecxixcnoricrn,
"u*
no
-n'?ororua*y
iunn"r
KaporalKa e cxeaNrlHax.
lJo3BereHueB crerreur np"goA*"
rrrrrxsHaqeHar?,
6o,rirseM uanix. E.n"'uol"aaeuae yBeflHrreHHp
,i
Hqrb nocre H3MeHeHHrI
nprrMe_
,uarrr6i ,"un, oro MHo)KecrBo
"ian.nogHaqenlrri
(I-r*-yrin) 6vlerraxrrM,)Ke,
* u n , " o o ( e c r B os u a q e H H t
Hbtx repeMeHHsix
Hcxo-t_
"
'r.pirru*
6y4er 3ar(,rrroqarbcn
.l{y^*-x^';);^;;'seeexr
B roM, rrro Ha KaDoraxHb,"
gi
6},lyr floArrepKHBarbcfi
o6"nau n BbrcoKrzx
suaqefir'rir
yqacrK', rAe 3HalreHrrrr
HA3KH'creneHsoenpeo6pasonu"il
"r"oi"r"rbcfl
u*aar raKoe xe BJllrflHHe
pacnpeAeJreur.re
ila
AaHHbrxr.tMoxer 6uri
drr
eHHs orprruareJrb'' fi ; ; ;;;;;
"d^ti;f"" ""1iJ",
f lt, " ;:',1l;
rlpuBecrrrK vBeJruqeHrrro
" luan"pi"""?' a,q"narb
ee seoAsopoAHori.
Orpuqare.lbHoacur,tMarpr,o"oa"
puanpuAa,rallrie
rrHorAaMo)r{er
Ennr, npu6na)Ke'Ho.rpeaop'ri"."a5,-",'
i" u,oprrnbrroe,ecr,rlrnpr
H n r a n p c o 6 p a 3 o B a r r r r e _i r]cr ,. :i "
Me_
X ; I i-ipao6pasonnrrlr
p " , r o " r r c \ o . l r b r er e p e r i e u Hbre j.o"rr)hHrr
6rrrr_ npc-{Baprrrenoiior ,,,,.r, ts
n,i, u1,,,.
.
;i :f,": ffiJi;T."iT, (?:t l,;,i;t"t);,# jfi 9: ni'eoopaao
".' u
uirr 6aHo
r,rr.tiruri
*o.o pacrpeAe,ren""
u
npeo6pasoe
a-
"-o'ff,il""ti:
H E N A P A M E T PqHE C K I ,EI M E T O A b I
napaMerBce npeAuir)'ulle crarlrcrnqecKpre Mero;r,blflB,tlflFoTcfl
xacIIpeAeJIei a x a p a K T e p I . r c r l i K ap
p t i q e c K I r M t iT
, . e . o H H o c H o B a H bH
IipIITepIIII
Hrrfi, napalterpbl IioropLIX II3BecrHu. Bce IICnc"'Ib3)'elIbIe
coBoK}'nuocreii.
(t, F tt y"2) crponrcfl nJrn ett6opot' II3 Hopr{ad'ibHblx
fl,1:r o6ocuoBaHIrfl Bo3!to;'I{HocrrIIIcitoJib3oBaHrIr3rI{x IipHTepl{eB
rle fiB,'IfleTcfl
E Te.\ C"lyqasx' KO|Aa IlCCJIe.l]'e\{agCOBOKyIHOCTb
qro o6telt nu6optlt Be".'IIIK
II coBoKynHopMa,'IbHofi,npn ,vcrtoB14Ii,
IIOCTb He OqeHb Clir-IbHO OTJIUqAeTCf OT HOpMa,IibHOll'
Cr'tP.lleT OOpa-
Tnrbcs K IIeHrpailbuoft npe4e"rnHotireopeue. I4uorAa, oAHaKo, IiccoBoK-vnHocrbMolKer cfi,IlbHoOT,rillqarbcgoT HopMa"'IbcJIeA,VeMafl
Itoii,'u.rir.txe o6lert out6opttu He,'Ib3qyBe,'IllqilTb.B raxilx cJy*tlZlflx
, a 3 b l B a e } l b l xH e n a p a cr'reAlero6parHrlca K Kareropfii{ xp}lrepl4eBH
KpHrepIIgMH. I'IX :vtoxso npiIMeCTaTIICTIIqecKIi]1il
r\leTpriqecKI{NIH
HflTb AJifl o6pa6orxlt r.rHQopmauttr6onee HH3I(lIx IIIKaJI,TaKHx,KaK
I1 nOpgAKOBbIe
HOMItHaJIbHbIe
AaHHbIe,B OTJIHqlleoT IueTpHrlecKIIX
crarucrilxe' He tpeB
rlapaMerpliqecKoii
llcnoJlb3)-eMbix
AaHHbrx,
5)'ercs HaKaKHX .lo,n),u1euuilo BHAe HcxoAHoro pacnpeAer'IeHl'1fi'
- HenapaMerpliqecl{I,te KplITepI4H' Boo6nle,
orcloAa Ii Ha3BaHIre
B r e x C d r t y q a q xt i,o f A a n t t 6 o p O u H a r C o B O I { y n H o c rIbI I { e e Tx a p a K T e p I I ' c r n K l r , g e o 6 x o l i r r l t t e B n a p a M e r p l l q e c K o Ma H a d l l l 3 e ,H e I r a p a M e r p I I qecKlie l{plrTepHIloKa3blBaloTcflI\IeHeeMoUlHblNIl{,qeM 3KBTIBaJIeHT'
H b r e n i l p a M e r p r r q e c h r l e .O A s a x o e c f l u n u 6 o p o u H a q c o B o K y [ H o c r b
e eH e a l r c e r c n e q H Q l r u e c x n xx a p a x r e p n c r l { K , H e n a p a N i e r p f l q e c K nM
To.{,broria3blBalorct 6o,ree &IotrHbr}II{.
HenapolterpHr{ecKr.ieKpHTepaHB reo/rornrt ulipoxo He rtcro,IIb3oBaJucb rr o6r,rqso He rIprIBoAflrcq B 3,'IeN{eHTapt{nxyue6uurax
c r a r r r c r r r K r r .O . x i r a r i oe c r b M H o r o t r p e K p a c H b l xK H H r ,B K o r o p b t x o l r E C a H b l F l e n a p a l l e r p l l q e c i ( u e3 K B H B a r ' I € H T bnI a p a M e r p I I q e C K I . I XI I p O '
I { e f } ' p , v } K e p a c c \ r o r p e H H b r xH a M r r . C p e l u H H x M o x u o H a 3 B a r b
riHr.rrl3
i r r r e n q 1 3 0 ] , E p e an n [ 4 ] r r K o H o e e p a [ B ] l i a p .
Mausa- Vuruu
Kpnrepr,rfi
liprrreplrii XlauHa - VHrHlr r{o)KHo ricfrolylb3oBarbKaK HeIIapal\ieTprrqeciirir:r
elinLIBa.'reur/-xprrrepHfl !"ufl frpoBepKH IrI[oTe3bI o
taBeHcrBe cpeAHrix 4nyx nuSopox. flpelnor'ro)KlrM, qro ubl IIMeetlI
g n e e u 6 o p x n o 6 r e u a t n v n n x o r u r { n p o B e p t i r b r r . { n o r e 3 yo r o M ,
qro oHlr rBirflrorcfl nur6opxaltn n: o;lsoii n roii )Ke coBoKyrluocrl{.
3HaI{eHLifiHa6lrcAesuii
O6lelauult
o6e art6opKu H pacno.'Ioi'KI.IM
B nopsAr{e Bo3pacraH}rr or }IeHbuero x 6o,rrueuy. Kaxlouy
u a 6 l r c A e n r i o n p r r n r u e M e r o p a H f , T . e . H a H M e H b u e M y3 H a r { e H H } o
fiplrfl]rueM paHr l, cr'reAyicqer{y tro BeJruqiiHe- y:awr 2 II TaK Aa.ree, Jo nau6o.rrurero Ha6lru1ettttfl, Koropoe 6y''aer IlMerb paHr
( n z + n ) . E c " ' t t io 6 e n u r 6 o p x u 6 u i . ' r t .Bt 3 f f r b l i r : o , l t t o i l i l r o i i ; . K e c o B o .K),nHOCTII
HayAaq\" To i\4oxHo oxiH.IaTb, qro ua6"rrc.LeHufloAitoil
ul
Ta6nuua2'22
Kpuruuecnue3naqenrs Ant l(pureplls MasHa-Vnrun [8]; snauennnnpuBeAenbl
AJrfl HuxHero Kpl{rl'rqecKoronpeAeJla; coorBercrBylourlrfi''npeAe.tlAr-fl BepxHeft
e l}l
xprrnuecxofi nJIolqaAHAaercs 3HaqeHleMfr-d:/ttlt-l
-:rl,
2 .01
.05
.10
3 .01
.05
.10
4 .01
.05
.10
5 .01
.05
.10
6 .01
.05
.10
7 .01
.05
.10
F .01
.05
.10
I .01
.05
.10
l0 .01
.05
.t0
1l .01
.05
.10
12.01
.05
.10
13.01
.05
.10
1^ .01
.05
.10
.01
.05
.10
l6 .01
.05
.10
t7 .01
.05
.10
I tz
0
0
0
0
0
I
0
0
I
0
1
2
0
I
2
0
0 0 lo l0
0 Ut l t l
I I It -t t ;
0 0 l0 lo
I I lz la
l4
2 I
0 0 li
1 z lL;D l 4
A Itr
0
2
0
J
^
I
0
2
o
I
i
o
o
(
h
0
,
4
0
2
4
U
3
5
1
3
I-r
I
4
5
I
4
6
I
4
o
I
4
7
7
2
6
8
3
6
I
J
7
l0
3
8
1l
4
8
ll
4
9
12
t0
l3
, u| , nl r o
li
l0 l0 l0
l1 lr
tzt9l z I 2 l 3 u
ls IA
t;
I t lr ll 5
3
l r ti
: l4
lu l8
lr)
l3 l; ti
l0 lo
I
4
6
4
I
4
7
5
z
5
8
l4 t4 l5
lo
lc
6
lz
t2
l
7
l
b
t;
Ii
l6
l5 IB
l e I t o t 1ll l-l o
l1
t,
l
'
^
7
l
6
l
4
l
6
t:
l9
ll0 lll tz 113
lo lo t7 lB
23
l
r
q
2
l
l
6
l
r
o
l
t
7
llt
ll3 ll4
l6 I7 l8
l5 lc 17
I ll -, l 3 l 4 l 5 l o l 7 l d l q 1 1 0 l 1 t 1 ,
2 3 21 26
l 4 I I A 1 7l i e
l
9
l
7
l
6
1
1
2
I
1
1
3
1
1
0
l
D
(
2B 29 J t
1 4l l 6 l l B
2 l tt ,2^ 3
l o l s lt q
: I t rl l 3 |
lc
l 9 20 o l 23
IL
l o t 7 I B l r l l 0 l t 2 l l 3 t 4 Il cl do
A
27 29 t t l
22
l o l 8 l e I r iI r al l 5 1 1 7ll 1r- e-81I o2A 026
I t,R
39
D/
6 l 8 [ 0 l t 2 I t1l l 6 l 1 81 2 0
|
qi
25 27 29
ta ls l7 ld ll0 ll9 113
l 1 5 1 7 1 8 20
27 29 3 1 34 JT, 38 +o
5 t i t q l t 2 l t 11 1 6l i 8120t 9 9
11
7 q II ^r-, ,I l 4 t l I r q ,, 124t ; i 29 3 2 o+ 37 39 4 2 4 4
e
33 35
t 4 l l 6 ITB2 l 23 25 27 29
5l7 l8 l0
,l
q
l e z t o 32 34 o t 40 42 4 5 4 8
f)
l i l 1 1 4l 6
.)( 1 2 4 34 q a 4 0 4 3 4 6 4 9
8 l l I t 4 l t 7 20
lze
l3l
1'7 I r y t 9 ,
4l
A
24 27 29 32 31
6 l 8 Iro 1 2t l (
51
t
.
)
9
40 4 3 46 4S
t 2 6 3 1 34
i9
7 l0 113
Cr.t
29 l e z'JO 39 4 2 4 6 49 53 56
23
10 l3 ll6
48
39 4 '
t 4 1 1 7 20 lzs 25 28 3 l 34
+
7 ta
^
,
63
56
+
c
49
3B
2B
35
2
l
25
8 12
l e z 44 4 B 52 D D 52
l ,,
l8
7T
59 63
25 29 33 o t 40
l1 t4 ll8
4B 5ll <1
3B A O
5 8 1 1 0 l 3 l 6 1 9 23 26 29 32 35
5B 62 66170
39 4 3 A A 5 1
I I D l t 7 20 24 28 32
l o l o 20 9,1 28 32
5B 62 66 70 7 t l 7gi
4 1 .tD 4 9
61
6 I 1 2 l 5 I B 22 t ( 29 32 o o 39 4 3 47 50
7,9
35 39 4 3 4 B 52 56 6 l 6 5 69
1 0 1 A I B 22 27
E'o
E7
lo
l 8 22 27 3 l 36 4 0 4 5 50 o+ A A 64 68 7 3 7 B
4 8 52 56 60 6 4 168
36 4 0
1 7 2 1 o 4 28
o 10 ID
1 6 20 25 29 3 4 38 4 3 4 8 5 2 57 62 66 7 l ztil 8 1 18lr
ll
!)0i 95
t 4 t 9 24 ,o 34 39 44 49 54 5 9 64 69 a q EO .351
oi) 39
4 8 52 57 6 I 6617011 t
7 l l t 4 1 8 23 9 7
B3l 8 B lo ?
t 2 1 7 22 2 7 o z 3 7 )42 + I 52 5 7 62 67 72
o 9 i 8 l 03
4 r l 4 B 53 59 64 7 0 t , B I
1 6 2 l 26 32
:917" " 1t l e761
-^l
8l
4 3 4 B D z l57 62
B l 2 l 6 20 2 5 6 0 lo + 3 8 1
t o l 9 5 10 1
56 62 6 7 173 781
t 3 l q o n 29 3 4 1; o l4 6 5 1 1
"wl
^-l
q
a
l
1 7 ; ; l 28 34 4 0 1461
0511 1
5215 8 164 6 e l 8 l d^ -/ ll o" "?1l
o / l 721 771
831BE
1 3 ll t I t ; ; l 3 2 13714i--9 |1A7 F.q l o / l
^^l
Y O I 02108
4 34
1 s l5 b l 6 l o o l t z l 1918^ , 41 l
l D l 2 0 i26 o r / 3 7 1
9Ll I
I 071l 3 l 20
6 2 i6 8 17 5 1d l l
1 8 l', aA l I 30 3 7 14 3 14 q l
"^l
'7('
B3l 8el9 1
e l 1 4| 1 9 1241-r" q lI 3 4 13 e 4l 5 15 0 1561D l l to :/ ll I
I 031t 0 l l 6 j
1612 t l , z l 3 4 14 0 14 6 15215 8 16517 r l 7 8 l8 4 1
i 141, t l 2 9
l 9 l 261 3 9 14615 3 15 9 1o o /lo I 8 0 18 6 19 3 1
ll
l2
lo
I4 t4
t6 t9
It
z
I
2
0
2
'l'l'
t3
lii
lt,
l;F,
I'u
3;i
itl
lrl 9?r
.91
,1,
'l'
tl
1 B. 0 1
.05
.10
l9 .01
.05
.t0
2A . 0 1
.05
.10
1
5
7
L
5
10
l4
5
5
8
ll
5
8
lo
li)
It)
1 0 l i ) 20
t 7 23 29
2 1 28 3 5
1 0 q11 6 2 l
31
l8
22 29
l 1 t l 23
l 9 26 33
23 . i t 39
ttl
Bel9.,ilol
37 42 4 B o + 60 6617t l 7 7 1
o3111oll17112+
Bele6ll "q3l
4 2 49 56 6 2 69 76 831
q 9 l 991
r07lr r + l i z t l t i s l t s e
4 9 56 63 7 0 78 85
64 701761831E e le 5 l l o ? l l o e
D/
33 39 A 7
l10lil7ll2{ll3i
tozl
4 5 52 5S 66 73 8 l 881osl
q,
59 6 7 74 82 90 e8lr 0 5 l l r r32l 1 l l 2 9 l l 3 6 l l 1 {
4 l 4 8 D + 6 1 O B 7418 l l 8 8 1s + l l o t l t o s l t t s
l l l6 l i 2 l l l 3 l l l 3 9
4 B 5 5 63 7 0 l 6 8 5 e3lr o l l l o 8
ts:
rzaliaolt++1
11111201
63 7 l 7 9 87 9 5 031
al
z5
36
42
27
38
AA
29
40
+t
"-l
p a B H o M e p H op a c c e f l H b tB f t o u: nlr6opox 6yayr 6olee u'rrl IIeHee
C , I I e l. lol .BOaBl eaJTlet ,r 'Hl buHLOr lCr T lP
i aa nHrrvODB' '
n"i'*"
i;-i-e
1'
ua6,lloaeHI'In
eepBoii elt6opxtt' a Yi-
i: - ^e, ,t^t^a o ' n n -
utII .{: It,i t^l
P; ; t Ha6n'oAc
.." J " ,op,jri t "'?" pi-1.^
i- \l;i:
I
v'{rHr'
""-u-";
i(t"';pu'iMo"uu
;il;R
"
ii;
i:;ii i"i:{J:',";;;iT;
I T M E C TB H A
n
T
' 4: 2 ! . R ( , Y r -r
t t ( nj t )
( 2.50v
Q I
lr?
[3
,rl* ^:rl,
3il
- npocro cyM\{a pallroB sa6nioJ'esttfiu: nepoofi
flepnuir tl"IeH
er,r6oDxu.KpuruqecriuJun'oua"r"'r, B3flrble lI3 Kouoeepa [8]"
s ra6n. 2.22'
npneeJ.eHu
I(l]Ilreplls
'pairone MaHga VrrB xaqecrsenpuMepa[cflo"Ib3oB^aulrr
a'rr$
f
Koacr
Hu paccMorpuMur"n""t. iion. z'zz B
cBxcrpyKrypHblx
iCural HeQrr u ras Ao6HBalorce-lt3
"IoByt-rIeK'
3aHHbiXccoJt'Hb]MI.IKyno,taMu'flpot.HosblAeJIaIoTC'IHaocHoBe
i i a p T } i'ceirc\a[qecKriMil
poBaHH'II]oAcTI.l,IIarourlixfop}l3oHToB,KoTopbIepeIHcTpIlpVMeToAaNlrl. lloreHrlua'rbHble ]r'r-leBo.r.opo'lHble
rorcq
6lonn Ha cbnaurax coJiflHblx li--YHaK"lollHLIe
,:IOBylllKI4 BK'rlrcqarur
B r-161, 2'^2-3nepefro,'roB II sa\lKuyrble aIlrI'lKr'lHHailv Ha HX ocflx'
OCHOBeCeuCtltllqeHa
nO"'lyqeHHble
ilrlC,'IeHbI npOrHO3Hble I'TIOIIaIH'
Hyx<Ho y3Harb'
n
o
6
e
p
e
x
r
a
p
e
f
n
o
u
o
n
"rlyu:llaHu'
cnux Kapr ,lBVx
ecrbr'llll)a3,'lII4qHHBpacnpocrPaHeHHI{nepcrleKTuBHblxy'lacTKCB
i r e ) K - 1 . )J . B yM t l p e r l l o H a M I I '
alt6opxit
Ta6,,r.2.23 raxx<e coAep)Kl'rrpaHfu o6t'eruuesnoil
Cyuua
pervoHax'
B
nepcrrenluunotin"roulaAefi AByx
na6nroAeHHti
Man'
paHroBnepeoitrpynnbl- > n 6):67 ' floerotvtycratncrttxa
t t a- v l l r s s p a B H a
B ( 3 i FI l : 3 1 .
T - 67-
El
8-201
I iJ.
T a 6 , l r r u a 2.23
flepcnexruenlre nnou{aAn aa ue$rr r ra:
co!,lsHoKynoJrbHbrx
cTpvKTypAByx perfioHoB
oooepexbfl Jlyfi3haHbl(.flo KapraM Mopcxofi
ceficmn,rec
xoir c;lyx-6ur)
t a 6 n . 2 . 2 2 , x a x u T o r zr r t t t l - T o 1 2 . E c " r r r3 a A a r b y p o B e H b3 H a q H M o c r r {
r y , : l } 0 l o , o r l l n p e A e r ' i r ,6ry l y r 1 6 l l 5 6 , r a x I { a K n H r n o 6 a p a e H l t B .
i l p o n e p a e v o e H a M I i 3 H a q e H u eK p H T e p l r qH e r r o r l a A a e rH U B o f l u 5 t1 1 1 3
{ p H T i r r r e c K r r xo 6 . [ a c T e i r , T a K r r r o 3 T o r K p i r r ep H i i H e n o s B o J l t l e r
v T B e p l , K A a r bq, r o o 6 b e M b r n p o f H o 3 o B B A B l x p e f H o H a x p a 3 J I I I q a IOTC'],
Bocto'tut:ti
I'
.\ 2
l'-
peeuoH
802
t7+
158
140
166
328
o10
99
l6
B
6
4
7
l0
J
3anaduoui pezuoH
rl
312
b5
i'^
't' .
I'v^
)'g
220
276
i54
473
666
t .:2
9
ll
5r
I
t+
l5
K p r i r r r u e c x u e 3 n a r r e u u r 7 o , n p l r n e . { e H H b rB
e Ta6n. 2.22, npuuuvaIOTCrr.
3a HrlKriiie !pe.{,enbr,T. e. oHir I]pHfoAHbr.].,'rf npoBepKH HV! ' I e B o i i f r r f r o r e 3 b r :H s : E ( X ) > - E ( r ' j
e t: E(X)1
trpH aj'rbrepHarr{BH
( C H n e o , ' r E o 6 o s u a q a e r < < I r a r e M a r r r l r e c K o ex ( H A a H r { e >r r>
<E(y).
xaparirepn3yer I{eHrp pacnpeleireHlrr, 3a KoTopbili MolKeT 6btrb
n p H H f i T OK a K C p e 4 H e e3 H a q e H i i e ,T a K t r M e , [ f i a H a . ) c o o r s e r c t s r - r c I q H e [ p e A e J r b rA i r f i B e p x H e f o K p H r r r q e c K o r o3 H 3 q e H r r f\l{ o x ( H o H a i l r r r
rro QopMyne
t l t t t- T q .
Tpo:
(2.51)
i J I f fn p o B e p K I il l y r ' I e B o irih n o r e 3 b iH 6 : E ( X ) <
f l o c n e A u s e t t p r r r o . ] H bA
e 1 :E(I)>E(Y).
- < E ( y ) n p r r a r r b r e p H a r n BH
B u a u e u n p i r M e p e , o A H a K o , N r b rx o r r l M [ p o B e p r r r b A B y c r o p o H Hroro aJIbTepHarIlByIi oTKJroHrirbil.InoTe3y o paBeHcTBe[pofHo3Hbrx nJroulaAeii B AByx pefuoHax, ec,"r[ oHH AJIfl nepBofo peilioHa
rH6o gHarlureJlbHo6orr,ue, nu6o 3HaI{[TeJIbHoMeHbule, qeI,I Te x(e
BeJrHriHHbI
Anfl Broporo perfioHa. Ha QopuaJIbHoM fl3brrre HarxE
HMeIOTBIIr:l^
fIInOTe3bIiI aJIbTepHaTI'iBa
Ho:E(X) : E(r'),
Hr:E(X)+E(1').
no
3saqesul rpaHrrubr
AByx xpurn'lectinxo6nacreirHaxo.r,flrcfl
u4
Kpnrepuri MaHHa- Vnruu norB.nflerct B HeMHoropa3,tuqaroCpeAu HIIY r'{oiliHo
ulfixct Qopraax B crarricrlrqecKor?
p l t r e p l l i i 3 H r e n q_ - T l i o i t t l , I t p H , "ILirepar)'pe.
l r a 3 B a r b r p u r e p u i i B H . ' I K o x c o H aK
repr.rr:r@ecrusAxepa. Bapxaur 3ure"tq ._ Trtoxlt Haa6o,lee I{Hrepeil,nfl lpoBepKI] peDei{crc e H , T a K K a K o H M O i I ( e r6 u r l u c n o , ' t b 3 o B a H
, a K H N Io 6 p a 3 o M , I I e B a A H c n e p c u f tn 4 n y x n t t 6 o p x a x I I t { B " { t l e r c f l T
aHa JIOTOM
npocrof O l -Iipl'lrepl'Ifl.
IIapa\,reTp}rqecKIIM
I4HorAa cflyqaercfl, qro ABa u,ru 6o.lee Ha6JIIoAeHufinpll paHilill'
p o B a H H Hn O J I y q e I O TO A U H a K O B b Ipea H r n . 3 r o s s n e H l l e H o i r l l r i l i l 3 B a H r i ec B f l 3 a H f l b l xp a H f o B . T o r A a c B f l 3 a H H b I Ig, ia 6 n r c A e H U f l Nn{p l t paHrH' paBHbIeCpeJ,HeMy3HaqeHl{iopi] IlilIicl,lBarcTCtlOAHHaI{OBble
foB, Koropble 6u.nu 5u npnnucagbl, ec,IIIl 6u Ha6nrcAeg,uffiie 6bl"'Ip.r
, ra5n. 2.23 Mbt }'loxieM
B r o q H o c r r i c o B n a A a r c i l { t t u l l .H a n p l z N { e p B
lo!'ro;xurb Ha6rloAeHue X2 paBHbIvt220, a ne 174 yctt. e.l Tor.la
ua6,rrcAenns Xz u I/3 6y4yr cBfl3aHHbIMll.KaNAor,ty 6yAer [pI{rttrc a H p a H r ( B + 9 ) l 2 : 8 , 5 . K p u r e p u r i , I t c n o , r t b 3 \ r l o u l ulllip o q e , l y p b t c o
c B f 3 a H H b r l r up a i { t a N l H ,H M e e TT o T x i e B I I A , q T O H p a H e e .
Kpr.rrepnfi Kpacxna -
Vg,'r,'rnca
HenapauerprrqecKi.rfi xpurepirii gKBfiBa,'renrHoclH HecKo,'rbKrrx
eu6opox 6u.ir pexolreHAoBaH Kpacx.riov ri Vsnu'rurcotu.fleiicrarzTeJrbllo, oH rrB,rirercfl HeriapsMerpr{qecKr.rM
aHaJrofoM o.ruo$aNropHofo .r.llcriepcuonrroroaHaJlrr3a.flpoqe.cypa ero BbrqucJrenrrror{eHb
uaiioMr.rHaercoorBercrByroqylo npoueAypy J,r'rf Kpr{repuq MauHa Vururi; Ha6,'riolenun H: nu6opor< xorl6HsHpyrrorcq H.[l{ o6r,cAlruqr o r c f l u 3 a r e M p a H ) K H p y l o r c r ro r H a H M e H b r r e r ox H a H 6 o , r t [ r e N r ] : .
A " r q K a x ( . l o i i n u 6 o p x u H a x o r r i M c y n , r \ { yp a H r o B :
,rh
p
' t n -- _ s p / l zr r r i l ,
zr\
( 2.;:'i
f.le R(Xro) -paur
l - r o H a 6 , r r c A e n u fsl , k - i a n l i 6 o p r e . O 6 u r e e q r { c , l o
t t a 6 . l i o l e u u r i e c r l N : l t t r , , r l e f l p - r { H c r o H a 6 n i o A e H a r si A - i r e b r 6oprie.
H y , r e e a a r n i r o r e 3 a , K o r o p y r c r p e 6 y e r c a t t p o B e p r . t r b ,r a K o B a :
BCe coBoKynHocrlr, lr3 Koropbrx 83trbr BH6op'rgs,rrMer.oro.[r.rHaKotsble paclpeAe,rretrur. A.ritrepuaruBa cocrolrr B ToM, r{To ro MeHbuefi r,tepe oAHa u3 coBoKylrHocrerl rrlreer ueHTpaJlblroe3HArIeHIIe,
orrurrHoe or ,rtpyfux. llpe4no.laraercf, qro Bce Ha6,roAesus 6ltnH
8*
llD
cc6pilllbtc,'ryqatiHbl\r
rr rrro Bbr6oprill
o6pa30Nr
He3aBricHMbr
;1pyror
.epyfa.
,II,.nacyunaurpaHroBNIoxHoBbrr{ucrurbcrarncrriri}. Kpacx,'ra.Ita,t,tu
rca
H _
j,IItt
bo,'iee,'left(afl
r.tMeer
Lln-I
Soplra
k
12
r t r l [ R r - , r ( \ ' - + -l ) ' 2 l i
.Y(\ +l) lJ
flp
i-1
Bbtqxcr'reHlt:i aJlre6palqcctitt
k
tr
12
N(/i+l)
E
i-t
2
'p\. R
-3(N+
nk
l).
(2.53)
3KBlBarenrHag
(2.54)
rl(pitrlrvecrue3HaqeHfitH ra6ymrpoBaHbr
roJrbrioA,riflTpex esrdo.poK,Ka)KAaffH3 Koropbrxcocrorrr 6o,{eeqeM u3 nqrtr ua6.,rrcAeHuri
(cu., uanpirtrep,[30, ra6,r. 0]). I( cuacrlru, crarucrirxa H pacilPeAe,'reHa
npr6nlrsure.nruorar 7"2 c k-l
creneHrMrrcno6ogsr,
raK qro sror Kpr{repaii uoxHo c ycnexoM lprrN,reHrrbAJrffperue.nns 6o.leecJroll{Hbtx
3a.u.aq.
orcop'
M f l , - n p o c r o e i r e . r r o .K c o x a r e H H l o , o K p y r J r o c r " ] i : ] - " : i t l . b
lIIKa"le I'{JIH
I'rHTepBa"IblloH
I{e
B
o6bIr{Ho
II3]{epgrcTcq
rnposariuclcTlt
creneHl oTCOpTlIpoBaHHocTI{
a B IIOpgAXOSOfi,
IIKaJre oT,HOrIreHrrH,
T
e
p
M
H
H
a
M
H
.
I
I
J
I O X a tyl ,M e p e l l H a f ' x o p o u a t l '
o6uquo BbrpaxiaeTCfi
r
,
n
a
c
c
v
Q
n
l
{
H
p
y e T c tT e p M l l H a M l I - y f " I o B a o
K
a
T
a
H
H
O
C
T
l
.
t
c
T
e
n
e
H
b
a
Ec,lu Hcnor'Ib3OoKaTaHHaq.
Tar, no,,lyyr,,toBaTafl,IIO,'I)'OKaTa.HHafl,
xoppeJlflqliH
'Jtn
roaQQHUlreur
o6blqHbIfi
TO
Barb 3rlr TepN'lltHtl'
o K a T a H H O C Ti I i C T e c
T
e
n
e
H
b
l
o
l
U
e
x
(
j
l
)
'
C
B
f
i
3
l
l
C
t
i
,
l
t
l
xapaKTepIlcTIrKII
.neilio orcoprHp oBaHI{ocrI'IHexpI'lroAeH'
B raxni c,'t)'I{aflx [c[o,1b3):ercfl pagroBblii xoeSQuuueHT Kopp e ; f l 4 u l r c n u p , l l e H a , r < o r o p l r r i , K a K o r c B L I A H OU 3 C a M O r OH a 3 B a panroB'
H u n , n u p a x a e r c r e l l e H bc x o A c r B a N { e x A y A B y M f l u a 6 o p a u l l
HexoroI'{3MepeHHif--sa
ttopflAKoBbIX
ua6opa
HMeerI
.1na
Mbr
,flvcrl
l { e p e 3X i ( a n n n e p n d r r n o n a c r s e o 6 b e K r o B ,K o r o p b l e o 6 o : u a q N M
p a H M H p y e MK a x ( (
l
'
t
r
s
r
3
a
r
e
l
t
e
r
o
p
o
r
o
)
'
Y
i
u
e
p
e
e
ioro Ha6opa) n
lepe3
g u i i u a 6 o p H s u e p e H a f i ,o 6 o 3 H a q u BH X p a H f u c o o T B e T c r B e H HrO
L
I
3
M
epferr
c
n
l
t
p
n
e
H
a
4(xr) }l R(i'i). KoeSQuurieHr KopperrsrlHr,r
p
a
H
f
o
B
:
H
a
6
o
p
a
u
l
t
c x o J . c r B oI \ I e l t i J . )A' B Y M f i
n
eS
lR(.x;)- R(ri)1,
(2.55)
:l
t'(nz -
HenapamerpfiqecKafl Koppersrlnq
B npe4sral'rui{x ttapafpa$ax no.1po6Ho npHBeJ,eHoBbrqflcd,renue
liosQQuqueura rioppeJrflr\vril, a ttapaN{erprrqeCxlrirxpr.rreprrrl3Haqur \ { o c r n u u 6 o p o u u o r o r < o e $ Q u q u e n T aK o p p e J r r r r n t ro r r l c a H B n a p a rpaQe, nocBflrr1eHHoMl-xpnrepHrc. OAaaxo eo N{Horr{x c,T}'qaflx,
IiofAa o6uqulrti xogSQHqueHr r(oppe.rirrlut{ (ua:oreaemtrri uHo14a
n r r p c o H o B C K l l vx o e Q Q t q H e H r o M r i o p p e r ' r f l u , r r t iu) e n p H r o l e H , x e , ' r a TeJrb_Ho
HlvreTbr.r.lpyffie Mepbr cBrr3eirnrex<1},nepelreHHbrllIl.
CvHraerca, r{ro crpyKrypHbre ceorZcina [ecqaH[Ka orpaNiaror
]'c,'IoBIrfl oca.lKoHaKorrr'IeHuf.Hanpnlrep, BbtcoKo 3Hepferlrqectiaf
4 r a t n r a , r r s a q o 6 c r a H o s K a B o K p e c ' r ' H o c r f l xn , ' r f l ) r ( an p u B o - 1 r r rK B b l BerpuBaHluou pa3p)[IeHrrro, B pc3\','rbrareiioropbtx o6pa:1'orcx
x o p o t x o p a c c o p r l i p o B a H H b r re{ x o p o t u o o K a r a H i { b r er p y 6 o : e p u l r c r s i e
flpti Hrr3Ko 3HeprerrrqecriHx\-cJroBrrflxord'ro)rieHHn
or.rroi.r{eHrrt.
6y,-. 4 ) ' r n p e / l c T z B r € H b rN { e H e er u l a r e . ; r b H oo T c o p T r r p o B a H H b rr\,{{ a T e p H a , T r o Mc 6 o . r e e l , r € ; t K r r M u\ / f r r o B a r b l \ { H3 e p H a t v r u<. D o , r n I I I ] o n p e a e J r fe r c T p y K T ) ' p H ) . r so p e J r o c r b r ( a K c T e r r e H b o r c o p r H-peor B
l t a H H o c T Hr . 1
o K a r a H H o c ' I In
r e c q a H b r x3 e p e l r . f l p e J . n o , l a r a e r c n , u l o
lsa csoit, oKaslrgaoulHii aHoNlar'IIrH
c r B a r e c H o c B g 3 a H b r ;t r e c q a H L r K n
arotl
c B r r 3 t r ( H a r t p r . r N { expo, p o u o o r c o p r t r p c B a u s t r f r n e c q a H H Kc \ ' r ! ' i o B a r b r M r r s e p H a v r r ) , H a : l r B a r r o rc r p ) ' r i r v p H o o 6 p a u e u H t r l , r .
I ( a : a , r o c s 6 t , t , o n p e A e d ' r x r bn o H f l T t i e c r p ) ' K T y p H o i r s p e , r o c r u ,
c o 6 p a n o O p a 3 r I b rr r e c q a H H K ar i r r s l , q r r Bu x c r p y K r l , p H b l e c n o f t c r n a ,
a raK;'r{e Bbtr{HcrHB3areM Mepbr cBfl3u MexAy srgMr.r cgoficrsa; l1 6
l\
B c r i o 6 r . ; a xn o j , 3 H a t t o N c{ ) ' M \ ' t b tc o l e p ) K a r c f l p a 3 H o c r l l p a u r o e o 6 r , €KroB aeyx na6opon.
B r a 6 n . 2 . 2 1 n p u e e g e H b tc r p y K r ) ' p H b t ex a p a K r e p l l c r l l x l l A B e H a A Ko,rt,rteKropauu.I(axIIarH necqaHlirioB, qBrrlou{Hxctt He(Fratlbttvlt't
r r , r i r r r s H l r x c p a B H H B a , ' r ccf l . t p y f H \ { . { a . I rr o r o , q r o 6 l t p a H x t l p o B a r b
I { x o r s a u 6 o , r e e n , , ' I o x ol o g a u 6 o " , r e ex o p o r x o o r c o p r r r p o B a H H oof
u o r H a n 6 o f l e e v f , r r o B a r o r o! , o H a t r 6 o , r e eo K a r a H H o r o . P e : y n r r a r u
p a H i K r . i p o B a H I r iqp u B e ^ l e H bBI r a 6 , r I I i u e .I ( a x u B K p t . r r e p t r tMa a H H a V u r t t r r , u a 6 , r r c - ] e H r r r r ,cro c B f l 3 a H H b r M rp{ a H r a r , r i i f l p f i n l l c b r B a l o r c f l
' r e x p a H r o B , r { o r o p b r e6 u r , r r r 6 t t i l p u t r H c a ) ' c p c . t H e H H b r3eH a r { e t { r r f l
ttbt 3tul\,1ga5,rn.leHutiNI B cr't\-qaflx,ec,,il,l6lt ogll He 6l,l"qlIcBfl3aHI ( o e S Q u q r r e n r r i o p p e " r r f f q r rC
r n r r p u e H a M e x { ! , } -t B } ' N r f l r r e p e } r e H Iitbl\'1U paBeH
, . ,_ |
6(162)
l 2 ( l 2 r- l )
| -
e72 :0.43.
1 71 6
O 6 , r a c r r H 3 , i ! r e H e H rxi fol e O { l r r t 1 l i e H r ap a H f o B o i r x o p p e " r r t \ n i l r ' r a K a f l i r i e , K a r i H 1 ' o 6 u r u n o r o x o a Q Q u q u e H r a K o p p e J r f l r l u-a o r f 1 , 0
(ilo,tHoecoorBercrBneNrelKrypaurauu) Ao -1,0 (nolHal o6parHas cBr3b Mex(.n)p
' auralnr). PaseHcreo noer!QuqlteHrapauronoii
r i o p p e J l f i ( l ' r l lH \ ' ! ' I t oo 3 H a q a e r , q r o - r B a M H o l K e c r B a0 a H r o B H e 3 a B H c r . { M b rP. a s e r r c r e o r i o l Q $ r r r t u c u r a p a u r o e o i i x o p p e , r n u u t r , H a I p H u e p , 0 , 4 3 , o 3 H a q a e r , q r o t t M e e r c g ,c- l a | a n n o ; r o x r . r r e , r b H a qc B f l 3 b
lt7
a(5o
(9
(O
.+
Ta6aE\a 2.25
paHroBoroKoe$apllqseuTa
KoppeJrcq[H
Kpururecxxe3Haqenuq
CnupuenaAnfl npoBepK[rfinoregbrp:Q
(olol
:)
Ht..i
t-
E
G
v,
f)
q
4
,.;
t-
.:f
\tr
I
a.t
aa
6
7
B
9
i0
ll
t2
!t
O
o
O+
cD
F-
O
a.l
IJ
lt
ra
o
.8000
.8000
. i 7t +
.6786
.6190
.5833
.5515
.5273
.4965
.4780
,1593
4,19q
IO
=
Fh
6O
l-
53
L;
o
B=5
6=
I
vcctco(o
o)
co
ts-61L.
3r
A:1
-, -J
e
rax!a
X'Q
Oi;
E>
:;
i7
i8
l9
20
2l
22
23
qA
25
zo
27
:8
29
30
.4265
.1il8
.3994
.3895
.3789
.3688
.3597
.3518
.3435
.3362
.3299
.3236
.3175
at l2
.3059
.9C00
.8286
.7 45A
Tl1?
.6833
.636{
.6091
.5801
.5519
. 5 3 4l
.5179
.5000
.4853
.4716
.4579
.4451
.4351
.4241
.4 1 5 0
. 4 0 6l
.397i
.3891
.3822
.3749
.3685
.3620
.9000
.8857
. 8 5 7t
.8095
.7667
. / JJ.)
.7000
.6713
.6429
.6220
.6000
.5824
. JO,J /
.5480
.5333
.5203
.5078
.4963
.4852
.4748
.4654
.4564
.448i
.4401
.4320
.4251
qltq
.8929
.8571
.8167
.7818
.7155
.7273
.6978
. 6 74 7
.6536
.632+
.6152
..)vr o
.9643
.9286
.9000
.8667
.8364
.8182
7qtt
.7670
.7464
. lzoa
.7083
.6904
.tJLtl
.5684
.5045
.5426
.5306
.5200
.5100
.5002
.4915
.4828
.6586
.6455
.6318
.6186
.6070
.5962
.5856
.*/.*+
.ooo/
.4665
.5479
. D/D/
.5660
F
\:.
o
't
k
>'=
I
P
o
F:;i
\5€-
o
F
: : F
665
Vv
r=ro'sol,==
-
:
:
q
;t
g
5 '=-
=
= * v =
:l
j-
5
-q
=
a
;aX
3i
':
E5-
.: :=
= =A
^*.{eEEF.iE
u
\r\J
(r)
:l
F>
o
Y
F F
ot
ao
o
a
-
3g
Eo
E,v8ul'E.o=F.
-s'6.vai
€
_ r c a c a r a u d z 6 & dFaX
=
g
e
"
F#:f
#
't E
I
st
&Iex{Ay cTeneHblo oKaTaHHoCTH3epeH n CTeneHbrotrx oTcopTr.IpotsAHHOCTI.I.
fipuesruuuri l-rpurepnfi 3HaqriMocru xoe$QnuaeHra KoppexfiIltlu He MolKer 6nrs npuueueu K r', TaK rax f-rpurepufi npHuenrercq B cJryqafix, I{ofAa nsr6opxa cAeJIaHaug coBoKynuocrl{, LIMeIoqeii 4eynrepHoe HopMaJrbnoepacflpeAe,'teuae. cqacrbro, cyulecrK
nyior ra6.ur.rubrKprrrr{qecKfix suaueHLrrl,no3BoJIflrorql.{x
IIprMo ocyl u e c r B l r r b r r p o B e p K yp a n r o B o r o x o s $ Q u u u e H r a K o p p e J r a q u uC n u p r'leHa; qacrarruo gru ra6nuqu Bocnpor-r3BeAeubr
B ra6n, 2.25. Kax
II B cil!{&€ f-xplreput, HyJreBar rnnore3a cocrouT B ToM, rrro ABe
ilepet,reHHbre
He3aBucriMbrr.rJrr{irro p/:Q. Has6onee o6qar anbrepH a r H B a- p ' + 0 ,
r a K q r o x p n r e p u i i A B y c r o p o H H r 4 i tr,r K a K o q e u b
ooJiblrl]te,TaK H orreHb MaJIbre (orpnqare.nluure) gHaqeHHr rrprrBoAflT K orKJroHeI{trrcnpoBepseMoii rfifioresH. flpeano.loxuM, rrro
lIpI'IHflTypoBeHb 3HaqHMocrr.ra:0,05,
AocraroqHbrr?, no HarxeMy
MHeHIIIO,AJrff [poBepKr{ 3HaqHMOCr}rKoppeJrsrlrir4MexAy oKaTaHI{ocrblo H orcoprnpoBaHHocrbro. TorAa Bepxuee Kp[TErIecKoe gHal19
rreHr.re6yaer coorBercrBozarr l-a.12:0,975
u Syaer paBHo0,5804
H u x g e e K p H T u q e C K o e3 H a q e H r i e , c o o T B e T c T B y l o q e e
A,'rq n:12.
al2:0,025, paBHo -0,5804. Buqac,reHsuri rooSQau,HeHrKopper{rc
"rrIIuH r'--0,43 He Bbrxor,Irr3a orri fpaHurlbr, rr runore3yo roM,
c T e I r e H bo r { p y f r ' r o c T HH c r e n e H b c o p r r 4 p o B K r rH e 3 a B H c g TA p y f o T
Apyfa, orK,'ronr.rrbHeJrb3r. Ec.[l-r ece )Ke Me;,r{Ayerr.t\,rHceoficrsal,rr.{
r r M e e r c f lc B 1 3 b ,r o a r r 6 o p x a , c o c r o f l r r l a g u s 1 2 H a 6 , r r c A e H l . rHr ie, R e qro6u ycraHo"rrercr AocraroqHo IrpeAcraBrrre,rlriorl Ar'rfl Toro,
B H r b g r o r p l 5 % - H o M y p o B H e3 H a q r . r M o c r r . r .
K p n r e p n n ( o , r n a o r o p o n a-
Cnrupuona
O A H a o q e H b l o r e 3 r r a q f p y t r n a H e l r a p a M e r p H q e c K HK
Xp l r r e p r r e e
B K r ' r l o q a e rx p u r e p u f i l ( o n v o r o p o a a - C u u p H o n a . H a p l A ! c 4 p y ; 1 1 Mr.I npIL'IO)KeHHflMr.r
UX I{O)KHO}rCnOr'Ib3OBaTb
IJrg npOBepKII COOTBercrBllfl nu6opouuoro lt frfrorerliqecKofo pactipere,reuI.rri,H raxrrl.t o6pa:oM, orrH Moryr c,'ryrl<r,rrba,rmepHarunofi oill.tcaHHofo
B b r r r r e1 2 - x p u r e p r r r . X o r s K p l r r e p x u c o o r B e r c r B u f l r r f i a 1 2 r a x n i e
gBd'ttloTct HenapaMerpuqecKlrMliB ToM cMbrcr're,r{To HX Mo)KHorillHMeHrrrb x Ha6.rrcAeHHrMc ,rro6uu rnrroM pacnpe!,eJreHr.rs,
KpHrepvu l(o"rl,roroposa-CuupHoBa flBJrflrorcr Hau,lryqrxaMlrB HeKorop u x o 6 c r o n r e J r b c r B a x .C a v o e 3 H a q u r e , ' r b u o e
u x n p e n M y i l I e c r B oc o -
"Puc.2.40.11poue.l1'panpoBeplifirxllore3blocoorBercrBllnnlt6opouuoropacnpeltole"lu (xHpHaa lrrHun) c IloMolqbio
; 1 c , r e r r r { r r( i o r i x : r : i " : r u n r l n i r n n o r e t - H o e c o o t ' r
l Ko.r\'loropoBa-uMlipHoB:l'
lip Ilrcp La
"16.r rpaOuKa
/flHH
R K-vll-YnflTlIBHoir dlop\le, o6lacrs
Hafl pa3Hocrb - 9To trpoBepselrag
3HarIcHufl
ctatucrlxa
or
0'0
K-C
!o
l'0'
I'LaKctruanb-
aKChMaJ'lbHat
pa3HocTb
cToHT B TOM, r{TO A,'Ifl UX LICIIOT'Ib3OBaHHfl
He OOf3aTe,'IbHO fpynnHpoBarb ua6,rnAegrzfl B npor.I3Bor'rbHbreKarefopl{a; no gtor:t [plitIr{He'
nprr npoBepxe orx.roHenufi
oHlr flB,Tsrorcs 6onee r{yBcrBr.rred'rbHbrMu
B x B o c r a x p a c r t p e A e d ' r e s r r rcl H u 3 K H M H q a c r o r a M u , u e l t x p n r e p u l i 1 2 .
Ha puc. 2.40 npounr'rrocrprrpoBaHorrpnMeHeHi{eKpHreprzn Ko,'r\{oropoBa-CuupHoea. I4s Hexoropoii ueusnecrsoli conoKylurocrll
essra sn6opKa H HylKHo npoBepnTb coorBercrBlle au6opouHoro
pacnpeAeJreHIrflrrrrroreruqecr<oriMoAeJIII.I(ar< nlr6opoqHafl, rali ll
fHrloTerliqecKarlMoAe!'itIHaHeceHbrHa oAHH II TOT)Ke rpaQnt< n riv:uy,rarueuoli Soplte, fi,lorqaAu noA rpa$uxalrn npHBeAeHbIt< 1,0.
H a x o A u i u n a r r 6 o " r l u r y t op a 3 H o c r b M e ) K A yB H a q e H u f l M Ipl a c n p e . q e r e Hur; 3ro u ecrb crarr.rcruKa Ko,rlroropona-CvupHoea (K-C I
3HaqeHIIr.rJIr crarucrtrlt
B r a 6 n . 2 . 2 6 n p u e e A e H b rK p I { r I , r q e c K l l e
K--C; oHH N,roryr 6urr rtcno.rb3oBaHbrAr'Ifl npoBepKlr KaK o.qHoc r o p o H H e i i , r a r ( I I A B y c r o p o H H e t ir a n o r e s . f , e y c r o p o H H r f l H y J I e B t f l
f l r r o r e 3 a . v TB e p l t { A a e r ,q r o K ! ' t a c c b r p a c n p e : . e , r e t i u l i . 1 1 3 l i o r o p t t x
n o , l y q e H a n r , r 6 o p r a , A , , ' r fB
l C e x s H a q e H H r.i f c o B n a A a l o r c K i l l c c a \ { l {
p a c I ] p e , I , e J r e u urrpi t n o r e r t r q e c r o i i M o A € a r Ho. i l u o c r o p o l l H t a I I ) ' J ' l e B a f l
f u n o r e 3 a y r B e p l n A a e r , q r o B C e l { , ' i a c c b lu t t 6 o p o u u o r o p a c n p e i l e , l e HI{g paBHbl }lr'lv MeHbIxe,tle\I K/'laccblfrl|ItTeTHqecKoilI'lo.le,ru, ecr'llI
nOr'lOlKUTeJIbHylO
pa3HOCTbnpOBeMaKCI'rMa,'IbHyIO
NIbI HCIIOT'lb3yeM
pneuorl crarucrlil(tz, ]L'tI{ tlro BCe KJIaccblnu6opouHoro pacnpeAe,renug paBHbr r.r.rtu6onluIe, IleM KJIaccbl ft{Ilorerllqecxoli MoJ,enlt,
OTpuIIare,'IbHy]Opa3HOCTb
eCJIII MbI IICIOJIb3yeM MaKCI.IMaJIbHyI'O
120
2'1
012
A
P n c 2 . 4 1 . K y ' u y , ' i a r u n n l r i i r p a c p u r p a c n p e A e . l e H u q 3 H a ' l e H l t i t c o ! ' I e H o c r t t e 6accerlr r e V a r i r y o r e p , c r a H A a p r u 3 o B a H H b t xI i n p H B e r l e H H b I rx r . r a c u r a 6 y o r 0 , 0 a o 1 , 0 .
\ l a x c r r r a r l H a q p a 3 H o c r bM e x a y K y v y J q r r e u u v o s t 6 o p o q H b t vp a c t r p e A e n e H t r eriv KyMynsTuBHbIr
HopMa,lbHbl\{
i l p o B e p r r e \ { o rci r a r n c r u r u . B
pactrpcAileHlte}I
-
K
C
paBHa
0,06
6 o " r r [ r u H c r e e n p r . I M e p o BM b ]
ltcnor'Ir,3oBaTb ABycTopoHHroro rilnoTe3y
6yaeu
Ir a,rbrepHaTHBy.
B
O6uqHo xpurepr.rilI(o,ruoropoua-Cunpuona ucrIoJlb3yercfl
rex cryqafx, KofAa rItIIoTeTHqecKaflMolerb lror'lHocrbloonpeAe,'Ie. H a ' T . e . n a p a M e T p b lp a C n p e A e , ' l e H HHf l3 B e C T H b(IH " I H n p e A n O , ' I a r a lorcfl ir3Becruuua) Il3 KaKr.rx-Jln6oAono,ruureJrbHbrxcoo6paxeHnii,
o r . l n q H b r x o r A a I I H b r x ,c o A e p x a u H x c f B c a u o i i n u 6 o p r e . H e x o r o p oe ycoBepIUeHcrBoBaHHeKpL{replrfl, n p HHaA,'Ie}Kax.(ee,II
u,r,rueQopc1' [24] , oAHaKo, Ito3Bo!'rflerricnod'rb3oBarbMeroA I(o,ruoroponaCnupHoea A,'rr npoBepxn 6,tn:ocrH au6opouHoro pacnpeAeJleul4fl
,I{ HopMsJIbHON,ly
H AI.rCnepCpeAHI'rM
C 3apaHee He OnpeAe"IeHHblNIH
t2l
Ta6rarra 2.26
3sar{eHufl
Kpxrepuql(o,rruoroponaKpuruuecrne
Cruupnona
I
n:l
2
3
,1
5
6
7
B
I
10
it
t2
1?
tq
15
16
T7
l8
l9
20
ll
.e00l.s50l
. 6 8 4 .17 7 6 .18 4 2
. 5 6 5 1 . 6 3. 6
7 018
. 4 e 3 1 . 5 6.624
51
. 4 4 7 .15 0 e .15 6 3
. 4 r 0 1 . 4 6 .8511 9
. 3 8 r 1 . 4 3 .6418 3
.3581.4r01
.33e1.3871
.430
.3231.3691
.4C9
.3081
.3521. 3 9 1
.2961
.3381. o / D
.2851.3251
.361
.2751
.3141
.349
.2661
.3041
.338
. 2 5 8 1 . 2 e.327
51
. 2 5 0 1 . 2 8.328
61
.2+41
.2791
.309
.2371
.2711
.3 0 1
.2321.2651. 2 9 4
!
.990
.900
.78s
.689
.627
.995
---91
q?q
.829
.731
.669
.ot I
.617
.538 .576
. 5 0 7 q,{ o
.480 . 5 1 3
.qot
.419
.404
.390
.377
.366
.346
.337
.329
.489
.468
.419
43'
.418
.404
.392
.3Bl
. 3 7|
.361
.352
A n n p o r t c r t i var{ l r l
l,;tn n)40
.226 . 2 5 9
2 2 .221 t < 2
23 . 2 1 6 a l 1
ot
,1'
.242
2E . 2 0 8 . 2 3 8
2e . 2 0 1 t a ?
2 i . 2 0 0 99A
28 . 1 9 7 t9(
29 . 193 ,91
30 . 1 9 0 . 2 t B
. 187 .214
JZ
.184 ol r
33 . l B 2 . 2 0 8
. t7s .205
JA
AR
. t 7 7 tn9
36 , 1 74 t q q
itt
.t72 .196
38 . 1 7 0 l q 4
3g . 1 6 8 . l 9 t
40 . 1 6 5 . 1 8 9
I .07
.287
.28l
.275
.269
9At-
.259
.254
.250
'LA
,.4 0
.238
.234
.23r
,11
oq,
. 3 2t
.3!4
.307
.3 0 1
.295
. ?90
.284
.279
.27it
,270
. t66
.262
.2sB
,^4
. 2 5i
.3{+
.337
.330
ln
:
.3t7
. 3 1I
.305
.300
.295
.290
.285
.281
.)77
.273
9AO
l 52
r. 6 3
ln.
7tL
cueri. 3ro )coBepiueHcrBoBaHrre n03BoJrser ficnoJib3oBarb u3.ito)IieHHbILiMeTo.l aHa,'IofI.IqHO
TOMy, Kar{ r{br HcrIoJIb3OBa,l[npouejly.
x T e 6 , 1 .2 . ! ' 9 .
P Y X ' l n r n p o B e p K r rr r i l o r e 3 o A a H H b r x ,n p u B e A e n r r b r B
C , r r e r y q , { u " r . r u e S o p c y , c H a q a . [ a n p v B e A e l , rA a H H b r eK c r a H A a p r H o f i ^ Q o p M e , H c r r o r r b 3 y f lr p e o 6 p a s o B a H H eZ i : ( X = X ) l s .
C p e " q H e eH . 4 u c n e p c r 4 fHl a x o A f r c q o 6 b r q H b n { o 6 p a 3 o M . ! , a . r e e
craHAaprHoe HopMar'rbHoepac[peAeJreHrleH 3Har]eHuffZ vay.ocntc+
H a r p a Q n K B . K y M y r ' r f l T H B H oorol p N , r e ,K a K 3 r o c A e J r a H oH a p H c . 2 . 4 l
.UIg 3HaqeHr.tirco,'reHocrHB 6acceriHe Varir-Vorep. Mai<crrMa.{bHaq
a6co"'uorHa.Rp:]s^H_ocrb
Mex<.tyABVN{.fl
KpnBbrMrrcoorBercrB\.er llpo6 e c H o u e p o v 3 5 r r 3 H a q e n r i r oZ : 0 , 3 7 , r , n e c o J e H o c r b D a B H a
5-3 uacru/rrlnu. KpijrH,iecKrre 3Har{eH}rr Kprrreplrn I(o"rl,ioropoB[]Cuupuora npHBeAelrbrB ra6r. 2.26, xotx ra6flr.rl{a Aoge:eqa ,[uu]l
! , o 3 H a q e H L I fnl : 4 0 . f l p u 6 , r u x e H H b r e 3 H a q e H u f L I I A 6 o , r t u r n x r t
\ { o x H o H a i i T r . r t o S o p M y a a M , y K a 3 a H H b r MB r a 6 " r u q e . E m n : 1 8
H y p o B H f l 3 H a q r r M o c r r .ar: 0 , 1 0 K p r r r n q e c K o e3 H a q e H n eK - C
panH o 0 ,1 7 . B t t q l r c , r e H u a f l c r a r u c r u r ( a K - C
p a B r J a ( 0 , 7 0 - 0 , 6 , 1) = = ,
i!2
i
. JZJ
.221 9L7
. 2 1 8 ,i + 4 .262
c)l (
. 2 + l .258
912
.238
, 2t 0 .2ir5 .2D2
I .36
i
i;
t
"'i
= = 0 , 0 6 . 3 r o s H a q e H u eH e f i o n a l a e r B K p r . r r r i q e c K y roo6 J . i a c r b .f l o 3rorly orK.IIoHHTbHyJreByrorI,Inoresy o ToNr, qTo Bbr60pKa rioJryqeHa Ir3 coBoKynHocTLtc HopMaJrbrrr,rM
pacnpe,qeJleHrieM,
HeJrb3F.
gJreNleHTapHbtx
Ha erolt If br 3aKaHqlrBaeMII3/'ro)KeHae
c'rarl.rcrriqeci{rzxlporleAyp, Ho He rroToMy rrro paccMoTpe,'rrr
lrx Bo Bceii no.'tHore, a [onpocry A,'rfi TOro, r{To6br nepeiiTu K ,4pyr]rM Bolrpoca\r.
Pnccuarpunaeuufi MareplraJl sBrffercn oqeHb KparI{HM H3,'roxeHIIelvIIIo,IyroAOBOrOBBOAHO|OKypca B NIareMarltqecKyloCTaTHCTHK\', I{ Koropouy 4o6auleHu as6paHHbref,'raBbrH3 6o,'reecneur.ra'rrbH b l x K y p c o B .A n r o p H e p a c c q u r b r B a ' {H a r o , r r r o c y M e e TB c T o , I b r \ I a , ' I o M o 6 b e r v i eA a r b c r p o r o e o 6 o c H o B a H r eo 6 c 1 r 6 g 2 e l { b r xB o n p o c o B .
C,xHaxo npe!,craB,'rflercfl,rrro rr3Jrolr{eHHoro
6yeer [ocrSTouHo,(r'rfl
I ] e p B o r o 3 H a K o N l c r B ac o c H o B H b r M rI.iIo H f f T I l f l M HT e o p I l H n p o B e p K I {
C T i I T H C T T i q E C I i I I XI I I N O T E 3 .
H p c : ; n r r u a r i H oK p a r x c e H 3 J I o x e H l r en p o u e . l y p n p o B e p K H c r a r l r cru..recIifix fri[ore3 lvro)Kerc,ryx(HTb BBe!,eHr.reM
e 6o,']ee cnoxHblli
x n o c r ' r e A y r o x r u xr , r a g a x . 3 r o r
K p \ . r B o r - r p o c o Bp, a c c M a r p r { B a e M b r B
\ r a r e p I r a . r I H e H c q e p n b r B a e rc o A e p ; { a H H f I u a r e } t a r L l q e c t { o fci r a r H cruKn. Vgnrrac u Po6eprc Bo BBeAeHr.ur
K cBoerl KHrlre [33] yr<a- )Kr.rBoiirr yBr'reKareJibHbrrl
3btBaIoT: <<cTaTrrcTr.rKa
IpeAMeT, Ho ee
n3vqeHr.ieoqeHb qacTo IrpoTeKaeTcJIHluKoM BflJIo>>.
I4snoxus ery
HayKy B KOHTeKCTe
reOJrOfHqeCKrrX
3aAaq, MOIKHOHaAeflTbcfl,qTo
3ra KHr.rranpe!,cTaBHTaHTepec Ad'It feo,rotoB, HMeroult{x AeJIo co
crarrrcrrrqecrrort o6pa6orxoii IaHHbrx.
CNhCOK JII,ITEPATYPbI
l. Aicltiso:t "I., A ne'"vapproach to null correlations of proportions: Jour. oi
i r r t ' J A s s o c . , 4 l a t l r e m a i iC
c aelo l o s v ,1 9 8 1 1
, 3 ,o . 1 7 5 - 1 8 9 .
2. Aichisott./., and Brown Al.-C.,1g69,Tlie lognormal distribution: with special referenceto its uses in economics:cambridge univ. Press, cambridge, lg'6g,
p. 176.
.^_ S.-4:h R. 8., Basic probability theory; John \\riley and Sons, Inc., Nerv york,
l97tl, 337 n.
ColepNrrr'..no,tHoer3Jrorieurre$u,roco$cxux ocuoB Teoplltr eepoaruocrefi r.r Marel,rarrr.tecxoiicrarrcrttKu.
| , F 3 A l g y / . I / . , - D i s t r i b u t i o n - l r eset a t i s t i c a lt e s t s :P r e n t i c e - H a l lI,n c . , E n g i e n-oorC
l l i f i s , N . J . , 1 9 6 8 ,3 3 8 p .
JTir iljrnrl ioAepxHr Harr6orrce
no,rsnil ncpeqeHbra6auq A,rs HenapaMerpt{qecKu.\
riprrTCprreB.
p r e s s , C h i c a g o ,l g 7 l , g 9 p
,(H.Ir:l
. - 5 . C i t o l l e sF . , R a t i o c o r r e l a i i o n :U n i r , . C h i c a g o
col€p;Nnr no4po6uoeu3,roxeHnepe3y.rbraroBcrarucrnr{ecKr{x
}rcc,reAoBai'lllit i 1s6sap1tflu rpyrlx cnoco6oeonpeAer,terrut
3aMriuyrbtxAaHIlbIx.flpunoAxrcx
n p t t r l i p b r ; i l r e o \ r r { t r r r .f l o c r p o e H H a al a o i H o B et J ' o c a n e x q n i r ,o H a J e r r o . q o cTl nil a.
, ,t e d . C h . t t t t e UR . F . s t a t i s t i c a l m e t h o d s i n g e o l o g y : G e o r g e A l l e n a n d U n i o n
L
: o l r d ( ' i - r1, 9 8 3 ,1 e , 9p . h r r e e r c ap v e c x H fni c p e s o . l : - V a Hpu" .O . C r a r u c r H q e c x u e
rrero:br B reoJ'lorillr.
I{.,-Mup, 1987,'i87 c. Heiurpe r"lanu sroir KHHirinocBsrqerrl,r
llenspailte'rpnqecKHM
crarHcrrlqecr{HM
r{pnTepnsM,KoTopbre aBTop peKoMeHAyeT,
Tali IieK oHtt o6,terqanr
BbrqltcJ'IeHufl.
Annals of r\{athematicalSia_
,. ..7_ Cc,cltranW. G., The test of goodness_of_fit:
t r s t i c s ,1 9 5 2 ,. 3 ,o . 3 1 5 3 4 5 .
t23
nonp trics t a t i s t i c s2. n d e d . : J o h n W i l e y a n d
g""f ,f::'nl.i Y;,i; ?d68l';a! arame
Do,t turrHcreo rr3 )'nonflHyrr,rx s' srori r"rl^4tse,en ap aMeTp
uqecriu.\ lip }rTepueB p acg stor'i rrHure.B qactHocrus Helr -fi
cMoTpeHo
co.lep)KuTcfl orteHb no,.rHoe ri:l,,ro;rieHlre,
IipuTepneB
cKaqKoB.
9 D u c h a o r t h I Z . E . S t a t i s l i c a r t e c h n i q L r e si n
t e c h n o r o g i c a l r c s e a r c h .M e t h u e n
a n d C o . , L o n d o n , 1 9 6 8 ,3 0 3 r r .
o . q H a r s d T y q u r ' X f i c a M b r xp ' a c n p o c r p a H e H H b r x
KHH. no crar'c'rrie, flperHa3HaqeHa
. a ! ' r f lf i c c d ' r e . q o B a r e n e xr le, , t a r o t r - l u i n p i r l r e H a r u c r a r u c r i l q e c x r i c
nporle.l\pbr. Eo,rluoe
B H H r l r a H I ' IyeA e r e H o ' ' r z r ] r p o B a H H r o s r i c l e p t M e H r a .
H e c M o T p g H a c . r o ] l i H D C T b3 T r X
BonpocoB, oHu craHoBtrcr ,\ocTlrnHbrr,{u
6 . , r a r o t a'.fr.ni,il."i,lii,i'.,r.".J]
pq 6.lecrguier,ry rr3.rtol.KeHr{ro.
r0. FisherR. 1.. Statisticaj
methods,na
Bo.vd,
Edinburgh,
1978,175p.
ori'er and
rJ xHIlre u3,'rafaercq
38oJttoqu,crarlrcrrrqccrioii
ltr,rc,ru.f,r. 3 H 5 nocssruenur
ri:.roiNeHrrrc
ocHoBTeopIrHnepoRrllocreir,
ee nourrlrii ,, a,oa,larr,,ii,^"orrai^"ru,u"
il3 Hlrx.
ll. Folh R. L. Siagis
t e x t L r i a i ; ; i ; ; i i y i n s e d i n r c n r a r lr,o c l i s .J o u r . S e d i nrentr-rp
y c l r o l o g y , l 9 S l . 2 1. o, pf . 1 2 7 - _ : l J 0 .
r 2 . f r e u n d J . E . , w r L i a r n s F . J . D i 'c t'i'o r r a r y T o u i l i ' e
of basis stalistics,
. \ c C r a r v I { i l J , I r r c . ,N e r v Y o r k . 1 9 6 6 .i S S
i..
l eologl'
oi l n t ' i . A s s o c . f o r , \ l a t h e m a t i c a C
relatiousbett'eenproportions'Jour'
1977
, 9, P. 5a3-562-.. ^
" 'rO'.'Krumbein
F' , 4 -A n i n t r o d u c t i oino s t a t i s t i c aml o d e l s
\V. C'.and'Gtallbil,L,
1 9 6 54, 7 5p .
nil{':,t:q#;[l]fi
"*];;Tl)
ii:'H"rif
nont'no
;,;;;;'itv.q."
"
5'.';'"'il;.i;i;.il;'
"9-69Yv-':P::'-T."-)),,:'':'J'1oi1l"'
lpail5un,t
@. Crarucrltqe'liIIe Mo'le'lll B
6- 10
clreAyer.o6parurr H? r'rt o;t:-:..
oco6oe BHHMaHIIe
teocrarucrltliu. Oco-6oe
,;;;;;;;;;mrrriu.
o6,qacru
LtlHJ"lau:le,ti?{I:l
petrographv'
oi
sedimentary
lGirual
.,t,
f
2t. Kruntbei, IV. C. anabitiiiii',t
. r.n. o I i " t ' C . " r r i ' - a t -t ' t , l n c , N e w \ o r l i ' 1 9 3 85' { 9 n ' d e c i s i o n s3,r d e d . I l . r c u u I t ,
Iirii".i.
2 2 . L a p t t rt . r . s L . i i . t i ' . ; ' i ; . ' ; ; i . ; "
' 8 7p '
e . " . ; J o i u l ' o r i c h ,I n c . ,N e r vY o r l t ,l 9 B 2 8
Brll.7[peIcTaBneHbISl(cnepHMeIITbInoI'Io;leIIIpoBaHlrrc.lolia3aTeJ'Ibc,tBueHTnPeacJbHoflreoPeMbI'
n r.tuuoit
'""";5'.'
v. 1' EdwardsBros' Inc ' Ann Arbor'
t{-i"c-. n. staiitillar inference,
, r i i c h ,1 9 6 16, 5 8P .
''o 3!'leMellraplloll cr3'III'rrl''c'
rolr npe,lcrao,naer co6oit oHUIiI(,'lonelu'o
if.p"i,ii
H a r . { t , ( H o e o c o 6 o e B H r l M a H H ec ' 1 e ' i ) e r o 6 p a t r r r ;
ll:.roxerure B BbIclreu;;;;a;;
.r. 7, o xoropoii paccr{arpuBaerct.Xr-pacnpenereHl'Ie'
r""
r a r"t4.'[tltitorl
norrnaliiv
-gi1h
H.' W.^"O;'tG-Hrfiitoloto\'-srnitnou test for
iil,,"lXii}'..iJ;i.Tf;L:;:Xf;..ui.i',?;"j;:i;:1'J:
ih-eAmericanStatisticalAssociaironl96T,
i:,e"r""i:1n*",,*Xll:l{]l,i,ilJ;
nJ*;,'i;";.;i
r,r.un'i,rla"iliirn..'rtii
(r.rHexoropnx rleuseecrHu)
Sopr,ry,ru crarucr'ueixri.\
iipr,reprreB
;"r1;i;"":.t"n_r
1 3 . G r i f f i t h s " / . c . S c i e n t i f i ci n e t h o d i n i h e a n a r y s i s
o f s e d i r n e n t sM
: cGi:rrvHill. tnc., New )'orlt,
p. rri;;;;.;'pi:..,ru,i n.p.ro 7: rputBrpttrc
S_Oq
19_6"1r oca!,oqHHx
frc. Ha_
'qHbre Mero,qbrHcc!,re,[o-BaHilfl
nopo-1,_L1.,lirrp,'1gi,t,"'[ii",
f taw't 13-22 rB,'rflrorcq-BBeAeHr,eNr
n nprunial"yrg cra'rcrur{y. oco6'ri uHrepeg
n erori xurre npaA.tuu.l.::T_H3.ro,*erJ'e
nbnpocrrn,cBr3aHHbr\c xoppeiirHbrM,ere_
NaMIt cTaTlrcTilqecKl.tx SKCneDHMeHTOB.
1 4 . G u e n t h e rl Z . C ^ C r i n c e p t so f s t r i i s t i c a l i n f e r e n c e . 2 n d
e c l . ,i \ i c ( j r a r y - I I i l l ,
I n c . . N e w ) ' o r k , 1 9 7 3 ,b l 2 p .
u,*iaroe BBeAeHHc .tTylII
;1.1qTex, xro xoqeT
" u e .B n r r u r e3 a r p o H ) T ' l r p o r i l ' ' noJysrrrrrltariclnr],\,ruHeop\rau u r r B M a J ' I OO
M6 r e
K p y f B o n p o c o no, ' r , r u r r oH e c o _
'
,D.epxauluxctB KHuraxraxol.o o6telra.
Statistical lables anC tormulas,John Wilel,and
S<.rrrs,
y*rrl,1nflfttrA.,
Inc., Ncrv
16' Hichs c. R. Fundamental-concepisin the
design of experime'ts, 2'd cd'
andWinston,
Nii" v-i,'igzi,"zs" p.
Llolt,Rinehart
P,r'x_o-s-o,qcrso
no
excnepLr,reura
il rac[epcroH]totrvaHaJri3y.B i.r. 6
,u,'raHflpoBaHurc
npI'rBoItrct rpaQrruecxaa
uHTepnpeTauri,83aut,rod,elcrnriu:;rx.1n1.x(.rrr.iropriblx
nr'raHoB
u nprrN{epbr.
17. Kellauaa F. til., ed., pen-g^uin_Honr:yrvell
book oi tables, penguin Boolis,
L l d . , H a r m o n d s r i o r i h ,E n g l a n c l ,f d b e , - Z -pS. ' " "
-s
tllaretlraruqecKHe
ra6rxrlbr, npr.rBeIeHHbrei)rofi Ku[re,.BL-rrltrc,rleHbl
Ha OBM $rrprrofi Eiectronic Data process'ingDrvision-oi'iion.y,u.it--cii"i'^ilta."li.y,,rbrarbr
ganucaubl
6u'ryu
Ha MafHr'rrrrori,r..-.ure,
u autaonrrnaoara'lt. IroaroMy o Hri.KMor.riHo
cKa3aTb,qTo Hx He Kaca,lacbpyr{a qe,{oBeKafi
OHII He coLepNar ol]jfiaroK,
o 6 u q u o B K p a A b r B a r c q f i xsc r r a K u e u . a r e p u a . n o_rITO
Ti .a 6 n . 2 . 1 1 , 2 . 1 4 u 2 . l B 2 - i r r ; t :
ruurn [x' flenuca B3rrrj r13xuurn
[17]-l-nrnauutu"o, c pa3perueHlr,au.r.opa.
18.Koch G. S., Jr.
R . F . S t a t i s t i c a la n a l i r s i s , o fg e o i o g , . u t d , , t r .
^
a
n
d
_
L
i
n
l
i
Dover, Inc., Neri'york, 1981,8b0 p. d.;;;;;;;;Hoe
r.r3AaHrre
npe4*an.raer codori
fiepeneqarr(y
oparfiHa,,rbHoro
AByxroMHuKa.
CoAepNur nolpo6uoe.n*oia"ra .rr_
TlrcrurlecKofo
aHann3areo,l-orlrqecKnx
AaHHbIx,B qacrHocTnAaHHbIxonp0608aHjtr.
Brrrn'iaer uoApo6uoeu3Jro)KeHr.re
nu6opouuux'&enr,noeroAos
arrcnepcnouuofo
aHa"qrr3au MHoxecrBeHHorlperpeccur.t.llo,upo6uo oa
r;?
?
" - ' n' 2 i1.Q" iQt-a. 1i0i a
. rettticee v a l t t r i i o n as n d e c o n o m i cd e c i s i o n sP
.4. lV. Petroleum
'
l
1
B
p
1
9
7
5
,
J
'
,
N
.
C
I
i
f
l
s
,
I l a l l , I n c . ,E n g l " e u ' o o d
pl(npCAe lt'HJtii,
B r;r. 3 npercraB.IIeHo nolpo6Hoe lI3"lollicHIIe B e p o t ' l l l o e r H b l \
HeC$:rl 'n1 . h . . . , , ,
i l p .a133BBeeAAKxeeu
n " r p eeuqaatroouI It It It \x(cffll n p u
John WrleY
26. Par;ctt E., -\lodern probablllty tileory and its applicaLion.
464 p
Y o r k . 1960,
1 9 6 0 , 464
S o n s Inc.,
I t . t c . . Nerv
N e r v York,
P'.
ancl Sons,
"""
Publ'
; ; " ] i ; , ; ; ; ; ; i C . ; . - i ; t t " d u c t i o n ' t o q u a n i i t a t i ' e p a l e o n t o l o g i 'E l s e ' i e r
C o . ,A m s l e r c l a n t1, 9 7 1 , 2 2 6P .
cra3.rleMeHT_:ipHoil
no_npfir'IoxeHtIIo
p} KOBO-1CTBO
Hacroqre"lsHoper{otreHl}'eMOe
. f J I . b C O A e p X { a T C t T a r ' l J ' I I l U b ln p O T I T C T H X HK 3 a A a r I a M 9 K O ! ' I O r u U i l n a ! ' I e O 3 K O J ' l O r l l H B
B erOii xUure. Onttcasli
itO,,lXuTenbHOCTlt XU3HII, T. e. TeMbI, He 3aTpaf[BaeMble
r'-"
aK)Ke MHOflle HenapaMerpHqecKHe l\leTO'lLI..
ig. i-oltiirsoni. E., iomputer applicationsin peiroleum geologl'. Hutchinson
RossPubl.Co.,NervYork, 1982,164p.
o6paueHo Ha nocrpoeHueIiapr.
BHuMaHlte
He6o,rliliaqKHllra,B xoropofi ocHoBHoe
29. Saaper R. and Sinclair A. L' F a c t o r a n a l y s i s o f s t r e a m s e d i m e t t tg e o c h e m i c a ld a l a i r o m t h e M o u n t N a n s e n a r e a ,Y u l < o nT e r r i t o r y , C a n a d a ,N l i n e r l r l o g i c a D e p o s i t a ,1 9 7 4 I, , p . 2 4 3 - 2 5 2 .
3 0 . S i e g e l S . , N o n p a r a m e t r i cs t a t i s t i c sfor the behavioral scicnces.I'LcCrrrv'
L l i l l . I n c . , N e r vY o r k , 1 9 5 6 ,3 1 2 p .
(J,lrra
quTaeMhtx
uraeMhlx K
{eloAaM
KHirf
HiIr n
no
o H
HenapaIIeTpHqecKI-Iil
e n a p a M e r p u r i e c K u r l xxlel(JAaM.
O 4 t t a In3
ts n
nepBbrx
epBbIX u
uaa6o,ree
aa6o,ree q
3 1 . a o n ' . l l i s e s R . , P r o b a b i l i t y ,s t a t i s t i c sa n d t r u t h ' D o Y e r ,N e N Y o r k , l 9 8 l '
nt,l
n
-"
tP
"
3 r o r c r a p n i r n e p e B o f ( 1 9 3 9 r . ) K H r . t r f i H e M e t l K o r o K J l a c c I . I K at B . l r e r c f l x o p o u r l ] I
BBe.qeHr.reM
n $u,rocoQcxr.re Borrpocbr crarucTtiKn. flepeue TpH rJxEbI ilocBtluLeHbl
I . I a B H brl l o 5 Da 3 0 \ , t o n D e t r e J r e H l . lBr cc'freedorn.
p o f lT H o c r t l .
Jour.oi Educational Ps"vhology,1940;
32. lY'aiher
H. .1i.Desreesof
, 3 / ,p . 2 5 3 - 2 6 9 .
Or.rilqrroe
ceo6oasL
rr3J'roxeHue
noHrruqcreneseii
33. Wallis W. A. and RobertsH. V. Statistics,a new approach.The Free
p r e s so f G l e t r c o eN, e w Y o r k , 1 9 5 6 .6 4 6 p .
3aHHirtare,rruoe
c MnoxecrBoM[pIIMepoB,tlcropntl, anerBBeAeHne
B crarr.rcrr-rKy
IoTOB O npolrcxox<.qeHlllr
npoueAypA l4x IrpU,'IO)KeHlltx.
Arff Tex"
craTHcTfiqecriltx
K]O NPEANOqUTAET
NOBCCTBOBAHI{M
E ATCMATI-IKE.
Hbre
Bonpocbr
YB.IICKATCTbHOC
" np"*.poi.-d:jlg;f_,1;dfi;;5;.Tl'"'ff.'i'j":',T":0,:1.."J;H";i"";
tt4er o6 nHr€p-[peratttJu
.q,aHHhrx
c -nocro"Hlroiicylrnaot.
l 9 K o r h . 1 . o . E r a m i n a t r o no f t h e c h a l : e i r i r u s l i a i
p r o c e r l r r r iec r
t2l
iestingcor-
-
frasa 3
M A T P 1 4 I I H A qA T T E 6 P A
B BHAecJIeAYIoqeii MarPlrlrbl:
f..;:"-., ]:ffi:;,
x':fii:l
COV6.-,v1
s2sr
lcovu_.,
3ra r"'rasa [ocBffilreHanarpuuuori a.ure6pe.EonruiugcrBo Me.
ror{oB' rloropbre6yayr paccMorpeHbr
B cJieAyroquxrr'raBax,ocHo-
BaHbI Ha onepallaflx c MarpHl{aMIr, qacro BL,]IOJIHfleMblxBbrqHc,'rgT e J r b H b r M I M a I i l u H a M I t . o c o 6 o e B H I i N { a r { H e6 y e e r y A e r e H o M a r e M a TflqecKIIll oilepaqutM, Koropble ,re)Kar B ocHoBe aHar'tli3a [oBepxgOCTCIi ]'PCHAA, ]n{CTOAA IdIIABHbIX
KO[,IIIOHCHT,AHCKPI,IMIJHAHTHOIO
aHar'r3a rr 4p. Buuucdrrr4Te,rrbHbre
npoueAypbl, cBfl3aHHbre c grlrMrr
N{CTOAAMII,TOqTII HCBbITIO,'IHAr\AH
6ES BbII]LICTHTCTbHbIXMAlllI{H B
€Bf3pI co cd'lolKrlocrblo u MHoroKparHocrblo npol{3BoAlrMbtx Bblrlltca.nre6pu Hx MO>KHOnpeAcraBlirb
"reiiuri. c nouour,rrc uarpuuHoii
B AocrynHoM H cxaroM sr.rAe. Taxalt o,6pasou, ecJrH rrurare!,Ib B,raAeer ocFIoBax,lH[4arp]iqHoir a.ure6pbr, oH cMo)Ker noHflTb ocHoBHbre
[poueAypbr, Koropbre 6yayr paccMorpeHbr Htrx(e.
K coxia,reuH!o, 6o,rluLHHcrBy reoJroroB nplr o6yueHr.rr.r
He nperroAalor liypc N{arprr,{Horla,'rre6pu, Hecuorpfl Ha ro qro gror Herpy,tuuri npeJ,Mer, no-BHA_H_MoNI|,
6o.,reenoJre3eH,r{eM pflA Apyrrir
MareMar;iqecKux Kypcon. Kypc rr,rarpuuHol'r
a.lre6psr B KoJrJleAX{a-\
o6glrlro HacbluleH MHoroqHc,rreHHbtMI,I
Teopeil{aMHH Hx AoKa3arevrbcrBaMH. Taxoe H3JroxeHrieHerrp[foAHo A.[s sror? xoporxori fJraBbr,
Ir Mid orpaHtlqxMct roJrbKo_TeopeMaMtr,Koropbre norpe6ynrcn e
rocreAyloqeM r.r3JiolreHnn.fipa sroM npeArroqreHue6yaei orAaHo
H e A O K a 3 a T e J r b C T B a Mr r, p u M e p a M .
MATPI,IIIA
Ilarp;rqa-3ro
H a 6 o p q ? r c e J rp, a c n o J r o ) K e H H s rsf r B H A e n p q M o Ta6.nnqtr,
ToqHo raroii >Ke, KaK ra6nut\a AaHHbrx.B rrlarl,ronuuort
p l i u H o f i a . r r e 6 p e r a 6 n u g a p a c c M a r p r . r B a e r cH
s e xax ua6op orAenbHbrx S.rrelieHToB,
a KaK eA[Hoe IIeJIOe,qTo IIpHBoAHTK sHaq[TeIb_
HbrMynpoueHrreM peAa npoqeAyp ?r 3aBr.rcrjrlrocrefi.
Bo oropofi r,raBe orMerJaJrocb,rrro orAe.ntguri sJieMeHTMarpxubl o6u,ruo o6osHaqaercfl 6l,rxsor?c np[nucaHHbrl\rri BHrI3y HHAeKcaMa.Sneuegraur
i\'raTpr.rubr
IIoryT 6Hrl !,ricnepcHr.rIr KoBapr{aurj}I,pe3y,'IbTaTuga6,rn4eHnii, xog$QllqueHrbr cr.rcreMu ypanHeHlrii H npocro .lrro6ue
qI]c,'Ia.
Tar, HanpaMep, B r;r. 2 rpe6oBaJrocb BbrqtrcJrarboqeHKH Ar.rcnepcHrt n KoBapr{r](ufi gnn coAepx{aHriri lraxpoa,,reMeHroB,nprlBeA e H H b r xs r a 6 r . 2 . 3 . f l o . r r y u e H H b rpee 3 y J r b r a r b rM o x H o n p e A c r a B n r b
t26
CoVy-v1
COVgr-V
CoV1,s1-V
s$
H a 6 o p q t I c e J I ( A o n y c r u t n l , s H a ' { e H l . l l i n e o e u eX,H n(X)
o t i ' it"'tn
v)'npeAcrae*
,reuHsrriB BHAe*orti"'uii,"o6oi"* o6o:Ha'raercx[X] ,
ltxll.
K B a A p a r H s t ec x o 6 x n s o r '
B arofi KHllre 6yayr npllMeHnrbctl
l e J I b H b I e g J I e M e H T b l " N { a T p l I u b l 6 y a l ' r . o 6 o 3B
Ha
r pBeH- b I M I t r
r ' II Il 'al rTebpcagr 3
y pa erBJcI a
8 1 , n " u n , , c u H A e K c a M uu, a n p u l t e p t l l : l o o 6 u r e
3KBHqanrcs u raKHe -v.noun"a 66ot"auent1fl'l(aK lnll' fxl'i' Hru
3"Ie{li
cHriaeoJl
KaK
6yxnlt,
-O-3Harlaer
rpeqecKl{e
-xii',
BaJreHTHbIe
M
a
r
p
I
lqa
e
c
i
I
I
I
iX]
\reHr i-ii crpoKr* iio-'.ron6Ua. HanpuMep,
n o p a , l r < a3 X 3 :
Li:rl
II T',u'. Ec'lH qHc'llo cron6qoe paBHo IIIICT-I$
ro.f,33:9, -t13:7, )hr:2
HHcrpoK, To xlarpltlra Ha3biBaercff xna4parnori, a ee 3"'IeMeHTbI'
H
a
3
b
l
B
a
l
o
r
c
r
A
I
I
a
r
o
l
l
a
r
b
H
b
I
\IH
;
:
1
;
,
(
r
'
e
.
AeKcbl Koropblx paBHbI
Marplru'exapal(repucruKpaca,leluesrauu.B buurenpltgeAeuHoti
IlpeAeJIeHI.IqMl-iKp03JIeMeHToBAlIaroHaJIbHbIMI'I'IBJI'IIoTcflAHcIIep.
- KoBapHauHa' B rofi
g.. ocrar'Ib'ble o,IIeMeHrbI
;;;;;i;t".u""R.
paBHbr cooTBeTcTBegno1. 5
SJIer\{eHTbI
/Ke MaTpHIIeAUaroHaJrbHbre
rr 9. gaqe Bcero Bcrpeqalorcfl KBaAparHbIeMarpHIrbI' Ho HeKBalparHble rolKe HepeAKI'I,HecMOrpq Hl To-qro onepaIIHH C I{IIMHIlo'1'qrrHeHbrCTpofHM OrpaHIlr{eH14flM.
OCO6eHgOr{aCTOI'rCnOJIb3ynTCg
. r n e c p o p u r i H e K B a A p a r H b I xM a r p l l u : B e K T o p - c r p o K aT, ' e ' r { a r p l l u r s
rtoo",1,<i lxnt, u uantop-aton6eu, r. e' uarprlua rioptrl(a rltXl'
n
v Y, c, n^b, , , x a u r u
rrplIXOAI'ITCfl I'IN{eTb AeJIO C AByMfi TI'IIIaMII KBaLp a r H b I X \ r a r p l i q . 3 r o c l t u l t e r p l ' t q H a nI \ I a r p I { q a , B K o r o p o H x i i : x i i v
liar(, Ha[pHNrep,NIaTpIiqaBI.]Aa
fl
2
L:T
:]
J-lnr'"rr",
A
y J r ' , , r n^r ,\ ryr \,r ^a h- ' , . H o l \ lM a T p l l u b l ' c n r ' l u e r p n u H o f i o T H O - C l I ' T e ' l b H O
r.raeliori auaronanli MolKer cJryxHrb Marpl.iua J.HCIepcuil t'l KoBa'
p t l a q r t i r ,n p r J B e . r , e H l {B
ag
brue.
t.)7
I : A l t H H q H a fM
l alpu[a -3ro
c u M M e r p H q H a fM
f a T p r 4 r l aB
, KOTOpOT?
t s c e A r r a f o H a " i b H b rseJ r e M e H T bpra B H b r l , a s c e o c r a J r b H b r ep a a H d 0 :
0
tI Il
T a 6 " ' r r ' r q3a. I
(
r
l'105 r)
r
.
B
a
f
i
o
u
u
n
r
,
1
9
6
4
B lurare
Ao6uqa 6extonurosHx rJInH
0t
lI Io I o l
t00lJ
S J I E M E H T A P H b IO
E N E P A I I H HC M A T P } I I I A M 1 4
c.rlo;xegtre !r Bblr{rrraHr.re
Marpnu rIoAqrrHflercfl 3aKoHaM o6rtqu o i i a , r r e 6 p b r ,H o r r p n o A H o MB a l K H o Nyr c , r r o B t r Hc:K . r r a A b r B a e M bnr. e
[rr
BblrtrTaeN,tbte
Ma,TpHrIbI
IO,rlKHbt IillIeTb paBHoe rluc.rlo cTpoK Ii paBHoe qll('.tocro,r6qos.
llpl
nunonHenrlH orreparrnu c"qoxierrHrrtC] : t,4] * [B] r< r<axi.
.noMy sdre\reHry-MarpHuu [,4] npu6an,raercff coorBercreynrqufi a"rervreHrMarprrutr IB]. Ec,'ru lrarpurlbr pa3Hbtx nopflAKoB,ro onepaqrifl
c,'ro)KeHusHeBbrnoJrHHva.BuquraHrze IC] : [1]-[B]
BbrrroJrHflercff
T a x H r { x e c n o c o 6 o r , r :x a x < A u r i 3 . r r e M e H M
r arpHubr[Bl elrqtlraercq
r l 3 c o o r B e r c r B y r o * a . o 3 d , r e M e H Tr uaa r p u u r r [ , 4 ] .
B x a . r e c r e e r i J r , r r r o c r p a r { ueu r a 6 " ' r . 3 . 1 n p n e e g e H a x a p a K T e p r { c r u x a A o ( _ r u r q6r e
r r r r o H u r o e o l ir , r u u t r B r p c \ r o p u o 4 o 6 u e a r o q z x p a i i oHax u'lara Bal:ion,trrHr.
/ - l o 6 n e a e r c r r p u o c H o B H b r xc o p r a r J . r r r H b ro:/ l r r H n p H M e H r e r c f l
. A , ' r r n p r i r o r o B r r e H r f l6 y p o n o r o p a c r B o p a , a p y r o r ?- B K a q e c r B e . r r r reitHoii i,trrHbt H noc,'IeAHufi lrcno.ll:yercs t(aK ,'reKapcrBeHHoeII
, K o c M e r u L l e c r i ocep e A c r B o ,A , ' r f l K e p a N { r l q e c K Hu_er. r e r i u 4 p . B c e a r r r
I a H H b r e n o ; ' r i H o3 a r r u c a r b B B H A e M a r p u u b r [ , 4 ] n o p n l x a 3 X 3 :
t n l _ -_
lnl
;:?l
t;,:
| 3q2
3B
4l
'l
+
H;3;I L;;;
:x28
flDocne
r,'l ll Hbl
o
105
2t8
bJ
80
2
220
/b
I
MaTpn'
14sMeHeHlieAo6ut'IH MOIKHOnpeAcTaBnTbKaK pa3HOCrb
e.
uu [A] u r',rarPuuu
[B], T,
iBl
[ 84 1024l
lz+orzt I lLsoz28 ol
OtuerHu,
qto
:
'Jair-il
-il
[;:;:
tAl
tcl
noJIoxI'lreJIbHble sJIeMeHTbI MarpI'IIrbI tBl-tAl
coorBercrBylorpocry Ao6uqu rlus.
MarpHII nopflAKa n X f t t
a.nre6pe, c-JIo->Ke-HJ'I-e
r B
e ooblqHol{
o6HqHofi aJlreope'
KaK
Kax ]i
T. e.
u accoqsarl'IBHo'
r._ e.
r.
KoMMyraruBHo,
KoMMvraruBHo,
[/];1[AJ;
9_.[,4]+[B]:[B]+lAl,
BbIqI{npn
MarpHIr
flopn4ox
(tAl+[r]) +[C]:[,4]+([B]+[C]).
TaHr.IH,XOHeqHO,CyqecrBeH.
Vusoxeune Marpl'tublHa KOHCTaHTy CBOAI{TCS K
Ha 3Ty KoHcraHry.Hanpuuep,
KaxAofo ee sJIeMeHTa
yMHOXeHI.rn
f3 t2f
ft 41
3.12 sl:16 lbl
6l
Lg r8J
Asanoruqso npoBoAlrrct AeJIeHHe MarpHIlbI Ha nocrotnHoe
qrIcJIo.B xaqecrs6 npocroro npllMepa npnltaeneuuqsrflx onepaquft
paccMorpaM ra6n. 3.2, coAepx(aqyto pe3yJlbrarbl H3MepeHvfl'Anu'
HbI Tpex ocefi a, b u c xpeuHneBblx raJIeK, B3nrblx I'I3 neAHI.{KoBbIx
orloxenuir, I,Isuepeuufl cAetaHbl n 4rcfiuax I{ Hx Hy)I{Ho nepeBec'
Ta6nnta 3.2
OJ
tBj
tcl
102 4l
r8e
165 el
I
1 2 1 I lI, : | 4 5 9
28 ol I u::
il_,["ix
"rllrreltH,at
rNHHA
oraoxesnfi
[suepeuun ocefi nalex n3 JteAHHKoBHx
O6uras npoAyKur.rrr
3a ABa roAa B rpex pafioHax61'4er npe,1craBr'rqrbcyMMy[C] anyx Marpur{lAl u [B]:
[/l
BocroqHuft
PahoHu, norPaHaqHEIeco luraroM
MonraHa
I-[esrp a.nr'Hr,tfi
ls
llpo4yxurtio, .4o6nryrc B cr'reAyroureM
roAlr, Tati)r(e Mox{Ho oxa'paKrepu3oBarb
rvrarpHilefi
[B] :
84 t02
I
lB1:| 240 l:l
fnHHa Ans
6]"poBoro
p a c T B o pa
PerHoH
ill il
,A,nHHa ocH,,u,IofiMbI
O6pase4
I
;
j
5
(r-201
3,4
4,6
5,4
3,9
5,1
99
I,8
4,3
Ao
47
t9.
4q
L7
o?
3,8
129
-
t{ro6lr I I O " l 1 , ' t 1 1 1 1 oMaTpi.luv, co.leplKaulylo
Tlt B Mrrr'r"rrrNrerpbr.
.qaHHble B Mr{Jr"rilIMeTpax,
HaAo y M H O X ( r r T b Marpuuy lAl na nocrofiHglror
nennuuuy25,4.
q4A
l-nrr[]a
l41
L'Jt1'
tal
l.'J
!-e r
99
| ;:;
A2
a r-)
:s,'+.ll
5,.1t 7
I e,g ' R
* r"
I_r,t4 c )
tvl
t3|l-,;::;:
55,89 1i,7tl
109,22r06,68
|
I 1 9 , 3 8I 1 9 , 3 8
i
7 1 , 1 2 5.9,42
|
l2!',46 96,52_l
i,jilLir'::
YA{HOXEH}IEAIATPI,|I
B c n o u s r r l u r3 a A a q y c 6 p o c a u r r e u M o H e r b r , p a c c M o r p e H H y r oB
r,l. 2, rrle Birltlllc,'lfr'lacbBepoflTHocrbIIoaBJIeHnflnoc.reAoBarer,rbHoc r n _ r e p 6 o e [ o c r ' r e p a l a 6 p o c a H r r f r ,e c , r a B e p o f l T H o c r bB b r n a A e H I { g i
rep0a npH oAHoM 6pocaHuH paBHa t/2. BepbarHocrb BbrrraAeHHfl
r p e x r e p 6 o B n p h r p e x 6 p o c a H r r x p a n ua i l r x t l z X t l z ,
wnv" tlzt.
AHa,'rorHqHyro3araqy Mo)KHo cQopuy"rapoBarb rrpr.rH3yqeHilil Jtrr_
ro"r-orn.recxofi xapaKTepncrr.rKli crpariarpaQuqecxoro" pa3pe3a.
I lpeA[ro,'roxHM,rlTo npu r.r3yr{eHHR
pa3pe3a B HeM BbrAeneHbrTp}r
J H T o ' l o r l l q e c K I I ep a 3 H o B I ] A H o c r xn o p o A : I I e c o K , c , ' t a H e r {r, r 3 B e c r H r K .
K a ) r ( A b r Hy q a c r o K p a 3 p e 3 a M O ) K H OO T H e C T rK. r O A H O M yU s n e p e q f i c JreHHbrxrrlrroB. B urore MoxHo nocrpolirb Marprluy qacror rrorB-JeHr.rflKaIKAOTO
Tr.ina nopoA B pa3pe3e Bcr,reA3a ,Ipyruun Tr.rrraMu.]
B
necor
Vs
flecor
C.raHeu
I,l: eecrHsK
se
f
11486
1434
CnaHeu
18
I I:s ecr a qx
n?lj
5t
3 r a u a r p u u a H a 3 b r B a e r c qM a r p u r l e l i n e p e x o . q H b r qx a c r o r H n o _
K a 3 b r B a e rH
, anprrMepq
, r o c d ' r a H e cuJ r e A y e r3 a [ e c K o M l B p a s , a u s _
BecrHrK 3a necKOM- TO/'rbKo2 paza; H3BeCTHflK
Cr're.{}r€r3a c,raHu e u 4 l p a 3 , n o B r o p e H H eu s e e c i H s r { a B c r p e r r a e r c o B i p u r , u r u
IIecKoM- ToJ'tbKo2 pasa,
9ro6rr [o_.[yrrr'rrr'Ir3 3THX qacror BepoflTHocr,, HyxiHo pa3Ae-
" T I I . I T bK A X A U i I
aHa"'lof nr{Hbl\ BepoflTHOCTfiNlB 3 a ] a q e o 6 p o n llu.a BCOO'ITHOCTCIT,
]
i' il ltltil NI|JH€T bI
AICITCUT MATPIIIlbI
HA CYMMY 3J'IEMCHTOB COOTBETCT-
Byrcuefi crp_oKrr.
Taxntr o6pasou no"ryuznrMarpuqy nepexoAHbrx
BeporrHocreri,npuee4eHHyro
HH)ie, xoiopaa co.lepx<ureeponruo.*
cru co6srrur?,sax,'iroqarcrrlHxcfl
B TOM,qro lopoAa OAHOTO
THla
c"'leAyer
sa nopo4oliApyrororuna.
9ror Bonpoc 6yaer paccMorpejlAeraJrbHoB c,reAyroqefir.naee
rrpn aHaru3eBper.reHHbrx
prrAoB.Tenept )Ke Hac HHTepecver
Ntar_
130
[
|
L
IltC,-.rli
l.rttu I'
l1:secrHrti
0,23
0,61
0,38
0,74
0,10
0,05
H:scc rHqr
o.o3 I
0.2e I
0, Ir7
J
.far.
fAe 6bl.li] OnPe;1e_ , i . e t, i i l r i l i B 3 a A a q e o 6 p o c a H i t l r N l o H e T b l ,
, ; I e H a B € . i - ; T f l T H o C T b I J b I I I a A e H I { f l I I o c . I I e A o B a T e . l b H or eCpT6llI f enpf r6l o
l BCno.
B e p O a T H O C T IBI l ) l I I a ! ' e H l l t l
ilontbKl l.t3BeIeHllfl B CTeIIeHb
OIIIIOflBT'IeHIJg
(ii lcaHltlt, NlolliHo OnpeAeIIiTb BepofiTHOCTb
n o p o i l B 3 a ' l l ' a H H o r II l l l r e p B a " r e '
"1,,o^t
p,,l-i*n"o,,t't TIocJeAoBare,'lbHocreil
B03BecTllB creneH" tii:!]ii1)^,.nepe'xollHr)rr
'il.,,o
i i r . r , , ,n.,,,r
l l l ' r t r , , -,'locrarorltlo
;eii
lI noryqllrb
iIocJIe /? Talillx nepe\lHo;l(eHilll -N'larpllil)'
; . i , : ; ; ' ; ; ; ; , ; ; . nt p ; 1 ,i o t o p u " 6 v r e r p a B H a) I a r p r r q IeP " ] ' ' A { acrep' lrt t u a
]larpllubl ]la
B cre[eu1] n - 3T'o npocio pe3y'rlbrar )']lHoilieHIItl
H
}')liHo 3tlarb IIpaO
I
I
e
p
a
u
H
I
i
3
T
O
i
i
B
b
l
n
o
J
H
e
H
u
f
f
n p . ( t 3 { ) , A U a r c ol . ( s
8 i l . r : 1 I ] e p t M H O l l i e H H f lM a T p l l q .
- 3To
)r\'lHollieCarnraqnpocrafl rpopua MarpllqH-oro yNIHoNieHIIfl
IIopflAKa'
o
'
l
u
H
a
x
o
B
o
r
o
r
r
M
a
r
p
i
l
u
t
<
n
a
,
1
p
r
t
n
L
,
*
l
B
]
[
'
4
1
ime ABy);
uarprrlier? [c]'
T l l ) O n 3 B e A e H u eI i o r o p t J x c l l o B a f l B " r l f l e r c f fx e a 4 p a r H o r i
c
'
r
e
A
y
n
,
u
r
l
l
N l o o p a 3 o l ' 1:
M
a
r
p
l
l
u
y
y
;
(
o
6
H
o
p
a
c
n
o
.
r
a
r
a
r
b
fit,,' ut L'\1
IB]
[A] [Pes"v"nrrar]
L l T ( r [ > i , rr o . t v l t l l r b
yMHoxI{Tb
3HarleHne 3J]eNIeHTactj, HyxHo
IiaiiiAblil 3.-leMeHr l-ii crpoxu Marpulrbl ['4] (HauuHas, c"leBa) Ha
(Haurtuar
c:oorBelclByrou,nii a.[eMeHr i-ro cro.u6ua varpuult
l8]
ilo.lyqeHIifl licKo\{ofo 3,'IeMeHra c11 BCe 3Trl IIpOI{3cnepry). I"lq
B e - l e l r u l f \ N l N I r l p v r o T c.f H i l ; ' I { e H a n p l l M e p e A B y x N ' l a T p l l l l n o l i a 3 a H a
.floc,le/loBaTeJbHocrb oneparlufi npH NIaTpuqHoM yllHoilieHlltl:
f r 4 7l f ' ? 3l
l: 5 8l l3 4 5l
Ls 6 eJ Ls 6 7J
C u a . t a , r a Y u H o l r { H Ma r r H a b r t r r B p e 3 y r ' I b T a Tneo ' l y v i l l t l :
[r
171fl
2 3l
lz s al.ls 4 bl
Ls 6 sJ Ls o il
. d a ; t e e , y N , I H o ) t i a f ie 1 2 H & b 2 1 , n o " { } r { 3 e u l 2 :
[1 4 71 fl
2 3l
lI z s a lt l. l a 4
-l
L36erL5;;l
r31
Haxoueq, yMHox(afl a1s H2.031,IIO,IyraeM
l3!rlt3: ;l
fr2
3saqesHe g,TeMeHTa
c1y np€!,CTaBJrreT
CO6OftcyMMy TpeX BbrqIIcJIeHHbIx
gnaqenuft I + l2+35:48.
flocneAoeafe.ntnocit 3rHX
onepaqnrt ueo6pax<euaHa npuBeAessoftHu)KeAr{afpaMMe.Orue-
THM, rrTO rax4trfi sJreMeHTc;i npol.I3B€AeH,L|fl.
MaTpr44 noryqaeTc
B pe3y_Jrb-Tare
c!'ro)KeH[s [por.r3BeAeuafi srel.IeHros l-fi crpoKLI Mar
pHrIH [A] Ha oJreMeurlri-r5 cro,r6qa rr,rarpnuu
[B].
Haxox.o.exre 3reMeHTa crr
HaxolKAeHhe
l;l
I
-t
I
l
B nrorepe3y,lbrar
,rno*Tf"
cgz
-l
I
6yaer HMerb c,re4yrcu1uften4:
t;l
[:i ;ltil
la
t5
60 72f
72 87
1
84 I 02J
Marpr.ruH3MeHHru
na o6parnuft
-__E_c_,r1u
lgpsaox nepeMuo)KaeMbrx
apyror? pesynlrar:
[B] . I.4l : I Cj, ro no.'ryuurtr
il2
|:irl
il
ti
l'iil |'lil
3X2 He'lb3r yM'
Heo6xoAlltrloorMerltrb, qro Marprl(y [opflAKa
quclo cro'n6uonnep'
rai<
xat<
Sxg,
Hoxarb Ha Marpl4t(y-nop"anu
(iuui He paBHo rruc"Iy crpoK nropofi l{arpl4rrbr
;;;';;d;ut
(nrtr).
mxn Ha MarPItuY
B peay,rlrare yMHoxeHI4s MarpIIubI noprrAKa
noptAoK
l r o p s A K a n X m r o n y q a e r c g K B a A p a r H a t Marpr{qa,ilpfiqeM
pesy.llrHPYr'ourefi
nopnlox
o
n
p
e
A
e
'
r
f
l
e
T
n e p e M H o x a e M b l xM a T p } l q
MATDHUbI:
F2
L+ b
il$:l:t't;:l
OAnaro, noMeHgB[epeMno)KaeMb]eMarpHIrbI MecraMIi, no'lyql{M
ttilus:t:[ii
48
L:: ;J[::z:,
,l:]
63-|
4t tnl
34
45.1
npor.r3O6uran $oprvry,raeJreMeHra
MarprI(bI IC], ne.nrrortr.eficR
BeAeHHeM
AByx Marplrq,I,IMeerc,re4yroqulieu4:
3t rt4 32 50r
yMHoxeHrieMMarpr.rr{br
Onepaurant/].tBl :[C] uaauraaror
[B] ua
AHa.norn,Iso,o Marpilr{e[.4] rooopart qro oHa
Marpuuy [A] c"rrena.
yMuox(eHaHa MarpI{qV[f] crpaBa. 3ro npocrefturzftcnoco6 onpeAeneHHfl
yMHoxeHHflMarpl{q.
132
Ma'I'puqH'19 I'Ix^npoII3ABe KBaAparHble
Ec,ltt nepeuHolKalorcfl
roro xe [optAKa'
,.rJnu. rar<xe 6yaer xeaAparuoit'uarpuuet't
ro B
MarprlublnopsAKoB*x'y^:.:r'
ec.runepeMHolKl'rrb
A;;;;;
npoll3BeAeHl.ie
e'
r'
Marpnuy
nopflAKa
ntrXf
,
]iunorut. noJyqHM
u*..t qnc.'iocrpoK' paBuoequc-JlycrpoK
fi;o;;
":p191^)l:lprrrlbr'
Ha'
pu"io"'u'ucny croJr6q'osiropoii^uarpttUlr'
' qtrc"tocTo",lotloB,
roptAKa
MarpHuy
ua
5X3
nofrrrxl
l\larpllqy
non*ap, yMHolKafl
5x2:
5 " x i , i t o . t y " r l MM a r p H u yn o p r n N a
cii:
n
\al
Z o*0p1.
(3.1)
oruetHu, qro npll nocJleAoBareJ'rbHoM
6o,lee
nepeMHox{eHHH
qeMAByx Marpuq
garou, T. e. [opsAoK
AeftcrsveraccouuarrrBsuri
BbrnorHeHus
ui:cyulecreeu.Tax,
t/l. tBl.tcl : (t.41.
tBl).tcl: I/1.(tBl.tcl).
133
r
M r : p u u 1 ' N r o ) K H oB o 3 B e c r r rB c r e f l e H b , T a K K a K B o 3 B e A e H H B
e
c r e r i e r - r bc o c r o u r n o n p o c r y B B b r n o , r r H e H nprqi r a y u u o x e H H i i . T a x ,
[ 4 1 ': [ , 4 ] . [ , 4 ] ,
[ , 4 1 , ' l A ) ' . [ A ] : t , 4 .l t . 4 .1t , 4 1 .
M a ' r p . ' . . - r ,rra r i ) r i e N r o l r i H oB o 3 B o J , r r r e
b l p o 6 u y r o c r e t t e H b ,q a u r e B c e u rBoa A r o B i : e n e H b t l z . 3 r a o n e p a r l l l f l g r i B i r B a J e H l ' H Ia' r 3 B , r r e r r e H K
p a r r - ; r ) - ; ,r i o p H r r i 3 r , r a r p u l t r , r[., r 1 ] t 'e c r b ] r a r p r i u a [ X ] , r { B a , r p a r r i o ropoii preeu [,4]:
[ A ) , i ": t r ] ;
[r], : [A].
f J : r - , . - . , r r < ; e n t rlep o 6 u o i i c r e r r c H r r t r a l p r r r l r , r . t o B o . : r b r r o c . : r o i t i t { o .
K c.il,rrrrro, H;l\{ Hn)iie iloHajlo6fircq.'lrrurl trpo6Hbie cretreHn IIIaI oropoit, Ilcti.riiol O H r i , r i i . r : r r xN , r a T p i l U l. ) r ' o v a r p t r r l l l , B C e - j . r e \ ' t e H T L N
q a u j , r . : . \ . t e t t r t J Ic, r o u u i r r e I r i l r . q a B H o r i l r r a t ' o u i i , , t u . p a B H b t H y . r r r c .I { l
C i l e l l l ..l' . - ' D H b l eC B O I i C T t s :Ill O 3 L l O , i l t l l o l ' , : l C r l i OO C \ r I I e C T B , i l g l ' bB O 3 t s e . { e I rr r e r : p o 6 u 1 ' r o c r e r c H b . E c " n u e o s e e c l r r J l r e l r o H a " [ b H y r o M a r p r r u ] '
[21] a -,t.tyqe,l)'to creireHb, To B pe3y"t]brare no"ilyLtrITcflAfiaroHa,iIbHarr tl,1;Tpt{qa c H€H}rt€BbtMr4 3JIeMeHTa\{rr Ha f,'raBHoft ALIaroHaJilr,
paBHbrh{rI KopHf M xBaJlparHbr}r r3 cooTBeTcTByroqux 3,'reMeHToB
HcxoAHoiiMarpriubr[,4]. HanpuMep,ecrrr t/] 3X3. rr:
MarpriqaroprAxa
:,'l,]":
,?
]
ffi' ['r ,.1
E 4 u u H u H a n N { a r p u u a- 3 r o A l r a r o H a , r b H a f M
l arpHI{a cflequa.rrbH o f o B i . r r a c o q e H b i r o r e 3 H b r M rc{ e o f i c r s a N 4 uE
. c , r u H e K o r o p a f lN r a r pul{a yMHOX{aeTCfl
Ha eAHHI'lqHyIoMaTpllU,y,TO B pe3y,lbTaTenor'1}rqaeTct Ta )Ke[cxoAHaq N{aTpI]ua:
t3ir ltB:ll:[ii;]
Taxlrtvt o6pasovt, eAHHHT{HaflMarpuqa coorBercrByer eAHHLIUeB
yMHolKeHr.r[.3ro ceoficrso oco6euHo Ba>KHoB orreparluflx,
o6br.ruoN,r
p acc NraTpHBaeMbrx B c,'IeAyroul€M p? 3[€r-re.
CBEPTKA
Ceeprxa - BeKTopHaf orlepallufl, rrlupoKo Hcno,'rb3yeMaflB aHad r r i 3 eB p e M e H n b r xp f l A o e , o c o 6 e H H or r p n o 6 p a 6 o r x e c e f i c u u q e c r u x
A a H H b r x .B S u e n u e c K o Mc M b l c r ' r ec B e p r K a o [ n c b r B a e r c n o c o 6 e s a l.r,vo.xeri
crs afl r{oMnr'reKcoBAByx sHepf eTuqecKilx Bo,'rH.P a ccltorpu iu,
134
I 4xx c B e p r .l rr lB
Bll::l lbl oob! 'rIbt zr . .. .-l1. . A
BEKI(ar
n,pueoar
r
r
,,
IC l :[a]" tBl
xa o6o3sa.laerctlonepqroryM
ber<ropa onpe'lernrorcs
liBa BeKroPa lAl:
lasai a2
Ic]
;;p;"ici:i-cs cv c2.i.1. i<otnoseHfrr
no $opvY,re
L
c, :
)
( 3.21
aib;i.
j:0
H a r p u u e p , r p e 6 y e r ' c r c B e p H y r b, l B a B e x r o p a
atf
u r u x r o . q b K on o A B a q a e n a i ' e ' [ ' a ] : f a s
-BAfl KOMfIOHeHTa cBepTKlI
?:i"'#;:
lal"1JfJ;
Co:aobo-o:Qobo,
B T O p J tK
l oMnoHeHTa
ct : aob;o I
1 peTbfl KOI\lnoHeHTa
cz:
:
aftrr
sobr i
a1bo,
-
z o b z - oI
arbz-r *
azbz-z:
Ho Hu a2, HV b2 He clEeCTBylOT'
paBHa
aobzt
atbt *
nO3TOMy TpeTbq
a2bs'
KOMIIOHeHTa
c z: a r b r .
T a x u u o 6 p a s o uc, B e p r K a[ A ] n [ B ] B 3 r o Mc,,lyqaeecTb
[ A ] . [ B ] : t c l : l a , r b oa o b r* a r b o a f t t f
3auerun, qro xorn xax [,4], raK v [B] coaepxar ro"lbKo no
;lBe r(oMnoHeHrbl,cBeprra [C] cortepxHr rpI'I KoMnoHeHrbI.B o6ueM c,'lyqae, ec,ru nepnliii BeKTop, yqacTBylouuti n cneprl{e, coTO CBepTKaCOJ,ep'
a BTOpOt- /?13,'leMeHTOB
Jep)Kl{T /? 3r'leMeHTOB'
>xur n* m-l
a,reNleHros.
P o 6 u H s o HN T p e i i r e n l [ 7 ] a a r o r i 4 H r e p e c H o er p a $ u u e c x o e o 6 l t t c H e H H eo l r e p a r r u H c B e p r b r B a H x s .1 4 c n o . [ l s y f l H x M e r o A , c B e p H e M
I R a B e K T o p a ,x a x , l n f t r . r 3K o r o p b t x c o . ( e p N { H Tr p l l 3 , r e M e H T aL. H a t{aJa crpouu ra6.rr.rqy HJrr.rMarpuuy, B Koropoti o4uu BeKTop onPere"tqer crpoKI.I, a 4pyrofi BeKrop - cro"l6qlt. S,leueHrlt s aroii
]\rarprrqe_ npoH3BeAeHHfl
crpoK ua cro;r6qu
bo
br
b,
1,,
:',ii,:',/,]
:',1:',
f l o " ' r y u e u H yM
l oa r p r r u yT e n e p b n o . I p a 3 A e " ' I s e M
Ha noJlocxu, Ha,' r.r.l H_a f l
rlTo
or Hil;.11Hefo J'IeBofo
xl ili.ltrlt"r 3"rte\{eHT
no,rIocKH
yf,'ra .qo BepxHefo npaBoro, TaK
e c r l c r o " t r 6 e u ,e c d r u I J A T Hc n p a B l B l t t t 3 ,
135
I.I eCTb CTpOKa, eCilil tl(Tll CreBa BBepX, T. e.
W'?x,1A
S,reueHrur BeKTopa [C] cocronr Ir3 cyMM sJIeMeHToBnoJrocrcr, HasLr:f.afr,
c BepxHero ,'reBoroyr,ra. HanpLIMep,
:
lCl
l a o b o a r b o* a o b r a z b o *
* a f t r f a o b z a z b t * a f t z a z b z f.
3ro s rotlHocrr.rror qJreH,roropufi HaxoAHTcflc fioMolrlbro [pHBeAeHHofo BbIIrIe ypaBHeHHr, 3altetuM, rrro, KaK I.t oxHAarocb, tIIIcJ r oq " r e H o B
n [C] ecrr 3+3-l:5.
t r l H c n o e a p a c c M o r p r . r M , r u c n e H H H fni p H M e p , f l p o A e M o H c r p a p o BaB oJ.HoBpeMeHHo,
KaK oAHH BeKTop rlroxer 6lrrl ceepHyr c Apyr u u n H o i r p a 3 M e p H o c r n .I l y c r l 3 a A a H b rA B a B e K r o p a :
[,4]:[l
3 5 7 2],
tBl:t6
2 41.
Cneprxa IC] 6yaer HMerb ceMb q,reHos.I,lcno,'rtsvsrpa0rrqecKr.rfi
Mero,[,,Hx Mo)KHo:g^afiru
rro cxeMe
624
lffi
Taxuu o6paBoM,
co: 5,
:20,
cr:18*
2
c,:30*
6+ 4-40,
ct:42+10+12:64,
c n : 1 2+ 1 4+ 2 0 : 4 6 ,
-?9
C 5 : =4 + 2 8
Cs:
B,
O E P A I U E H 1 4MEA T P I T qH C I , I C T E M bYIP A B H E H I , I H
B A a s s o u p a 3 A e n e M b r o n p e A e r ' r n Mo n e p a q u r , oH a A M a r p i r u a M H ,
o 6 p a r H y l o o n e p a q u n y M H o ) K e H r z r3, H a f l n p H 3 r o M , q r o D p s ] l o e A e O4uaro, ficnoJrbr€HH€ oAnoft MaTpHrrbrHa Apyrylo HeBbrrro,'rnr.{uo.
3yq npaBlura MaTpHqHOfOyMHOXeHAfl, MOIKHOBBeCTI{COOTBeTCTBylouee lloHsrue, AJrs qero Heo6xo4arraopeul.trb MarpurrHoe ypaBorHocr{re,rrbHo HeuseecrHoft rtiarpnusi [X].
n"enuet/l . [X] : [B]
Heo6xoAr.rrlronoArIepKHyTb,r{To 9To oAHa Hs uaH6oIee Ba}KHbrx
onepauuft uarpauuofi alre6pu, Koropafl 6y4er HeoAHoKparHoHcloJIb3oBarbct B AaJlbHefiueu, B r{acrHocrH AJIfl,peuenHff ct{creM
y p a e u e H u f tB A H c K p r . r M H H a H r HrorM
rpeHA-aHarrv3ax.
fIpnaeAeHHoe Bbriile ypaBHcHHe peixaercfl c rroMourbroHaxox(r , e H u f l M a r p l r q b r [ A ] - t , o 6 p a r r r o i i n r a r p u : g e[ A ] , K o r o p a f l ) ' j l o B , r e r B o p r e r c o o r H o u r e H r 4 r[o, 4 ] . [ A ] - t : I l ] .
Tar KaK yMHoxeHHertrarpr.r.
IIbI Ha eAIzHaI{HyIoIlIaTpHIIy,[I] ee He Ir3MeHfleT,MbI MoxeTT yMHo.
Nr.rrr o6e ,r{a'crr.r
ypaBHeHr.{nsa lAl r, a peary"rr,Tareqero N{arprrqa
q
a
c
r
r
. ry p a B H e H H f H
l c q e 3 r r e r .B r o x e B p e M r rM b r H a x o [,4] a,rrenori
He.r,r3BecrHori
Marpuubr [X] 'lepea Marpgrlbr [B] n
Ar.llt.Bblpax{eHne
6hrs
isa-apainofi. hcxoto
Aorr)KHa
Lts
[.4]-'._-MarpHqa LAI
o6e qacru ua rtrarpriqy,
o6paruyrox [,4],
t,4].lXl:[Bl,-yr'rgoxrErr,r
I,fiii: : xr,roryrrHM
"'i !1r
; f fl;:;tfIiLrfl,l
ffiI r
lxl : [4]-'. [B].
(3.3)
Taxuu o6pasou, sa1\aqa,o6p-a,tuan
yMHoxeHuroMarpHtL cBoMarpnuu [X], onpeAeJiennolicoouiouear.iel{
4lircs K HaxolKAegi.rrc
(3.3). B HeKoropbrxc.tryvairxo6faiuyro^Marp[rly safirn He,,rb3fl,
TaK KaK B npordecceo6pauleuHaHHofAa npuxoArlrct BblnoJrHrrb
Ae,'reHHe
Ha HyJrb.Heo6paruruaflMarpHrraHa3brBaercq
BbrpolKAeHHoLr,Ho raKue Marpnrlbrs sroft rJraBeMbrpaccMarplrBarbn6 6yaeu.
I I P O I I C A Y P Y O O P A U I C H H gM A T P H U M O ) K H O N P O I I J I J I I O C T P H P O B A T b ,
peuas clrcreMy ypaanennft B MarpurrHoft
Qopnie. 3HaqenHn HeasBecTHbIX
B s r o M c r y r { a e X r : 2 y t x z : S . f l o n u i a e n c s H a i r c u I , I x .H c noJb3yq yMHo)KeHHe
u o6paqesue MarpHrl:
4n * l0x, :36,
lOxr*30,12:110.
3ry cucreuy ypaBHeiriifinro>xso3arrucarbB MarpurruoftSopue:
LlJIH
lcl : [6 20 40 64 46 32 8].
136
e 6o"rluliucrBe CTaTHcrItCoeprxa He OqeHb[uHpOKOLlcnoJ'tbSyeTcg
JIl1lxb aHa,'lH3Bp_eIIeHqeCKHXOnepaU,Hfr,I.ICKJIIOIIeHIIe
COCTaBJISeT
ufix pn4on.^Mu eule BcrpernMcq c eroti npoueaypoii, KorAa 6yaevr
paccMarprBarl QH.utrpaqurc (cru. r"rl.4).
t , 4 l . t x l: [ B ] ,
137
rAe [.4] - Marpi{qa Ko3QQnqueuroB,
HeH3[X] - BeKrop-cror'I6er{
Becrubrx,[B] - BeKrop-cro,'r6eq
npanux qacreii ypanueuafi.
B uaureuqacrHoMc,'ryqae
f.i
l:l t".l:f .?:l
LlO 301 Lr, l Lll0 l
9 r o 6 s r p e u u r b 3 T o y p a B H e n u e ,H e o 6 x o g r . r u oo 6 p a r a r b M a r p n u y
[ . 4 ] , r o r . l a n p o r r 3 B e A e H H eM a r p u q [ , 4 ] - ' u [ B ] l a c r H a M B e K r o p
.peureHrar[X].
Bosr\aoxHo, quTare,'rrcHe [oHflTHo, nor{eMy cr.rcreMyypaegeHufr
M o ) K H or r p e A c r a B l l r bB y K a 3 a H u o i l u a r p r u H o r l Q o p m e . L l r o 6 u y 6 e At4rbcflB oror'i, noperioMeHAyelrnepeMHolKHfbMarpr.ruy [,4] N nexrop-cro,l6eq [X]. B pesy,rlrare AoJr)KeHno,lyqnTbcrr BeKrop-cro.[6 e u " ' r e e n xq a c r e i i y p a o u e u n r : r :
[+
[;fi:J:[4x1*1Qxs
[;-*14:):[
,0.,*,0.,
]
Tenepl peurr\r cucreMy l,paeueuuri c rioNlourblo o6paureHnq
i ta r p t t M a r p u u b r [ A ] . f l o l l e c r r N r N { a r p u ( y [ , 4 ] c , r e a a o r e A H H H I I H on
Ha
u s r [ / ] H B r , r f i o . i r H I rB] rc e u e o 6 x o g , t r r t o roe[ e p a q u t r o A H o B p e u e H H o
o 6 e u x M a r p r r q a \ . L I e . , r oa r u . r o n e p e u r t i i- c B e c r l l A I I a f o H a . : r b H b r e
Marpullbr [A] x eauHl{rraNI,a Bce ocra"IbHlle - K Hy,'rflN{.
a.rreMeHTbr
3ro ebrno,ruflercn c rroMorrlbroAe"reHIIacrpoK MarpHrrbr[,4] ua xoncraHTbI, a rari;{ie IIX cr'ro)r{eHIIflIIJII tsbrrnrraHlif. fIoc,re.,logate,rrHocrb orlepaquitc.nelyrcqaa:
J)
D.
4.
r38
,(
I
1 0 30
I
0
Orr
1
0
otr
5
I
lf
JL
tl
l0
0l
0,25 0
01
0,25 0
-2,5
I
Ilarpuuy [,4] norreutaeupfiIo]r c e,l!ru r r q H o ilir a r p u q e r l[ 1 1
flepryro crpoKy Ae.rrnrHa 4, no,lyvaen
r t p H3 T o l t I H a M e c r ec 1 1
Bstqrrraenus nroporl crpoK!r yAecrrreIrerrH)'rclcpByro, no,ryqaerr0 ua lreCT€
O21
0 , 2 5 0 I Le;rru nropyro crpoKy Ha 5, no,'ry-0,5
0 , 2 qaelt I Ha N{ocred22
I
I
|
I
I ,5 -0,5 I I'uHoxaeu Bropyrc crpoKy y.a 2,5
f
0,2 lnsL,rrrraeM
e e u 3 n e p a o i i ,n o J v q a e M0
| -0,5
L
J rravecreay2
ll
- f - 1 r 0 l: f r 0l Jl
[_i,3 3,;]L r o s o j l o
rorcfl c"'reAyIouHe paBeH"
T a x x a x [ , 4 ] - ' . [ A ] : [ 1 ] , r o Bbrno,'tHff
CTBA:
lA)-'.tAl. txl : IAJ-'. [B],
t / 1. [ x ] : t l l - ' . [ B ] ,
txl : [/]-'.[B].
Vr4HoxHe Marpllqy lAl-t
Hylo Marpuuy [X]:
nu Marpuuy [B], uafi,1eM Hell3Becr-
-3:l]
[-J:i [,fi]-L3l
IAI-'
]
3 a r e l t , y M H o l K a nH H ) K H r o rcor p o r i y , n o r ' r y q a e M
?
Mu no,ryul'l,rH o6paraylo Marpiluy. A"'rt{ ilpoBepKII npaD{1.'TtrHo'
yMHo;,llrrb HcxoAHyIo Marpnu)- [A] ua
cru o6paur,eHur Aocrar_o_rr_Ho
no.rryrreHHyro
Marptruy [A]-1, rr B pe3y.lbrare Ao,'riKHaro.rvqilrbcfl
e l u H H q H a rM
r aTpirqa
llOx,f30x,l
Blrno,rHtts gro yMHolKeHile,BbI y6e;1nrecl, qro clrcreMa 3anrlIIo IIpaBH,laM yMHo]lielrHfl MaTcaHa npaBli,rrHo. .[,etlcTBI{Te,'rbHo,
pu[ noJ]q4€M
+ l0
1 0 30
[i
1 0 .. |i ' , l : [ 4 x , + l o x , l
LlO 30J Lr,J
|.
;
IBI : [X]
Berrop-croJr6eq X coAepN(Lrr IrcKoMbIe Heu3BecrHbre Jq:2,
cx z : 3 . B c n o n a u s a s ,q r o u M e H H o3 T r r 3 H a q e H H t y A o B , ' r e T B o p f . Jur H
xoAHbIMypaBHeHuflM,l,tst y6ex4aeMcq B ToM, rITo HaUJII{ )cy H x2
IIDABIiJIbHO.
PaccuorpuM exre or,uH npuMep
ypanneHuiic
^peueHlrr cu.creMbr
rroMoulbro o6pauleuur MarpHqbt. SarH[reM npuBeAeHHbre
HlI)Ke
)'paBueHHfB
l M a r p H r r H o i iQ o p m e u uafiAev x1 H x2, o6paulaq.\,rarpuuy cHcTeMbI:
2xr * xz -- 4,
3 x r+ 4 x 2 : 1 .
rrpH o6pauleHnu tratKparxo 3aIItIrrleM oI]epauHIl, BbIIlo,rrHseMbre
puubr:
I
lil;;l:fil
i3
2' | l - ' l : l 4 t 5- l l 5 . l
4)
L3
L- els 2t5J
-;,1
3
t-;j;
til:l_;l
t39
l
'
Cne4oeareJrbHo, snaqeHttq Hea3BecrHbrx6y4yr
---2.
x1:S
1q trg2a
3auersM, rITo olrricaHHaffnpor{eAypaorrenbHa[oMHHaerKJraccnqecxrifia.nre6pauvecxafiuero;1 perueHlrsclrcreMbrAByx ypaBHesnfi. B caMoMAeJre,perxeHlre cucreMbr ypanHeuufi- nall6o;ree
BaxHoe npr.rMeHeHr.re
npoqeAypbro6pau,enur Marpnq. B 4aHHolr
c,'IyqaenpeHMyqecTBoMaTpHqHbrx
MeTonoBno cpaBHeHllro
c MeToAalrHo6uquofi anre6ptt 3aK,trrcqaeTcg
B ToM, rrTo oHIr 6olee
cHcreMarH3rrpoBaHbr
r.r Jryque noAAaroTcfl apofpaN{MrIpoBaHrno.
bo.rluruHcrBo npoueAyp, orucaHubrx B cr'reAyroq[x fJraBax,nprr.
BoAHrK peueur{roctrcreMypaeueHuft.3rH cucrervrHo6srqHosanu.
CbIBaIOTCfl
B MaTpI-II{HOM
Bl{Ae II peUaIOTCfiOIICaHHbIM BbrrII€ r\t€T o A o M . O n e p a q H r b o 6 p a u l e u n n M a r p u u M o l K H or r p r r M e g r r r bK K B a A .
paTHbIM M^arp^HrIaM
,rrc6oro noptAKa, a He roJrbKo K MarpHrIaM
rropr,AKa 2X2, paccMorpeHHbrr,rB npr.rMepax. V6e4lrrecb B 3rolr,
ooparuB rrpI,lBe.IegHylo
Hr.rxe Marpnuy noprAra 3X3:
[;::]
Ec.nn uu saxorrlM o6parurt AriafoHaJrbHyro
Marpt{uy,To gaAarra oKaxercfl 3naqr.rreJrbHo
npoille. O6parnar Marpnrla- 9To npocro AnaroHailbrafl. M_arpl{qa,HenyneBbregJreMeHTbI
xoropofi - 06parubre BeJn{qr.IHbI
coorBercrByroulnxsJleMeHToB
o6paulaeuoftuarpflrlbr.PaccuorpuMMarpr{qy[A] nopaaxa3X3:
':l
:6'"1,1
[l'
tl
I^
€c'
c.ryqatx He o6ssare,rlHoo6pauarb N{arpHuY,
B Henoroprr-\
nn rpe6yercq ro,rrbriopeut{rb cucreMyypanuenufi.B paccltotpeu'
sreN.{eHros
rnrarprrqh[X], yaon'
r{oMrlpnMepeMbrucKa!'II{3HaqeHHff
ypaeHeuHrc
"qerBopEloueii
f +
[r,, 3oJ
I
U
f 3 8I
l:Irrol
C sroii ueJrbro rror o6paru.rrrr Marpuuy [A] u HaITIJIIIMarpiluy
{X], yuuoixun LAI-I Hq [B]. Buecro 3roro MoxHo 6si"ro_n_ptMoI'Icl r o , ' r b 3 o B a r bM a r p i r q y [ B ] n o M e p e r o r o , K a K M a r p u u a [ A ] n p e o 6 '
MarpHuy. c
srofi qe,'Iblo yAo6Ho
pa3oBbrBa,'racbB ell,HHriqHyrro
r.icrroJrb3oBarbTari Ha3brBaellyIo paclIIHpeHHyIOMaTpHIIy, COCTOg'
cro,r6uos. Berrop-cro.l6eq [B] sanurr,raer
ul!'ro H3 /2 crpoK v n{l
cro.n6eq pacufipeHuoft uarpnqbl, ocraJlbnaq qacrb een*l-it
o6paqaercn. tr4cnona3ys oror cnoco6,
r{arpr{qa flopsAr(a nXnpeur,rM Ty x(e 3a.u,aqy:
t.
4,0
10,0
10,0
30,0
38,0
110,0
2,
1,0
I,0
2,5
3,0
9,5
I1,O
1,0
0,0
2,5
0,5
v ,ll
llepnyro crpory BblqnraeMrre rropol
A
1,0
0,0
0,0
0,5
2,0
1,5
Vrtroxennyrc ua 5 eropyto crpoKy BbtqrrraeM rie nepnori
.).
1,0
0,0
0,0
1,0
tn
3,0
Bropyto crpoKy Ae.'run Ha 0,5
U
att
l 0 l '1".,
Ir, l
Vt uarpuu lAl tt [B] cocraBrlneDt
Marpr{uynopflAxa nX (n+l)
flepsyro crpoKy AenrIM sa
pyrc- ua l0
4, Bro.
1,5
a22
Hexoropste xolvr6Huaunl.IAoBoJbHo c,tox(Hblx onepailufi craHoeCJ'lIIBxOrIfiU{HeB HIIX N{aTpflIlbIAIIaroBflTCt OqeHb IIpOCTbIMLi,
ga rrbHbjg; H a np rruep, p accMorprrM -y N{Ho)KeHr.re
[A1-t : [A]'h :lAl-'t' .
E c . t r u [ A l - N r a r p n r r a [ o p s A K a 3 X 3 , r o r p o n 3 B e A e g u ep a n n o
:
:{
Ii' "1,]-'
l^
tl
V rru
0
I
It
w
00
[40
-
r f
-
V ozz
0
I
V ass
cron6eq nonyuenuofi
Taxxn o6pasort, B pe3yJlbrare n*l-tt
xrarpurrbr coAeplr(fiT perueHl4ecllcreMbI ypasHeuaft, a HcxoAHaE
.
IlIarDgua sa NreHeHae.u,nsuquofi
.II,.riao6paqeHI,ts i\{arp}rq r.i3BecreHpnl MareN{arHirecKIIXnpoMeroAoB cogAaHbl
ueAyp, 3ac,'rylKrrBarcuaXBHriManfiq. Aecsrxu
ypanneunfi
pe[reHus
cncreM
lr
cyqecrBy]or
corHn nporpaMMAJrrr
ntrx aepcufi. Hexotoptte LI3 HHx npeAHasuaqeubl c[equaJlbHo AJrn
Marplrq qacrHoro BHAa, raKrrx, KaK pa3pex(eHHbreMaTpHrIu (r. e.
MarpHIIbI, coAepx{aqfie Muofo HyJieBbIxeneueuron) uJrH Marpnrlbl,
o6.naAarculue HeKoropbrMn TllnaMrl cuMMerpull. So.nruruHcrBo BbrqHcJruTeJrbHbrx
rIeHTpoB HMeeT cTaHAapTHbrenporpaMMbl B cBol{x
6u6luorexax, npeAna3naqeHHbreAJrfl BbrnoJrHeHuff
Marpr.ItrHblxonepauufi. I-Ieo6xoan,rto3apaHee c HHMrr o3HaKoMrlrbcfl, npelKAe geM
n o r p e 6 y e r c q B b l n o , ' I H r r np a 6 o r y , o i l e p u p y r c 6 o r l r u u l t n M a c c H B a a{}r AaHHbIX.
t41
i7
I
T P A H C I I OH P O B A H N E
,I{eKoroporiIIoc,{eAoBaTerbHocTrr
onepauHir.O n p e 4 e , r n r e J r bc a M B o detA, lAl unu
o6o3Haqaercs
JllrqecKu
O l e p a q n a 3 a M e H b rc r o , r 6 q o e M a r p n u b r c r p o r i a M r r H a 3 b r ) l a e r c f i
T p aH c n o H f l p o B a H L I e M .
l-Ianptu
r ep, rrarpHrra
att orr
l
azzl
tl3:l
Iloc"te TpaHcnoHIlpoBaHlIfllrMeeT BHA
3il
O t l t e t r l M , q r o I r o c , . t er p a H c n o H r r p o B a H l nf i e p B a f l c r p o K a c r a . T t r j
nepBbrM cro,r6qona, a BTopafl crpoKa - BropbrM cro,r6uopr. Ec.llr
o6o:saqrrro Marpuqy uepes [l], ro MarpH(y, no,'ryqeHHyrrp
l aHcnoHHpoBaHHeM
M a r p u r r r , r[ , 4 ] , o 6 o s s a q u n [ A ] r . l l p u r p a H c n o H r . r p o A;; nepexo,t,HT
B a H H T3I . n e M e H T
B 3 r ' r e M e HoTj i . B o u g o r H x 3 a A a q a x ,
p a c c M a r p u B a e M b r xn r , r . 6 , q a c r o 6 y 4 e l r r r o , ' r b 3 o B a r b c r r e M , r l r o
B e K r o p - c r p o K a M a r p r r q u [ A ] n p n r p a H c n o H n p o B a H H rni p e B p a u a e r ct B BeKrop-cro,r6eq Marpr.rubr[,4]r. Bexrop-crpor(a rr Ber{ro.pcro,r6eu, lo,'ryqarorcq oAHH u3 Apyforo rpancno:HapoBarxueM.HanptrMep,
Il
234lLl
Lil
lloexe 6yae:u HMerb MHofo cJryqaeB,KorAa Marplaqa yMHoxiaercs Ha Marprruy, rpaHcnoHl{poBaHuy}o
x r sefi. Ec"ru uarpuua [Xf
IrMeer n crpoK u m cron6uoB, ro rpancrroHupoBaHHaflx nefi [X]'
6yaer lrMerb /r? crpoK u n cron6\oe. Vl\aHoxatr Marpurly [X] c,reea
H a r p a H c n o H u p o B a H H y rxo u e f t n a r p n u y , M b r n o r y r { a e M K B a A p a r H y } o ,
cuMMerpHriecKyroMarprlqy [opflAxa ntXl?, Ha3brBaeuyrolrenuureil
- [por.I3BeLeHL{eM
MarpHUbr[X]. Vrunoxax rr.rarpaUy[X]
rr,rarpuu,efi
c n p a B a H a r p a H c n o H u p o B a H H y l ox u e i i N { a r p n u y , n o , r r y q a e MK B a A parHylo cl'IMMerpnqecKyloMaTpHIIy llopflr].Ka nXn', Ha3bIBaeMVIO
6o"rlurori Marpilqeii - npon3Be5eHueMrraarpilqlr[X].
oII PEAEJI I,tTEJlt4
Harrreft noc"re,qner?
flpex4e ueu nepet?rH K H3,'ro)KeHi.rro
rer,ru"
xacarouteficq co6crseHHltx sHaqeHHfru co6creegHHx BeKroDoB.
ocraHoBuMcfl KoporKo Ha onpeAeJI[TeJIeMarpHIIbr.Onpe4e,rrareJrb
3TO quc,'lo,npunr{cblBaeMoe KBalparHol.j Marpilue B pe3y,[brare
I to
taa
Qzr
OH ertqucnflercff KaK cyMMa z! u,renoe elr4a
(-
l)u ari, a:i,... ani,r,
( 3.4)
T A e n - q l r c r ' r oc r p o K ( l t , r a c r o , r 6 u o e ) u a r p u q t t ; i 1 , i z , . . . , i n . H e K o r o p a g[ e p e c r a n o B K aq n c e " l 1 , 2 , . . . , n ; k - q u c , r t o r p a H c r t o sHIur? nap a,reMeHToB,Heo6xotrtINIbtxAr'rR Toro, ttro6bt pacnoJlo,>KI.IT
HbH r e K c bB
r flopfAxe 1,2, ..., n.
KaNAnfi q,res eroii cyiln{br coAep}KHTno orHoivr}r3,qeMeHTyrI3
r<a>x;toficrpoKH u Kax(Aofo cro,r5qa.
fipoqeac BbrqncJreHufloirpeAe.rrre"'rfl Haq[Haercfi c ou6opa no
i T p O K rgr , r l O 6 p a S O B a H I Ipf a
l 3,'InqHbl\
o A H O M y3 , r e M e H T yU : X a X < 4 O iC
r o u 6 u s a u u r ? . S , r e l t e r i r b r K a > K A o r oq . [ e H a c y r l r M b Ie r t 6 u p a n r c R l t s
, c r p o KB e c r e c r B e H H o M
n o p f l A x e l , 2 , . . . , n , o A H a K oK a > K A a fKf o M 6lrHarrilq Moxier corepxiarr, Torblio tlo o.{,HoMy3I€M€HT} Hs Kax(aoro cro,r6qa. HanpnMep, B Nrarpnue riopsAKa 3X3 tuoNuo BbIe r, o a , ' r e N { e H T b I
6parr xou6uuaqltlo attaztazz. O6parure BHHivtaHttq
p a c r l o , ; r aaf r o T c f i B n o p f l A K e B o 3 p a c T a H H qH X r l e p B b r x l l H A e K c o B
n o M e p o B c r p o r i . K a ; r r a s n o r , r 6 n H a u n rc o A e p x n r p o B H o n o o A H o M y
a,rreMenryus xaxiroii crpoKII r.r Kaxi.qoro cro,r6qa. Tpe6yercn er'rS o a r r B C e B o 3 M o N i H l r er o v 6 u H a [ r n l . c o c r a B J r e H H b rrea K H M c l t o c o 6 o e r . E c . , r u \ { a r p r r ( a r . i } , { e e nr o p g . q o r (n X n , T o r a K u x x o r r 6 l r u a q u i i
6y.aer n!
Tax xax nopfl.r.oriyMHo)KeHHnqttcerrrHe B,'tufler Ha pe3y,'lbrar,
T. €. Cl ,azzazt:a22Q1ia3i:4s3A22411
it T. A.' 'IO MoX{Ho npolI3BO,'lbHO
i l 3 N r e H i l r br r o p f l . l o i i 3 J e ! r e H T o Ba o r o 6 p a H H u . r x o u 6 n s a u r r n x . l l o [ b r r a e ] r c n e r r 6 p a r r 3 , , r e N l e H rrbarn , q r o 6 r t u x B T o p b r el l n r e K c b r , r , ' r t r
H o N r e p ac r o , r 6 u o s , p a c f i o " r r o x i u , ' r u cBb n o p t A K e B o 3 p a c r a H H a .f l e p e craHoBKy NIo)r(HoBbinoirHllrb, IreHRfl ,'r106bre
.{Ba coce.IH}rxa,teMeHT a M e c r a M r r . B l , r n o " l n f i f l o n e p a q r r r o ,H y i K H o c o c q H T a r b , c K o , ' r b K o
cAe,rraHonepecraHoBoK, Heo6xojlltN,rbrxr,,'rr roro, qro6u HHxeKCbr
B Hyx{Ho}r nopflAKe. Ec,qrr .q.rs 3Toro norpe6oBapaclro.roiKr.LryHCb
. r r o c bq e r H o e r r u c , r or e p e c r a H o B o l i( r . e . 0 , 2 , 4 , 6 , B , . . . ) , r o n p o u3BeAeHHe3THX 3.leMeHroe 6epercfl c tto"rro;^t<rrexbnbrM3HaKo]r.
E c . r y n6 u , r o H c n o " ' r b 3 o B a HHoe q e r H o eq H C , ' r on e p e c r a H o B o x ( r . e . l ,
ro nporr3Be.leH6
u e p e r c r c o r p l r r l a r e , r r b H b3rHMa K o M .
3,5,7,...),
B uarpuue noprlxa 2X2
f oazt, t
I
ut1
ozz)
coAepxaulHx
JlIolKHo gaftru ro"rIbKo Aee xoM6lrHar{Hu a"reMeHTots,
r43
no oAHoMy 9,'leMeHry r.r3 KaxAoft cTpoKH rr3 KalKAofo cToJr6qa,Q r r d z z H A 1 2 A 2 1B. r O p U e I I H A e K C bBI l { " q e H eA 1 1 A 2 2p A C f I O J I O X ( e H
Bb I
ecTecTBeHHoM
rropsAKe rr [epecraHoBoK He Tpe6yIoT. Lhc,ro nepecTaHoBoK paBHo Hy,'Fo, rioSToMy 3HaK npor.ISBeAeHr.rg
noJroiKHTe,lbHbIr?.oAHaKO SJreMeHTbI
B qJIeHaXArz Lt Qzr HyXTHOnOMeHflTbMeCTaMU, qro6br HX BTOpbreHHAeKCbT
pacnoJroxuJrr4cbB HyxiHoM rropsAKe. 3ro rpe6yer oAHofi nepecraHoBKll, rroeroMy pe3yJrbrar
6yaer c orpuuareJrbubrM 3HaKoM. I4Tarc, olpeAeJruTeJrbMarpi{qbr
nopfAKa2x2 panen
Att
d r' q- lI : t
Otdzz-Qtzdzr.
n e p e c r a H o B oHKe r p e 6 y e r c a . f l e p e c r a H o e x uAJA
O . 1 1 A y A 3 2 :d 1 1 A 3 2 d 2 9
A pA 23A31: A,pd, BsAzs: A t t dt zQzg
O,pA21A4: d,21&12A3s
A 1g A 2 1 Q 3 2 :A 2 1 ds d 4 2 : A 27 A3 2 A1s
A 9 Q 2 2 Q . 3: 1 A 13A s t A z z : d s t A n A 2 2 : A 3 1 4 2 2 d1 3
ft:1,
k:2,
k:1,
h:2,
ft:3.
s H a Ksuat *
s H a xguax *
s H a x-
Vrax, B orIpeAerHTeJIe rpH IIoJIo)KIIT€r'tL'Hbtx tI rpll orpi{Irare,ilbHblx q,'IeHa. Cx,raAnrnaq q,'IeHbI (c cooreercTByloxlllMH 3i{eKal\ll'i),'
rIoJ'tyqr]M
! A 1 1 Q . 2 2 A- * A 1 1 A 2 s A g* 2 Q n Q z s d s t - a 1 2 Q 2 1 a 3*3 Q t s a z f l z z - a p Q 2 2 a g 1 ,
B xaqecrse q[cr'IoBofo IIpr{MepapaccMorprrM
MarpHuy
TeneprpaccMorplrM
I{arpHtly 4eiicreure,rbHbIx q ttce,T
32f
4 rl
L+sl
11
paBeH
Ee onpe4e.rureJrb
03J
li
ll: * e.B)-(t.4):2.
l+ ul
Tenepr paccMorpnM6o.ueecJIoxHbIfiuplrMepMarpr.rqbr
nopflAKa3x3
eu etz o"
azt azz
dsr
qJIeHoB
nprIBeAeHbI HLIIKe:
azt azzl
12 rl
.l,pyrllx
asz
oupeAenl{reJrb
[lecrr qJreHoB
BbrrJrrAflrraK:
(4.4.3):48,
( 4 .I . 0 ) : o
(3.1.1)-a
(3.2.3):lR
(2.2.0):0,
(2.4.1)-8.
I
azzl
aggl
3 A e c r 6 y a e r 3 ! , u n n 3 . 2 . 1 : 6 , x o t l t 6 u s a q u f i ,K o r o p b r ec o A e p l K a r
no oAHoMy gJieMeHry r.r3Ka>KAoilcrpor{}r H KaxAofo cron6[a, HHAeKCbr Koropbrx pacfio,TafarcTcf B lopflAKe l, 2, 3. HaqllHaq c
BepxHefi, BbI6I.rpaeMIIo oAHoMy 3,'reMeHTytis-r<axg,orl crpoKl{. CHaq a ! ' r a u 3 l e p B o l i , 3 a r e M H 3 B T o p o f t ,T p e r b e r l ,. . . , n - f t , H c n o n b 3 y f
[pLI 3ToM He 6oJlee onHofo s.rrel{eHTaI.r3 Ka}KAoro cTOJ6qa, }1KaKOM6nHaIIHH,!.{OBr'IeTBOpgIOqI{e
x{eM Bce BO3MO>KHbIe
STHM VCJ'IOBIigM:
flepnufi, Tperr.rfilr ntrblfi LI3 3rl{x q,rrenoB rpe6ylor
verHoro
LLLTCTA
OIICPAIIHfi,AJIfl TOfO IITO6bI IIX BTOPbIEI.IHAEKCbI
PACNOJIO}I{[.:rr{cbB noprAKe Bo3pacTaHI{n.fina Tofo rrTo6br uHAeKcbrocT?r'rbHbrx gJreMeHToBpacfioJrox(I.lJrllcbB nOptAKe BO3paCTaHHs,Tpe6yercq HerrerHoequcJro o[epaquf{, I.t no3ToMy oHH orpl{rlaTeJrbHb],
Crn a At'tea fl,, [oryqae M:
lAl:48-0
+ 3 - 1 8+ 0 - 8 : 2 5 .
3HaKa KaxAoro rLIIeHaHaM Hy)KHo BbrflcHr.rrb,
,[.nr onpe,qed'IeHufl
qro6br Bropbre
cKoJrbKo nepecTalloBoK HeooxoALIMOBbInO,rrHr.rTb,
,ueHa ay(r22a3g
B
IIoptAKe
l,
2,
pacnoJloxuJlHcb
3..II,ng
I.lHAeKcbI
Sror ueroA Bbrqncrenlis onpeAeJrl.ireJrronucaH flemoQpeqilo
s uoHofpaQun
l5l. Eo.uee o6qerpuusrblft noAXoA, LIsJro)KeHHsrrl
f u p n u V u n e p a [ 2 ] , o c n o u a n H a r a K H a 3 b I B a e M o M e r o A ea J r r e 6 p a u qecKI,Ix AoTIoJIHeHI{ft,HO rlo cyqecTBy Ma,'IO oTJll.tqaeTcflOT ll3r'rox{eHHofo.
Teueps MbI yxe yMeeM Bblqr.IcJrflrbonpeAenureJlb KBaAparHot?
Marpltllbl, Ho eule HescHo, qro gro raKoe. Onpe4e.nureJluBo3HLIKasaAarrax, HO qaqe BCerOOHr.rHetBHO yqacTBylor
IOT B paSJrLIqHbIX
ypaBHeHIlfi. ql,Irare.nu Mof He saMeTI'ITbI'lX IIpIt
B perueHH?tCPICTeM
t44
l0-201
d,11d.22Asg,
A11d.2slg2,
Apd2gAs1,
Q.12d.21lgg,
AgA21Ag2,
49d22O,31.
145
paccMoTpeHIIII 3rofo Bofrpoca, Ho cKpbITo oIIpeAe.ry['lTeJII{IICilO.IIb'
.soBa.rrrrcbB npoqecce o6paqenfifl
Marpuubl. Peurult cllcreMy AByx
ypanHeHilli:
atfit *
rpe4crae,rnr,.u
.".::f;'
&pa2:
0.1,
p a H e en p u M e p e :
o a npuBeAeHHoM
f t r p o n e p H ua r o n p a B H J ' I H
'nl f"'l:f.?il
In
Llo 3ol L',J LrroJ
(3.5a)
ure"Tl
I.f,
3 s a nes aterrrt e o 6errx,npo6nx p a BHbI oIIpeAe.rl
|:
*oo'.,
"1':;;;#
";l l;;|: ti;]
loo',',
(3.56)
Hrrcnrtrerl Bbrpax{eHr.rfl
[Jtfl x1 paBeH onpeAe,txre.{}o
ro):40.
I l ?l
l?l:138.30)-(rro
l0 3ol
A l u y ; x e B b l f l c n u r ' r r rq,r o B e K T o p - c r o n 6 e ( H e r l 3 B e c r H b l x t r r x z
,Mo>Ker6urr nailAeH c rroMourbrco6paueuuq Nlarputrbt.OAsaxo nul
MolKeN4uafitu HeH3BecrHbtec noilIournlo 06stqultx a,rre6panqecKIIX
npeo6p a sonanuii. flo"'tyuHu
. - -- - , , j , - L b r o r . , - f t r z b "
"t
orrorr- oLzQzl
V
..
"'
:
ertb"-brdz,
orr,r.u- orrou'
H e r p y , l n o 3 a M e r l l r b , q r o 3 H a M e H a r e J I yH 3 T H x a u p a x < e n u i i oAIiHaxoeur.3ro onpe4eflIlre,'rbMarplrtrbl [A], r. e.
I A ] . - :::
:','"1:
atrazz- &zzazt'
(3.E)
npeAcTaBIITbKaK onpeAe,'IIrTe,'IH.
TO)KeMO)KHO
f,anee quc,,IIITeiTH
rlnc.lrrre"rl BbIpaxieHfifl AJrfl,xt \'lo)KHo npeAcraBIITb KaK otrpeAeJII{TC,']b MATPHI{bI
I B Ai,':li: "ni"l:b1a,,-a2b1,,
A
tIUC,ililTe"Ib
Bblpa}IieHKfl
!'JIfl' x2
'B, :l::: i:
I'{,,
(3.er
KaK OrrpeAe,lliTeJlb MaTpHI{bl
:
artbz- azrbt.
(3' l0)
Sror lterol NIolKHoo6o6ulurl ua .nrc6ue cucreMbl ypaeneHnli.
T a x o u c n o c o 6 p e u e H H r i c H c r e N r b ry p a e H e u n l ' rH a 3 b r B a e T c tIlI p a B H .nOrr4
KpaUepa, i<OrOpOefr'tacHT,tITo sHaqeHne lrc6otl Hel,t3eecrHOii
.tl B cricTeMe coBMecTHbIxypaBHeHHt .paBHooTHo[IeHI'IrcAByx onpeAe,rlrre.reti3
. s a u e H a r e J l b- o n p e A e J I H r e J I b ,aNr Ip u u l r r < o : Q S n q n iHron (e HaueM npttMepe Marpllubl IAJ ). 9uc,rrlre,Ilb onpe^ei
f
t cron6e(
y
roropoii
J r l r r e . r b ' r o r 1x e n a i p u U t r x o e Q s u q n e H r o n ,
b).
t{acreft
(nepop-cro,r6eU
ypae,ueuuil
.3aMeHeHcro.n6ilolt npaBblx
146
I
9lrc,rure,tl BbrpaxeHr.rtr,Jtfl xz paBeH
: 60.
: (4'o)--(r0.38)
,1 ,?:l
(3.6)
(3.7)
1?l:,0.30)-no.ro):20.
\
/
301
ilo
tr4rax,xr:40/20:2,
a xz:60/20:3d.
o6Pun"" c nonaoiqurc
paxIeHHt MaTpllu Mbr Irau,'lH TorlHo TaKHe 3HaqeHI'lt HeH3BeCTHbIX-
HbIE 3HAq EHI,Iq il CObCTBEHHbIE BEKTOPbI
CObCTBEH
Teua, r xoropoii Mbr rrepexoAnM,- co6crseHIrHe 3Har{eHl{s It
co6crseHHlre BeKTopbt- Har6o.qee rpyAHa B MarpulrHoft anre6peKoropoe qBflrercfl He
TpyAHocrl cocror{T He B rrx Bbrr{uc,'reHxu,
6o"ree rpoMo3AKHM,r{eM Apyfxe MareMaruqecKlle trpoqeAypbl. Cxopee Bcefo, TpyAHocTb 3aK"rloqaerct B HHTyI.ITHBHoMIIOIIUMaHHIT
orux BeJ'rHrrHH.
K Hecqacrblo, n 6o,rlurHHcrBe pyKoBoAcrB 3Tzi reMa
I{3JIafaeTCflB CTpOfrX MaTeMarriqecKfixrepMHHax, He BCefAa noHflTHbrxHeMareMaTI{Ky.
noHsruli o co6clseHHblx Bel(Topax
Oqegl xopouee H3J'rox{eHLIe
rr co6ctneuHr,IX 3HaqeHr.rflx,cofipoBoxAaloureecq reomerpauecxofi
uHrepnperarrueil, 6uno noAforoBJieuo foy"tt4ou AJ'IqcryAeriroB reo'rpaSuvecxoro Qaxy,rlrera llesculrbBaHcKofo yHIJBepclrrera. flpnreMbr ocHoBbrBaercnHa srorl pa6ore,
BeAeHHoe3Aecb H3r'ro)KeHHe
a r a K ) K e H a c r a r b e l o y , r 4 a [ 3 ] . M s r 6 y a e u p a c c M a r p H B a r bM a r p r H3 KoopAl.rHarToqeK B HeKoTopoMrrpocTpaHcTIiy, cocTaBJreHHylo
Be, H l{HTeprlperl.rpoBarrcsoiicrsa co6crBeHHHx sHaqeHilfi H accoqimpoBaHHbrx c HHMH co6crseHlrttx QyHt<qHilKaK reoMerpnqecriue
c n o f i c r e a p a c [ o J r o ) K e H u sr o q e K . T a x o r ? n o A x o A r p e 6 y e r p a c c M o r peHufl MarpHrr Hu3riux iloptAKoB. Oluaxo rrHTyrirHBHbre
rrpeAcraB.IIeHHfl, no,lyqeHHble
AJ'lt
3TO|O
C"lyrrafl'
N{OX{HO SKCTpanOJIlIpOBaTb
Ha Marpr.rubr6o,rlurux nopflAKoB, Aa)Ke Ha raKue, Bbrqucd'IeHut{
A,nn
npr{ pyr{HoM cqere. C.rre4yer
Koropbrx flpaKTnr{ecKIIHeBbrnorrrHHMbr
3 a M e T H T bt,l r o M b I B c r y n a e M B T a K y r o o 6 . r a c r b , n x o r o p o i i o q e H b
qacro .u.axe uau6oree MourHtre 3BM oKa3blBalorcflHe B cocroflHgrl
10.
| 1J
t+ L
.IIPCOAOJIETb
BblqI{C,'IHTCJIbHbIE
TPYAHOCTU.
TAK KAK MbI Y)KC NO3HA.
.KOMIiJIIICb
C OnpeAe,'IHTeJrrMtr,
To MoxeM LIx HcIIo,IIb3oBaTbAnR
BBeAeHUTIIOHrTtiii CO6CTBeHHbTX
3HarreHr.rfi
u co6cTBeHHbrxBeKrop o B . l l y c r b A a H a c H c r e M a y p a B H e H r i i i ,B a n l r c a H H a sB M a r p r { q H o f i
QopMe:
l , 4 .l t x l : 1 " [ x ] .
( 3 . 1)2
rorrbKorerepb [B] :1,[X].
HyNgg saftru BH_aqeHHfl
1,, yAou.nerBopflrorqne
3roMy coorHo.
(3.11) nrox<Ho
{rreuuro.
VpaeueHHe
3arrcart e $opn,te
(tAl-rul).[x] : [0],
( 3.13)
rge ft[1]- eAaHri_quas
Marpurta[/], yrranoxeHnaa
Ha qricJrol, (no-n
plAor Marpnubr[1] raroii xe, xax
noprAoK Marpnrrbr
t/l).
Marpnqal,[/] nopnar<a
3X3 HlreerBrrA
LIII:
[s;:]
(3.r4)
Hcno.nssyn trpHnrrylo 3altHcb, fioryrrrlM c,'reAyroulyK)CI,ICTEMY
5',paeHeunft:
(art -
I ) x t + a t z x z* Q 6 x s : 0 ,
(ar, - lu)x, + d2sxs:0,
a e f i r * a e z x z* ( a t t - l , ) x 3 : g .
Qtzxr *
(3.r5)
peAe"'IilTeJIIr
KoropbIX flBr'tflIorcfl qticJIHTer'tgMHgrHX oruoueHufi,
€c_TbHla'r€Bofr cro,.r6eq, oTr.{ onpeAe,'ruTeJrltpaBHbr H-v.[rc. Taxullt
o6pasolt,
rvr-
to1
rAr'
143
i-I att
dn
&b
0r, -
I
CIys | :
2,
-'esz
0.
( 3 , 1 7t
o"L l
, nosrolly MoxiHo
o 6 u q H o x o e f o u q u e : H r b t a i i H a N rH 3 B e c r H b I H
HaXOXAeHHqSHa.{eHI'Iii,
tsocfio,lb3oBaTbcfl3TI4MCOOTHOIIeHHeM,U,J'Iq
yAoBJrerBopflroulllx 3aAaHHbnt{}'c,'roBlirrM.,[Lnl eroro npeAcraBHN{
onpeAel;rre"rib KaK nod'rlHoNria.rbuoeypaBHeHI.{e.PaccnaorpuM cHaqata o[peAe,IIIiTe,'1b
MaTpLIIIbInOpr4na 2X2:
dnazr
L
ap
drz-
-fl
1
flpegcraenM otrp€!,err,rre!'rb
B BllAe
h
)
(ar,
( a z z- x ) - a u d n : 0 .
floc.ne repeMHox{esus
noryrrHNI
(a,r ?")(azz f) : (anazzl a cJlox(}rB3TI.IABa ypaBHeHI.ifl,rIMeeM
(anazz) - (anarz) - (a1l) -
(au?r)-
(arzlu)* 7"',
( a z r l ' ) * 1 " 2:
0.
Ai1, TO nOC,'IeAHee ypaBHeHI{e
Tar xar r\{br sHaeM 3Tl:qle,HLIfl.
B BHAe
I{OX{HOIIpeACTaBI{Tb
(3.18)
1,,2
+ a t l u* a z : 0 ,
o6uquoe
tAe ai - cyNrr'rbrcoorBercTByIoqIIX snaueuufi a;;. 3ro
xopsrr Koropofo BbrK B a A p a r H o ey p a B H e H u eB u A a a x 2 + b x + c : 0 ,
rnicJrfllorcfl no Qopuy,re
-b+ V'br-4ac
(3.19i
Ec,rrr qurare.rb He3HaKon c sroii Qopuy.noft, a raKxe c pa3,rroxeHHeNl KBaAparHOrOTpexq.rreHaHa MHox{HTe/'r[,oH i\lo]KeT BocpHbIM y.Ie6HHKoMa.nre6prt.
arbcs a,teN{eHTa
noJIb3oB
B u q ; r c . r n l r r e t r e p b c o 6 c r e e H H s r e3 H a q e H H f lr r a r p H r d b r[ o p f l A r i a
2X2.il',,crr
rl7 - 6l
rr -^,rr-- |l - - [ J_ l 6. It.
Nrarprlqv
e Qopue
C H a . I a , r anpeAcraBuM
3anucas 9To coorHorxeHlieHHar]e,ro,ltvr{HM
lAl.txl: [0].
'
lott'o,.r
2a
flpegno,roxurlr, qro y erofr cr.rcreMbr
ecrb HerpfiBr{anbHbre
perueHHfl,r. e. qro cyulecrBylor xi#o. flo npanu"ry Kpauepa 4,rrn
peueHrrflcncreN{btypanueuuiiHerr3BecrHble
HaxoAtrcfl Kar( orHorxeHr.rs
B csqsr{ c reM qro B Nrarprrqax,onAByx oripeAe,,'iur€"{€ii.
l'rJ-
I A-xl | :l
( 3 . 1l )
B srox{ ypaBHeHurnpou3BeAenrreNrarpuubl xoe$sHqueuroe
{aii) ua BeKrop-croJr6eq'HerasnecrHbrx
[x]'paeHo npbriseeaer{Hro
KoHcraHTbr
l, Ha sexrop-cro,r6eqHeu3BecrHbrx.
3agaua norrrrr raKas x{e, KaK H pe[reHuecr.rcTeMb]
ypauneuufi
t A l . t x l: [ B ] ,
I'rarpuuu [A]
eexrop, ro o[peAeJILIreJIb
Ecnu [X] - HeHy!'IeBofi
paBeHIIy,'tIO,
T. e.
(3.16)
'-;'
r.4t-rrrt:[
_;ir]
r49
IIp Hpannrrearr onpeAe.rrnTe,rb
Hy"qrc,ilo,ryqaeNI
1 7- ) .
| l o e x a e q e t { I I o I i o H q n T b c B b I q H c , ' I e H H e M c o 6 c T B e H H br{ro6bi
Ix3HaqeHHii
pu.t*orpHM elue oAHHrIpHMep'
-6
- 16* 2
I e p e u H o x e H H e , t a e r -: 2 7 2 - l T ) . + 1 6 ) " + i .+22 T O : 0 , u . r r ;?: u 2 - ] , - 4.)
-2:0,
u J I I I l o c . r r e p a 3 " r r o N i e H l g, t e e o f i q a c r r i y p
;r rbaJM
- caoB6Hcer nHeHHf H
XHo) i I i r e J u ( ^ " - 2 ) ( f + 1 ) : 0 , q r o o n p e ! € r - r f l € r; 1 a a
3rra*
t l e H I J t7 q : 1 2 , ) ' z : - 1 .
3 r o r n p H v e p 6 u " n o u 6 p a u H a M t r A , ' r f l y- nnppuouueepH,r i s e s r { r . i c r e H r . r i i .
Tenepl >Ke paccMorpuu 6o.lee c,roxHsrii
B KoropoM ucI r o J b 3 y e r c f l c n c r e M a . y p a a H e u u i i , r { o r o p y r c M b r H e o I H o K p r , f H op a c _
c M a r p u B a , ' rB
u b r [ i e .I l y c r s A a H a M a r p u u a n o p a g r < a2 X 2 :
4
rr ,r ,rr-_ | [10
flonropreu
l0l.
301
4- )"
10
t0
30--r
l0
30-e
I
^'
J-,rl "l:(:-11(3-1)+24:0
1,2-5i*30:0.
rorcn no Qopuy,re
Bbrrir{c,'rrr
KopHuaroro YPaBHeHrs
( I 1 , 9 ( - 'lut o
u
|
z
^
tuL-
5+V'=es : 2 , 5 * 4 , 9 i ,
2
b-V -v, :2,5 - 4,9i,
^
---nnz:
20:0.
*t-3a)!v=1a"=a:T
2a
2'l
33,4,
_ 34+VW6
-_-_--'-'
lz : 0,6.
Mu uoxeu npoBepnrb3 T X 3 H a r I e H H t , n o A c T a B U B I i X
!rHTeJ'tb.
vqurlteag ouru6xuoKpyfJreHufl , noJrylraeM
B OrrpeAe_
10
: ( - 2 9 , 4()- 3 , 4 ) - ( 1 0 ) !(0 ) : _ 0 , 0 4
30 33,4
l0
4 -- 0,6
(3,4.)
(29,4)- (10)(10,y
: - 0,04.
l0
30- 0,6t-
t_
Taxnu o6pa3oM,co6crBeHHbre
3 H a q e H r i fH
l aii4eHu BepHoc roq3HaKOB.
HOCTbTO
AO AByX AeCfTI,Ir{Hblx
150
-t) ^
rpe6yer
Mur nu4tlu, r{ro Haxo}KAeHIreropHeii 3Toro ypaBHeHufl
ql'lcer'I'TOtAa
OTpI{UaTer'lbHblx
I{3
r<opirefi
KBaApaTHbIx
H3B.rleLreHug
trIcno,rlsyr$oprray,ry
Ar'rs onpeAe,rreHHrxopHefi KBajfparHoro
4-33,4
10
I
l2-L
^1 L- , 2 -
yp aBHeHi{fl, rro!'ryqaeM
lr:
BL,IqHC,ltlqroropltit,
no,[yquM
-o
: (4- t)(30-1)- 100:0
1\2- 3 4 ? \ +
- b+l/br-4,0c
l--u B'-li:o'
I
I'TJIYI
1:
t241
|
I n r - L _ 6 3 1|
b
^io onpeAe'll{re"i
Io .l;:T.t"tf
M Hy.rI
llprzpanHae
r zrl-
'g"rIH
!,alee
4-7
l0
"."p;;";;;";^-'ty2,
K
a 3 a T b , K a K H e N l O f y T e O a U U X U y f l A O I I O " I H I ' I T e " l b H b l e O C ' I I O >: K H e H I ' l q '
Marpulrbl
;;; s uairci co6crBeHnbre sHar{eHI'Iqcr'IeAyloqeii
n;t;;
r
Bce [poAe,']aHHbreB npeAbrAyilreM nprrMepe Aeii-
CTBHg:
no-
qucJIa, coAep)Kaul]e KaK',neiigraure'rrIAe fr, lz - KO!1II.r'IelicHble
q a c r H , B K . r l F o q a r c u r uq ea c " l o i : ' l - l '
K ctlaHyIo, TaK Ir MHIIMVIO
HMeIor
Aelictsurenr'Hlte
crblo, cuMMerpllt{Hble }larpHIrbl BcerAa
, ' e 6 o , ' I l l u H H C T B eH a u H x B t I t { H C " l e H l I i i '
c o 6 c T B e H H b r 3e H a r I e H I t f i H
3HaqeHIIf BeliTopaNIIi iI CO6cTBeHHbINII{
CBfl3aHHbIx C CO6CTBeHHbII,Iil
MII,}ICIIoJb3yI.oTcfllioBapuaqrloHHble'KoppeJIqIIHoHHbleI{JIIIaHaJIor n q H b l e M a T p H I I b [ ,I i o T o p b l e B c e f A a C I I M N l e T p H q H b I '
3HaTenepn pacclrorpriri iipoqeAyp_y BbIr{IIc,'IeH}IfiCO6CTBeHHbIX
qesuii l,ra inrarpriqblnopflAKa 3X3:
Bl
rl l : 0 - 4
-.20
-+o
B
|
|
t2 -26 J
L -oo
IlpupanHue aeM Hy,{Fo coorBercrB}'Ioulllli orpe!'€'tlIir0rb
2 r-).
0-).
-4
-4
B
I
-20 l:0,
-40
B-r,
- Grt t2 -26 - )"1
-l'3 +2]'"2+8]":0.
nocJie qero rlo,'Iyqltlt
lDt
3ro - ry6nuecxoeypaBneHue,r.rMeroulee
rpr.r KopHs.Fagno>xHs
ero Ha Mnoxr.rreJrx,
MoxeM sanr{carb (f-4) (f-0) (t+2):0
E
KopHafu:4, ?uz:Q,}us:-2.
noJIyqI{M
Xorq usroxenHbre[pueMbr npr.rMeHr.rMbr
K Marprrqe.nrc6orono.
ptAKa, HaxoxAeHr.re
xopHeft [oJIHHoMoB
BbrcoKr.tx
creneuefi flBr'rgercq HerefKolisa4auer?.
O6uqno co6crseuHsre
sHaqeHrirHtxonrrrcfi!
He c IloMolqblopeueHr.rflrroJrr{HoMl,IarrbHbrx
ypaeneHuil,a c IIoMorqbroMeroAoBMarpur{Hbrx
npeo6pasonauuii,cyuuocrb Koropbrx
cocrol{TB rroc/'reAoBareJlbHbrx
npn6,rnxeHi.rtxK co6crseui{trM3HaqeHHflM.3ra lreroAbroKa3aJrucb
rrpHMeHr.rMbIMH
ToJrbKo6,raro4apx.
14cnoJrb3oBaHrn
6ucrpo4eiicreyrouiHx 3BM, nosBoJrflloi{iix 3a
BecbMaxoporrcaftnpoMelr{yror(BpeMenr.r
nafira npu6nnx<enuoepeuIeHIte,a 3aTeMyToqHHTbefo B TelteHLIeHecKoJrbKr.IX
MHHyT.
lerrepb, K9rla Mbr noryrlnJrH npeAcTaBJreHHe
o npoue.u,ypeBbrrIHc'IIeHLIg
co6ctgeHHutx sHa.IeHLIft,Mo)KHorro[blTarbcfl noHflTb H Hx
cyuluocrb. Marpizl(y Mo>KHopaccMaTpgBaTb KaK Ha6op sHa.reHr.rft
KoopALIHarroqeK B n-MepHoM npocrpaHcrBe. Marpuqa
nopsAr(a.
2X2 coorsercrByer n,nocnofi nonepxiocrn, TaKofi >Ke, KaK Jrlrcr
6yn,Iaru.Taxnu o6pasou, Marpr.rqHbre
oltepaqun MoxHo rpaKroBarb.
reoMerpllqecr<n.Tar, Marprrqa
F n c . 3 . 1 . J o a s e x r o p a ,o n p e a e l r e H H b l e
aMlr nopflJ.xaMarpHUblzXZ
3,leMeHl
Prrc. 3.2. 3.rnllnc, onpe'le'reHHut-t
9 . t c \ r e ial l1 l1l r l r r n H u b ln o p R l l i r z X z '
Co6crgeHnlte Beliropbl Marptlu,bl coorBgl'
CTByTT InaBH!'IM nOJIyOCflMSIJItrnca
t4 Br
|
rr r. f, r-_ |
18 4l
ottpeAeJrrerABe roqKr.r["'rocnocrr.t
c KoopAr.rHaraura
(4,8) a (8,a)Srlr roqKll coorBercrByroTAByM nexroparr,rHa KoopAr.tHarnofi
i,rrocKOCTH,BbIXOASUIUM
H3 HaqaJIa KOOpAIiHaT,KaK 3TO nOKaSaHOHa
pHc. 3.1. Oruerrnr, qro B KaltecrBe KoopAlruar roqeK MolKHo r4cnoJrb3oBarb u cronbqu Marpurlbr, qro He Buecer cyrqecrBeuHbrx
HsrueHeHnftB Haurn paccylxAeHlrg. Ens, ofipeAe.rreHuocrrr 6yaera
Aeficreoearb co crpoKaMr.r.
flpe4ctannu ce6e, qto ABe rorrKl.L're>KarHa s!'i.{trncec qeHTpoM
B Haqale KoopAliHar. TorAa gJrr'ralc 6y4er npeAcraB.rrrrb Kpr.{Byl.o,
IlpoxoAflulyrc qepe3 3TI{ ToqKH. B pesy.irilare co6crneHHbreBHaqeHwfr Marprtlbr oKa)Kyrcfl paBHbrMv AnnHaM 6onturoii u uanoft nolyocefi sroro g,rrJrnnca.B HaureM npr.rMepeco6ctaeHHne 3naqenrrfi
pannu hr:12,}uz:-4.
Heo6xoAutrlo orMeruTb, uro orHoIIIeHHt no.nyoceri Mo>KHoHcIIo,'rb3oBarbKaK Mepy BbrrrHyrocrrr g/'Inr{trca,uro rpa$ruecr{r.{ noK a 3 a H o H a p a c . 3 . 2 . f l e p n o e c o 6 c r s e H H o e3 H a q e H H ex a p a x r e p t i 3 y e r
6o.ururyn floJlyocb, AJrrlHaroropoft or ueHrpa .qo calrori yla,lreHioft
o r H e r o r o q K r . rx p l i n o i i p a B u a l 2 e 4 H u t q a l r . B r o p o e c o 6 c r e e n H o e
s H a q e H i ] eX a p a K T e p H 3 y e TM a , r y r c n o . r y O c b ,H a x o i l q l q-pasHa
ylocq Bo BTOporl uernepra KoopAHHarsoii flJrocKocrr{.Ee 4,lllHa
4 e.quH r I r l a M u 6 e p e r c n c o 3 H a K o MM L r H y c .E c , r u 6 u r 4 e e 4 a u H u e r o r r K a
6ltlu 6.nuxe Apyr K Apyry, To orHorreHlre [oJryoceli llsN{eHr..trocr
t52
coorBerPrrc. 3.3. VA"'linessulir 3JlJll.l[c'
KOTOpOIt
CreyrOUtll'r MaTpllqe, 9'leMeHTbl
gaAalot
TOqKn c pacc oflHl'IflMI.IMexiAy
--ltttr,
M e H b l r l l t M l l 'q e M H a p l ' r c ' 3 ' 2 '
Co6ctget:Hste
BeKToobl
noJlyocnvfl
qBntorca
Puc. 3.4. Marpuqa, cogePxaxr.aq paBHbIe cTpoKH'
npITBOAATK BblpolKAeHHOMy snnlrllcy - [ptMot{
TJIaBHbI\1fi
3'[nHnca
ecr'rlr
6u. HanPunaeP'
Iu,lrMtlMarpnqy
BbI6paHbI TOqKI'I c
: [3 :]
rAr
M arpllllbl
oo co6cTBeHHbIM I'I 3HaqeHI'lsMI'I
o6paayrc'
KOOpAlrHaraua,
6yayt uI{cJIa}q:14, Lz:
- -2.
153
3ro noxasauorpa$uuecKr.r
Ha pric. 33. Eo.rlruas noJr).ocb
AaH_
HOI-O
3,rr"rHI,ca
HalrHoro60"rrrueMa,'rori.Ec,rll .rsc olr6pauur,re
rouKri coBfiararor,T. e: ABe crpoxrr Marpur{broJriuariond,
To tsropoe
co6crneusoe3HaqeHHe
craubezrcs pinurrn Hy.Tio,]r paccMarpH_
gaer4lrrio,rr"ru''cBbrpo)KAaercl
n nprryrc. Orolry .ryur6 oru"uuar,
Hanplril4ep,
NraTprrqa
l - + BI
rnt_[+ BI,
xapaKrepucrirqecr{oeypaBHeHr.re
xoropori tur-ln.+0:0
Aaer co6crBenHbre
3HaqeHr.rq
7q: 12,)"2: 0.
c]rlyaunn Hso6plx<euarpaguuecKirHa puc. 3.4.
-urix
,Ine
-..11:.::
BbtopaHHbre
ror{Ku coBrIaAaror,
.repe:
npoxo.tltr'6o.rouagno-
Jyo9;b' a nepneHlllKy,'ttprraf
x u e i i M a r ' r a f l o c b p a B H a H \ . . .ttr , l .
l l p o r r B o n o , r o x s s r xr ip a r i H H rci . r y u a f io n u c i , r i a e r c n
" rrurpruefi,
coorBercrByroueii,reyN4
nepneulrrriy,rrrpHbrM
BeriropaM panHoii
Hanpu,vep,MaTprrua
AJ'rrrHbr.
t . q:l L
l-4
BI
a 4)
rrMeerxapaKrepxcrurrecKoe^
1,,+ 0l_g0:0,
xopuu xo_
r o p o r ol r : * 8 , 9 5 , i , r : - 8 , 9 5 _ypaBHeHue
.
c"ryuaii rpaSnuecxz npeAcraBrreH
Ha prrc. 3.5. !,aaHue
__
?"o"
Bet{Topbr
flBdrqroTcfl
paAr{ycaMuoK-pyxHocTu,B tioTopyronpeBpa_
TlIJct
3rtr'lunc. Hx p,nuua paBHa co6craeuHuM
3HaqeHHflNI.
3aueruu o,u,Ho
BalKHoeceor?crsoco6creeH"i." ,"rua"r.rii, xoropoe qtrTaTe.irb
Mox{eTnpoBepi.rTb
Ha npHBeIeHHF,rX
paHeeflpr{Mepax.
cyuua co6creeuHurx
sliaqeH'rruce.gu'paBHacyMMeAr4aroHa,,rbHbrx
s.IIeMeHToB
Marparrl'r'Koropafl Ha3brBaercq
cdrreAoM
uarprqu. oro,
csoricreo no'rre3Ho
r{crroJrb3oBarb
i1/rf npoBepKrlnpaBlr,rrbHocrr.r
BbI-
qr.rcr'reHrrrco6crBeHHbrx sHaqelrHii Ha 3B,Nl, a raKiKe rnfl KoHTpoJq
e b r q n c n e t : ; t r i n p t t I I c n o , ' l b 3 o B a H I I I IN t e r o A a t . t a B H b l x l i o \ ' l n o H e H T .
B c n i : v a t t l , t , t t r o ) t b t o r t p e A e " q l t r ' t lci o 6 c r e e u H b l e 3 H a t t e H t l f i K a l i B e J n r q n ! l { , 1 ,: x o . r . f l u , u e B \ r a r p u u , y c l l c r e M b r y p a n u e u l t r i ( 3 . 1 3 ) . T e n e p u ,
t{ofAa:il ,: Be,iluqllsr,trtalijleHbl, N{6)KHo BepHyTbcfl K cllcreNIa}l
y p a e u e u i r ; t I I R b r r i l l c . : i l r T bB e l i T o p H e l t 3 B e c T H b t rx . ! , " 4 1 \ l a T p l l l ( b l n o pttlia 2. :2 nepnoe co6creeuHoe 3HaqeHlleno"lytlll\1 ll3 ]rpaBHel{lifi
It ^r r , , 2 ,
L
ot,: I
[.''l
I
i
t-
o.::--7rl l-.'rj
tlzr
f0l
I
I
(3.2C)
L0j
! , , i t r . l o p o r . o c o 6 c l e e H H o r o 3 H a q e H l t f l ) t a r p l l r l H o e , v p a l l H e H l l ec o c l l i i , r M "r. . . - i a H a . ' r o r I I r t H o . f ] o c , ' i c B b l r t t t c t. e H l l f l J l t a l o H a ' i I b H b l x 9 . l e \ I e n n o r r r vi , i r ( H Ou l i i r r t H e t l 3 e e r l r t { b t iei e x r o p c n o } 1 o l ! b l { l o 6 p a u l e t i t i x
: \ l a r p . r 1 r r , i .3 r c , r B e t i r o p I i a 3 b r G a e l c n c o 6 c r e e H H b t N l B e l i r o p o r a ( a r a t i r pricrtirl€ctirr\i Il.rill f.rraiiHbl)l aetiropolt). I(a;x;10uy coi,lirie -:ta0irri€
crBeHHov .' Betiropy coorBercrBver co6creeHHoe 3uzlrlcHllgM?Tpllllbl.
Criorur,.l ,'N,rarprIuL't co6creeuHlrrx 3traqeHltii, It.lrr crpol( (cro.'t(;q o s ) , c ' i ' 1 . ' , r r . i o1 ' : r o i i N l a r p u t r b l r t c o 6 c r s e u t i b l x B e l { T o p o B .
T a n l r r r . lo 6 p a : o l t , u r o 6 i , t B b l q l l c i l u l ' b c o 6 c ' r e e H H l t e B e K T o p b I I i
c o 6 c t s e s f r . r e 3 H i l r r e n r r f l i , r a r p t t u t t n o p f l r l { a / 1X / u , H y ; l i H o g a f i t t l l t
xopHeri e€ xaparirepttcrHqectioro ypaBHeHIlr II peurtrb // cflcreM H3
paccMarpl{BaeN'lble Ha\lll
i, coBNrerrnbrx vpaBHeHuii! K cqacrblo,
rrpuMepi,nr Marptitt ilopflLKa 2:;.2 se rpe6yror rpol'lo3Alilix Bblrllrc"neHrrfi.
Ha.rHev c paccltorpeHllq Marpuubl
tt7 -6 I
,l
rt r, 'rr-- |
l-trJ -_l0r
BcrrovHnl,r,r{To r,rbryx{e Bblquc"'ttt.lrtco6crBeHHbte3HaqeHl4fl3ToI"t
N I a r p l I U r , tI:t : * 2 , 1 , 2 : - 1 .
i N { a r p l r u YA a e r
l l o 1 c i a H o e x a n e p B o r o c o 6 c r B e H H o r o3 H a q e H r l f B
-6
[r7-:
-6
ll5
I
-lo-zj :f+s -18J
L nt
I
C o o r s e r c r s y r c t l l a f l c r r c r e M ay p a e H e u u l i I i M e e r B U A
15x1- 6x2:6,
4 5 x 1 - 1 8 . 1 2: 6
n uarpuunoiiQopue
I rr
145
P u c .3 . 5 .M a r p u q a ,
3J'reMeHrbi
3araror nepneHArrlil."tnpHbre
BeKropbr,
orrpe^
i9t-gp9ti
: e , t t e T 3 . { J H n c c paBHbt\4r.r
no,'lVocf\11t.
T. e. oklt\,)xHocTb
Ial
-?,I[;l]=l3l
Flerpyauo BIlAerb, qro Bropoe ypaBHeHHeMo>xHo noJlyql4rb II3
Ha 3, nogroMy AocTaToqHopeul'{TbOAHOIt3 HltX,
nepBofo yMHo>KeHl',lefut
.qro6u nor'IyqeuHblepeureHllfl yAoB,'IerBopflJttrtr ApyroMy ypaBHe155
I
HHIo. flpocrofi noA6op Aaer_cJreAyroquepelueHHr: J/d:2, )(z:5,
9TO KOOPAI,IHAT6I
TICPBOIOCO6CTBEHHOIO
BCKIOPA, COOTBCTCTBYIOqC.
ro [epBoMyco6crBeHHOMy
3HaqeHHrc.
B leficrsurersHocrH r{Meercs
oecKoHeqHoe
MHo)KecrBopelxeHl]fr',rat< KaK peneHI.IeMtBJIFerct
Jrlo6oriBeKTopBr.rAa
l:):u13l
rAe P -,'ilo60e quc.rro.Mn xe orpaHnrrHflI{cb
ro,'rbKooAiiHr{ 3HaqeHHeM
9:1. llosxe yBHAlrM,qro rinTepecnpeAcraBJrflror
ro,rrbKo
xoopAnHar BeKropa, a oHr.rnpH yMHolKeHriH
BeKropa
9-1"9T:11"
Ha !'IIOOOeqIICJIO
He I,I3MeHgIOTCff.
aJIeMeHTbt
Kr'roHa6ontuofi noJlyocn SJIJIliflca.Ecnu paccuarpuBarb
To
nJloctiocru'
Ha
ToqK[
KoopAI'IHarbl
KaK
co6crseHHoro BeKTopa
tBJlflIolqylocfl
rloJlyocb'
ottpeAeJlser
BeKrop
co6creeHHuft
nepeurfi
6li'ccexrprEcoftyr.na Mex{Ay AByMr 3aAaHHbIMI'lcrpoKaMn MarpI{IIbI
aerropa'tlt't.
A.tinna [oJlyocu paBua nepBoMy co6creeHnoMy-3Haqe'floAcTaBJrflfl
IIO:
e iradrpnuy Bropoe co6crseHHog 3H3r{€H1{€,
ilrzlo.
JyrrHM
f4-t-_+l 8 I
4-(-4)l
L8
I:l^-i
i18
-6
I
Lns - t 5 . 1
ypanHeHliflnpriBoAsrcflK oAHoMyypaBHeHlrrc:Bx1_1sr:
:0,^O6a
peuesneMKoropororBJrsercr BeKTop
I
i', I
^| I
't
lr, ): Lsl
f"l-[-r I l,
I
1",l-L
f 4
I
s
8
4)
I
I6 8l
IAI:le 6l
.II,.nanepnoroco6creeuHoroBeKropanorlxqlrM
8 l
f(6-14)
(6-14)l
L 8
f_8
4_t2j:Ls
8l
-81
I l,
l-8 -8
j
Ls
f"l : iII
r
Lt,I
R
- lt
c co6crseHnbrMll
sHaqeHus,un
hr:12, hz:*4.
flo4crao,rnfl nepBoe ug Hlrx B rrcxoAHyroM a r p i t qy, [orytrtrM
l4_t2
l / l : 1 3 5 ' , ccJt€'
ne'
paeultfi --l/l:11?,
xoropufi LIMeerraHreHcyfJla HaKJIona,
H ons"IJIII[ca
no"Iyocu
rraefloft
K
nepIIeHAI'IKyJItpeH
,qosaierrHo,
lreururyn no.trjtoco(cr'l. puc. 3.2). ..
peAeJrser
'
Tenepr npouine4eu pacqerbl4,rr nropoil MaTpuubl, cTpoKH Koropofi otlpe,u,eJltlorroqKv, pacrloJioxeuHble6nuxe Apyr K APYrY'
ITCMB NPCAb]AYIIICMIIPHMEPC:
Xors sH'racJreHr{snpn yBeflHrreHrlu[opsAKa sHaqrireJrbno ycJIOXHsroTcr, paccMoTpeHHbreMeToAbrMoxHo npr{MeHflTbK MaTpH_
qaM nopqAKa nXn. [IpeNae ueu nepefirr.r K
Bbrqr{cJrEr€,rrbHbrM
ocIIeKTaM npo6neuu Haxo)KAeHHqCO6irseHHbrx3HaqeHuft, paccuorpHM HeKoropbre Marpr.rrlbl c ueJrbro npoBeAeHr.rsreouerpiruecKoro,
a'Jailwsa 9TAX BeJII{qHU.BOSI\40XUO,
UiO 9TO no3BOJIUT [OHfrHee
o6rgcnHrr reoMerpriqecxuri cir,rncn co6creeHHnx eHaqeHHft.
L H a q a J r ap a c c M o r p r - r M
MarpHuy
rr .r .rr-_l -l B
L6 6l
6yaer aropofi co6crseHHltftnexrop
Peureuue,ta
Marpuqa cr{creMbrypaeneuufi,orBeqarculaflBropoMycc6creeHHOMyBeKropy,HMeeTBnA
*6 I
17- (- t)
1
6
(
-t)J:
L 4b
[8 Bl
Ll
llepBoro co6cteeHHofoBeKropa'
Tarnu o6pasou, yroJl HaKJloHa
aoa"u"n""r +'S;f u"*"op AeJrLrr[o[oJIaM yron, o6pasoeaunufi4ny,Il,.rruna6o'riruofi noiryocu pasna 14'
Mfl 3aAaHHor*"
oxllAarb'
""*ro1iuiln.
u cJIeAoBaJIo
sHaqeHl,Irc...Kar
co6crneiluorrily
T. e. IlepBol,ry
BeKropy, uaft4euuotuy B npeAblAyqeM'
eror sexrop napaJIJIeJIeH
narirn'
nor.rMe'e,HO r.rMeer66nturyro li'lsy. AHaloriaqso Mox*o
co6cr'
BropoMy
coorBercrByroqnfi
aextop,
;i"p;f-;"?i.tuun""n
3rofi rrlarpi.rqecoorBercrayer co6crseuHHfiBeKroD
BeHHOMy 3HaqeHHIO:
Bosepaqascb cHoBaK pr{c. 3.2, y6ex4aeMcs, qro co6crsesuuitr
nopgAKa' xorq'
Sror uerog nPIiMeHHMH K Marol{qaM 6o.lnuero
paccMor'
npuuepa
BbrKJIaaKu cragoBgrcs 6o.nee c.troxHrtutl. .[,na
f "'l -- |tI
L', I LI J
BEKTOP MO)KHO ITHTEPNPCTHPOBATb
KAK XAPAKTCPI,ICTTIKY
YIJIA HA156
:Ll-rrlI
l;;l
lof
pI.{MMarp;ruy
t")
Ha p -. 3.6 ua
-
tii;l
i"l!ifi?li1,;
il1,,',i
1;fi1';3.x
;:n*;t,";r3;
:iii:fr
t';
",:ffiH"
lli,1,;:i;:iil;,ff
:r:d;#ii'J,"#;L:';J:",1i.*r;*":",';ti::
;'
;
;;
;
:::iii"''
f,|.il,i:{ii:#::}'"i^"r
if:if#';j:j:
i:Tlf
ll,ili'Tl: - i;,; Ji;rftll'u;
.,o6cr
ee
rrIrl,-*"J.,,,0p
";.",,':[];,0,,"",
i,
t.l?i]tt"ax co6c'neHHbrx
.it:t,.
rreHHbrx
3Haqenriii-iico6cr.r.:..iropoB.
crBeriHhrf.nr{.ni,o'lt,::]:t^-*tptrqa crrrlrlerp}rrr}ta,
ace rpn co6-
zr:II.3
-
::
.-,
Bo(roD I
0,69
0,43
0, ,t8
IledrT oD l
_n (A
-n
l(l
n !r
) . .- 2 , 6
BeKrop.S
-0, 4;
0 ,B 8
_-L),l i
L rroorno
C
6 eeqI t
Ha prrc.3 7. Bce]'Ka3aH'bre
'ct.
u,.ri;il" 1tffi:lr?"[1"6paNeHu
Bbiue
I-lpaeoMepHoe
p a c n p o c r p a H e H u ep e 3 - \ . . r b r a _
Crordeq
Prrc. 3.7. Co6crseHHHe
nopraxa 3\3 p a c n o J o x e H b l B T o M ; ' l i e
Be(ropbrMarpr.rqbr
qro u BeKropblpllc. 3.6.
npocrpaHcrBe,
y r r a , o 6 p a s o g a s H o r or p e M t i
Orrterxrr, qro nepabn'l co6craeH
Huitor;Xfl,,
R?1S:lnouutton
ToB sroro aua"ru3a Ha Marpuuu 6o.rruux [opt,[,KoB Maret\,IarllqeCKU OTIeBUAHO,
HO HaIIIH BO3MOMHOCTI'I
HarItlAHOrO npeAcTaBJ'leHHtl:
yxie rrcqepnaHu. O4Haxo rIlrrare,'rb Moxer ce6e npe.qcraBr.rrbcoBoKylHocrb roqeK B rrpocrpaHcrBe 6oree sttcoxoii pa3MepHocru,
nepneH'
B HeM rpe6yeuoro qt{c,'IaB3aLINIHo
a raxlKe cyurecrBoBaHr.Ie
A I I K y . f' ilp H b r xH a n p au n e u u i i .
3Aecr Mbr orMerHM To,'rbKooAHo Ba)KHoe csofrctso co6crneuHbrx BeKTopoBMarpurr o6ulero Br{Aa, He rB,'trrotrlt4xcscIMMerpttqHbIMII.
Cror6errI
Fuc. 3.6. Bexropr,rB TpexMepHoM,npocrpaHcrB^e,
onpeae.qreMbre
S.IelreHT{1[{lt MaTp u r r b rn o p r a K o3 X 3 .
1i)li
Ec,ru sH TIIrareJrbHoH3yqn!'rusry r!'raBy u AerairrbHonpopa6oTa,rH npr{Mepbl (a rarxe o64yrrla,ru Bo3Mo}Kuocrb KoMnJreKcHoro,
Mero.loe e 6o,ree cJrolKHblx sa4auax),
npuMeHeHHt H3,rro)KeHHbrx
K TOMy, qrO6u nepeiiru K H3y[OArOToBr'reHbI
TO y)Ke AOCTaTOqHO
qeHItIO COBpeMeHHblx
N{eTOAOB,
npH}IeHfieMblXB
BbIrIllC,'IliTe,'IbHblX
reoJrorhr{ecKuxHccJleAoBaHfirx.Mlr nonsrtaJH,cbH3,rrorrrrrbB ylpoulesHor? Qopue ocnoBbr uarprunoli a,rre6pur. KaK orNte.IaJlocbB
rperleft r,'IaBe, crarHcruKa c,'tfiIIIKoM c,'ioxiHat HayKa, qro6u ee
tvio>xlto6lt.[o us,roxllTb B onHoii r,taee HrH aa]Ke s oAHoft IiHHre.
Matpavuaa a,rre6pa rox{e Aocraror{Ho c,'Iox{Ha, u ee HeJIb3t xoporuo H3,rloxr.rrbHa Hecr{o,'rbKnxcrpaHII4ax. O"q,uaxo.
HaM I(axerct,.
!;;!'r
{iTo qHTaTejrb no.lvtl1n
{_e^Ko-Topoe
np€AcraareHr.re O MeToAax MaT_
alre6pu, sro
.*i-?e3
rpyAa ycBonrbocuoBbr
l-TT,9i
_nosBon,i"
Bt'IqrcdlItreJIbHbIX
MeroAoB,
Koropbre'6ynyr li3JroxteHbl
AaJIee.
laana 4
AHAJI I,I3 TIOCJIEAO BAT EJIbHOCTEI'I AAH H bIX
CNI4COK .III4TEPATYP
bI
l. Dalis p. t., Th
of matrices,2nd ed' John wiley
york, Ig73,5en;na.thematics
and Sons,
ll-..:-Nu*
ro reopurMarpnr{.
c MrrrrManbHbrM
*:X;3ilT.5;;Xtfipfl::.11-"ftvue6uar<
Ko.,ru-
2 o;!;"
i "';;;'"i^ffi:,"l,l"1#,lii
, c:j:
.ii;, J,!?t?f
flfil;;,: ;;; ed: Bro.
F?:.lf
Monterev,
ci.,'r-rjdz',
*:
::ll. c-o.,
;. "
K'ura tB'lsercs oinrru s3 Har.tnyqulix
pyr(oBoAerBro
;r''ipr'##;;..?t#t"u"
3' could P' on the.^g"eographic,interpretation^or
eigenvalies:
ration:Trans.Insr. Britis-hdrcolraptersj;;.';;;
an initiar expro.
1967,58_86 o.
t'lHrvHrusHbrir
B3rrra Ha reopr.lio..ioo.rs.n;or;,.rra,reHrrfi
u nexropor c HcnoJrb3oBaHHeM
reorrerp'qecK"-..::i.4gi_"Jt--M;;.p;;
orJraq'ofixni.rru,npe4uasuaqacrllrlHo
"roii
":'ii
fiIi
#t):"tN
"no'o'bsan l ^l{.- P'u.rog,u.r-o.-r lr iiror.
": york, Igdfl?tii'|.'"alvsis-a practicalapproach:Ma.tffi'rl'oo'prtr.
Lo., .lnc.,New
(-olepxrrTnpor{eA\.Dhr
k
jXT"
;ol;&?""
T.il;,fi
3;ifi
:Hiil?Ti
lffli"",1i",gll5$.;1"ff
:fJ.XT
1"*1
)'fJl#:
$ttlifrezzo
tslal
groM
B
A. "f' Matricesand iransformations:
Dover,Inc., New york,
cxpouuou neDeu3qagr.ltH3Becrgofoyve6Hrra
c,oAepxarc, TpaAuquogHbtir
o'qsoceu-ecrpo"o"v
ffiltj#rtlr*:
*vp.i'
"l"pit,il'i
a.,rreop'l
ni-"i"nfr&""p'Mephr
theorv
andrinear
argebra
: Hor
t, Rinehart,
ft,f3;;f:^rnc"
1;Jl liS#?l?il',%il
N.*-voii',
i"e;i:'i
;?
"ill
;:
flil
J:::gl
Bsoaubr-ri
*ypc . nb,l
j analysis:prentice_Halt,
T"ft
,, ,o,:lt,;S:opr'yliiri-rienal
"^",
"tri::";t:"ff
f
f,,
f
N.l"
ieb;,
,tf".,"u1gt:ggg
;66";
_cl, ;',iJ"? l,'iiJ;e'ne
-;;;;'.;;
Bonpoco',
cBrsas'hrx
"x?y,:,9:l.t.xl*t,y.:::f
€BepTrrI.
.l"bld:;**";
c oneparrrerr
NOCJIEAOBATEJIb HOCTH T EOJIOT Hq ECKI{XAA H HbIX
B srofi r!'raBe MbI paccMorpnM MeroAbI HccJIeAoBaHsfl.
AaHHbIx,
rioropbre xapaKTepn3yrorcq cBol,rMnoJIolKeHHeMHa rprMofi. Anq
TAKilX AAHHbIX
CYUIECTBCHHYIO POJIb HIPAET
MCCTO, 3AHHMAEMOE HC-
3HatteuueM B 4aHuoti noc,leAoBareJlbHoKoropblM onpeAer'IeHHbIM
crg. MgoxecrBo AaHHbix raKofo runa r{acro Bcrpeqaercg B reo'lorlru. HanpuMep, oHLI Moryr npeAcraB,'Irru co6oil noc,'reAoBare,'ibn I'vIllnpt43HaKoB,reoxIzMLIqecKI.{x
Hocrb sHaqeg[ft ,]rLtroJIort{qecKI.IX
HeparornrrecKl{x xapaKTepncruK npo6, nsnrbrx IIo pa3pe3y I.IJ'IIIB
6ypouoii cKBaxLIHe, gHaqeir[fi gJleKTpt]qecKoroKaporaxa ueQrrHbrx cKBax(LIH,3apen{crpnpoBaHHbtx nplr6opal,rH. K atori o6uteit
K a r e r o p l t r l M o x H o o r H e c r H T a K x e A a H H b l e ,H 3 M e H f l o l q H e c fcl T e q e Hr.reMBpeMeHI,I,HaIIpl.iMepH3MepeHHtlcToKa BoAbI B peKe, xapaltTepricrrlKu Ao6nqtt ra3a Il3 criBaxiLIHbI.Me'roru lr3yrleHrq nocJleAoBareJrbHocreiioAttoittepHblxAaHHbIX MoxHo orHecru K aHaJIlI3J/
Mofyr
BpeMeHHbrxpg,rl,oB,HecMoTpflHa ro qTo [oc"tIeAoBaTe,rIbHocTI{
ea
, K H n p O C T p a H C T B e H HSbaI eB H x a p a K T e p r r 3 o B a TKba K B p e N I e H H b IT
cl.,tMocTi.l.
llpexi4e qeM [epexoAnTb K fi3'to]tieHulo MeroAoB Hcc,'IeAoBaHHfl
TaKnx lrocr'reAoBare"rssocrefiH paccMorpeHl'llortptlMepoB I'{3 reoJlo['uH, ocTaHoBulvlc.rrHa pa3JIHqHblx TLitrax [oc,'IeAoBaTensnocreii
npfixo.4ljTcgBcTpeIJaTbctlteOJIOfy'3rO UOXer
;f,?HHtiX,C l{OTOpbIMI{
6rttr, nocrreAoBare,tbHocrl a6co"rrcTHorotiHblx llsuepeHnft KaK 3Haqenuii usyuaettoft nepenreHuofi,TaK I'I sHaqeHilft iIIKa,'ibI,BAorb Koropoli p acfloJl.ox(elrblpe3y,'Ibrarbl l{3Mepenuil. B KaqecrBe npl{Mepa
patocMoTperb3HaqeHlis Kapora)KHoii xpnnoft 4;ra 6yponoft
MOXTHO
HK B a ] K r H t l B O B p e M e H H .
c K B a ) K H H bII{ I { 3 M e H e H I l eI p o A y X T I I B H O C TC
B nepeou [pLIMepe nepe,laeuuoiiflB,rrercq [pi{3HaK, nslvlepReuufr
B OMaX, a eAIIHUIIaMU[IKa,'IbI Uan{epeuuti flBJIfIoTcF ,'turpu. Bo
B T O p o M n p n M e p e n e p e M e H u a s- T o ) K e n p n 3 H a x , u s l a e p a e n t u f i e
IIKaJIbI Iasuepeuuii flBJIflIorcfl AHu,
,lurpax HeQru, a eAIlHI,tqaMI,I
mecrubr n!'rn roAbl. llpr ;rio6oft Qoplre 3anxcll cyurecrBeHHblABa
l b I p a x ( a e r t f lB e A I I M o M e H r a .B o - n e p e l t x , H 3 M e p t e M a sn e p e M e H u a fB
urxa.ntt UJIHllIKa"lbI otltomesufi; 1000 ,r ueSHr.ruaxuHTepBa,TbHoft
Trl B r,Ba pasa 6o,rrrue, qeM 500 I, a coltporuBJleHuee l0 ON{ a
Aecrrb pa3 npeBbltuaer co[porxB,'IeHI'tee I Oiu. Bo-eropltx, ltuTepBa,'1bl'BAO,'1bKOTOpbIXpaCIIOJ'IafarcTCfl
AaHHble' TOXie nMeIOT
onpe4e.,reuHyn Be,'IilrlHlly.f.ny6nna CKBaIKLIHHs 900 M B .4,ecqTb
pa-a npennuraer rny6nHy B 90 lt, a AecflrI.IJIerI{eMei(Ay 1940 u
rITo H Aectrl{J'Ierl{e Me)K'
1950 r. ltMeer ry x{e npoAo"lxiur€ilrrHOCTb,
lAl
Y
Ay 1950 u 1960 r. Ha errtx 3aMeqaHl{rxBBlrAylrx rpnBrra,lbuocrr,
He cToIt,'Io 6rI ocraHae,'nlBaTbcfl,Ho, KaK MbI yBHAI.IMn Aa"lrUeirIreM, AaiIeKo He Bce reo,rotuqecKae fioc,rleAoBarerrbHocrH
o6na.qarcr
TaKr.rMrI
cBoircrBaMLL
B Kaqecree rrpuMepa paccMorpr.rMrrocJreAoBare,'ibHocrb
crparrlrp a SH.lecxux AaHHbrx,o6p asooa uHyro Jrr.troJrof
uqecKr{MH p a3HoBrlAHocrflMrl fopHbrx rtopo!- cJrara]oulnx ocaAoqH.y]oro,rqy. Taxori noc,rreAoBareJrbHocrbro
Mo)KHo cr{r.rrarbcepHIo (cHlr3y BBepx) H3Becr'
HgK- r"rlruirctlrri c,'raHeu- H3BecrHgK- fJruHr4
crnfi c.nageq- ttecqaHHK- yfo,'rb - r.rrnHllcrbrfi c.uaueq- HgBecrHgK. Mu
xoruNt
KaK-TO OCMbICTTTeHHO
OII[CaTb 3Ty nOCr'IeAOBaTe,]IbHOCTb,
O.qHaKOHe
r.{ox{eMeu6parr A,'Ig Hee lxKa,'iy. OqeeuAuo, uro oro u3MeHeHHe
"IliToJrornqecKHxnpr.i3HaKoBnpoucxoAr.tTB TeqeHHeonpeAe"'reHHoro
B p e M e H I 4H, o y H a c H e r H r { K a K o r oc n o c o 6 a e u 6 o p a c o o r B e r c r B y r o xleii BpeMeHHoitrura,ru. Mu MofJIH 6u Hcno"rr3oBarb l,{otrlHocrb,
HO OHa MOXeT Or{eHbCHr'tbHO
II3MeHffTbCfl
OT MeCTaK MeCTy,AaX{e.
rropoA ocraercfl Heusil,{eHHotl.
ecrru rrocJreAoBareJrbno,crb
Tarau o6pa3oM, Hcno,lb3oBaHHeMorrlHocTunopoA BpgA JtI.rIIoMoxieT HaM B
Ha[rHX HccJreAoBaHHsx.
Tor Qarr, uro r.i3BecrHflKB pa3pe3e cronT
Ha TpeTbeMMecTe,a yfor'Ib - Ha [IecToM, He I]MeeTToto 3HaqeHl{fl,
Koropoe Mo)KHo6uno 6n Bbrpa3nrb qlrcJroM (ro, uro HoMep 6 s4eoe
6 o n n u e H o M e p a3 , A , r g H a c H e H M e e r c u u c l a ) . A g a , t o r r i q n o J r u r o ,totnqecKritl cocraB cJIoeB He Mo)Ker 6utl nupaxeH Ha .Ilacu'Iogott
rrlKaJIe.Mo>Nuo ro,rbKo gaKoAI.rpoBarb tlpr.rBeAeHHyr,o
noc,rreAoBare/'rbHocrb, Hanpr.rMep,TaKr{M o6paaou: l-2-l-2-3-4-2-1,
rAe u3Becrnsx o6osuaqaercfl rrnQpoft l, rnusucruft c.naHeq- 2,
recrraHuK- 3, yro.nr - 4. Ho raKafl, ycJroBHocrbcoBepueHHo ltpo*
rr3BoJIbHaH He BbrpalKaeTHuKaKrix cooTHo[Ienufi IrleN4y pa3HoBIrAHocrgMH nopoA. Oqesr4AHo,qro oTa flocd'reAoBare!'rbHocrb
craBl]T.
IrepeA uccJreAoBare,trMr.I
6o.rluree qficJro pagflHqHbrx npo6,'reM,r{eM]
sro 6nino B paHee paccMorpeHHbrxrrpnMepax.
I4naercrcs, oAHaKo, Apyfue Bo3MoxHocru. flycm,
Harrpr4Mep,
Hac HHTepecyer HeKoropafl a3MepseMafl xapaKTepHcTr.rKa,
BxoAflulafl B nocJreAoBareJrbHocrb.
llpegno.noxaM, rrro Mbr ycraHoBH,'IB,
3naqeHus coAep)KaHrrft6opa n xax4ofi ,'rnro,'roruqecxofipasnonHg,H o c r l { p a c c M a r p u B a e u o i i c e p } I q . M u v o x e u } r c l o , r b 3 o B a r bu K a , t y
p a c c r o a u n r ?M e ) K A yn p o 6 a u u B M e r p a x u c q r i r a r b , q r o p e m a e l r 3 a r.ny6uutr HrH paccrorulrt. I(poue
Aaqy, cBs3aHHyio c r.r3yrreHueiu
T o r o , M b I M o ) K e M p a c c M a r p H B a r b 3 a B H , c H M o c r cbo A e p x { a H n n6 o p a
sTtrM SHaqeHLieM
oT MecTa, 3aHr.rMaeMofo
B IOCJIe.ILOBaTeJTbHOCTH.
E.[tzsKo cBq3aHa c npeAbrAyrrruMIz3a1a.t.a a*ailuga [oc,'reAoBaTe,rrbHocTrl,
I(oTopyrc Mox(Ho oxapaKTepn3oBaTbnpllcyTcTtsHel,IHJt{
orcyrcrBneM _HeKoroporlnepeueuuofi u.nu nepeMeHHbrxB HeKoropbrx
, a r r p r . r M e pn,o B T o p H o er l o f f B e e M e c r a x . F I a c u o x e r i l H T e p e c o B a r bH
. r e H u es a e u c s u e t l o r S a q n r i m u x p o Q a y H t r e o 6 p a s q a x n o p o A , o r o 6pauHtrx lpu 6ypeHurl cKBax<r{Hbr.flpyroii
K,rracc 3aAarr- 3ro,
] . c r a i r o B . t e H r r ei l c c , r e . l o B a r e J b H o c r i rM u H e p a , ' t b H b r3x e p e H , u a 6 , q r c , "
162
.EaeMbIx Ha nepeceqeunu unu$a. B groNr cJryqae MbI MoxeM LIc'{IOJIb3OBaTb
Mr.rJL'II.IMeTpOByrO
[IKaJry, HO OHa He [OsBOJIfleTOqeHIiTbr
'qTO qAIUC BCTDEqAETCfl -
OJII'IBI'IH ]-I,IIII [,'IAII,IOK,IIA3.
,[,aHurie, i<oropue Mo)KHo oxapaKTepu3oBarb He[pepbIBHbIM
,pacnoJro>KeHr{eM
B [pocrpaHcTBe LrJrrrBpeMeHH,rlacTo Ha3brBaIoT
ptAaMrr, r.rJrEIoc,leAoBaTeJrbHocTffMH,
uJrH rlerrtMH. flpupo4a paccMaTpI.IBaeMbrx
AaHHbrx [peAonpeAe,'rfleTTe 3aAaqr{, Koropble AJIff
fitlx Mo>KHonocraBrirb. fcso, rrro Mbr He IlroxeM l{3Bd'reqb
uuQopMautrrc o BpeMeHndrx uurepnailax v3 nocJreAoBareJrbHocrllcrpatnrpaQauecKlirx AaHHbrx, TaK xax npenlenuda [IKaJIa, coorBercrBylour,as eroft nocreAoBareJrbHocrr.r,Heu3Becrua. B crparurpaQuqecKHX 3aAaqax qacro l{c[o,'rb3y]or BMecrc epeueun6ft urKar'rbr
npocTpaHcTBeHHyro,
Ho IIpI,ISToM HaIJI] 3aKJrIOqeHLIt
He Jryque, qeM
rtro
B3flToe B HX ocHoBy rrpeAloJro)Kenr.re
o roM,
BpeMs, tpe6yeuoe
,q.ra o6pasoBaHrifl ocaAKa onpeAe"reHHoftltoulno,crll, MolKer 6brrb
,r{3MepeHo.
B ra6,r. 4.1 npune,qeHaKrrracc[Quxaqur pa3,'ruqubrx MeroAoB
.aua.[H3a AaHHbrx,Koropbre 6yayr paccMorpeHsr s eroft r.raee. llptt
3ToM Mo)KHoBbrAeJnrrbrpn runa pflAoB. B nepnolr H3 HHx paccroqHHe Mex{Ay na6.rrc4eHuqMu [3MeHrercff ?r noroMy Aonxuo 6nrr
,oxapaKTepn3oBauoa xax4oft ToqKe. Bo nropou npeArio"rrafaercfl,
Ta6nnua
K;raccu{uxauuq paccMarp[BaeMHxs grofi r,'raneMeroAoB
no Tr.rny[epeMeHHblxIl I{x pacnonoxeHurc Ha JruHItI{
NEDET(EHHT,IX
Ha6JbIeHtrr,
HepefynqpHo
DacnoJroXEHIHBIC B trDOCTPAB.
CTBE
.rIepeveuuue,usue- trIHrepnonnuuR
peHHble B uHTep-llo.nnuouua.nluas
.gansHoii rrrKareI.r,rnpefpeccns
,luxare otHoureguit Cn,raiuu
pasHa6rrcAesus,
HOMepHO H pefynspHO pacnoloxegHbte
B npocTpaHcTBe
4.1
f l p o c r D as c r g e H H o e
p a 3 M e u l e H H eH e D a c orlaTpHBaeTcg
Oproroua,rruar no- Aeroroppenqquq B
JIHHOMHaT'IbHap
q e - rIepeKpecTHaq
Koppe,'rsIIHs
rpeccHfl
Cxo,rr,sqIrlne cpeAHHC
<Dumrpa[ua
r.r
CIJ'I AXI'I B AHIIC
3oulraponauue
AeroxoppeasqHq rj
nepeKpecrHar r{oppeJI'lIIIlfi
lloayeapaorpauuu
Unexrpa,rluufi auaiI u3
Ileperreunue, Hsue Psar,r co6lrrufi
H o N r H - I(-C npurepnlr
peHrrble B
rra,trltofi
rqAriosoii
i:irri noIuKa,'Iax
AnroaccouHauuq u Aeroaccouriaqus E
nepelipecTHaq
acco- rrepeKpecTrrar ac.
unaqHq
COTIH
AIIH'I
Arranrrg no.{craHo-A n a " r n s B 3 a r ! I 0 3 a BOK
MEH'lCIIOCTII
I-{ennMaprona
IJ,enu&laoxona
Kpurepuu cKaqxoB KprireprrrcKaqKoB
I l.
IDJ
Y
qTo ToqKrr pacno.[o)KeHbrB rrpocTpaHcTBepery"'rrpHo ]r paBHoMepHo'
II, KpOMe eJ.rrHCTBeHHOft
nOCTOflHHOf.{,
HuKaKUe qtlc.loBbre XapaKTep r . r c T H K lrpr o c r p a H c T B e H H o f op a c [ o , 1 o x { e H H fA a H H b r xH e y q a c r B y t o T
B aHarrrse. HaxoHeq, B TperbeM ,cyurecrBeHHa "rlilrrb noc,rreAoBaTe"lbHocrb sa6ntoAenari, a u-x npocrpaHcrBeuHoe pacnoJro)KeurreHe.
l r M e e T3 r r a q e H u t .
3tu uerorxlr Mox(Ho r,raccuQrzqlrpoBarbraKx{e u no rarral{ He-.
o6xoAuraux Ha6"rro4eHHii.B oAsrx cryrraflx rpe6yercfl 3Harb HH'
TepBar'r NIe)KAy ua6,rrc4eHnflMAuJtvt lrx ornoueHHe: [epeMeHHafl
lto ueroropofi urKaJreH Bbipa)Kena B BeAoJrlKHa6url ltsrr,repeHa
uIecTBeHHbIXqlIC,laX. B 4pyrax uc[or'rb3yloTcq HoMHHa,'tbHbre
]rit]I
nopflAKoBbreAaHHbre,H Ha6nrc4euur rpe6yercfl Juurb HeKoropbrM'
o 6 p a s o u p a c x . r a c c a S r . r u n p o B a r bB. n a e r o g a x ,p a c c M a r p r . r B a e M b rBx
arofi r,raBe, Kr'raccbrHe paHx{r.tpoBaHbr,
T. e. cocrogsve A Henb3ft
cqHTaTb B HeKoropoM cMbrcr're6onee u[poKi.rM H,rH o6r,euJrrouluM,.
qeM cocrotsne B utn C. Horr.rnua,rrubreAaHHbreo6urqso npeAcraB,tflIor ueJrblMuqr{c,laMH,6vrnaun HJrHcHMBoJraMu.
B eroii rJraBe Mbr paccuorpuu MareMarur{ecKrre MeToAbr,nc[oJlb3yeMble flpu aHaJrvse noci]reAoBaTe,rrHocreft
AaHHbIx. oAuaro,
paccMaTplrBaeMbre
3Aecb MeToAbrHe rrcqepnbrBaaTBce cyuecTBylou]Iie Bo3MOXHOCT?I.
cXOpee HX MOIKHOOxapaKTepr.l3oBaTb
KaK ocol
6eugo nepcnexrr.rBHbre
npn Ko,'ruqecrBeHHbrx
r{cc.teAoBaHuflxB HayKax o 3erra,re.[pyrue MeroAbr Moryr oKasarbcs 6o.lee rroAxoAflnrlrMn Ailv 6o.riee MorrrHbrMn n cneqn$uqecKux ,clrryaungx LrJrrr r^jtfr'
HeKoropbrxoco6lrx nocJreAoBare,rtsocrefiAaHHbrx.lfa saru B3r,rlJ,.
- XOpOUee BBeAeHrre.
3HaKOMCTBO
C OnriCaHHbrMr.I
HH)Ke MeTOAaMH
r o6uupHyro o6,'ra'crb aHarr.irltr{ecKoro lrccJreAoBaH14q
reo,'roflrqec K H x A a H H b r - rO
. 4 u a x o M H o r u e H 3 o r r j x M e r o A o B6 l r . n u p a e p a 6 o r a H b I c n e u u a , r H c r a M ue o 6 , ' I a c r g x H a y K u , n a , r e K H Xo r f e o J r o t n l l , H r r x
onucaHHe, npucnoco6,reHuoe K l,t,ctro,rlb3oBaHl{rc
B IlHxeHepHoM Ie.le, e 6uo.rtont{r,rK,'terKH, K arailt43y pblHoqnblx ornorueguri u,.rn
peuenofi Tepairlzu, TpyAHo npucnoco6irrb A,'rfl peueuus reor'rorrirtecKl.rx3aAaq. Hexoropue H3 orr{x N,reroAoB
onepupyror c HenapaMeTpaqecKr.rMIi
craTircTIrKaMH,IlorrTtr He paccMaTpI{Baer{brMHBo
BBoAHbr-\crarr.rcrnqecKilx Kypcax. Tar, xax 6o,ntunHcrBo feo,'IofoB
Ile 3HaKoMo c ocHoBaMI{ aHa,'tH3arlocr'teAoBare"rlgocreii AaHHbtx,
TO MbI nO,'raraeM,rtTo r.rN{6yaer [o,'re3Ho npoqecTb npuseAeuulrrl
s r e c r o 6 s o p p a a H o o 6 p a 3 H b r xM e r o A o B H [ o A X o A o B . K a x B f i A H o u : ,
r a 6 n . 4 . 1 , 3 T I { M e r o A b r o x B a r b r B a t o r n o c J r e A o B a r e r ' r b u o c rpua s , q u q IIbix rr.rrIoB H npeAHa3HaqeHbrAJrg orBera Ha pflA nonpocoe. FIt
oAr{H H3 MeTOAOBHe H3JrafaeTcr SAecr, [cqepfibrBaloule, oAHali0
paccMoTpeHHbre
SAecb npr{Mepbrra rrpH,'ro)KeHrzg
MoryT rro}{oqb leo.lory nu6pam sau6o,ree rroAxoAfllullfi n,tero4Arrs peiueHAfl,sa1asn".
Cnucor< ,'rr.rreparypbrnoMo)Ker uafirH AeraJrbHoe u3,rolKeuue cneI{HaJrbHbrx
BorrpocoB.
PacciuorpeuHble MeroAbr Aalor BogMoxnocrb noJryqr.rrb orBerbr
Ha prA Bo[pocoB, a rrMeHHo:Mox{Ho Jrrr cqiirarb ua6,lrc4enufl cJry164
trafiHbrMI.r
HJrHB nux o6napyxllBaercfl Hexoropltti TPgsa; ecr'IH
ro xaxosa ero Qopua; Mo)KHoJu o6uap\'}lirrb
cyil{ecrByer,
TpeHA
u u3MepI{Tb IlI.IK,lbI Il nOBTOpeHIlg; nO3BO.Ifl}OT.:'lu .r.aHHble cxe,laTb
oqeHKH Ii [peAcKa3aHHff; MoxHo .l]l oueHUTb 3aB]lcllMOCTII \leiliAy
[epeMeHHbIMI.I u yKa3arb ]-Ix clt'ry? Xorlt eolpocbl Talioro pora H
He tBHO CTaBflTCfl B nOC,'IeAylOUIeMlI3,;lO)I{eHUlI, llllTaTer'l!O pelio'
efo
MeHAyeTCfl npoAyMaTb ,cyulHocTb Kail{Ioro MeroAa' a raK}Iie
qTO
gaAaq
3aueTllNl,
rttna.
pa3.']l{qHOfO
pe1geHn1{
[p!I
BO3MO)KHOCTI.{
HaMI'l 3aAaqi.{ Moryr IIoMoqb B peueHI.IIl MHofHx ,1P:"rIIX'
su6panuue
npuxoAltrcn HMerb .tteJo He rorrbl{o c auar'Ill3n\'l noleolorau
cleAoBareJlrHocreft AaHHblx, Ho lt cpaBHHBarb Me)li,ly co6oii pas-
pr4u ua6,un4euuil.Har.ls,uHufi ilpuMep- crpartlrpaQu.-rrrrrHbre
qecKag KOppe,'Isunt npI,I I.{3yI]eHII}I pa3pe3OB IL'llt iIplI 3JIeKTpflqe-
cKoM Kapora)I(e cKBa)KuH. flpuuuua,
i
i
1
no
roropofi
reo.norrl
IlC[O,'Ib3yIOTKOppe,Isqh]O,-flpOCTOe ]Ke.rIaHI{eycKOpHTb nO.'IyqeHHe feoJloruqgcxllx BbtBoAoB ti3 saxo,quposauuori uttQopltar{utt'
x p a H f l I q e i i c f ls 6 a H K a x A a H H b I x .K p o v e r o r o , f e o J o r l l c r a / I K I t B a l o r B Tex c.lyqafix, I{of,u,aHe MofyT cBollcs c 3aAar{aMfi Kopper'IflIll.ril
M I t C H J I a M I p. Ie u t t r b B o n p o c 0 6 g t l e t t a a " r e H T H o c r.l [l B y x p f f A o B H a 6,r roAeHufi . C"ra 6oe cxoAcrBo, c,'lIl lr1KoM He3Ha ql'lre,'lbHoe,qro6 bI ef o
Mo)I(Ho 6u.no o6napylKHTb BI43yaiIbHo,Moxer 6ltrl eblqereHo 3rl1rIpU I'iCnoJib3o3aHllll
MH MeTOAaMI'I,
AalKe eC.IIH3TO HeBO3MOX(HO
reo,'lorzll!{
no3Bo"qsIor
MeroAbl
npI{eMoB.
Ko.[fiqecreeHHbte
Apyrl4x
[epeMeHHblX' r]TO fiBr'I9HeCIiO"'IbKO
pa'CCMaTpl'IBaTb
OAHOBpeM€HHO
e r c g M o I I I H b I Mc p e A c T B o Mp a c n 0 3 H a B a H I r t l l 3 y l l a e M b l x o o L e i i r o B .
Haroner{, B ctrJy a6co,rrctsoit ttunaptlauruocrr onepaqNfr B BbIr{rrcr'rurer'rbHofi
nporpavMe Koppe,usuuottuuii aHar'ttI3 6pocaer estreo3oB feo,rofy. Ec,ru lioppe"IgtrrloHHbte3aBacHMocril, oqeBHAHiJIe
c pe3y"IbTaTaMIl,[OJiyqeHHbIMlI uauttuOil,
.'IOry, He COf,'iaCylOTCfl
reo,ror o6ssas onpeAe/'u4TbnpIIqlIHy sroro pacxolKAeHllg. O6ltqso
rlo3BoJlger BbIflBHTbocJlo/iiHeHIIfl
6o,lee rurareJlbuoe HccJIeAoBaHHe
He 3aMeqeHHbleIIpH nepBoHaqaJlbHoMl{cc!'IeAosaHIIH.
I{ CMeUIeHI.Ifl,
3ro se o3garlaer, qro reo,'Iof Ao!'Ix(eHu3MeHHTbcBolo uHTepitperaq r { r o r a K H M o 6 p a s o u , q r o 6 u t o H a c o f J l a c o B b l B a J l a ccb p e 3 y n b r a r a uaruuHt't. CoeceN'I
xilr, notyqeuHbiMIr c noMourblo BbIqi.IcJII.ITe"IsHofi
uaoOopor, rlMerculuecfl B Hacroffulee BpeMfl B Ha[IeM pacflopn;i{eHHn flpofpaMMbr aBToMatnqecKoii Koppe,rflu]ru AoBoJIbHorpy6sl lt
cocraBJIeHbInpocro B coorBercrBnl{ c xoAoM l.tttclell, [cno.nb3ye\lbrx reoJlofaMu. oAnaKo no Mepe npoAo,lxeHat tlcc,'IeAosaatiftno
KoppeJrflqfir{Mox{Ho o}KI{Aarb, uro 6y4yr co3AaHbI BecbMa no.'Ie3Hbre aJrfoplrrMbl, Koropbte no3BoJltr 3HaqureJllHo o6.lerqum pa6oTV reod'lofa.
E6"rtruyro qacrr, MeroAoB cpaBHeHrigAByx urv 6o"treenoc"leAoBaTeJrbHocrefi:noxso pas6url ga LBe 6o,rsurue Karefopl,lH. B nepBoji Hs Hux flapbl AaHHbrx Mofyr 3aHHMarb To'lbKo oAHo no,'io)t(enire, LI Hall]a 3aAatla- oIIpe]leJrr.irbcreneHb cxoAcrBa Me]KA] 3TItB xaqecrse npaMepa N{oil(Ho
r\.rirAByMg troc,rreAoBaTeJIbHocrflMu.
l0r
p a c c M o r p e r b c p a B H e H r . rAen Q p a K r o r p a M M b rH e H 3 B e c r H o f oM H H e p a J r a
c ller'rbroefo r.rAeHTuQuxaquuc HeKoropbrM prAoM craHAaproB.
Cpanueuue co craHAapraMH npoBoAuTcfl He roJrbKo no r.rHTeHcriBH-ocru orpa>Kenlrs,Ho H rro coorBercrByrouleMy efi yr.ly orpa)KeHrfl.
Hanplluep, HHKar(nx BbrBoAoBHeJrb3fl cAe,rrarb,ecJrn cpaBHHBarb
I.IHreHCr.rBHOCTb
OrpalKeHIlfl peHTfeHoBCKHX
.lyuefi noA yfJroM 20
20" c nsreHclleHocrorc orpaxieurlfl rroA yrJroM 20 30'.'!,axe
ecrrH
B e . n l l q H H ar i H T e H c H B H O CO
T rA. tr r H a K O B aC,p a B H e H U e
C O B e p I X e H HJOr r r ueHo cMblc,'ra.
T o r $ a r r , q r o A a H H b r e ,a H a , r o f n q H b l e[ p r r B e A e H H b r Mg,a n l ] c a H b r
B BHAe noc,rIeAoBaTe,'IbHOcTH,
He HMeeTSHar{eHLIq,
TaK XaK raX4rtii
3 , I e M e H Tp r r A a p a c c M a r p r r B a e r c f lK a K o T A e J r b H a sI { H e 3 a B H C l r M a f l
n e p e M e H H a f lH
. u r e u c H e H o c r b o r p a x { e H t r r n o A y r d ' r o M2 0 2 0 " x a p a r Tepri3yercfl o4Hoft nepemeHHor:r,
a sHTeHcuBHocrbno4 yr,ron,t 20 a
30" - apyrorl. Mero4tr cpaBHeHnr raKHX [ocJreAoBare.nlnocrefi
M b r p a c c M o r p n M n o A p o 6 u o e r , ' 1 .6 ( c u . x u u r y 2 ) , r A e y K a x ( e l r
MHOfOMepHbre
KpHTepr{HcxoAcTBa It paccMoTpriM 3aAaqH Kd'raccHSnxaqilu I.I AHcKpHMnHaHTHoroarailuga. B eroHt KJIacce 3aAar{
no.10)KeHrreHa6"rrrc4eur.rfl
B frocr'reAoBaTeJrhHocTH
cr'ryxHT AJrg efo
u4eHruQuraqtzIz c 4auHori nepeueHHoii r{ He r]fpaer 6o,rrrue unraNoii oo,rrir.
Hao6opor, HeKoropbreH3 onr.rcaHHbrxB AaHHoft r.lase MeroAoB
o c H o B a H b rH a p a c c M o r p e H r . r un o c J ' r e A o B a r e , l t H o c r e f A
i aHHbrx KaK
nsr6opox rr3 HenpepbrBHoro
M H o x i e c r B au a 6 , r r c g e n v f i .A n p u o p N H e r
H I I K a K H Xn p H r { H HC q U T a T b q, T O O A H a H 3 C p a B H [ B a e M b r x B e J I H T I I I H
Jyqlire Apyroft. Taxue MeroAbr, KaK B3arrNIHarKoppe,'rflrrr.rfl
H accoIIHarrng, Hau6o,qee6nr.rgru feo.rlofaM, Ho, K colKa,'IeHHIo,
HX [pHMeH e H r i eo r p a H i l r r e H r r oT, a K K a r i o H H H e A o n y c K a r o r n e u e u e H u i l t r l a c u r a 6 a o A H o r o p a 3 p e 3 a n p r . re r o c p a B H e H H rc. rA p y r t l M . , [ , , 1 a i v H o r u x
T r t n o B n o c i l e . ( o B a r € r ' I b H o c r ep
i ra, c c l { a r p a B a e M b t xB e r o r ? r r a B e , I t 3 M e H e H n f lr v r a c u r a 6 a H e r p e 6 r - e r c f i , i l r r o 3 T o N r yr p y A H o c r e i i H e B o 3 H r l x a e r . O r 1 u a x o c K o p o c r u o c a r K o H a K o r r , ' r e H u fHl ,a n p H M e p ,H e f l B ,rtrorcg nocrotHHL,rMrr,rro3Tolry crparnrpa$fiqecKne AaHHbterpyLHO I3yqaTb C nOMOXIbIO
MeTOAOB
CyUIeCTByTOTqHX
KoppeJrrultoHHoro
a H aJ ' t i t 3 a .
MaIIflzHaflBKax rrlu yx(e orN{eqaru B r,t. l, nst.Mc,{LITeJIbHaq
.rrrercg MorrrHbrMopyAXeM peueHlrfl crolxHbrx 3aAaq. OAuaro oua
r.iryna Lr Mo>Ker trpr.rHr.rMarb
6eccntrrc,resHbreAaHHbre I{ BbrAaBarb
cro,'rb xe 6eccuncJreHHbrepe3)'J'rbrarbr6es Ko"'re6aHuft.Muoxecreo
npofpaMM aHaJrH3afloc,'rerfoBaTe.llHocreiipe3y/'rbTaTon na6"lrc;eHrrii ttox<go ,'iefKo lto/ryqfiTb n3 pa3JII,tqHbrx
IicroqHHxos, Ecr'II,INe
r r c n o , r I b 3 0 B a T3bT l l n p o f p a r r ) . r b rK a K < < q e p H H rt iu l r . t x > >H
, e noHHr.!taq
r xr p a H H { e u u i r , r o
n p o i i s B o l i i I M b I XB H H X o n e p a q t t i i I r H a J r o ) K e H H b o
Jerxo c6urrcq c nyrn. Mu Hageeucs, qro onucanue MeroAoB rr
nprriirepbraroii r,rasrl 6ylyr .qocrarogHbrivrlrA.rrf roro, uro6u onpele.inrrb o6,racrr lrpI{NIeHI.i\tocrtlKax(Aoro MeroAa r{ noMoqb roH r r \ i a H r r r on p o r p a N r M . O , l , H a t i o B o r { o H I { a r e " t r t H oci ir a A H I t a H a r ' t r r 3 a
Ilcc,rle.loB3Te,'Ib
.LoJ'IxeHIIO,IalaTbct Ha cBolo HHTyHUlrlo'cro,rxuyeB BliAe nocJlert1tlgbC salaueri, B KOTOpOiiAaHrlble npe.],CTaBJ-leHbI
j,oBaTe.rlbr]ocTl.r,
Bbr Mo)KeTec qeJbi'o ]'nopqAoqeHl'lt Ba[Iero Ilcc.']eAoBaHur 3a,qarb ce6e c,le4yIo[IIie Bonpocbl: a) ua raroti Bo{Ipoc
(eonpocu) s xoqy ornerurt? 6) lialiots rllrI Moux ua6,rrotreultt:i?
O6pa3OnanHOii1lOlyugliilotattt
a) rraKOB TIlir nOC,'reAOBaTe,tbHOCTll,
Ua6'rrc4eUltR
natt?
Bnt ltox<ere AoBo,'IbHo6ucrpo o6napy>t<urb,r{To orBer Ha trepnttfi eonpoc N{ox{Hono,rYq}trb JIIilub lloc"le qerKllx oTBeroB Ha BTo'
poil u rperuir. Ec"rH yuecrb 3To ,ro Haqa.la IlccJIeAoBaulifl,illo)KHo
u 3 6 e ) K a r b q a c r r { u e H y x H o f i p a 6 o r l t . B n p o r u e H o M c , ' I y q a ec n o c o 6
c6opa AaHHL,txMox{er npeAorlpeAeJ}ITb \{eroAbl, Iioropbie Hy)liHo
IICIIO!'Ib3OBaTb AJf
qTO
B
CBOIO OqepeJ.b
cli'lbllO
H H T E P N O J ITf lI H O HH b I E N P O U E A Y P b I
'!
'l
106
lIHTepIIpeTaUiiil'
of p aHnqHTO6,racrr ucc,leAoBaHIlfl.
1
I
il
Mnorue LI3 oIIIIcbIBaeMblxHH)t{eMeroAoB IIpHToAHbIA.iIl AaHHblx
pacllod'lo)KeHHeB
M npocTpaHcTBe; HaoJlrcLeHilf
c paBHoMepHbIM
oAHofo I{ TOfo )Ke aHTepBacoxpaHeHHer{
c
upoBoAl.rTbct
lioJlxHbl
! ' r a H a n p n i r a o rvi r v H a n e p e c e r l e H l i llll H o r o r n n a . K o H e q H o ,H a n p a K HanpHlvlep
TIiKe co6,'ircAeHHeSTOIO yC,rOBHt r{acTo HeBo3MO)I{HO,
H'r,IlrIpH _aHailu3e
npn MHofHx crparurpaQHrIecKIIX IICcr'IeAoBaHLrflx
,t-asgux us 6ypotux cKBax(l.lH,a raliiie ,u,,rl on6opoli, co6paHHLlx
no MaprupyraM B cna6o o6sa>ressov pafioue. llo:rolty ueo6xoAuM O y M e T b O q e H I ' I B a Tpba C C M a T p U B a e M bnl e p e M e H H L I eB T O q K a x c
peryJrrrpHbrMpacnoJlo)KeHueM,Hcno"1ib3yflI'Ix 3HarIeHHs,nO.'lyrleHHbIe AJIfl pa3r'll4qHblx[HrepBaJIOB. JT]l BOnpOCbI I13,{aralorcfi B
r , ' r . 5 n p r p a c c M o r p e H H Hn o c r p o e H l l r I I 3 o . l t H H r a il il .p o r p a M \ { b I n o rrpeAHa3HaqeHbt
crpoeH14r t.rso"uHHI.ll?
A.itfl pery"lapHoir cerH Ko,Hrp o J r b H b l xT o q e K H a o c H o B a H u us a 6 : t l 0 l e H H f t , H e p e f y " r l f l p H op a c n o iloxeHHbrx B rrpocTpaHcrse. Bueulititli eug, u ToqHocrb nocrpoeHnfi
uara IIpHMeHqe'
riapTbl e 6Orlllloii crerleHu 3aBucflT or Be,,'lnql4Ht'I
llofi cerg H or a,rfopllrMa, HcIIo,'Ib3oBaHHofo
L,'tfl [o,'IyqeHI{t oueH o K B e e y 3 J r a x . C e f i q a c M b r p a c c \ I o r p u M o A H o M e p u u t ia i r a , r o r a t o f t
3aAaqH.
B r a 6 , r . 4 . 2 n p H e e g e H b rc o A e p l K a H l l f lM a f H I . { nn n p o 6 a x I i 3 B o i l
penu Crpuru Vorep. B cessu c rpyAHocrrro or6opa npo6lt 6u,ru
IIHTepBar'laMI].
Mecra or6opa upo6 6lt,.lu
B3qTbr c pa3r'IHIIHbIMH
HaHeceHbIua a:poQorocHIl\!KII, nocJle rlefo r',lexl-v HIITIrIaTeJrbHO
.
lvil'lH3Meptr]lHcbpaCCTOgHUfl
I4s 6o,'irrxofo quc,'ra r{eroAoB, c ttoMou{blo I(oropbrx Moxiao Il3
IIepery,'itpHO paCnO,'iOX(eHHblx
AaHHblx nOJ'IyqllTbOUeHKIIA"rIt peMbr nolpo6Ho pas6epeu ror''lbKo ABa.
ryatpHoro pacIIoJ'ro)KeHIJfl,
Iiepriufi - nau6o,ree npocrofi. 3ro'verox,'npocioir .rttuefisoit ltulloi-iytlIlTb
TOqKaMu,nO3BOJIslouIHIi
TepnOJIfliIHIiMe>KAySaAaHHbIMI'I
x qriax. Prrc. 4.1 rl.r'lxlclptipv€T ';r\r
o u e H r { r r B n p o i \ ' t e x < y r o q r t b rt o
-
Puc. 4.1.
Ta6tuaa 4.2
Aoa,(qarr nrrvrepeerficoAepxaHlq MarHuc B BoAax
p. Cepunr Vorep (paccrocHfis ficqncrrrorcs
or ycrbs peKlr Ao mecr oaarun npo6)
Paccr3ssue, lr
Co,u,eDxaHI.Ielrarsxg,
0,1
1820
2542
2BB9
3460
4586
6020
684I
7232
l 0903
r l09B
11922
l 2530
l 4065
14937
t6244
t7632
l 9002
20860
2247l
Me)KAy
r/r
64L
8,61
5,24
5,73
3,81
4, 0 5
2,95
oAHori ToqKu B lrHTeprro!-lflrIHoHHou
npol(eAype TIjeorrpeAeJreHr.rfl
6yerca r{crroJ'rb3oBarb'roJrbK
A oB a 6 , ' r [ x i a i i u ] H X 3 H a q e H L I g . E c n l l
ucxoAHble Aa rIHbIe IoABepxeHbI 3Har{uie.rbHoMyB,lutHHIo cI|LIailHOIIbIX H3MeH€Hll,i.'rr.r IIO/IyqeHHbleB pe3y,'IbTaTeI,lHTepIIOJIflqHII
Bbre 3HaqeHnr{laKxe Mofyl' HMeTb HeAonycTr.rMyro
cJyrrafiHyio I.r3MeF:qaBocrb.o6a ST}I MoMeHTayrlHTbrBarorcflB MeroAax, npeAHa-
., <-7
3,84
2 ,8 6
1,22
1, 0 9
2,36
SHAI]CHHbIX
IY
,94
2,05
2,23
o4,
0,87
|,26
- v )-------:::---T
(x, - xl)
-xr - Xi
|
AJLfr HCNO,IIb3OBAHHfl
6O"ICC
ABYX
NCPBOHAqAJIbHbIX
3HaqeHr.rftH ocHoBaHHbrxHa nporlelypax ycpeAHeHllfl, HcnoJlb3yloulr.rx B3BerxeHHbre
paccrosHHfl. oAsaxo MeroAbr ycpeAHeHI-Ifl,
Koropble 6yAyr paccMorpeHbl I{Hxe, IIpH H3dro}KeHHH
npoqeAyp crJla)KHBaHHflAaHHbrXTaKX{e LrMerorHeAocTaTK["Hanpuuep, 3HaqeHHe
nepeMeuHor?B [epBoHaqaJrbHoiiroqKe np].r riHTepno"ltulzn He o6fiycpeA3aTeJrbHocoxpaHseTcfl, TaK KaK llor'ryqeHHoeB pe3y.rrbTaTe
HeHHfl HOBOe3HaqeHHe MOXeT nDeBbrrrraTb(U;tU 6anr MeHbrlie)
3HaqeHI,tqB 6,,IH3,,IeN{auIHX
Tor{Kai Hs-:a e,rHtHrg 6olee VAaJIeH-
npolle.lypy. flpello,roxfiM, qro Yt u Yz - Ha6,rroAaeMbre
sHarreHriff
B T0rriiax Xr tI Xz, H MbI XOTHNIOIIeHI,tTb
3HalteHHeY' S T.}qXeX'.
C q u l a q 3 a B l i c u M o c r bB r l p o N r e l t l v r o q H b rrxo q K a x , ' r r . r H e i i H o f3i ,H a q e Hne Y' B ToqKe X' ruoxuo buquciurr ilo cneAyrour,eii$opnay,re:
v-t -
JIuHeiiHaq t{HrepnoJlsqut
TOqKaMH
IIOC'1e;XOBaTe,'lbHOCTII
-NAHHbIX
HbIX TOIICK,
Ec,rH nepnoHar{a,ribHbre
AaHHbre pactro,tox{eHbrHepefyJIrpHo H
npoMe)KyToqHble 3HaqeHI,lfl Ao,1)KHbI6 bITF,Bblr{HCJIeHbI
ii
A,'Ig Ka>KAO
IIapbr Ha6JrroAeHuii,ro rrpuMeHeHue.rHHeiiHoti r.iHrepno,tflqHr,r,
orpa)Karoqeft paBHo\iepHocrb lr3MeHeHHflnepe\{eHHori Me}KAy Korrrpo,'IbHbiMrr
ToqKaN{[,Bno,rrHeonpaBAaHHo.o4HaNo B rro6ofi SaAaqe,
B Koropori ltprrxoAr.rrcffl{cnoJrb3oBarbHHTepnoJrsuuFo
Ha6,'rroAaeMbrx
AaHHbrx, BcefAa cJIeAyeTI{MeTb B BIrAy, r{To AJIfl no,'IyqeHuq OIIeHOK
HeJrb3flLrc[oJrb3oBarbrro6oft MeroA. To.rnocrn nolyqeHHoro pesyJIbTaTaSaBIicaT oT [,'ioTHocT]r[epBoHaqaJrbHblxAaHHbrx,ucnoJrb3OBaBUIAXCffnpl{ noCTpOeHLIECeTH, W HnKaKafl HHT€p[O;'1fI{Iifl He
( 4 .1 )
l{Huvll cJIoBaMH,Mbr lpeAno!'rafaeM, qro pa3nocrb MexAy 3HarrerlLtflM;,w.
B AByX COCeAHT.TX
TOrlKaX rBrrreTcfl .ltr.rHefiHoiisyHxqHeii
pa3Aensrcqero HX paccroflHr.rfl.3Ha.reHrie B ToqKe, Jrexaqerl rocepeAltHe Mex(Ay AByMs Ha6,'rrc,I,eHI.IrrMH,
HaXOAHTCfl
TOTTHO
rrocepeAUHe Me)KAy 3HaqeHHgMLI
B AByX npr.rJrexaqux ToqKax. E,ruxair6yAer roqKa, 3HaqeHne Koropoil 6nuxe
Ueii roqxoii K Ha6JIIoAeHHro
B c e r o K 3 H a q e H H rH
Oa 6 r l o n e H u g .
Hecuorpa Ha flpocrory npoqeAypbr,rruHefiHofi nurepnoJrsr],firr,
B O M H O T H XC . n y q a f l XO H a 0 6 " r a A a e T H e K O T O p b T M H e A O C T a T K a M r r .
B c " n y u a e ,K o f A a q u c r o p a B H o M e p H op a c l o J r o ) K e H H b rrxo q e K r r p n 6.nttgure,rlgo paBHo rluc"'ry roqeK Ha6.nrc4euuliu nocne4Htre 60,'ree
Hr'rn MeHee paBHoMepHopacnpe,r,eJreHbr,
3ToT MeTOAAaeT yAOB,'reTBOpHTeJbr{brepe3yJibTaTbr.oAHar(o ecJrH ToqeK Ha6rroAeHr.{
fl He-
IIO3BOJIHT HaM yflyr{Ull'iTb pe3yr'IbTaTbI aHar'lIl3a,
eC,IlId IICXOAHbIX
HailpHMep, N{br MOf,rtI 6U OrleHUrl COAepAaHHbIX HeAOCTaTOT{HO.
)KaHIIe MafHLIfl B peKe c HHTepBa,'IoM 500 M HJII{ Aa)Ke c }.rHTepBaJIOM 5 M, OAHaKO COBepIXeHHOflCHO, qTO 3rI{ HOBbie 3HaqeHHr He
HHsopMaqlIH o pac[peAeJreHHr.rl.r3yAaAyr HaM AorroJrHr.rre,'rbHofi
qaeMoro sJreMeHTa
B noToKe.
Tenepr Mbr paccMorpul,r MeroA rro"ryqeHr.rfl
paBHoMepHopacnoB [pOCTpaHCTBeAaHHbrX,OCHOBaHHbTX
Ha UC[OJIb3OBaJIOX{eHHbIX
UeX4y trOC,leAOBaTeJrbHbrMH
TOqKaMI{,B KOHr.lHBCeXHa6JIIOAeHHft
Topbrx 6n.rru no.nyqeHbroueHKu. SToT MeroA Ha3brBaercflMeToAoM
NIHOTO 6O,'INUJCTOqEK, IIOJIYqAIoIIlIiXCfl TIOC,'IC I.THTCPIIOJISIII'IH,
TO
66.nlurag qacrb [epBI{qHbIX AaHHbix He HcloJlb3yercq, TaK KaK Ar'Ifl
r69
r63
ifl
JL
JO
43
Hblx nJloula Aeil u AeJIeHHflcyMMbI Ha Be,'lliqHHy nHrepBaJla' BLI6pauuoro AJII noJlyqenufl otleHKu. Haq-a.nlsoe 3naqeHue B oqenneaeN'IoftToqKe rIocJIeAoBareJlbgocrl{nut6upaerca raKl'lM xe' Kali H
s 6rr.{)KafiuleftnpeAuecrBylouefi AaHHoiirollKe.
Pasrr.IqHe rr,r6xay 4eyua ltporpaMMaMII Bblcrynaer oco6enHo
fiBHOB TOM C,'Iyqae,KOrAa I{CXOAHbIe
AaHHbIepa3po3HeHbl'H Me)li6onee oAHoit
floryrlarb
Ay AByMfl Ha6,rro4euurMI'InplxoAl'Irct
3HaqeHllfl,
llblqHcJIsIoTCt
orleHKri. flpu ;rnHeitggft [Hrep11o,'tflUu]I
p acrroJroxeHHbreHa flpfl Mofi iuunu, coeAr1gs1oxleiigae 6.lgx<afturlte
3aAaHHbIeroqKr{. Hao6opor, B MeroAe [ptMoyro/rbH]iK9B CTpOflTCg
o u e H K H ,p a B H b l en e p B o M yH a 6 l r l o A e H I . { } o '
r o H d M e r a M o p $ H s M aB o K p y f u H r p y 3 H B a 6 l t " ' i a
flpn irsyueHHr.3
K KoHTaIionpo6oBaHa cKBalKlrHa,npo6ypeHHaq IIep[e_HAI'rKyJIflpHo
l'y HHTpy3HHC BMeUIanUll-IMI{[opoAaMI4. I(epu pacroJIoJII{' H BCe
KpltcTaJrJrbIfpaHaTa, pacnoJIolKeHHbIeHa noBepxHocTH,H3BJIeK,'1H
cneKTpoxHMI{qecKIl\{MeroAoM Ha coAepxiar1 npoaHaJII{3HpoBa,'riI
TaK H coAeprrlre xeJre3a. Kar paccTotlHllfl MelKAy KplIcTa,'lJIaMI'I,
B luHpoliltx [peAerax. Aasslte,
x(aHr.re)KeJIe3aB Hrrx KO.rIe6a,'IfiCb
noIyqeHHble B pe3y,{bTaTe sTOfO 3IiCnepHMeHTa, npHBeAeHbi B
Ta6h. 4.3. Xe.irarentrio 6bt,'Io 6u norry'Irttb c I{x noMolqblo o6uy}o
B COCTaBefpaHaTa, oAHaKo 3TI'l AaHHbIe KaIraprr.IHy r.I3MeHeHUft
u He noAAalorcs rpqMoii ItH'
)Kyrcfl AoBoJIbHoHe3aKoHoMepHbIMIl
[poBeAeH]rq_ aHailu3a
Tepllperarll1lH.B Ka.IecrBe nepBoro [Iafa
CerH. xeilareJlbHo
r\{ox{Honocrpoirrb Hx oqeHK}I AnR paBHOMepHOft
MexAy roqKa}ll,l eu6parl paccrosHl{e 0,5 lt.
B Kar{ecrBer.rHTepBaJra
3,qecl MbI craJIKLIBaeMctc noJIo)KeHlleM,orJIlir{arcurul{cg or pac-
48
Pttc. 1.2. I l o c , ' r e J o B a T e , ' r b H o c TAba H H b I x , p a c c M a T p r r B a e M a qK a K cryneHuaran
Synx.
uufl liJrrr <ripuBaq npqMoyIoJ'IbHHKoB>
JU
40
P i r c . 4 . 3 . P a n H o : u e p H a x n p o c r p a H c r B e H H a f l r r o c J r e A o B a r e J r b u o c r b ,n o n y q e H n a f i H 3
I r e p a B H o M e p r r op a c n o , ' r o x e H H b r x, q a H H b r . {n y r e M n p f l M o y f o n b H o r o H H T e f p H p o B a H H n .
f l l o t u , a ; , uJ a u r p r r x o B a u s o iol 6 r a c r s r a K a r > x e ,K a K r { d a p u c . 4 . 2
uprNioyfo,rbHtrKoB.I,IcxoAsure AaHHbreMo)KHo [peAcTaBurb B BIr.],e
cryneHqarol'r $i'nxqrin, HMeroueft B lrHTepBar'reN{exAy noc,'reAoBaHa6,'rroAeHHflMr.l
TeJrbHL,rMrr
rrocTorrHHoe3HaqeHue. flplrlrep TaKor?
Qyur<qun npeAcraBr'reHHa prrc. 4.2. Ecnu rpe6yercfl rr3o6pa3l{rb
pacnpeAeJieHlre
c p a B H o l r e p H o i rc e r r r c , u a / I o n o c T p o h r b A p y r y p
cTyneHrraTyrooyHKulIIo, Ho TaKy]o, rrTo6br n/'roxlaArl rrpflMoyfo,'rb6bt.\H paBHbr coorHr.rKoBc paBHbrMlrMeN{Ay co6ofr ocHoBaHHfM:l/.
BeTCTBeHHO
nJOIqaAffM I{CXOAHbTX
npgMOyfO,'rbHHKOB.
TarOe paCIrpeAe,'ieHLIe
npeAcTaB,'reHo
Ha pHc. 4.3, rAe noryr{eHa riocreAoBaT e J I b H O C T bp a B H O M e p H Op a C n p e A e , ' r e H H b r ,3\ H a r I e H H r i , K O T O p b r e
C O O T B e T C T B y I O T , I , a H HnbpleMA,c T a B , ' I e H H EH
IM
a n p e A b r A y U I e Mp H C y H K e . O 6 e s a u r p r r x o B a n g b r en , ' r o u l a A up a B H b iM e ) K i r , cy o 6 o f t . 3 r a n p o u e A y p a H M e e TT o n p e u l l y [ I e c T B o , q T o o H a y r { n T b l B a e TB c e A a H H b I e
BHyrprt HHrepBaJra,coAepx{aqefo ror{Ky, A/'rfl Koropori rpe6-vercff
noJryqHTboueHri\' 3HaqeHrrqr{syrraeMoftBe,'rfiqxHbr. Kporue Toro,
r p a Q H K O M ,p a B n o c K o i l b K y r r r o u ] z A b , o r p a H r r q e H H a f[ r o c T p o e H H b r M
H a n " [ o x l a , q i t .o f p a H L l q e r i n o r 'nr e p B o H a q a , t b H b r xr p{ a o H K o } , r , T o H a 6"rrcAeHl.iqlr,t:cnoJrr,3yeN{blM
A/,Tflno/'tyqeHlIgotIeHKII B ToqKe, Ao.xxil eJ i r ] H eT o f o } r H T e p H b I 6 b r T r ,r r p r r n l r c a H bBr e c a , f i p o n o p u r { o H a J l b H bA
B a J r a ,K o T o p r r i iri n r o T B e q a e T .
Hecltorpn iiii ro rrro reoper!iqecKli no.[\'qeHrreoueHoK illero;\o]l
I I p f l M O l r O I b H I I l i O tO
s q e H L Ir l p o c T o , O H O I I p O A C T a B J S e TH e K O T O p b l e
r p y A H o c r r t n p r t n p o r p a M M u p o B a H r r r r1.4 c r o , ' r b 3 y fnf e p B , v r on o . t y q e H H!'l,O OI{eHKy,
BbltlllciltleII
npoIt3BeAeHI.Ie
paCCTOflHIIf
Ta6"ruua 4.3
Co,qepxanue )KeJte3a B rpaHarax D3 KepHa cKBaxBHbt,
npo6ypeHuofi a"'rMasnofi xoponxofi
fnyoHHa, cM
0
J
l0
l4
23
30
.lo
4B
59
66
6B
81
94
96
102
.1,OC,'ICA\:IOII{€-
ro ria6JrroAeHllflHa efo BeJ[rt{LIiJy,r{To AaeT Harvrn.lou{afb 11pfl\roAafiee npoii3BoAlrM Te >Ke Bbrr{lic,.'ieHr{ff,
AJrfi Bcer Ha)'fo"rrbH14Ka;
6"trogenuit, noKn He no,'IyqHMoqeHKy B nocr'reAHeii roqKe. 3ra
OUeHKaOnpeIe,'IfleTCflB pe3y,'IbTaTeCyI{MHpOBaHIIff
\')Ke HailI,eH-
I lo
CoAepxaHne
xcJe3a, ib
14,21
lo
aq,
t 7, 2 2
15,87
13,62
16,31
141
, 3
13,95
r5,00
14,23
16,81
I ll, 93
r6,02
1 7 8, 5
t 7, 0 2
15,87
f,rry6ltga,
t2l
130
163
168
205
239
251
283
297
322
335
370
408
116
cn
CoIepxaHHe
o,/q
Ncle:a,
19,84
1 69
,4
16,72
192
,0
20,41
1 68
,8
18,74
r6 , 6 7
18,56
1 88
,7
20,8r
24,52
2 5, 0 3
25,tl
23,28
419
425
49cl
443
117
22,56
19,00
2 0 ,5 3
1 9, 0 8
22,83
21,06
474
493
502
522
550
558
?4 cltl
i)/ I
27,9F,
25,03
26,27
586
596
1 9 ,i 2
99 9t,
26,8E
21,li
ta
ot
r7l
lan
e
cMorpeHHOfOBbrrrrec,'ryqafi fi3yqe'rtfl COAepxaHfifi
trrar'Hs B BOAe;
fia6lroneguii sHaqra
reitHo 6onsure, qeM ueo6xo4i.ruux oqenoK,
'a HalIIa qe'Ib - coxpaHltrb' HacKo,'rbKo
aro Bo3Mo]KHo,IrcxoAH],ro
t t H Q o p v a q H r c .B o r o u c J y q a e M e r o A n p s M o y r o r , r b H H K o B
rrpeAcraB..IIteTCfl 6O,ree rIoAXOAgrr{I-,INr
A,.rrr nOr,tyqeHI.rflOrIeHoK, r{eM MeTOA
.naseirsoil rrHTepfio,'rfi
u,rra. OAsa rio qvtiurenrc peKoMeuAyercff tror,r\,qrrrb oqeHKil no
AaHHbru ra6,r. 4.3 lr tert, Ir ApytrM *""oaunn"'i,
3areM cpaB't'trb rlo"ryqeH'bre pe3yJrbrarbr
AJIfl yacHeuHa pa3Jr'q'f
Mexijly 3TilMll NreToAaMU.
B r e o , t o r r r r { f i p o r { e A y p b r c p a B H o M e p H b r Mi l p o c r p a H c r B e H H b r } I
- paCnpeAe,leHUeNI
qa'{e BCenO ,,Cno.rrb3OBa,'rr.lCb
rrpn, ,,OX.OTOBrie
( t t c c . n e 1 o n a H u ap a s p e ' e o " , ' s l n n c e i i u
A
a
H
H
b
r
x
:l,lT:l!'.tHqettiHX
oypoBbIX
fypna,rax ,rr Ap.) AJrr npoBeAeHr.tflBpeMenHofo rpeHA_
aHaJlt3a. Sror lteroA
, B C ) ' U r H o c r n .R o r o e r c , H e r { e M H H b t M I i a K
fipoqeAypofi cr,,rax,BaHufl, r{ A,rrq cBoefo npHMeHeHHr
rpe61.er
p a B H ' N l e p H o r op a c r r o J r o ) K e H rA
r rar H H b r xn n p o c i p a u c r e e . T a x f i e
neToAbI aHa"M3a..BpeMeHHbrxpfiAoB, KaK aBToKoppeJraqnouuufr
rr
r a p M o H n q e c x r r i i ,r a x x e r p e 6 y r o r A d l r f lc B o e r o n p l i M e n e H t r q
paBHoMepHoro pacflpeAeJ're'rrf AaHHbrx. B uacroqqee
BpeMfl MeroAbr
aHa,'tH3a epeueuHdrx pffAoB, no-BnAHMoMy, 6o,ree '*ourno,", qe\{
Apyrlle MeroAbr r{3yqeH}rr rroc,rreAoBarenrtrocrefiua6,rrc4euHir, rr,
BepoflTHO'e 6nfixrariilree BpeNrrruarilyr
rr'poKoe
rrpHMeHeHre.
OAsaro gTH MeroAbrrpe6yrcr 6o,rsrurrx'l,raccuebsnH$opi,raqufi rrro
,
orpaHuq'Baer B.3MO)KHOCr''HX npuMeHeHr.rfl
x crparilriaQauecxnlt
nocd'IeaoBaTed'IbHocrfiM
lI al{aJrr{3yxopouo pasnegaHubrx pyAHbrx
rvrecropoxAenuii. Heroropblg pesynlra^ru 6u,ru no,ryue""
npn rryqerrr'rlr[ocJreAOBare.nssocrefi H
M Hepa JroB, Ha6.rrrclaelaux e ui,rr'Qa"x.
J.eT, ecJIIHHa6,'ll.oJeHIIRAe.qaloTcq To"'IbKo
ts TOqKaXIi3MeHeHIlflcocrotHHs.
,[,agsue, Bxo!,quue B 3TI'{ rtocJIeAoBaB CyuIHocrl'I,TaKHe X{e' KaK Te'
TeJIbHOCTll,
IOTCf tlpH aB-rOKOppe,rfl
KoTopbIe I.lcno,'Ib3)'
q n u } e s a a M H o i i r i o p p e r ' t f l u I { uT. e n e p l , o l r{aKo, MbI 6ylert Il3yqarb He pacIIoJIo)Ke'fl{I{e cocroggtlti B noc,'IeAoBare,'IbHocrll'
a npupoAy rlepexo.I'aHs oAHOro cocrotHHfl
B Apyroe. Mtt pacctltorptlM Nlero,r,bl,Koro'
pble coBceM He ilcllor'lb3yIOTIIHQOpMaUIITO
o [o,rlo]'r{eHuusa6no\eHnli nHyrpu nocd'IeHo 3aTo [o3Bo!'ItIoT no,'iy- ,
AOBaTeJibHocTI.l,
vnrl uuQopN{aIII{to o reHAeH(IIu oAHoro \
,cocTogHHflc,rleAoBarb3a ApyfHlI.
.[,anurie ra6n 4.4 [peAcraBr'Iqnr crpa-
ua
paspes,rso6pax<essuft
rurpa$nuecrrrft
pttc. 4.4, B KoropoM ocaAoqHble [opoAbtr0f
B nocJIeLoBaTefibHblx roq- L
oI]peAe.rrgJr]Icb
K a x , p a c r r o , I o x ( e H H b tHxa p a c c r o q u l r a 0 , 3 n t . t
K a x A a s f l I - I r o . [ o n l q e c K a q p a 3 H o B l l A u o c r l5 |
6u.na orueceHa K oAHoMy H3 qerblpex Bsa- F
HMHo rrcKJrroqarcqHxApyf Apyfa cocrofl- E
wttit - necqaul{Ky, li3recrggKy, c,'IaHIIy n 0 L
6u.nn o6oenaqenbl
]'rJIIo, Koropble yc,'IoBHo
-4,
iooreercredsHo B, C, n D. Moxso nocrporirb Marpllqy [opflAKa4X4, s xoro-
Ho ero 6y4er noApo6no
pucct,oorpino
**u.
pa3 .[,aHHoe
copofi yrasunaercfl, cKoJrbKo
.croqulrec,'reAyer3a ApyrI{M.Marpaqa rarrrarpuqeiinepexoAiioro Tn[a Ha3brBaercfl
Hbrxqacror. flpulrepu raKtx Marpl{q ttptBeAeHbrHrixe. llcc,'re4yeuuft crparHfpa$nuecruii pa3pe3 coAeplKl4r63 Ha6npleF{rtt, rloaroMy I{NIeercn(n-l) :62 nepexo4a. MarpHuy c,ireAyerql{Tarb or crpoKa
ri cro.n6qy. 3ro, Harrpr{Mep,o6osHaqaer,
r{TonepexoAyH3 cocrotHIISA e cocloqHte
C coorBercrByer s,'IeMeHrMarpHIlbI ats,
IIENI.{MAPKOBA
MnorHe reo,'ror[q.ecK'e ]rccJIeAoBaHHr cBs3aHbr c u3yqe'rreNI
ttocJreAoBareurosocreftpe3y,']braroe Ha6,nrc4euuft, *oropo,6
trpeA_
c r a B r I I e H bBI 3 a t r M o u c r ( , T l o q a i o u { r r M r { , AAppyyr r a , c o c r o s u H q N { a .
B
' xa_
qecrBe np[N{epa Mox(Ho IrpHBecTH
ro.reqHltli noAcrler coAep}KaHlrl
MHHepaJioB
' ' o l e p e c e q e H u r ou , r u s a , I ( O f A a H a r ' I H q Hreo r o n " r a
ugoro MrrHepaJraorIpeAe,.rqercocrorrHr.reB
AaHHorl roqxe. flpu Hsyue_
HHU crparlrpaQrruecnllx pa3pe3oB l,,rrr cKBalKltHL,r,
cexyureit soHtr
P Y A H O T O T C , I A , H A 6 N I O A A I O T C f l T I O C J I C A O B A T E T b H O C T AT H T O J I O I H q C C K U X
TIIfiOB IOpOA' t(oroDbrM MO)KHOAarb aHa,rofr.rqHyro xnaccuQaxau[]o.
Ha6"rroleHufl nu ncpeceqeHtro Mo,r*ro flpoBecTil c paBHbrMlr
HHTepBar'laMH I'I.[I1 ]Ke pacnorTox{rJrb rrx nlloH3Bor'tbHo,
KaK aro
o6ut.{Ho
A e , ' r a e r c t [ p r r u 3 y r { e H f l r {c r p a r u f p a $ u u e c x u x p a 3 p e 3 0 B . B n e p a o l r
npl'lMepe Mbt N{oxeM oNilrAarb rrofiBr'reHuflo4Horo
H Toro xe cocToflHLIfl,T. e. HeCKoJrbi{orrocJreAoBaTeJrbHbrx
Ha6.lrc4enuft uoryr
norracrb B oAHy rr ry xe r{arefop'ro. 3roro, oqeBHAHO,
ue nDonsoilt72
I
cl
cl
a. l
;All
Al
Al
A]
t'
c
A
A
c
n
c
D
B
I
B
B
I
U
8
I
c
c
c
A
A
A
c
v
A
A
A
L
c
D
A
A
A
A
T, e. gcJIIt Mbt xoTltM 3Harb, cKo,'IbKopa3
Prrc. 4.4. Crparrarpatpu'-reocyulecTB,'rflJrcflrrepexoA H3 crpoliH c Ho- c K H f t p a 3 p $ , B K o r o p o M
I'lt
M e p o MA s c r o ; r 6 e q c H o M e p o n tC , H r s ry n N - ,THTO.'IOIAqeCKIteCOCTOTH
ALIM, rITo trepexo.u.lI3 cocroqHtn A s co- B3aHlrHO HCKrrOqarOr Apyf
Apyfa:
croflHrre C npoa:ouren 5 pae no ecefi noA-necvaHHx; 8-u:eecrcJIeAoBaTeJIbHOcTr{.
AHaJIOril.{gO, ?illreeTcfl u t x ; C - c n a n e 4 ;D - y f o a b
IIrrb nepexo.rr,oB
ri3 cocrosHrifl C e cocroggue A e erofi noc,[eAoBare,'rbHocrn:3To glrcJro- 3JIeMeHTNrarpriqbr, crorurufi na nepeceqeHuu crpoKu C w cron6\a A. Marpriqa
l/
J
I
I
4.4
Ta6ru\a
Ha Bnc. 4,4,
CrparurpaQuuecKacnocreAoBareJrbxocrb,
flpeAcraBJrenHafl
3aKoAl.tpoBaHa
c noMot{blo qerHpex B3aHMHo}lcKnt()qarcqBxCOcroqHfift:
necqaHlrK(,4), r.rsnectrnr(B), caaneu (C), yroal (D)
(Bepx)
CCBCAA
CCBCAA
CCBCAA
AABCCA
AABACA
ACCADA
ACCACC
ADCAC(HEs)
ADEAD
CCBCD
CCCC
ilepexoAHblx r{acToTtBJrfleTcflxoporxHM crroco6oM BbrpaxeHr{fl c,IeAOBaHrrfloAHoro cocroqHl.Ifl3a ApyriIM:
B
A
t)^
D
n
Cylrlrn
no cro.r6ualt
B
C
D
5 0 -l
l- r8 0
105201
5 2 18 2 |
I
s 2 -l
l- o o
237285
CyllunocrpoKatrr
23
7
28
A
0,78
0
2
u l | 0 ,r 8
Dt_ 0
Al-
Lrs
poflTHOCTHOM C\1rbIC,Ie3TH rIHC,4a f B.rrflFOTC'OqeHKaMH yCnOnnOfi
e. BepoqrHocrll roro, qro cocroflHltei robeporruocrl P(jl;),
".
gBHTcg BcJIeA 3a AaHHbIM
s Hacrosulltii NroMeHT cocrossrrer'r i.
( M r r n n e , r n H e o 6 b I I { H o eH, o 3 K B t . l B a . r l e H r Hoo6eo 3 H a q e H u e( P ( l * r ) ,
Koropoe MolKHo ct{HTarb BepoflTHocrblororo, qro 3a cocrosuttert i
6yaei c,'reAoBarbcocroflHi'te i.) 3ro o6osHaqenne 6yAer HcIIoJIb3oBaHOnO3)Ke.
0
0,71
0,07
0
cyM:lIa
0,22
0,29
0,64
0,60
-l
0
0
I
0,il |
0 , 4 0_ l
1,00
I,00
I,00
l ,00
ir
cl
0,37
0,ll
o4J
63 O6uar cynlra
raNoe-"r[6oApyroe cocrosHue.B ee6yaer c,rreAoBaTb
cocTosHileM
O6qar
BCD
Orcio.qa, HanpttMep, BIlAHo, qro ec,'ttl B HeKoropoli Toqxe N{bI
I{axoAliMcff B cocToflHuvrc, To BepoflTHocTbroro, qTo ,'IIiroJIorllqe'
Ha 0,3 N'{ BblIrIe rali)Ke ecrb c, paBHa 0,64.
cKag pa3HoBHAHOCTb
'Bepogruocrb rofo, rITo 3Ta,'inTo,rlofuqecKag pa3HoBilill,Hocrb
6yler
coirognnent A, pavua lB%; ona paBHa 70fo Ats cocrotlHlltl B II
I l0/0 - AJIS cocrofiHHn D. Tar xar ?rH qerblpe cocrosHilfl 83allNIHO
ItcK,'IrcqaIorApyf Apyfa i{ flcqepIIblBaIor Bce cocToflHHfl'TO Ji]lrOJrorrlqecKaff pa3HoBHAHocrbAo.rt)I(Ha6ttrt oAltoii Ii3 qerblpe.\. flo3 T O M yC y M M a ,3 a A a H H a f Il I O C T p O r i a Mp,a B H a 1 0 0 0 / 0 .
Ec,ru ltrt pa3Aer'IIiMcyx,IMbIrlo crpoKar{ nepexoAHofi Marpllllbl
qacToT Ha cyMNly o6qefo qlc,'la IIepexoAoB,ro NIbI noJlyql{r{ orHopaSHOBI'IAHOCreii,
cliTeJIbHyloAo,rIo Bcex qeTblpex ,rIl{ro,rlornqecKIIX
npeAcraB,'renHbrxB oroM pa3pese. Sror $axrop BepoflrHocreir HaSbrBaeTcsMapfHHaJbHbIl,{,Iir'ilI QHticHpoeauHbl}IBeKTOpOMBepoErHocreri.
tr
3auerrrn, r{To cyMMbl crpoK It cyMMbI cron6qoa oAttHaxoBbl rlptl
ycJroBr.ru, qTo pa3pe3 HaqHHaerct lt KoHllaeTct B oAHoN{ I.I roi\{ x{e
cocTogHr.rI,I:B [poTHBHOM CIyr{ae ABe CTpOKH H ABa CrO.n6Ua Or,rUTIAIOTCSHA CAI.IHI{IIY.3AUCTNU TAK)KC, IITO B NPOTHBONO,{O)KHOCTb
TeM MaTpHUaM, KOTOpble BbMIICJIq,'IA paHbIXe, MaTpLrqa [epexoAHbrx qacroT, Boo6qe roBopt, ecJIH [ocJIeAoBareJlbHocrb Haql'{Haerc g H K o H q a e T c f l B p a 3 H b l x c o c T o E H I ' I g x , H e c H M M e T p H q H a ,T . e .
aiit'alt
TesAeHqurc c,{eAoBaHI.Ifl oAHofo cocroflHllfl 3a ApyrilM Mo}KHo
B b r p a 3 H T bB B H A e M a T p l { I l b l , n p e B p a T H B r i a c T o T b I B A e c f T I I t I H b l e A p o g,'IeMeHT l-ft crpoxlt pa3Ae,'I[irb
6rr-n,ru npoueHrbl. Ec.rtu xaxAlti't
Ha cyMMy 3!'reMeHTOBl-il CrpOrtt, TO noryrleHHafl Apo6b BbIpa3IIr
oTHocrrre,rlbHylo BenlirrHHy, xapaKTepn3ylouyrc, cKoJIbKo pas sa i-u
I t*
B
I
l
D L 0,08
Hanolruiru, rlro B f,'r. 2 coBuecrHafl BepoffTHocrbocyurecrBJlei{ilfl AByx cO6lrrtili ,1 u B paBHfl.rrcb
P ( 4 , B ) : P ( B I A )P ( A )
:IJH
, )l P ( A ) .
P ( B I A ) : P ( , 4B
T a i l i i r ' r o 6 p : , : c r r , B e p o . a r H o a r br o r o q r o c o c r o t H n e B 6 y 4 e r
- . r e r o B a r b 3 a c o c r o f l H r r e r ,Ar , p a B H a B e p o f l T r r o c r !ri o r o , q r o p e a J r H 3r'rorcfl o6a cocrosans A rr B, peleuHoii ua BeposrHocrb ocyu{e-
iiffi
i:r:?l:'Jil:,,i;
Ec'rir nepon*o crir ocvirecrBrreH,s
co6brr'fi
P(A,B) : P{A)P(B) rr
P 1 8 i . 1 ): i P ( A ) P ( B ) ) l P( A ) : P ( B ) ,
: . e . R F i o t r H o c r r ) T o r - o .r t r o c o c r o f f H l i e B 6 t ' r t e r c n e . q o B a r r 3
, a co:TOfliliitrl'l ,4, eCr., fltJOcr0 BepOflTHOCTT
.B OCybO|O, qTO COCTO'HTIe
'JecTBirTCf B 3TO\r pa3pe3e, rr 3Ta BepoflTHocTb 3aIaeTCq COOTBeT''iBylol]triM 3Jre]leHToM n
QuxorposaHHoM BepoflrHocrHo\{ BeKTope.
175
-
Ec"rE sce BepoflTHocrnpeaJrrrsarlaa
cocrosnufi B p a 3 p e 3 e H e 3 a B H ct{[,tbl,TO TaKOe}Ke cooTHorr]eHl.re
BepHoH I|qtfl.B C C X B 0 3 M O > K H b I X
nepexoAoB,
Hanpr4Mep,
P ( B I A ): P ( B I B ): P ( B l c ) : P ( B I D ):
P(B).
3ro noseonfler Harvrflpercr(a3arb,r]To Marpru,
BepoflTHocreri
nepexoAa Ao,rrxnaBbrrJrqAerb
raK, KaK ecnu'6u uu.ioio,'"i,iruroru_
qecKHXcocrossnrt
roqKe crparurpaSn,u."noio'
u"r"pnu.ru
1 ^o4nofi
6amu 6u coBeprreH'o
He3aBrrcr4Mbrvrz
or JilToJrorr4.
B
Tor{Ke,
pacroJroxeHHorlnuxe B..HerrocpeAcreeu'ori
6;;r;;;;;."Mr"p",.iiu
onr"blx
BeposrHocrefi--nepeioga
AaeM
6yler cocrorrb us crpor<,Koropbrr_:
r'rAeHrrrqHbr
3aAaHHoMJnexropy ubpoot"o.r.i.-A;
#;!.o
.rpururpaQauecKoro
npr.rMepa
oHa^liueeinz4
A
va
B
BCD
A I- 0,37 0,l r
B 10,37 0,ll
c I o'37 0,ll
D l_0,37 0,ll
I,JMCCTBI.I,U.
0,41
0,44
0,44
0,44
0,08
0.08
0:08
0,08
i'-" - -
-^-{-y-Mo)KeM cpaBgnrbsry Marpr(y" o}KHAaeMuxnepoaruocrefi
nepexoAa
c ua6,rIoAa-euoiiilarpHqei? nepexo4Hbrx
Bepoflr'ocrei.r,
Koropyrc N{HAeficraure,rrb'oHa6,rn4aen
',pH npoBepKerunore3 0
TOM,qro BCeJrriroJror[qecK,e
cocroqHi,q^HesaeHcaN'ri
or HenocpeA_
cocrosnaa.
oio ;;;;;;;;";
::::119
_"peArxecrByrorrux
n'onoou1oo
KpI'ITepHg
yt' npwle' cHaqaJlaorHoue'rrq, xapaKTepl.rgyrorq'e
BepofTHOCTIt[oflBJreHr.rfJrr.rTo,,rof[qecKprx
TArroB,[peBpal4aIOTCrr
rlacrorbr,Arq qefo lpoBoArircfl
B
yMHo]KeHne
r<aNlori
ao_
orBercrByronlee
o6qee qucJroco6urufi:
"r.p-il"^nu
O x u a a e l r r r e B e p o q r H o c r H nepexoxr
-0,37
0,37
0,37
_ 0,37
0,ll
0 , 1I
0,ll
0,1I
0.44
0.44
0,44
0,44
O6u1ee ulrcao
(18- 8,5)2 r
B,s
,
t
-
(5
10,4)2 rr- -i0,4-
n-7.0\2
7.0
(5-5,0)2
- 1r- '
5,0
(5-
l0' l)' I
loJ
|
'
(5-9,8)l
'
( 1 8-
1 9 ' 3 ) 2- L
t2,\
_.)noo
9'B
,creneseitceo6o,u.st
ri 5fls-uox, I'ns,-AeBrrru
Kpurnuecroe 3HarreHHe
sHaql.i3Har{eHlte
ecrl 16,92;npoBepfeMoe
ro ypoBH, 3Haq[Mocrr4
re.rrtirO 1tpeBbI1rIaeT 3To qIiC,'tO, nOSTOMy MbI MO>t1eM 3aKJIKIIII'ITb"
qTO rr.{[OTe3a O IIe3aBuC]l[IOCTIi [OCJIeAOBaTeJIbHbIXCOCrOgnnft secraTscrllqecKlr 3HaquMat TeHAeHulIs A'rIfl
BepHa, r. e. cyqecrByer
HeKoropbrx COCrOgsufi HMeTb npeA[OrITeHHe B CJIeAOBaHI{I'I3a HexoropblM ApyrHM COCTO'HITeM.
Iioc.'relb-eareJlbHocrb, e xoropoii cocrosHl{e s oAgofi TolIKe B
BepotrHocTHoM cMblcJle JIHIITb qacrHqllo 3aBl',lcltT__ornpeAblAyuefo
cocrofHllfl,
Ha3bIBaeTCR tr,tapxoncroft uenblg. HaSeaHHaq TaI( B
qecTb pyccKofo MaTeMATVKa A. A' Mapxor:a, oua flB,'IteTct npor,leiKyroqHbrM SBeHoM Me>KAy no"'IHocTbro onpeAeJIeHHblMI{ (Aerep\{IrHripOBaHuttruu) U COBep11IeHHOCJIyqaftHbIMIi nOC.;leAOBaTeJIbl{O-
[;glfa=[,ij"frf"lii
*i]
Kpr.rrepurt,
onrrcautnfie rr. 2
#:.."-lly
191enufiMarpr.irlbr
.1r_-111ouuHaer
Ka)KAbrrl3,'reMeHr
qacror
riep"*o4u
pHlo, B KoropytoBxoAj.rrxar na6.nro4e"uoe, cocraBJrseri(arer.o_
TaK rI oN(r.iAaeMoe
qlic_
d'Iolepe_\oAoe.
Oru quc,racpaBHIzBaroTcg
no 6opryr""-^*".'..
t':
s (O-E)s
(4.2t
rAe O -_na6,rrcAenHoeqncJronepexoAoB
u3 o A H O f o c o c T o q H H f
'n.peioao"
Apyroe, E - quc,ro o>KaAaeMbrx
rT3 OAHOto
ts
cocToqHil,
176
l e 3 a B H c H M b I 'K p H T e e n D V r O e , e c , ' I H n o c J I e A O B a T e J l b H b lceO C T O t I H H fH
"o,ffit*"d.
creneHeft cBo6oAbI, r$e m-qlrc!'Io cocroqgl'{ft
@-t)2
'(oa",
crereHb ceo6oAH repflercfl B KaxAoft -cfpo-{e' raK KaK cyMI{ c ApyrllM}I
M a B e p o r r H o c r e u t s x a x A o t l r c r p o K €p a B u a 1 , 0 0 ) ' K a x
Ox(IIAaeIlMeTb
KaTerOpHfl
y2,
AO,'l111Ha
t<a>t<p,af
Tr{narvlrlKpilTepI4fl
npt'l]{bre qacToTbIno MeHbIlIefirraepea,rs ugtu nepexoAoB' B arou
Kp!IKoHcepBaTHBHbIft
npIIMeHI{Tb
riepe 3To He Tar{, HO Mbr MO)KeM
t"'I1:lLIy
A"1fl
rIpoBepseMyIo
BbIilI{cr'lHB
repufi He3aBnclIMocrlI,
q
acrorbl oollrue nqttt'
o
l
K
I
I
r
.
a
e
M
b
I
e
y
K
o
r
o
p
b
l
x
x
a
r
e
r
o
p
u
f
i
,
ueiupex
[op' noKa t{-\
Ocra,rrsue Karefopul'I MoxHo xov6uHt-tpoBarbAo rex
qacToTbI
ngTb'
flpeBblcflT
oxrrAaeMble
.
(ur..opr"
eKrloqa'Ior nepexo4u-A-A, A-*C, C*A u C'-+C'
H3 Bcex sJIeKortrduuupyeMbleKarefopl.lll Mofyr 6urs o6pasoBaHbl
nepe-tr
KoM6uHaIIuft
D
crpoKu
3.rieMe'roB
Bcex
B,
;;;;
"i6oru A-jD, C*B
u C'->D.' flo,'ryuaeuaq crargcrl'IKa y't
""^"""ajr',
Ha qenl Maopaeiea yKa3blBaer
cton,{u.Haur crparurpa$rnuecr<rrft
3 fal B U C H M O C T b
KOtsa [epBOfO nOpgAKa' T. e. CTaTIICTUTIeCKa
cyulecrByer MexAy AByMfl coceAHlIMI{ToqKaMLI.CyutecrnyrcT TaKNe cgor:rirsa MapKoBocrl{ Bblclxllx nopflAKoB' HanpHuep, noc,'IeAoBareJ'rbHocrlMaprooa BToporo [oprAKa yKa3blBaer Ha 3HalIIiM]'Io
MI'I AAH'
VC,TIOBHYIO
MC}KAYTOIIKAI\{U, II PCAIUCCTBY}OUIH
3ABI'ICHMOCTb
soil na AByx npeArlecrByloulfixrlarax.
C norr,rbnrrrcMarpI.IIrbInepexoAHblxeepoarHocreft MbI M O X e l l
oueHllrb,T. e, [peAcKa3arbJIHroJIorunsa O,0 u (Ha gea g a 6 , r n Aeurzn) Bbrue sexoropoii 4auuoft roqKll. flpe4no"'toxuu' I-ITO MbI
HaqaJrl{c n3BecrHsKa(cocroruue B). VxasauHbieHHxe BepoflTl2-201
t77
1".#" J#:tffi: ?:.; fi :f#;i'11o n.lo" oFHre' coorBercrBvro'{e
e
,4
B
C
D
Cocrosrrue
(necvarrux)
( r r : n e c r H n) l . i
(r"rnHa)
(yro.rr;
%
0
7l
29
0
cooTBeTcTB\'e.t
uecc yMHoxeH}r' u cyMMllpoBaHl,IflB ToqHocTI,I
uepexo.la
Ec,rn
Marplrqa
BepotTHocTefi
yMHo>KeHsrc.
oaarpruqnortly
pe3yJlbral
ro
(r.
e.
aoseoArrrcr
a
xeagpar),
ce6s.
ia
u*"bXuar.a
ttofiua"" varpuueft Bepoflrnocreftnepexo4oBBroporo noprAKa B
c,reaosarenbHocTl'I:
0,220
o,7B 0
0,71 0,290
0
o,lB 0,07 0,640,I I
0,600,40
0
o
llpe4no,Tox(riN{,t{ro c.ryeAyrcqafl
__
ToqKa AeiicTBaTe,TbHo
.eT
B r,'rHHy; Mbr llroltier{ 3aTe;\r
IIonanaonpeaenrtrt BeporTHO,CTb
ea.qauuoli,r,,To.rrorfi
rrofiB,'reHlrff
qecno,l pisuo;;;;;;r"
E cJre,l]'rcx{eir roqxe;
L
Cocrogsrlre
A
c
D
necvanux)
uenecrunx)
rJrvHa)
yro,rr)
18
7
64
il
p:
q u lo1 n Inl oc.reroBar e.,r
fi3BecTHflK-traHa__aaeecTHflK
k"til
bHocr r,
l* ;,u' :l:^o-:l:..r::
:I9. H uevc[ K
Ouan"nuar"B KaK
"Xt^f -+P (B
c) x p (c x B) : 29ols
y 701, 2olo
jc-l'I{b B,qBar'ara
l Ll,fi
lfiliiHl
CTpOr{KBaApara MaTpuqbl ral(}K€
3aMerulr, qTo cyMMbr 9./reMeHTOB
cocraB,'tslor 1000/0.
Ha"rnqne eHaquN{oilMapKoBocru BTopofo [opflAKa MoiKHo npoMeisly
Bepl.trb rorlHo raK x{e, KaI( MbI IIpoBepfl,rlIiHe3aBu,cl{MocTb
y2.
Ecttt
I(pareplrn
c
iroMoutbIo
cocrogHI.IflMLI
floc,'reAoBareJrbqbIMI{
I\{arpaHee, To"[bKOI]CnOJ'lb3ys
BbIKJIaAKIi,npOBeAeHHbIe
nOBTOpHTb
puuy nepexoAHblx BeposrHocreii nroporo rlopsAKa, To MbI y6e4uir'tgg B ToM, rITo 3Ta nocJleAoBaTeJlbHocrb
He IlMeer sHaquMofo ceoftcrea 6url uaproncrofi qe[E'Io BTopofo floprAlia.
Mu tr,Ioxelt oqeHlirb BepoflTuocrb cocrotHug ua .urc6o\{ Iuare
6yAyuero, lpocro BosBoAs B crelleHb MarpHuy BeposrHocreii coorBercrByloiqee r{Hcro pas. Ec,rn N'larpHua Bo3BoAllrcq B creIIeHb
IlocraroqHo 6o,rlruoe qllc,'Io pa3, To oHa Aocrllfaer yctoflul'lEofo
cocroflHr.rs,B KoropoM Bce crpoKLI craHoBflrcs paBHbIMIr$urcuponOJ_VBaHHOMyBepotiTHocTHoMyBeKTopy, IIJII, ApyTHMIZCJIOBaMI'I,
r r a e r c r H e 3 a B r . r c H M aMt a r p l i q a n e p e x o A H b r xB e p o t r H o c T e i i ,x o t o p a R '
lre h3MeHfleTcqIIpn [oc,'reAyrorqr.IxBo3BeAeHI]flxB cTeIIeHb.
B npuneg,euHoMBbr[re rrpuMepe Bbr \,ro]Kere y6e4nrlcn B ToM,
rrro HagBbrc[rue fiepexoAHbreBepoflTHocTr{cooTEercTByIoTnepexoi . a M r r 3 o A n o f o x a x o r o - " r a 6 o c o c r o r H r { f l e c ? 6 a , H a n p f i M e pn e p e i : o -
3*x.'ff""rJ,:ft.{'*-iy.:"
cocroqHrin
;:;:il#X1-?"""'J".T:;;:::::^*!;;;;;;#i"-*T',,.:?:l;;l':
B
e
c
r
H,
K
B.p;;;; ;;;;,;; fi i ;;;";;;,;".,.1:,,::T*:;
ff ff
:Tffi;ff
P (B -+ B) x p (B -> B) : TIvk
x Ttol.= E1ok.
Tax rar Apyfrie [epexoAbr
H3BecrHrK*rlecqaHriK
]r rr3tsecrHrri_l'ro,'ib I{MeioTH}',?e:rlleBepoqTHocTnr,
,o ,r, ABe noc,,reAoBaTe.ribHo_
crlr f Brrrgrorcs
eAr.{HCTeeHHO
UOr*o"r"irr'
rrocJreA.BUrili'"oar""u,
Koropbre[pr{Bor,flr or a3BecrH"nu
ir-".ry }rie B ABa ;;;;.
Bepo_
nooooa
Ha nBarrruru
uo,rri.
,,ru".*"*, 61':er
;;1p1il;.;?"lll,
Hoe''
i'ioio.,,
cocro'Hrre,oyae
u..,,o..
i . i Jf':;lgjf";*#,!;:;lrrorr
P (B-.4-*B):
0olo
P(B-B.-B):b0o/o
P(B- C-BI:
2olo
P(B*:D-B):
0o/o
52rlo
To xe p accy)^riAeH
npHMelrrrrh
onpene./reH
rifl BepotrrHocrlr rlo.rrB.reHrrs
":.^yglno
alo6oii rn,rdro.r,o.cxori
^{j-rlpa:Ho.uano.ii,
crycrfl
trBa uafa, ec,ii{ itcrio.l'Tbit3 .arc6orc
cocrofiHltfl.
Oluaxo Her H\,/i\-fbtpacctrarpilBarL,'uauuora.rorrr*u,a
"rrro,roa,,,,ac^ofo
ilcc,te-qo3iTe''bl10crr'r
IrHAirBilr)'aJrHO,
rai-;,r,,.,,,ano,ooa'eltrtirr
,,3ir 3T,]].1
[p0r78
.I.AM TECI]AHIIK-TICCqAHIIK,
II3BCCTHflK-I]3BCCTHffK
I,I f"TIIlHA-IJIIj!IA.
OqeeuAno, trro grrr nepexoAHbreBepofiTHocru cBfl3aHbl c MouIHoc t t t o s b r 6 u p a e \ ' r b r xc r p a r u r p a Q r r q e c K n xe l r i H l { q H 3 a B H c f l To r p r l c c r o t H u f l M e x A y n t r 6 o p o v u u r \ { Hr o q r { a M r . rH. a n p n u e p , q a c r o r b t B n o . - t b
r r a e u o f i n u a f o H a . l t r l r a r p u r r r r rr r a c r o r n e p e x o J o B 6 y r r y r y A B a u B a r b c f l , B T O B p e \ , I gI i a K E H e A H a f O H a J I b H rq, ar eC T O T bOI C T a t O T CHge I i 3 \ i e qepe3 Kax\ALte
Her_HLIt\,ru
B cJyrrae, ecrri ga6.lnAeHrrfl trpocoAr.ir'Ir{cb
0 , 1 5 l t . 3 r o B 3 H a q r l r e r ' r r , H ociri e n e g n y c u , ' l r i B a e rM s p K o B C K o,€c B ( i r i c r B o , o A H a K o B e c r r r r ac n e q r r S n u e c r l r , . uor6 p a a o l t . B u 6 u p a r r r o r x o -ltqee paccro-flHue xrex(Ay roqt(aMr.rolpo6onaHlrg, I{br craJrKHBaer,rcfl co cleAyrcureir npo6.ueuoli: ec.rn r.ra6,nrcAeHlrff
pacnoJroxer{br
CJII{uI(orvr6,rHsKO,r'iaTptiUa flepexoAoB oTpa>KaeTr,lanulru o6pa3oM MolqHocrl 6o.lee MaccllBHbrx,crparllrpaQuqecKux eAI{Hnu;
ecJtu x{e paccrosHrifl N{ex(Ayrosrialn{il orpo6onauus c,'ruurrioMBe,'IHI{rI,TonKue eAHHHrlbrMoryr 6i,ttt uo,ruocrbro rrponyuenbr.
l2'
179
BloxeHsue qenr Mapxona
Tpy,uuocrefieu6opa noAxoAffrqefo r.rHTepBaJ'ra
onpo6onauua
$roxHo H36exart, ec,rlr na6nnAeHl{f fipoa3BoAtrcflToJ'rbKo
TofAa,
KorAa npoucxoAur crreua cocrosnafi. CrparHrpaQa.{ecxHfi
pa3pes,
HanpliMep,Moxier 6url npe4craBr'IeHKaK IIocr'reAoBare.'rbHocrb
'no-r,cTLJIaroullrx
nopoA, KaxAat H3 KOTOpbTX
,'rlrToirorHqecrilt
oTr'trrriI{a or HenocpeAcrBeHHo
fipeAuecrByroqeii.B ra6n. 4.5 npe4cras.tieHbrSarrHct{nocJreAoBaTe,rlbHocTH
ropHbrx nopo.{, nepeceqeHl{brK
cKeaxuuoii, npo6ypenuoft n !,onuue Mu4neHg a LlIorraHAHlr.
CxeaxfiHa 6sua npo6ypeuana 480 Nr B KaMenHolroJrbHbrx
orJro>i(eHlitx[eHc?rJ'rbBaHcKofo
Bo3pacTa,cocTotulHx i.r3 [epecflatlBaloulllxcff To"IIlI, |,TIIHbI, tlila, [ecqaH]IKa a yfo,'IbHblx n/'tacToB llJtrl
IiopHeBbrxsoH. 3rH ocaAKH HHTepnperrlpoBa,'Incb
KaK or,'roxenHbre
B AeJIbTerr"rrocKo['r
paBHnHbr,noABep>reHHofir{acrbrM 3arorrJreHIIflM,
TaK qTO MO)KHOO;fi[AaTb, qTo HeKoTopbreJIHTOJTOfITT{ecKtle
pa3HcBHAHOCTTIMOIyT HaXOAr.rTbCtr
B npeA[oqTprTe"rrbHbrx
oTHo[reHr{r\
npyf c ApyroM. !,annne B3flTbrus 6o,'rruoro qrrc,TacKBaxrrH, H3y,qaBur.rxcff!,ayroHolr.
Marpnqa nepexo!,Hbrx qacror r"irq qerbrpex cocroffHlrft, no;ryqeHHar A/'rfl pa3pe3a lllor.nau4cxoli cxeaxuHbr, npHBoAHTcRHlrxie.
LoBepr.[eHno oqeBii21Hapa3Hr{rla Mex(Ay 3roft r{ paccMorpeHHoiipaT a 6 , r r n u a4 . 5
lloc.nenonarelbHble JtHToJror[qecKge
cocrogHnq, no.rtyqeHHHe
B cKBax(HHe,
-s
npo6ypeuaoft B yronbHbrx nJtacrax ,ll,oarnu Muilenn
lllorraH4ur{: 83a[Mfio
.HcKJrrcqarcullre
cocroflHnfl: .4 _ nycroft cJraneu,B _ craHeq c ncKonaeMbrMn
ocrarKaMxnpecnoBoAHbtx
paxoBrn; C-aaenpoanr, D - necqaHuK
x E-yroar
Hn{ KopeuHaseonal uxrafire BHH3no cro.rr6uaru[l5l
{ Bepx)
BDCBEBBACEACDAEEAAAD
ECDEAAECECBDACAACEDC
AACACCADAAECEADDEAED
E E A D D.4 C C D B A
ADBCCCADACBCDCBDACDA
D C A A D,A. C A D E A
AAEECtsBBCCBCDAAEDAAA
C D D C D,.{ E E A .4 E
DCCDCBCAEDACCADCAEAA
C A A C A. E A C A B B
DEEAtsADDCEAACDACABAE
C C C B E C C C D A B
.1, D A A A D A A A D E
BCDEBCCBECCCCAAAEEAB
E B E A A D D A A D.4
AEADBCCBEECCEBEADCCE
,ADEADEEAADAAEADCDDA
C D A A B C A A C D A
DCCDEACDDAEEACCDCAE
CDACACDACCAAEADCDDA
,180
qJIeHbI
B TOM' r{TOBCe ee AI',IarogaJIbHbIe
,:{ee MaTp}rqeft,coctogulat
He Mox{er crleAoBarb
6urt uynrMH, raK KaK cocrorrHrie
;;il;;i
BepoflTHOCTeft'
nepexoAHblx
ivlatpnqa
-n-oJlyqarcqacror
.sa caM[M coooH.
o,'reMeHraMarpI.IIIbInepexoAHblx
,ihi'.i
A."eHHeM riaxlbro
r{e
gJIelvIeHToB
o6raAaer-feM
crpoKn'
cyMMy
Ea coorBercrBylouyo
I'13
[epexoAbl
B
Koropblx
."oilcrsort.- llocneA6sare"'Ibnocrll'
lu*r
B"loxeH'
Ha3blBalorcg
geKoropofo cocroflHtlr s ce6g -3allpexreHbl'
rlpeAcraBrfler cneufioHux
HbrMlr MapKoBcKl{M,i"utnotu'
1i11li3BCefAa noHtrna reoJlorall'
qecKvlo 3aAaqy, rp)'AHocrl xoropoii He
HHbIX'
touru* s a n liCrr crp arurp a QllqecKIIXAa
"ruu'u
B
Cyrrlrtt no
crpoKaM
ABCDE
A
t-
-l
0 11 36 2t 52
3 6 4!,,3|
F
I 3i
zsr4533l
;l
E l-
2823 e
ll9
Cytutltr't no
cro.n6uall
r
37 9{ 78 68
120
oo
94
78
68
396
O6uaq
cyM!14
6yxnauw A - tnu'
JIHrOnOrnqecK!{ecocrofHHfi 3aKoAHpOBauu
opfaHI',I3MbII'I MeJIKyIO nopry'
irrbl, He coAep)Ka[IHe HCKOnaeNIbIe
L; B - ratnu, coAepixaurlle paKoBI'{HbInpecuoBoAuoi{ Qaynu'
cootnopoAbr.
E -yfonb i.rxopeuHue
trnu"iii,' p-
"'.i*r"il--n'
flepexoAiblx BepofrHocreft HMeer BHA
aercrByloulafl MarPfi(a
B
A
A
B
c
D
E
DE
BC
0,09
l-0
| 0,78 0
10,36 0,02
10,37 0,01
l- 0,41 0,34
0,30
0,ll
0
0,58
0,l3
0,18
0,ll
0,48
0
0,r2
CyMMbt no
crdoKav
0 , 4 3- l
0,00 |
0,14 |
0,04 |
-l
0
1,00
I,00
I ,00
I ,00
I,00
D C B A C D E CC
Mapruuartuttft eeporrsocrnltft BeKropltMeerBI'IA
A C D E A B D CD
A E E C A B
B E B
E D C E D E A E B
C E C D A C E C.4
D A E C D A A D D
D A C B E C A E A
B C A D A D E B
(Hxs)
e l- o,ao-l
Bl 0,oeI
c l 0 , 2 4|
D I 0,2tJI
r' l_o,rz_l
Kpnrepnir12, uAenruunufi(!.2), MO)Ker 6urr ucno,'Ib30BaH
.qn8 npoBepKll MapKoBcKoro cBoI{cTBaBfloxeHHOii [ocneAoBaTeJIbt8r
Hocrr-I.3ro Ae.raercflcpaBHeHueu
ua6,rrcgaeuortqacroruofi Marpr{qbr [epexoAa c o)Kr.IAaeuoiilrarprqefi, ec,'in rrocJreAoBareJrbHbre
cocroflHlifl HesaBHcLIMbI.
O4uaxo Qrexcuponauuur?
nepo.Rrsomslrr?
BeKTopHe Mox{er 6urn ucro,rbgoBaHA,'rflorIeHKr.I
cron6qon oxn4aeuoft Marpl.rrrbr[epexoAHbrxBepoflrHocreii.flocr<o.nbKy[epexo.tbr
rr3 HeKoropofococror*r4s.B ce6r sanpeqeHbr,rrau,qonxuu 6u,ru
6nt ilcno,rr3oBarbrar<oft-uu6yAboKo,'rbHbrfi
nyrt AJrflor{eHKtIqacTOT IIepeXOAOB MeXAy He3aBilCUMbrMrr COCTOflHHTMT.T
nplt ycdrrotsHr.r,
qro raKr.re cocroflHufl He Mofyr cJreAoBarb ga caMr.rMa co6oli.
!,"na uaua"ra npeAcraBHIr,t ce6e, r{To Ha[Ia roc,leAoBare,'tbHocrb
gBJIfleTCfl HeKOTOpOtT UeH3ypfipOBaHHOu BbrB AeI{CTBI.ITe,'TbHOCTH
6opr<oii, r.r3B,'rerreHnorl
Hs o6rrqHofi nocne4oBare.rrbHocru,e roropoii
nepexoAbr rzs HeKoroporo cocrorHnr B ce6l voryr HMerb Mecro.
Marpuqa [epexoAHbrx nepoaruocreri eroft rocJ€.u,oBOTeJrbHocrn
AoJrlKHauMerb BrrA, aHa"rroru.rHlrfiyxe Ha6,lroAensorl, ucKJiroqafi
AHaroHa,'rb,Koropafl 6yaer coAep)Karb orJrriqHbreor Hy,rrfloJIe[reHrlL Ec.ru 6u uu BblqucJm,rrxMarpr{qy BepoflrHocreii lepexo4a na
erori tuarpuubr qacror rr 3areM Bo3BerH 6u ee B AocraroqHo tsbrcoKyn crerleHb, To Mbr oIIeHI.i"rrH
6rr uarpuqy [epexoAHbrx BepofiTn xoropoil nocJreAoBare,'rbHbre
socreir [oc,'reAoBarer']bHocrll,
cocrosg,rIeMeHTbI
Ec,rz gareHr or6pocurl AHaroHa,rrbHbie
HLIfl He3aBHcHMbI.
u IepecqllTaTb BHeArrafoHadrlbHbre
BepoflTHocTlr, To B pe3yJlbTaTe rto,'ryrrurcflo)KlAaeMas Marpr]qa [epexoAHbrx eepoaruocreii
,l,"rn B"ro>Keltrtoiinoc,reAoBarertbr{ocrn,y xoropoti cocroffHufl He3a-
ABaUDE
'3-l
tl
A l- 'og8rolf 'o?3"n '3
zn I n ?
2d 23
T
O6uiaq
c vI'1If a
AHaf OHa,'lbHblM 3a'Ie]{€HcoorBercrBylonrne
Ill:rr 2. OueHHeaeNI
no
c}'ltl{
H a I l A e H H b l e Ae!'IeHHeN{
TaNr flepexoAHbie BepoflTHOCTll'
crpoxarl ua o6urYn cYMNI)r:
D
E
ABCD
Al - 0,208
0 ,1 9 2
Bl
C
LT:I
Dl
I
0,203
0,200
L l
lllar
CYltnst no
cTpo(arl
-t
I
0,208
o ,t g z
o,z oa
o,2oo
I
I
o ,i e 8
0 , 1 9 8_ l
nepexo\HHx
3. flo.,r1,uaelt Bropyrc oUeHKy lvlarplrllbl
TOT, IIC[OJIb3yfl
3'{eMeHTbI'
AHaroHa'''IbHble
[oJIVqeHHble
qac-
yMHOX(eHIi-
Ha o6uryro cyrurMy5396'-BueauaeM AHaroHarIbHbIx
3arert
".p;;;;;;t;t
na6,'rr6^esibleTIaCTOTbI.
ttcxoA'ble
ereMeHroirOHaJIbHbre
cyMNIa'
flaxoArrcfl HoBbIecyMMbIrlo crpoKaNln o6uas
BIICIIMbI.
I(ax auunc,rrurb qacrorbr nepexoAoB u3 KalKAoro cocroflHufl B
ce6s, ec"ru era uHQopMarl,I.iflHeAocryrlHa? Mu 6yaen,t npHMeHrrb
AJrfl 3Tofo MeroA npo6 H our[6oK, nlr6upax A"rrsHHx raKue gnaqeHr{t, Koropne, 6yAyur.t B'craB"rreHHbrMH
Ha ArlafoHaJrrzMarpxubr rrepexoAHbrx iIacToT, He H3MeHsIoTcs npi,l B03BeAeHr.rHr\,laTpHllbrB
crerreHb. BseAIzarosaJrbHblegurreMeHTbl,
oAHaKo, 6yayr n3Meurrrbcfl
Ao rex [op, noKa ne 6yAer AocrlrrHyra ycrofivueaa NoHcpurypailux,
coorBercrByroqa fl MoAe,rrliHe3aBucIlMbrx co6ltrHii.
BHeArIaroHa,lbHbIe
Ha nparruKe coBceM Her Hy>KAbIBbIrIHcJrfiTb
3 . r e M e H T bM
r . s t u a . { u H a e Mc r o r o , q r o r r p u [ n c b r B a e M, l u a r o H a , l b H b I M
Ha6,'IIoAeHHOft
,r'talpltqbl [IepexoAHbrxrraCTOTHeKOTOpOe
3,rreMeHTaM
npoli3Bo,'rbHoe 6orruuoe qHc,ro, cKalKeM 1000. IIpocy\,{MupoBaB
Kax{AoiI cTpoKII Ir paSAe/'i[Bpe3y!'IbTaTbr
3.rreMeHTbr
ua o6qyrc cvuMy, ucro.rrb3yeM noJryqeHHbre3HaqeHIIfl B haqecTBe oqeHKu nepe^
xoAHbrx tsepotruocreli, crolulux Ha AuaroHar'rn. STlr BepofiTuocrn
B ile3y/rbB03BoAsrcs B KBaApar n yr,rHo)KarorcsHa o6uyrc cyxrN'r\r,
Tare no,'IyqaIorcfl HoBbreor{eHr{uAuafoHa,nbublxr{acror. 3rll noaue
B }ICXOAHyIO
MaTpHIIy nepexoAHbrx LracToTH
orleHr{r{BCTaBJIflIOTCfl
nepnuri r{Hr{,1 erofi
3aTeM sTOT npoUecc ltoBTopfletcs. vxaXieu
npoueAypbl.
I I I a r l . 3 a n H c m e a e [ ' {H c x o A H y } oM a r p u r { y n e p e x o J H b r x r { a c r o r
co gHarregneu 1000 Ha Kax{AoM Mecre .!,HaroHaJH:
I 120
1036
l 094
I 078
1068
5396
,063
|
8 looo-l
e
l-
Cyvust no
cTpoKalM
CyMvr'l rlo
CTFOKA}I
-t
|
V I s+ 2222 45 13 |
; | 29 i 4521J 3 I
E I - 2 8 2 3 e B 2 t 2 -l
.l
R
il:
B
ABCDE
35
r- 233 ll
1
I
28i99
21
+
353
235
316
2e4
280
52
o
1178
O6uraq
cylll \14
Ao rex IIop, noKa oueHKHnepexoAnblx
3ror npouecc [po.d,o,'ixaeM
H3MeHflTbcfi'
Locruxieutte
qacror Ha AIIaToHaJII'I
He nepecraHyr
'20
.'rIC.-ro
urepaqrtiit
npnuen
rrreiauuft,
1O
oi
Ao
,ioii u.", fped,ver
3Ha3aBIIcilT or rofo, xaK 6,rusKli 6u,'tti nlt6paHulte HaMH Hayfa'll'
BIIA MaTpHI{bI nepeXOAHbIx
qeHltrr x Cta6ti,ttHltU. OxOnqare,rlgliii
LiacroT c oileilellHL,I)11{AIIaf oHa,iIbllblMll qacroTaNIIi ilp llBe;IeH HI{>lie'
b
ABCDE
it,
.4
81283+!0
c
t
E
1 l ' , : , 1 : ' l n: ro c t i . , ' i i l i ' r :
flo
CvutILI
cTp oK3 ll
l-
66 l:
3'' 21 52 -l
186
I
i
l-
s+ !
!
:g
2s!3
lf 15- 13 |
3 len
+.17
9 8 13 I
123
13;
4i
l3e
1:3
95
8l
rt
52{
O6iila n
c \''ll\I a
TJ J
t82
3ry rtlarpurtyMoxHo npeo6paeonarb
B..oxuAaeMyloMarpur{yre,
pexoAHbrxBepoflrHocreftrHnorera.recxofinaapr<oaixofi
not,ru40"rTe!'IbHOCTH,
pa3AeJIHB
raxAufi ee SJreMeHT
Ha cooTBeTcTBvroruyrc
cyMMy no crpoKe.
raKafl,Marpuqa Marro rrurepe-nu,,rn
9{IuIo
Kar{ oHa xapaKTep'3yer
60.nlruerllnor-eruqecKyro,
qeu la6n,oaenHylo Br'roxeH'yrouocJreAOBarerbHoc*.
fipyroe Ae,'ro- rupr""uro.
HbrecyMMbrrro crpoKaM...np" Hx BbrqrrcJreHlru
lrcrroJrbsyeicn
rr,rap_
lusa.nruuii BepotrHocruufinexrop
iffiff
l
Mu uox<eu refiepb Bbrqrrc!,rr{Tb
o),Kr.iAaeMbre
BepoffTHocrrrrr o}Klr.{aeMbIe qacrorbl rr.illoreruqecxor? nocneAoBaTeJIbHOCTU
He3aBIrcHMbrx cocrorsuil Aas_MapfaHaJrbHofoBeporrHocrHoro
nexropa. ^[tnr
NPOBCP'CM THNOTC3YO HE3ABI-ICHMOCTH
TIOCJICAOBATCJbHbIX
COCTOqHHH, 3aMeqaff, qro. HanpHMep. ecJlH cocrosHlte
,4 He 3aBHcr.tr or
cocronHun
:'p (A)p (B). Tax iuri i"1ii" i p
B, ro o
!!!ul 3,'reMeHTaMH
Wl
Mapfr.rHaJbHoro
3aAaHbI coorBercrByloqr'rMI'I
BepoflT-
ro o(eHKayc,roeuoi?
BepotrrHocru
roro, qro co_
:g^.ll:io,Bel(ropa,
crorHrle
A oyAer c,reAoBarb
sa cocroflHHena
paBua p(AlB):
B,
: (0,355)(0,074):0,026. Oxu4aelrlre BepoflrHocr'r
J..r.sBcex re_
pexoAoBIIpUBeAeHbr
HHXe:
AB""DE
Ils
4
q
q
l - g , l ? q g , q ? q g , q 8 3 0 , 0 6 4 0 , 0 5 5_ l
I 0 . 0 2 6 0 , 0 0 6 o ,o r z o ,o re o .o i i I
I q , 9 8 3 0 , 0I7 o , o s s 0 : 0i 3 J .o i o I
E I 3;331
3;313
3:313
B:BBB
B,BBi
I
oxugaelrne qacrorbr HaxoArrrcsyMHo)KeHrieM
erori aroii uarpnqrr
ua o6Uyroc)/MMy,paBHyro524.
ABC
ir:
4
B^
c^
2
E
l- qq,q
I
lq,6
| 1
q,!
3
3,5
|
l_ 28,8
DE
13,6
3;r
B;s
6,8
6;3
43,5
B,e
2s,s
22',5
ta;e
33,5
6,8
2 2, 5
1 7, 3
14,7
2,3,8
6,3
1 8, 9
14,7
i2,6
3auerulr, qro gra Marp,qa c,MMe''pHlrHa H
!HafoHaflbHbr€
9,rleMeHTbr
ocralorcs Heu3r\{eHHbIMtr(c Tor:I:ocrbro
Ao ouru6cx
1.31
oKpyfJreHllfl). BneluaroHaJrbHbte o,'reMeHTbIecrb ox(HAaeMbleqacecnu rlpeATorbl nepexoAoB AJrfl sJloxeHHoft noc,'reAoBareJrbHocrl,I,
cocTotHHflIroJolKfiTb HesaBHcrjMocrbMexiAy [ocJleAoBare,'rbHbiMH
eJIeMeHToBMarpHI{bI,To ee
uu, Ec,ru orB,'Ieqbcgor AI,raroHaJIbHbIX
M o x H o c p a B H u r b c u a 6 , n p A e n u o f t u a r p u u e f t n e p e x o A H b l xq a c r o r ,
rar( KaK cyMNrbrcrpoK n cro.l6qoe y HHX oAHHaKoBbre(cuona c
r o q H o c r b l oA o o u u 6 o x o x p y r n e u u n ) .
flpuuenna AJrs cpaBuervrfl crarLtcruxy y2, [oJlyqaeM 3Haqeuue
,y:(m-l)r-m
c r e n e s e f i c e o 6 o A u r ,r A e
Xr:172. I(prarepuii lrMeer
(purnqecKoe
r i - q f i c . t o c o c r o . a H n t i ,H J I HB a r o M f l p a M e p e \ r : l l .
3 H a q e H r 4X
e ' c 1 1 c r e r e H s n a zc e o 6 o A s I L l y p o B H e M3 H a q t l M o c r l ic ( , :
: 0 , 0 5 p a B H o 1 9 , 6 8 ,r . e . B b t q l t c . r r e H HsoH
npee a q e H H e3 H a q I i r e J I b H o
qr0
rlo3aKJIIOql',ITb,
IIO3TOMy
MbI
MOX{eM
I{
KpIlTHqeCKOe
BbI[IaeT
3aperIICTpl.{pOBaHHble
COCTOflHHS'
r'lHTOJIOfHqeCKIie
C,'l€AOBaTeJIbHble
a cKopee orpax{aIor
s LllouaHAHrr, He fln,'rflrorcrrHe3aBLIcI{MbIMI.I,
ceoficrso cu,rruoft MapKoBocrll flepBofo [opqAKa.
Ec,la xpurepltft nor<axer Ha Ha,'tIIqueqacrnqHofi 3aBI.lcl'IMocrIr
cocToflHxqN{llHeKoTopoli noc.leAolaMexAy I]ocJIeAoBaTe,'rr,HbiMl.l
Te/'lbHOCTll, TO N{OX{HO IIpO.n,O,'l)KIITb HCCJIeAOBaH}Ifi C UeJIblO yTOrlHe-
H u s e r o r i 3 a B l r c u M o c r u .f l p o c r t t e r p a Q l t u a u 6 o l e e 3 H a q H M b I xB e porruocreii Harrolu.tHalor Kaprt.IHKIl, xapaKTepl'13ylolrluenoBTopeoHI{ TaKX{e Moryr 6ltrl o6Hapyxeubl
frrts B [oc,'reAoBare.r]bHocrt{;
, c r r o M o u l b r oa n t r a p a r a r e o p u l r a s r o a c c o [ u a q u l i . n n s
npoBepKII
3HAlI}IMOCTH
BCPOfTHOCTC14 NCPCXOAOB MCX{AY
LIHALIBVAYAilbHbIMII
, r r a p a M r lc o c r o g u u f r n p u N { e H H M b r , v o ; l u Q u x a r r u K
ll pllrepun y2. He,Koropbre aBTopbr HaxoAflT, qro co6crneHHbre 3HaqeHufl MarpHr{bl
,fiepexoAHbrxBeporrHoctefi rs,'tRtorcq rlo.re3HbIMII ItHAHKaropaltII
rlHK,llrquocrr.r.(Heo6xo4Hnao orNrertlTb, oAHaKo, qro BbIqucJ.reHr{e
co6ctseHHsrx Ber(TopoBacraMMeTplluttofttrlatpuqu, Kaxofi trB,Ilgercfl
M a r p u r r a n e p e x o A H b r xB e p o q r H o c r e f t ,c o n c e l r H e n p o c r a f l s a a a u a . )
3ru nonpoclr e Haueft KHr4feAaJree ne 6y4yr pa3BlrBarbct; I{HTepecvrcu1Hrlcflr{HTare!'rbMoiKer o6parnrrcr
K KHHfe Keuenn H
Cne.'l;ra [30] u;ru KHr.rrelllaapqaxepa [49], nocBsutenHofi xo.rlt,recrBeHHbIMMeroAaM ir3yrleHr.rflocaAKoHaKolr,'reHlrg.
Kparepnn rHna
B KHIrre
X2 Ann BfloxeHHbrx nocJreAoBaTensHocreftnpeAcraBd'reHbr
fyauena [22]. Coorsercrgyrolrl]re reo,'rornqecrue npo6.aeMbr pacc M o r p e H b lB c r a r b r r x [ 1 5 ] u [ l 6 J ; r r , t o x n or a r ( x e p e K o M e H A o B a r b
pa6ory'Itopna [541.
NOCJIE,IIOBATEJIb HOCTH CObbITINN
paMu He paccMorpeJir{eure oAr.rgr{Hrepecsnft rufi BpeMer{Hrirx
AoB, HasbrBaeMbixnocJreAoBare,'rbHocrsMnco6nruft. flpauepauu
reoJrofnqecKHxAaHHbrxTaKoro poAa MoryT cJrylr(HTbHcTopnqecKne
cBeAeHLIgO 3eM,'reTpflCeHr.rsx
n I(a"rHQOpHI{H,3arrI4CIrO ByJIKaHHqecKHx H3Bep)KeH[sx a Cpe4rseMHoM Mope. Xaparrep]IcrnKll oTI'IX
,psAoB c,'reAyrolque:a) co6urut pa3J'rHrralorcflMoMeHTaMI,I
BpeMerdo
g:i::"rocyr{e
crBy
cBoeMy
"i'itJ##'
it'Si;f/"':
Ift :a."''?T
rporcxoAnr
e oa,.uHror xe ,i;;;;;j;i,T,T;oTr.r rrrK.KHe
aea He
.r.;'""r'#'#??fltf:.?:'" ." 6";'i;#; in .oo p,...\rarprrBarb r(aK ro-
,c,roxsltfi crparoByJrKaH,Bce ero H3BepxeHrrflorHocHJrr.rcb
K B3pr,rB.IIoMy rlltty, H npu srou-ntr6pacbrBaJrocborpoMHoe Kor[qecrBo ByrriaHur{ecKofo relJra. Xort craplte,
pefyr'IflpHo npoBoAllBulfiecfl
3a[trcH coAep)KaT yKa3aHufl Ha OTHOCHTeJIbHVTO
!r npoMOTTIHOCTb
ro/'r )Kr'rre,'IbHocrbuseepNeHlt fi . aJ'rfl n p a KTuqecxll x ue.nerl Mbt MolKeM
.cqirrarb ganucfi KaK orHocqquecq x co6utugl.t, npol43orrleAuilN{
MfHoBeHHo.AHa.[ns acropr{H ByJIKaHaMo],r(errrpo,'rHTbuexoropstri
cBCr Ha nplrpoAy MexaHvsMa useepNeirufr r.{ Mo}Ker rrpuBecrrr K
rrocrpoeHuro Susu.recxoii MoAe,rrHByd'rKaHoB
[611. KoneuHo, Mbr Mo>Ke\I TaKlKe HaAetlTbct, qTo TaIiOe Ir3yr{eHue Mo}KeT npI.IBecTI.{
K
ironB/'reHnrorexHo,roflrll npeAcKaaaHHrrusBepxieHril s 6yaynrenr.
[4:yueHze pflAoB co6urnr? npec;'re^(]erHecKor'rbKoo6t,er<runsrrx
qe"reii. O6uqHo r{ccreAoBare,'rfl r.rHrepecyer cpeAHrifl qacrora riofl.BJeHHtrco6r,ttlrfi, T. e. qHc,{o co6utlrfr 3a Her{oropr,rfraHreDea.rr
BpeMeHIIK
. p o n r e r o r o , 6 u s a e r H e o 6 x o 4 r . t MH
o c c r ' r e A o B a rpba 4 r i c o .6rrurii 6onee AeraJrbno. Lle,rl rarofo accr'renoBaHil.E
- BbI.aB"lteHHe
raxol'r-nlr6o 3aKoHoMepHocrr.t,Koropor? lloryr noAquHrrrbcg co6rrrun. !,onorHHTeJIbHat lrHsopuaulrq N{o)Ker 6utt
HcrIoJrb3oBaHa
Ar'Iq yroqHeHrrfl qacrorbl rroflB,'reHl.rrr
co6brruir, .q"rq olIpeneJleHtIf
'oco6eHnocrer'reu6opouHoti cxer,,rlr,
rpeH4a rr Ailn
l.ul o6Hapv)r{eHr.tfl
'ycraHoB.aeHrifl
Apyrlrx cltcreMarnqecKHXceoricrg prAoB.
TaN r<ar ptglr co6lrtHil HrvrerorOqeHbnpocroli BHA B ToM cMbrc- HeT>>,
Ie, qTo oHu cocTofiT H3 XapaKTepr.tcTHK
Tr{na <<Aa
TO A,'lfl
IIx ll3ytleHliq Mo)KHoI{cno,'lb3oBarbIIpocrb]e H B To )Ke BpeMfl oqeHb
MorqHbreaHaJ[rr]rqecKHeMeroAbr. Koxc u Jlbnuc pacciraarpHnaror
MHO)KeCrBorpa$nuecrux MeroAoB, rlodle3HbrxArt r.Iccr'Ie.u.oBaHI.ifl
psAoe co6urur:i. 3ru uero4br rrrJftocrpr{pytorcfl B npuMeneguit K
, q a H H b r MH s s e p x e H u f t B y r K a H a A c o . n p e g c r a B J r e H n b r M
s -r a 6 n . 4 . 6 .
H a p n c . , 4 . 5 u s o 6 p a > x e H aK y M y r ' r f l r r i s H a sK p H B a Ro 6 q e r o q u c J r a
u : a e p x e H r r i i l , n p o u e o r u e A r x H xB n J r o r bA o M o M e H r aB p e M e H [ l . o H a
coortsercrByerHa rpaQuxe ror{xe c a6cuaccofi /. Oror p}rcyHoK
x o p o r r r o_ o r p a x i a e r r r s M e H e H H n
f l C p e A u e i ic K o p o c r n r r o f l B J r e H Hcr o
r6urrrfi. Hax,qog np:rlroir, coeAuHflIorqelinro6ue ABe roqKg Ha KyIr,rylrrnaHori xpHeorl, paBeH cpeAHe.MyqHcrry co6srruli 3a eAr.rHr.rqy
BpeMeHr{,B KaqecrBe roropofi ntr6paH r.rHrepBa"t MeNiAy srrrNrr
AByMt TOrrKatvIH.
Ha plrc. 4.6 npe4craB.[eHa rr{crorpaMMa qr.ic!.ra nsrepxeni.iii,
[poucxoAuiqux B tlocJleAoBare.'ibHbte
paBHble ttHTepBa,'rblBpeMeHH.
I IiCTOrpar,tI'{?
trpf}rO yr(a3brBaeT"rroKaJ'rhHr,te
IIeprroAbrQ,rrcxryaqrili
o r H o c [ r e , ] b H o c p e 4 u e i r c K o p o c r r r n c r r B , t e H r r ful : n e p x e H r r i i. t r 4 s p t t c|ritia BIIAHO,qro fllcrofpaMMa r{yBcrBltrer'I},Ha Ii ,l,,iHHeau6pauHoio IrHTepBaJa, nosror.,ry npn aHaJIl3e p.sAoB 6lrsaer [o/,re3Ho
Itli(,Tb 6olorue qe\i oAHy rlicrofDa14Ir\r.
3unliprr.recriar Qyurruru" aanreniHocrr By.rrr(aHa noJyrlaerct,
e c . r u ln p e ; l c r a B r r r bB n p o r l e H T a x3 a B u c r r M o c r l Y ( o r u o m e n i i l q u c , r y a
B p e M e H u b r xl r H T e p t s a , r oAB" t l t H H e eX x o 6 u l e u y q u c , r r yu H r e p s a , r o s )
c r X ( a " u r r H bBi p e M e H H o f or i H r e p o a . l a ) . i l o , r y u e H H a i 6 y H i r q n n x a -
;:Hr"il#Tr#ilr#Lri?lsjiitrf
;Tiffi
#;
ii-T.I:;fi
cyMMapHbrx ,lrrn
upa*egHbrx
cocrotTb
13
s'a,reHl.ft
6mrus.fiauuHee oA"o,i
"nraou,t'"
co"rpur{reprr3yrcqHx
O"pi.'riirf'l"?::
not
- I' obrrb
npocronpboOpasoeu.
f,l3ll"e ApyroueopMbr.
wroAeilH nocne40e-aril.nr'ocreii
co6_srrafi Mo)r(HO HCnor,rb3.Barb.
u"oo,*o,n-"'"r-r,
iii:{;,*f #T3l"lHi#':{**"'it:1"*
uiIi:X;:T3J#
t 3l'ifi' !,i;'J,".p"F11:1.
:l#,,f"fl:?:
"'.. [.u"u'
t;;;';
Bepr'A,-{11eft
{;,i;;;li$i;5:i#Tli,3i;':lrroBbrx
uAuaxo o6ocuon
o6pasoeau rrii.
aHu"
np *""
-n ";;;;"
crleroBarenbHocrlrcooo,ir,i'
IrccreroBaHun no"
"'r"o"Ja""-a..ocaAoqHblx
Jt:?{oB
ercs oqeHb
naHHbrr.rflBJrflI*' o1.,i,f.",^"^tp?HcrBeHHbIM
crosHcrBe.*bbo.",Ynlu
"pyAoarn"r^
-6asapyetin^1a[pelno,roxeHrr o ro-
xi#;";t4::;
i!l["'TTd*#3ilitXi:*'tl?il','J.ilffi
ycrroBHe,sar n'o.rarcqe._.i i6
*, * ;;: 3:f; "".
Jo"J"TiJ,trf.H;
"
"' ;
}ou.JffJ'1':{un"o'i-'o.r."ao'iur.nu"o.rn.
]"'ffi
nnoua
rJf#X.
i!, ff:;ifr"XtX
",'"I;;;; ; r'rLE
i.u:i. "f, y.d
"i
4.6
Ta6aaqa
.4,aru nteepxeHafi nylxaHa
Aco s nePIroA1229-1962
ff.
foA"r
I Ito
I 239
1240
1265
r269
1270
1272
zt J
97 I
281
286
JU5
QOi
.JJ I
,rJi)
340
346
r369
lD/i)
i A1i
1376
1377
I 387
I 388
1434
I 438
r 473
I485
I 505
I 506
1522
I 533
1542
I 558
1562
j ooJ
l 564
lo/o
r;32
I 583
I 581
1587
I 598
l6l I
t612
l6l3
I 620
16 3 1
r637
I 619
r668
lo/D
r683
l69l
I 708
I 709
r/b)
r772
780
804
806
814
dll)
826
827
828
l 829
l 830
1854
1872
t874
l 884
I 894
r 897
l 906
t9i6
I 920
1927
I 928
I 929
l 9 3t
1932
I 933
r 934
I 935
I 938
r9 4 9
I 950
r95I
r 953
1954
r 955
r956
1957
r958
| 962
r87
a,5. K1'uy,rRrrnnanKpHBari
Ll-ttr r u c J ' r a, B B e p x e H H i
EyrKaHa Aco, or-.
Hece.HHbl\r roAy l.I3Bep)I(e.Hus
Log
70
50
80r
30
qn
,I
rbu
@
o
t0
qn
o
5
:: 4 0
Jon
10
0
1200
r0
4 0a e r
t0
1400
1600
1800
foA co6urrrq
ttI
Prrc. 4.7. 3vnnpuuecran QyHxuttl Aer'
Te,rbHoclt ny;rxaHaAco.
Prc. 4.8. .Torapu@rr 9urtuptt.tectiojl'
ry,rxaua A:o.
SyHxquu.qerre.:bHocru
fIo BeDTHKanbHofi ocu yKa3aHbl npoqeHrhl
oT qHcJla I{HTepBatoB Mexay lt3B€DXe}tHt'
6otbue
MH, uMeroulHMH npoaotxllreJlbHocrb
ueioroDofi saaaHrioll, no ropH3oHraJbHofi
nDoloJlxHTeJIbEOCTbHFTepBana
Bepruxaasual ocb pHc. 4.7 s\ecb nn:!.areEa e g a s a o r a D g ( b ] r H r I e c K o Mg n 6 g 1 : t 6 e
' : l20t-
30
i rsF
rol
ol
aa
" toF
ol
; ;t
1 200
a
a
l-'o
n
. e
.:,
r409
r 600
co6btT h i
1800
Pac'4'6'rucrorpauva
B noc,.r.;:::?J:i:iJ-."?:1,""1,T;l?.f;r"ibnpoir3.rxeArr'x
Tepu3yer Bepo.flTHocrb
_Toro,qro co6utpte He npolt3otrr,{cpaHbrue
MoMeHraBpeMeHuj: ji^t":.
4.2 npegcraB,rreHo
npor{earHoeor_
HoIIleHLeqacra iluleg-n3nooMexny riseepN"uu"rnu,'noiopo,e
npeBocxoAr?HeKoropoe3a^aHHoeurcno
ru".' g;;- ;;A;#,;;o'cxovnr cnyuafr'o Bo
py"i.u,,o
ro
Aenre,,rbHocra61,Aer,,r{erb
"p.:y::il,
oKcrroHeHrlua,t
bHylo
Sopuy.
ry x(e caMyro SyHxr{urcMo>KHo
r.rso6paalirl_,e
.lorapi.reuriuecKoMMacrrra6e,ucnont:ya log y xar
rpyHxrlrrio_,y.
,rlorapuerr,tHue_
cKafl oMrr{paqecKafl
QyHxrrusaeare,rruilru oco6euuoJoS6n"
or"
H3yrreur.florxnoueuuft or c.tyuafiuofi
eer
rltlorca ua rpaQrrre .q*
KaKyKrroHeHr4e
o.,'111*Jl:".*919?"]u,rPeAcrasrr\srvrEnnx o.r.
rrpflMola JrHHH (puc. 4.8):.
Plc. 4.9. Ceprra"lluax Koppe,ltquq
nporoJxHreiuuocrefi Mex,4y nocfleuao6paxeHlrnMlt
BynaoBare"rbubrrlH
x a H aA c o .
H a
neprlrxarsHoil
npeAcraBJreHa
ocu
frDo,tor'IXilr€JlbHoCTb
noKor
treDe.q
l-M
):iBepxeHheu.
Ha ropd3oHTanbHoii ocH nocne /-ro
TpeyrorHHxalta
H3BepxeHriq,
qeM oAFDencraBJIeHbI cKotrneHltr 6oree
Hor:l Toqliu B o.n.HoM x rort xe Mecre
a
aa
=
I oA
Isg
4 0r e r
20
a
^^a
1 0-
aa
aa
a a
a
aa
a
o
aa
oo
a
a
a
a
a
a ta
a
a
c
a
a
l'
a
oo
2A
t
30.
,- t. ner
,[,uarpauua paccetnllt ceplta,rluofr Koppe.{tq[It uJuI aBror,iopIIHTepBa"r]OB
N{e)it.(y
penflIIIiH II€pBOIO[OpgAKa IIOC,IeAOBaTeJIbHbIX
co6ururrMrl npeAcraB,TeHaHa puc. 4.9. Creneno coorBercrBlI-flr{erI<,r,yA,rrrgofi HeKoropofo Ii HTepBaJIa u A,'unofi Helocp eAcrBeHHon pe,u,IuecrByloulefo I.IHrepBaJIanpelcraBJIeHa Ha rpaQtrxe roqt{aNIll c
rAe lt - BpeMt noflBreHll.fl
KoopAI'IHaTauuXr: ti+t-ti, Yi:ti-ti-r,
c o 6 H r l t q c H o r l e p o Mi . H a e r o M r p a Q u x e H e y ! , a e r c r o 6 n a p y > x l t r n
3a
riaxofi-"rH6o 3aKoI{oNIepHocrIIB c,'reAoBaHHIIoAllofo I.tHTepBaJIa
p
a
c
c
e
t
l
n
i
i
f
lc
T
a
x
a
s
o
A
l
t
H
a
x
o
s
o
i
l
n
p
r
.
1
A
i
i
a
r
p
a
r
{
N
{
a
A
,
'
I
I
I
H
e
.
ApyrHM
l89
lor
rr
cKopocTH noEBfleHIifl co6blTHft. Ecnu ti - BpeMq II,IH paccTosHHe
oT Harlafla psAa Ao i-ro co6uttis H N - o6qee quc.lo co6tlTfltl, To'
Mbr MoxeM Bbrqrrc!'rr.rrb
ueHTpoIlA S uo Qopnry.rre
)rf
:lrF
lp
o
or
e6 lL
o
!
N
t-
OF
s: -!-F r,.
i
ttttlrtlr
OOC
O
OO OF
@OO
O
CC
O
0102030405060708C
ooo
cor!@Gfig
a
Oo
Oc:cO.
ElEii-i'i;f,aclo"",q
4.I0. lloc,re:oBare,rb'ocrlr co6urrrr)i,Koropbre ,,poacxo.(flr
<MfgoBeHHO>
B
npocTpaHcrBeHHOM
r_rJlr{
BpeMeHHOM
KOHrnHyyMe.
lIIra;t a
t r J H p a c c r o t l l H e p a 3 A - e - . r e HHr aa l 0 o r p e : x o a , x a x A o M y
tr3 Koropbrx nocraB.
. J l e H o B c! !o9o. ir.tl su e T c t B H q
eHcJo (o6LITtrr:i.^ll:o6paxerruaa
q x c n a c o 6 b r r r f t H a o T p e 3 o K n o o r H o u e H [ rnoe e o x y n H H H , e \ - T b n p r M a f l D e r p e c c g r l
x c"ep"tusau orDe3KoB
'6ontruor?
(4.3),
u'
^l
v-
Alrclepcgeir u orgocuTe.lbHo BbrcoKori KoHueHTparlueft
ToqeK B6,irr3H oceft TunrrrrHa /^Jrfl,pffAoB cr,ryqafiHbrxco6t*Hfi.
B 6o"ltruuHcrBe HccJreAoBaHHfr
nocreAoBare,,rbHocreirco6bITHr?
paccql'ITbiBaIorIIa ro' qro yAacrcfl on,flcarb ocHoBHbrer{eprbr
pac'
cMarprrBaeMoro sBr'reH}r
fl T aKj qro6br 6u,r, ncxprtr
ue@asnve^cxrzfi
xaHlr3M ITDOCTOaHCTBeHHOfO
I-rr'IHBpeMeHH6ropac[o.roxeuug co6bltnfi' cna,{aJra Mbr AoJr)KHbrpaccruoiper.b Bo3MoxHocrb
rpoqB JreHHfl,
'TpeHAa B lIcxoAHbIX
AaHHbIX' r{To Mo}KHo cAe,rarb As Mfl cIIoc o 6 aM i l .
llocneroeare,rrbHocrb Mo)KHo pa3AeJir.{T_b
Ha HeKoropoe q,,c,rlo
yqacrKoB pannoft AJrHHbr,rar qro raxgufi H3
Hr{x co4'epxa" uecKoJbKo Ha6,rrcAesufi.rluc"rroco6uruir B npeAeJrax
xax40io yqacrK a c r a B r r r c t B c o o r B e r c r B H ec p e a u e f i T o q K e p a c c M a r p r . r B a e M o r o
'J'qacrKa.
Bat6upan B KaqecrBe gasucr.rl4orlnepenaeHuori]rn'
srraqennq
KOOpAr.{}rar
ueHTpOByqacrKoB, a ''cila co6urufi. B npeAerax cerMeHTa B KaqecrBe sHa.reHrriiapfyMeHTa x;, MO)KHO
nocrpo"rr ,rH_
Hr.rloperpeccnn. Ee yr,rouofi xberio,rtrreHr Mo)Ker_
Oiiri'nponepe"
r { a o c H o B eK p r . r r e p u rA N O V A , n p u e e 4 e n n o r o e r a 6 r .
4.12 c qe,,rbro
onpeAeJreHrrq'3Haq'MO J'rIroH OT,'Tr.rqaeTCfl
OT Hyrfl. Sror npoqecc
npoHrrr,rrrocrplrpoBaH
rra plic. 4.10. K coxajreHr.iFo,gror xprirepur,r
He oqellb e$SexrrreeH, rax KaIi nprr pa3Ae,,IeHrz[
[ocJIeAoBareJrl,Ho_
.tn,T_1
reprercfl HeKoropoe qacJro creneseil ceo6oAu.
:_lp_e3Ku
rrMerorcfl KprrepHrr, c'eilra,'rb'o lperHa3Har{eHIIbre
Lna o6^apyxieHllt rpeHAa B cKopocrtr ocyqecrBJr.euus
co6srrfiil, o' xoroplrx
Hcnorrrb3yercqMeToA Cp_aBHeHHs
cpegHeli Toqr{a noc,leAoBare,lbHocrri c ee IIeHTpOH40nt.Ec,rH noc,'reAoBare,,rbHocrb
orHoclrre.rrbHo
3Tr.rpflAbr 6yAyr or{eHb noxo)irtr, Ho ec,,trr rir{eercfl
9flopo'A"r,
TPCHA'TO IICHTPOH46YlCr CMCUTATI,C'
B HANPAB,,ICHHH
YBC,-.IUqCHHg
19C
B Kpx3ry craruc'ruKy B cBorooqepeAbMoxuo HCrro.rrb3oBaTb
repun (4.4):
I -\
tn,r{
/
t"o'
7-lC-
L==-T-\"-
z
t
J'
(4.4',
o6qag A"II.{Hanoc,'IeAonareJlbHocrli;Z - cras1aprl{3llporAe IBaHHaq HopMaJIbHanc,ryuafiuafl Be,IIIlqrlHa.3uaqultocrb Kplrreptlff'
\{o}Ker 6urr ycrauoBJreHa no ra6Jr[iqe HopMaJIbHoropacnpeAe"le'
H r 4 r ,a H a J r o r H q s o frta 6 n . 2 . 1 0 .
Sror rpurepufi ouent rIyBcrBIITe,reHK IisMeHeHlIIocKopocrll nosBJIeHur co6Hrur?. Hanpuuep, ecJIIl [osBJIeuse co6uruil tvto>xHo
onitcarb Sopuy,ttoft
r,
I t:E
^a+Ft
t
(4.5!
r o H y J r e B y l of n n o r e 3 y M o ) K H os a r l n c a r b K a K p a B e H c r B op : 0 . E c r l t
r{To MoAeJIb3KcrIoHeHB pe3yJlbrare npoBepKri Mbr ycTaHaBJIllBaeM,
i{HaJIbHagr.ruro p orJrI,IqHoor HyJrt, To, cKopocrb noflBJIeHIlRco6lil. I,Iuesso pea.qu3arlllto orofi'
tuit vt H3MeHsercr c rr3MeHeHr.rerr.r
BO3MO}I{HOCTI'IMbI H NPOBCPgCM.
Ec.[[ e cKopocrl'I rroflB,'IeHl]flco6urnfi TpeHA ue o6napyxeH, ro,
Mox{Ho cAeJrarb BbIBoA, qro rroc,teAoBareJlbHocruco6urnii Mo)KHo
paccMarpr{Barb KaK crar{HouapHste.C,re4yrcilree, qro cJleAyer nponOC,IIeAOBare.'IbBepHTb'- 3TO IIpeA[O,tO]KeHUeO He3aB14CHMOCTII
urtx co6utilii. 3ro Mo)KHocAeJlarb c fioMoulblo BbIqHcJIeHuffai]ToMeXAy co6blrll fl KOppe.rrgrIHoHHOii
oyHKrlHi.IAr'rt AJrHHHHrepBarllOB
vn. tr4nuutt cJIoBaMH,HaAo paccMarpaBarb IiHTepBaJIbI Me;lix)t
co6nrnsua KaK rrepeMeHHllo x;, [pI.rHHMa]oIqyIo3HaqeHIIeB roqp a c r r o J r o x r e H H QBM n p o c T p a H c r B e .L C J I I I l i H '
r{ax c paBHoMepHbrM
OOHapyx{LIrbcfl
repBaJrbr He sB,.rflForcsHe3aBr{cr.IMbIMH,
TO AOJI>I{Ha
reHAeHqr4f K roMy, qro6u 6oruuue 3HaqeHr.rsX (a.rrnuuue r.IHrepsa 6crriluMH 3HaqeHLIfllvM.
BaJIbI Melr(Ay co6urllauN) c,rreAoBaJIH
Ma"qbie
Aua,uornqso Ao,'rxHa 6urt u reHAeHqHfl K ToMy, qro6u
3HaqeHHsX (r<oporxrle I.rHrepBaJJu)c,re4oeaJrvsa ApyrIlMII MaJbI\tH 3HaqeHr.rguu.Mu MOXeM BbIqI{C'{I{TbaBTOKOppeJItIl[rO
AJIfl nO'
3Harlegllii ,tara U UpOBepIiTb HX SHaqHMOcTb.
CJIeAOBaTe"rIbHt'IX
O6ltqHo ror'rbKo nepBble Hecxor'tbKosuaqeuuii Jlara upeAcraBJlrtor
IrHTepec.Ec,[ti ugilox{eHHbleBbIiIIe MeToAbItlo3Bo,lgloTycTaHoB}ITb,
qro BHaqeHIis aBroKoppertlruoHuoii Qyut<utzlt HecyqecrBenHo orqro co6bITIifl IlpollcOT Hy,llfl,To MbI MOX{eM3aKJIIOqlITb,
JIHqaIOTCS
BO BpeMeHHllr'Ilr npOCTpaHCTBe.
xoAu,llr He3aBI.ICUMO
l9i
Ec,nv ltu ycraHoB'tli, irro [ocJleAoBarer,Ib'ocr],I He I,rMeIor HH
"IpeHAa, HH aBTOKOp_peJrsrItlH,
MOXHOno[brraTbcfl npoBepr{TbfHnore3y_o roM, rrro co6urng noAqnHeHbrpacflpeAeJreHr.r'ro
nvaccona.
HanouuaM, rrro B rJr. 2 pacnpe4e.r,e""e hyuaaon, onp'a*n"roa"
KaK Ar4CKpeTHOe
BeporrHocTHOe pac[peAeJreHHe,xoropoe Mo]KHo
'c.rrr{rarbnpeAeJ'rbHbIM
cryrlaeM 6nttol,tnanlHoro npl,t yclonuu, lrro n
(tlucflo ucnurasufi) cranonurcq oqeub 6onwniv," a p (neponr_
HOCTbycnexa B oAHOMr{CnbrraHr.r[)cranonatcq oqeHb ua,troli. Mnt
Mo)KeM npeAcraBr.rm ce6e, qro Halr epeueuHnfi pflA noApa3AeJrs/ ? H H r e p B a r r o ep a a H o r i A r r H H b r E
. cnu co6irriln npoHcxoAflr
:cryqaHHo'
::-T t1
To rIHcJIo IlHTepBa/'IoB'Koropbre coAep)Kar B ToqHocrH
H y ' l l b ' o A H o , r B e , . . . , x c o 6 r , r r u f i ,6 y a e i n o 4 u u u a r l c g 6 n u o u a a n r .
HoMy pacrpeAeJreHHro.
EcnN ulr HairHeMyMeHbuarb A,,rr.rHbr
HHrepBaJroB,n 6yler yoe,'InqnBarbcfl, a BeporrHocrH co6srrurl 6yayr yMeHbrxarbcq.
BHHo_
MIiaJIbHoepac[peAe,'IeHHeB groM cJryqae yx{e He foAr.rrcfl
AJrfl rroAcqeroB, tr yAo6Hee ro/rb3oBarbca picnperle.rreHlreMllyaccoua,
rax
H€rr He rp_eOyercr rorrHbrx cne4euur? o ee,,rH.{HHa
p.
x
n
h
I?I
l J M e c: r o a r o r o r p e 6 y e r c f l 3 H a r b n p o r . r 3 B e A e H H
n pe: L , K o r o p o e 3 A e c b
-xapaKreprr3yer cKopocrb rrorB/'reHrrfl co6urnft.
llyaccoHoecrar
BepOflTHOCTHafl
MOAe,tr,OcHOBaHa Ha cJleAyIOUIHx Ao[yqeHr,rqx:
a ) - c o 6 u r i r q r p o u c x o A f l r H e 3 a B u c u n r o 6; )
c o o b r r u r H e u 3 M e H f l e r c r c r e q e H H e i dn p"e6rpuoe*unno; .nr)i - nef e
" "pno"x" n
t u" o c r l
nosB,rreHuffco6rirfiq B HeKoropoM HHrepBaJre nponopriaonaJrbHa
ororo HHrepBad'ra;r) eeponrnocrL Toro qro 6o.rreeqeM
TJ:rHe
ABa
coorJrrrr npoHsoli4yr B oAHoM H ToM xe BpeMeHHoMr.rHrepBa,le,
trcqe3ar,oule
MaJIa.
VpaeneHne A,'rq onpeAeJreHHflttyaccoHoBcKofo pacnpeAeJreHus
ts 3TOMnpr{Mepe HMeeTB}rA
^o
031-
1=6
noL
;;t
7,=2
ozL f---1_
|
o r r-
--r---L-
i;0" , :u---
l;lf0 2 -l-..t-FfrL -- 0,6
P
0 . 5I
n?
0,2
0,t
0.0
2468"1012
qHc.no noggnexri
co6uttnq
Ha tsHTePga'
Puc. 4.11. flyaccoHoocxoe pacnpe'
AeJreHr.rec pa3nLIqHbIMI{3HaqeHlifM}i
I. nocrooenuoe no qucJIaM floqBreHHq co6uruft
ru Bnyrc Qopruy c IIoMoIIlbionpeo6pasoeauna
KyMy,rrfl
Yi: tilT,
,u,o l-ro co6urHx;
rAe /i - BpeMfl or HarIaJIa rIocJIeAoBarer'IbHocri'l
I - o6qag ',Irvla pn4a. 3ateu Bblql'Icd'ItlorcsrpII oIreHKIt:
l.
KC+:Ii*u*!-i
t;
- ' " )' j '
: lrn max{r,
2. KC+
+l
(4.7\
g. KC+ : maxl(C*, KC- | .
c r o r i c n o c o 6 n p o n e p x u c o o r s e r c r e ' f f p a c n p e A e d , r e H 'psx 4 a c o 6 l r i u i r
nyaccoHoBcKoN{ypacnpeAe,'reHuro.Csaqa,ra pflAbr flepeBoAflTcfl
B
pa3flepnHfi r<purepnfi- 3To npocro I\{aKcl'lMyMrIo,'1oxI{Ted'IbHbIX
socreii MelKAy Ila6.trcAesirblM psAoM I{ ox{uAaeMbIM' HcxoAfl u3
- 3TO MaKCHNIyM
OTpI{qaBTOpOH
ilyaccoHoBcKofo pacflpeAe,'IeHl'1fl;
3Hat{s
a6cO,'lIoTHbIX
erO
6Oruuee
il
rperuti
t6.llHOfi pa3H6cTr.r
qeHufi AByx rlpeAblAyurrax.flponepaenaafl crarl4cruKa KC sareM
3HaqeHl]flMH'rlpliKpl.ITI',IqeCKI'IMI'I
cpaBHEBaeTcflc AByxcTopoHHI'lMH
KpuTHqeCKoe
npeBblnaeT
Ka
ECttu
CTaTHcTI4
2.26.
e ra6,r.
Be,tr.eHHbrMr.t
6O"rlure, qeM oxgAaeMoe
oTK"lloHeHI4e
3HaqeHHe,To NIaKCIIMaT'IbHoe
a nu6opre, [o,{yqeHHoii c,lyuaiiultm o6pa:oNl u3 nyaccoHoBcKoro
p
' a cn peAeJleHI.Jfi.
MaypH tlleii,r - 3ro rIepHble, coAep)Kalrlre xpeltnnii, TJIIIHbI
p a H H e r o M e r o B o f o B o 3 p a c T a ,B c r p e q a F o u l u e c fHl a r e p p u r o p H H I I I T a i o n K o " r o p a A o ,B a l i o u u n r n M o s r a H a . I 4 H r e p e a , l x a p a K r e p u 3 y e r c q
6eHronlrroebIMH c,'IoflMu, Koropble 3a,'lefalor B
MHoroqrIcJIeHHbIMLI
MecTax s BaftON{uHreU MOuraHe I{ O6Hapyxl'tsaloTcfl
HeCKOJ1bKHX
cocroflT I'I3
npra 6ypeiruv Ha rTJrtt .nureiiHyto IJII'IHy. Eestonutlt
KaK npOAyKT pa3pyileHHs By"IBO3HI'IKaIOIIefO
MOHTMOpIJIJIOHI]Ta,
q aHAe3HToBorococraBa. B ra6l.
IIeIIJIa pI{OJII{TOBOTO
KaHHqgCKOTO
MexAy rrocdreAoI'IHTepBa,roB
MoxlHocrll
3naqeHl'ir
4.7 nor4soaflTcfi
s O6HaxeHI.lH
Saraionoutnn 6egrOsurOBbIMIIcJIOflMI,l,LI3MepeHHbIMu
192
t 3-20 1
P(X) : e-\ Lr lXt.
(4.61
qro cKopocrb ,'o.rrBfleH'r co6urnfi
3auernlr,
l, sAect flBJrflercfl
TOJTbKO
napaMerpoM pac[peAeJreHr.rfl. Tanfiqnue
I'yaccoHoBcKHe
qacrorHbrepacnpeAeJreHun
f l p e A c r a B J r e H bHr a p n c . 4 . 1 1 . p a c n p e a e JreHrreflyaccona npunaeHrercn flpil perxeHr.rH
TaKHX 3aAaq, KaK OIIPCICJICHHC
IIACTOTbI TCNCQOHHUX
BbI3OBOB HA
KOMMVTATODC
WilLI
onpeAeJreHuenpoM_exyrKa BpeMerr[ Me)KAy c6oqrun e B;r.rHcrH.
te.rlsoft cllcreMe. Kaxercg B[OJrHeB03MO)KHbTM
ero I4crIoJIb3OBaHlle
nplr I'ISyqeHnLrpflAoB reo,rrofuqecxux co6Etrvr?,onacaHnblx B HaqaJre gTOfO pa3Ae.ria.Ec.nN UU CMOUTI.I
ycraHoBlirb, trro Halrra [oc,rrenoA!*rHrercq nyaccoHoBCKOMypacflpeAeJreHr.rro,
AOBaTeJTbHOCTb
ro
Mbr MoxeM HcnoJrb3oBarbxapaKrepucruxu eroio
ilacnpe4e.neu'n
BeporTHocTHoronpof Ho3r.rpoB
,q,Jrr_
a Hrrr AaHHOrODffna.
KpHreplrfiI(o,ruoropoaa-Cuupnosa
o6ecndqfri., HaM rpo-
193
Ta6nnaa 4.7
Mor4nocrr (n rfyrax) uHrepBaJroB
MexAy
lrocJreAoBareJttHunau
6eurouuroBbrMLcroqMu
B MeroBbrxorJtoxeH[sx Mavou
lllefi;l
-Bafiorrtrar)
no @pemour Kanrplr (rurar
(Bepx)
29
l1
6
5
l0
5
lt
t4
476
t6
8
234
l0
15
226
354
4
l7
5
4
(Hus)
Maypu lllefi.l no Opelronr l(aHrprz (rurar Barionrasr). Oru c.roa
rrpeAcraBJrflrorcKon,'reHrrsrerrJra B pe3y,,]brare 6ypHr_ix H3Bep]Keuuit nynxanoe e I44axo. llpe4lo,laiaercr, qro coAep)KalraflcJ{
TaM
qepHat fJrI{Hd orKJIaAbIBa,lacbc trocro'Huofr
cxopocrsro, Ii 9TV rroc"qeAogare.lbHocrbsgaqeHltii N{oulHocrr.r
Mo)KHoaIIa;.rr:t3r]poBaTb
}(aK
pr1 co6r,rrwfr, aTaJrornqurrii HcropurrecKoMypaAy, o6DasosaHiroN.ry
H s B e p l K e H u r u HA c o .
l l p o e e p l r e s r ' , A a H H b r eH a r p e r ' i l B 3 H a q e i { i l r r c i i o p o c r r r r r o r B . r e H l r f f .E c , r u r p e n 4 u e 6 y A e r o 6 H a p y > x e u ,r r p o B e p l T . eH a a B r o r ( o p peJr(rrro nocr'reAoBarer'rbHbre
HHTepBaJrbr
Mex{AV bo6urugnau. C6;.rcHLrre: a) BogMox(uue eSSer<ru or HeoAr4riar<olJLlxcxopocreli
ocaArioHario[r'IeHEflUepuofi f,TuHbi Ir 6). aoslrox{I]0crb rporrB.rr|iJHri
aKTrrBHocrr.r
6o,ree oAHoro BVJrKaHa.
K P I 4 T E P H 1 4C K A I I K O B
Ilpoc'refiurafl
noc,reAoBareJrbitocrb -- aro
Iroc,jcJoBa,i.errbHUCTrr
Hii6rrotrerIIIit, pacnorolKeHIIbIx B iroiltl.ir(e Hx rofii.ileHrt{,
iii,}ilireM
TaKarr, rr]'o KalK;Ibrfi ee e,'tex,teHTnpurIii..{e}KrJt.orHo\Iy
li:J _Iilvx
83aHrvroitCK,irrcqaloildr.i,y,lpyfApyfa coclcrrrrrii. i--;iccr,iO:,pirr,r
1.i).,,rli_
HoBar)'Io rJopoAy c KoIll<peullfl\'llI c ue,ritrt'JIlor'rr'rriaB iiiix
ricri(iirile$Ibtx ocr;lrKoB. .[,po6,'ieune ,.ortxletulii
,.BJtrc.ra,i ]rcnbt iaHrlrl\,rH,
Ilpfiqe\1 Kax{Aoe Il3 Illtx lt,\lceT I.B:l B:j:iij},iot.tci{"ljG{ii,:i,,}illilx
IICXOjIa:
r i o H I ( p e r { r 1 rn1r i 6 0 c o l e p i l ( i i r I r c i i o f i u e r \ i L r eo I T a r r c i , , a l i i i o
IIer. ncir.neA O B a T e J b H O C T bl a K I l X I I C X O j I O BI I p t r i . I 3 y q e H r { f fI i l j i l i O j j l r O D O r I b lt s r e qeFlrie IH'I COCTaB,'rteTtpCUeUnCit prili
CIreqrieJ,r5ilOr.0urfilr. A{u l,tOx(eM rlocrpoui'b
aHadlorlrtlHylo roc,'reAoBare.rrbHocrb SKcIrcllHrIeHT a J r b H o , 6 p o c a a x , r o H e l . yr r o T M C u a r r i l b I ] ] a A e ] r r j e r e p 6 a n , r i l
ir"ruuru.
ilo,ryuetiHar
rocJreAoBire,'ir,uocrl
65rrr,er. HiiJrouuIraro c,,.re.ry.ynu{uti
pnr,20 t'o6slruir:
f Pf f PfPPPf Pf prfPPf f f .
KoHe'rno, llHTyllqliq IIoACKa3brBaer IIaM, qro e eloii
194
iioc,,reAoBareJrb-
uocrn AoJIxHo nofiBuTbcq oKoJro Aecqrli rep6oe, ri Mbr MoxeM ottpeAe,'riri'b BepofirHocrb BbrnaAeHfifl3rofo (u.tu nrc6oro Apyroro)
qlrcira rep6oe. B saurelr lpuMepe Mbr no,tyqunu ll rep6oB; cqfiTafl, qTo MOFIeTanpaBlr,'rbHafl,l!{bl IIo,Iyr{aeM BepoffTHocTbBbIIlaAeH I { g 3 r o r o q g c J r a r e p 6 o n B n o c J r e A o e a r e n t H o c r u2 0 H c n b r r a u i t i ,
D a B I I y F o0 , 1 6 , u " r u n p u 6 . t u s u r e . n t H o l / 6 . B e x c n e p a H r e H r e a, H a d ' r o , b r M o x ( e Mo ) K r r A a r b9 , l 0 u 1 1 n u r a 4 e f u q r { c M p a c c M o r p e H H o M yM
uuri rep6on, T. e. IreMHorgu 6o,nrule oAHor.'i
rperfi or quc.[a l{c]rbrraltoAr][rHfiIorcg 6uHovira.ro;lrii. Pe:y,rilarul 3Toro gKcIrepr,IMeHTa
n o l { y p a c i l p e A e . [ e H a ] op,a c c N l o r p e l r u o u ye r r . 2 .
Oasaro npr.r oroM Mbr He yq,'In [opqAKa, B KoropoM nonBJlffIorBITIiJIflAe!'ra
racn rep6r,t. Beponruo, ec,ru 6rt [oc,,]eAoBare,'rbHocrb
<rlu o6paaona:
rf f f f f f f f f f PPPPPPPPP,
' T o a r o n o K a 3 a J l o c b6 u r i a u o q e H b c r p a H H b r M ,x o r g B e p o f l T H o c r b
rroJiyqeHr.Ur
rar(ofo xe KoJiflqecrea rep6oB B ABaAIIari{ HCTIbITaHI{sx raxar xe, KaK rI B fipeAr,r.qyxieMrrplll{epe. .[I,pyrorl xpafiHafi
c a y . r a r i- [ o n c p e M e H H o en o s B , ' r e H [ er e p 6 0 n I I p e i x e K :
f Pf Pf Pf Pf Pf Pf PIPf Pf f ,
Tollic BLrf,rnAr{TorreFrbueo6ltuHo, xorg RepoflTHocrb BbtrIaAeHHtl
q a H n o i o r r r r c , r r ar e p 6 o r o c r a , ' r a c b n e u : l t e H H o f t . B g r r r r l t p L I M e p a x
r e I l p o l r o p q H f l ,B r l o r o p o i i n u n a 4 a n r
H a u t e i i o ; l c 3 p e t j H eB r , r 3 b r B a eH
q ,r o B b I n a A e rep6ut, a noil;;1oi( hx norB,'teHngM
. u fipe,trno,'IafaeM
p e [ r K ] l c n y u a t ? H o ,a B A B y x n o c J e A H L r xl r p n r \ r e p a x
Hre i'cp6a H,T11
3To rlpe-lloJlo>rieHrieKa)r{ercrr Becbr.{aFrenpaB;ionoAo6FIbIM.
I,1r,r r,iox<eu npoBepr.rrbrnriore3v o c,ryuafiHocru e:oir Iroc,'reAotIHC,'la CXarlKOB.LKatlKIl OilpeAeBaTer'iblJOCTIiIlyTeM IICCr'ie.lORaHI'ifl
'fcx
cirqrorcq F:aK Hel]pel]brBarcu{ilecr{ lroc.rleloBareJlbllocrlr oJ,Hiix H
, { ( e c o c f o a H u i r . f l e p a a n r o c , r e i l o B a r € " I i b H o c r b c o . q e p > K H TI 3 c x a q x o s ,
r3roiinfi-roJibKo
19. CxaqKH B [epBoft noc.lteAosr2, u rperraie.t rrlroc] il nolqepKHyTbI :
f
I
P
rIP]'PPPIP
l0
ff
PP tff
ll
t2
l3
\{lt uilixer,r BLrqricJIXTb Beporrr-Iocrb rofo, q'r'o J.aHilvro Iioc!'IerotsilTe,'rbltocrb cKar.IKoB B SKCIIepr.{MerITec AByMr{ Irc.rioiiiiN{ri (rep6 ri"rir
peur{a B aroi\{ ripur,,Icpe) NIoxiHo cqr.Irarb cJlyt12ii"oii. C eroii rieJrblo
Bblriuc.rlflercfl rtr.icJlo Bo3Mox<HbIX na3Meu{eHlIir lt1 cocroRvvvl I u nz
cocro;urii.r 2. O6uee qLICJio cK::iqKoB B noc,'relloBare,rruoctu o5o3Haqaerca uepc: U; rrMelorcfl ra6,rrrqur, Koroirbrc coAepx{ar Kpl'iIIiq e c K I I C 3 u ' r r t c H l J i lI i u ( ' d l c c t ( a L I K o BU n , l g r p u x c u p o n a u v 6 l T 1 " 1 1 2I l
3aArirHoro ypoBHq 3HaqI.IMocrH a. OAuaxo ecJlu KaxAoe I{s sllaqeguil tlr Yt I'LzrlpeBblilIaeT Aectirl, To pacilpeAeJleHue seruquul't u
aIIIpoKcHl!{xpyerctl
HopMar'lbl'lblM pacilpeAe"Ie.qoBoJbHo xopouo
IIIreM, I'l MbI npll HCnO,tb3OBaH]'lH3TO|O CTaTHCTIIqeCKOfOKpHTeplif
13.
r
i
vi
MO)I{eMHCIOJIb3OBaTb
Ta6r'rHr{brCTaHAapTHOTO
HOpMar]rbHOfO
DaCn p e A e J r e H H. fC
l p e . a s e eq u c , T oc K aq r ( o B e i , ' r 1 ' u a r i n o rni o c , r e n o e a r e J r b HOCTI.I
c n1 ICII€XZMLILI n2 HeyAaqaMHpaBI{o
;,
2n' rt"
(4.8)
nr*nz
fiHcnepcna
cpeAHero rtr4cJta cKaqKoB Bbrqric,'rffercq no QopMy,'re
2nrn"(2nrnr-rtr-nr)
_2
U
I
( n , I r t r ) z( n , I n r - l )
(4.e;
VxasauHlre Qopuy,rsr no3Bo.rrflrororrpeAeJrHTbcpeaHee (rrrc,rlo
c r i a r r K o BH c r a H A a p r H y r o o u a 6 x y c p e A H e f o q H C . r r ac K a q K o B t r p H
BCeBO3MOX(HbIX
pa3N{eqeHHqXtL1 U tt2 B3aI{MOltCK,.'lrcqa}OUHX
-tpyr
I P ] , r a I I c x o A o I ] .B o t , I k c , ' i H ey K a 3 a H H b r e
x a p a K T e p n c r r r K HN, t b rM ( ) ; r i e \ f
n o Q o p u y , r e ( 4 . 1 0 ) n o J r y q r r r bx p n r e p v i t Z :
Z : (J -0,1oi,,,
I
l';1e [/ -
(1.10)
ira6Jr]olaeMoe q[cr'lo cKar{KoB.
Mu uoxeu rpaMenr{rb oror Kpr.rrepwia
gnn npoBepxr{rnnoreebro
cnyuaftilou p acnoJroxeHtrHoJreMeHToB
nepBofi [ocJIeAoBareJlbrlocrll,
coAep)xauefi pesy.ltrarbr lrcnbrraunft npn 20 6pocauvtqxMoHerbr.
Hy,reaan r[nore3a yrBepx{Aaer,qro Her cylqecrBeuHoropa3rr.rrrufl
MexAy sa6lroAaeubrMrrr.rcroMcKaqKoBn cpeAHriMrrncJroMcKaqKoB Arq c,ryvariHofirrocJreAoBareJrbHocrn
Tofo xe o6reua. Mu ucfio,'rb3yeM
AJrfl ee npoBepKr.rABycropouurift r{pnrepr{ft. Hyneean
rurrore3aorBeptaercr, ec,'rr{B 3Toir nocJIeAoBareJlbuocrlt
lrMeerct
,rU6O C.NUTUKOM
MAJIo. TIr6o CTHuIK0M MHoro cKaqKoB H IDIIHIIMa.
ercr aJIbrePHarI'lBa
Ht: u *o.
Bu6par 50/o-uufiypoBeHb3HaquMocrri(a:0,05), MbrrroJryqriNr
rpaHr.rubrKpurriqecKoft,
o6nacru -1,96 k + 1,96. Cna,ra,'raBbrqr{c;'IaM Cpe!,H€e3HaqeHI,Ie
I{ cTaH.q,apTHOe
OTKJIOHeHpie
AJIfl qucdlacKaqKoB B cryqafiHori nocdlreAoBareJrbHocra,
r.rMeroqefiny rep6on (n1:
: I l ) u n 2 p e I I I € K( n z : 9 ) :
. I I e i r , . r yl 6 e 4 t t r r c l _ , r- { r o s r o n p o c r o Q o p u y , r a ( 2 . 2 8 ) , i l e p e l r l J i i H r r a n j l j r t r B e r ' r L t q l . t lU
t b,r o t t t o c r i r e , r b H oK o r o p o f i M o x H o c t l ; o p M ) , ; l H p o 3 a i b r r i l p o B e p r { r bp f l , I ,c r a r f i c r l r q e c i i l r x f a [ o r e 3 . F l a n p l r u e p . I l p r r
c . r 5 ' u a r i r r t ; lpr a 3 N , r e u e n t r rHr a M M o x ( e r n o r p e 6 o n a r b c f l n p o B e p r i i l r l r n o r e : l b r o r o M , r { T o n o c d ' I e A o B a r e " l b H o ccrobA e p ] K r r r6 o , r e e q e N {c p e A I r e e r ; t I C J , t oc K a q K o B ;
B STOM cJiyqae
HvrrteBafl funoTe3a
rlrBa rlofyT 6lirl ganr.icaHbr
Tax:
It aJIbTepHa-
y:2!!-fl:10,9,
o?- U
T. e. cJilruKoM 6O,{btxoe qHCJIO CI(aqKoB rrpaBoAnT K OTKJIOHeHT.iIO
rrrnore3br. 3ror
xpHrepuir fl8,'rflercs oAHocropoHHuM. Hao6opor,
Mbl MoxeM Irox(eJraTb onpeAe,'IIrTb, He coleplKr.rT JIIr flocJIeAoBaTe.nbHocrb HeBepofrHo Ma./roe qrc,rro cKaqKoB. B eroN,r cJryqae coorB e T C T B y i O X I a Sr I J [ O T e 3 a U a J r b T e P H a T H B a3 a n r ] c b i B a ] O r c f l B B U n e
HstU>-4,
H1: IJ1O
H C J I H T U K OHMI l 3 K O eq H C J t OC K a q K O Bn p H B e A e TK O T K r ' r O H e H nHi oy resoii rlnore3br. Sror xpnrepuil raxxie .rrBd'rflercs
oAHocropoHHlM.
rHIrore3y o
HapyueHI.IH c.rIyEc,'tu l,tot xorllM orKd'roHr.rrb
"rro6olt
qafiHocrlr B noc,reAoBarelbHoc'rH, To A"qq
sroir ue,tlt noAxoAI.rr
ABycropoHHzti t<pnrepuii A,rrsilpoBepKlI rurlore3bl:
HO:TJ:
np14aJrbrepHaTHBe
Ht:U*4.
IJ
( e+ i l ) r ( e + l l - r )
_
4,6.
Crarucruxa Z pavua
Z:
Ho: U -<C,
H1:U24,
ll +9
(2.il.9)(2.il.9-il-9)
: t';,lo'n:r,o.
u-0
U
Tarrlu o6pasou, qlrcJo cKaqKoB B rrocdleAoBareJ.-ilrHocrn
tenol
t u e c T a H A a p T H o I oo T K J I O H e H HOTTTC p e A H e r O3 H a q e H u f lB C e XB O . I M O I K H b I X c K a q K o BB T a K o r i n o c d ' r e J . o B a r e , r r b H oHc rInI e n o l a A a e r B K p u TrlqecKyio o6racrb. C,retrosare,rblro, yKa3aHHoe qncro cKarIKoB He
!.aer ocHoBanrfi gnr orKnoHeHr4quy,reuoi'i rilrrore3br r rplrHflTlrt
IlpeA[OJIo)KeHus,IITO nocJIeAOBaTe,]lbHocTb
He tIBJIff
eTcfl cIyIIaft Hoii.
Hao6opor, Aalor coBepIrIeHHoorJrnqIpyrue nocJreAoBare,/rbHocrn,
Hbre 3HaqeHufl KpHTepHs. Tar KAK tx1 v flz ortHaKoBbr Arq Bcex
rpex [ocJreAoBareJrbHocreft,ro a u og TaKxe oAr.rHaKoBbr.nnn
BTopotl fioc"rleAoBareJrbHocrr.r
3HaqeHr-rflKpHTepHfi
2 - 1 0' ", 9
'--4,2,
z:2,1
.l,JIt TpeTLeIi
z
t 9_ 1 0 , 9
o:____:
L r
3,9.
I
O6a grn 3HaqeHHt pacloJrox{eHbr 3a KpI.rrliqecKHMH IIpeAeJIaMI{,
r.r Mbr AOJIXHbI OTKJIOHIjTbrr.rnoTe3y o clyuafiuovr pac[oJroxeHnlt
aTe,'IbHOCTeiI.
3JIeMeHTOB
IIOCJIe,U.OB
196
la?
l,-{
|['
feolornqecKfie [pI'IMeHeHHfl3Toro KpHrepl'ifi He BloJlHe oqeB H A H b IT
, a K K a K O , 6 u q U On p l I x O A H T C sp a C C I v I a T p u B a T1bI O C , ' I S A O B a c O C T O R I I t t f6i ,o . r t l u r n U A e y x . C r p a r H r p a c p r u e T e J T b H O C Tc HT I u C J I o M
nepeCeqellHqUl,'Iudla c6ltxuOgeHIio
HanplIMep,
pa3pe3bI
LIJIII,
CKIze
coAeplKar He MeHee rpex cocro;inuii, xoropble He"rrb3t paH>KI{poB a T b H U K a K H MO c M r , r c J r e H g uol r6 p a s o u . M u p a c c u o r p f i i { c n o c o 6 b i ,
qacTb I]OC,{eAOBareJIbl"lOCTeli
rlplBecrll
C [OMOlqbIOKOTOp6IX
.ilioxipg
CocTotHl4ll'HO npex(jle NIL'I
I( IIOCJIe/I,OBaTe,IbHOCTH
AI.{XOTOMHqeCKIIX
l,
lti
1r
iiti
tl{
t{
lr
lr
li
ill
liI
I
I
I
f lp l i T C p l t u
O C T a H O B L I M CH
f l a I e O T t O i H I I e C K O Mt I p H M e p e I l D l l ) Y 1 e H e F I l l K
cocTosHl]tlMl',l'
C
CI'ICTeMbI
AByMt{
cKaqKoB npI.I H3yqeHI{H
ocranerMarLIrbI o6pasyrcrcn npI'I Kpl{cra,'IilllsauIIII
O6uquue
I
l
p
1
4 OTB
e
u
{
e
c
T
B
a
M
H
TOqHO|O pacnJiaBa, o6oraulennofo !'reTyqulvrE
o
1
H
o
Bpeo
6
y
c
.
n
o
n
J
l
c
l
l
a
M
r
r
M
b
l
.
I
4
x
c
r
p
y
r
r
y
p
a
B e p A e H r . r Hr p a u u r u o f i
UesHOIi Kpt4CTaflJIll3aI{ueil KBapI{a n flO,rleBoro igllara B sBTeKrHr{e6e:
IipollcxoAqr
cxorl roqr<e. Ec,'pi KprrcTaJrJrH3Aqr{ff rrefMartrra
IITO
lu|laTa
fi
I]oJlcBofo
KBapua
3epHa
TO
N{O)KHO
IIOMeX,
AOnyCTIiTb,
BO3IITiKaIOTtl C,'lyuatlUllX TOtIK;lli BHyIpIr OXJIaXi.r.arcUIefO1.]acll,'laea. 3ra ctttyau"x (clyuaiiuoe o6pasonaHue sepeH) ocraercq Hea s x a e H H o i rA o r e x [ O p , I r o K a p a g n r r a B s a T B e p l e e T . O j I H a x o n p u g y T cTBr.ie oAHofo KpIlcTaJIJIa, HanplIMep IIoJIeBOTOlUnaTa' MolKeT cTilO6paSOBaHHe 3epeH IrOIIeBCI'OtltlraTa
MyJIlrpOBaTb AOIIOT'IHLITeJIIUOe
Hao6opo'r'
crpyKryplrl.
necrpofi
Bo3HI'IKFIoBeHI'1rc
K
npnBecrll
H
II3 I\{2fNlb]
pocT oAHOfo Kpl.IcTaJIJIa MolKeT JloKa./ibHo llcqepnalb
Hyx{Hble cocraB,'lfiIolidxe Il IlpllocraHoBllrb KplicraJl'[ti3aLlHrc' B pe3),'JIbTaTeItefo Bo3I{LiKaeT IIecTllafl Mo3aIlKll U3 I(Bapqa I'i noJIeBofo
lli1aTa. Eo.lt uryro Ir,t]1.y Ilo,'itrpoBaHHOrO Ief\laTI,ITa MO)KHO paCcMal.pr.rBarb rirtK oKHO B feo,'roffiqecr(yrc x)'xHIo, n xoropcii cryAel{TaMAaHaBo3MoxHocTbI-i3yqeHH'3Tllxa,'IbTepHaTi-tBHbIXIlpoqecC O n . l l O . n U p O B a H l { a t 1n O t s e p x l t O C T bn O p O A b I I I O 3 B O J I f e f d ' i e f l ( o \ r C T a HOBHTb l(OHTaKTbI Me>I(A)/ C"lafarciill'lMU ee 3epHaMl{' nO3'IOMy ilHHtrr], trpOiJenertt{att na Hei'i, npllBOI114T I{ nOC-TpOeHltl{l liOC.lteligLtalllIIa'ta. JliitlHu lla IOJIi'ipOBaHT e , r l b H O C T3l te p e H I ( B a i i U a I { I I O ! ' I C B O f O
rtit''lt gutiCiilt<a ti:;
i
l
i
O
)
t
:
e
T
llOii tr.nri'l':
P A C C i , l a T p H B a T b C nK Z X C " ' i 5 ' V
BO3tvtO)KI{uXilo{tr'ICAOEaTe.llHOCreiiB TeJie ttef},{ii'[]1Ta' fl3 IiOTOpOfO
6br.[a nse.[eqetia 3T'a rr'Irira. lloc,re;cua'l e,lbHt]crb :je'pell xual)l\a I.1
r r o J r e B o r o i l I i l a r a B A o , I I b J I I I H H Hy K a 3 a H a s r a f i , ' I . 4 ' B ' F l a u ' l s a , q a rja -- rr3yqHTb cKaqKl{ oT I(Bapl{a K nojlleBon'I:f lulliiry, IlpoBeplirlr
H Olrpe/I.e"iili'ib, HeT Jitl Tell'lelic"lyvaiiuocr.b Ilor.iJ]elloBale,'1bHOC',il.I
floc,fieAosarenstlocrt100 3epeH norenoro unara (Il)
rioflytlei!Hatl npll
Ta6tuua 4.8
n xra"pqa (K)'
nepecetieHTI{ nervi;i1ari'
Pnc. 4.12. Ilocnerlosare,'t,uocrn sa6nrcAenufi, xoropafi aHaJruBHpyercsMero.rtoM
CKAqKOB BBCPX H BHI.I3
ulr]] K clrc'ieMaTI{qecKoMy
cJreAoBaHHIO
OAHOTO
COCTOflHHfl
3a caM}rM
co6orl unu, uaolopor, TeHreHui{rr oAHoro cocroflHrirr cJlenoBarbHer r o c p e A c r B e g H o3 a A p y t a M . B u n o . n u u r e H c c J I e A o B a H l roer H x n a H Hbrx c lror\,lolqbloKpuTeplrfl cKaqKoB I.I OUeHI,ITe
Tpu a,rbTepHaTr.lBbt.
r errepb p acc[,rorprir{ cTaTHcTrrqecKyro
rrpo[eAypy Hcc,,reAOBa]r]rq
c K a q K o B B B e p x I I B } I I 4 3 .o H a U C n O . n b 3 y e T C
Br iT e x c d n y q a r l x ,K o f n a
Mbl IlMeelI AeJIo He c AByMfl pa3JIIlqHr-rMIicocroflFluflMH,a riorJa
nocr'rerlyrolUee r1a6"rrcAegue 6o,rr,1ie rrJrLl NreHbrue, rleM nDe^{brAyqec. IIa ouc. 4.12 nso6paxeHa ritrrnquar noc,,rrejloBsreJrbrroor]:,
r(o_
1O]]}'Io
TiO}KHO
I]O3TO\IY II BCib
I{OiIi;I() PACCMI}TPIIBATb KAK CAII.
H C B O : ] ] I O ) I (H b I .
llpa paccuorpeH14li ro,rbr{o pa.:nocreii Me}r(Ay 3Haqe}uirnvu{B
coceAHirxroqKax Mbr npeo6pa:yeM raHHyio noi,iegonareJibHocrb
ft llocJIeAoBaTe,'IbHOcTb,
ltr{erculylo ToJIbKoABa cocToffuun (unurpu,
'lr:O6pae C J I I II I M e I O T C p
' I a B H l r l e3 I I i l r t e H H f l ) .f l O C . r t e n O B a T e J l bj iut O
, u
)KenHVroHa pr.ic. 4.12, wst MolKeM nepenxcarb B Bnlle
+++-0-+--0+.
nK!iln K
i l l l K n K n n n I ] n n q K { ! l K n n n K n nn rn n
n K K I ]K K
nnn K
n n Kn n n n n K K i! \ n n K K K
ii ii i( ri ii ( ( n ri n
i i K i i i i i i r i i i i i n (n x n n K n n r n n K n n n K Kr Knn K
(KoHerr)
l9
-YI{ACTOK CDEF
r i r ' r r i c N a q o x s H r i s . l { H r e p n a n I I N { c } K r r op a c c M a r p i l B a r r n l r 6 o x a i <
r , , r . ' l ho t
l e : x r r - 1i / 1 " r ,i r o i l t r a ; i < ; , t r ; i i l c rcoK t iq o K B l t H J , . l u t 6 o K a K
r r z r c r bo r p e 3 x a I I f t , u s o S p a > x a r o [ i e f oc x a q o K B B e p x ,
np]IqeMo6qee
Liirc"aa)
cI(aqKoBr-rcr2ercil B !'IIo60t{ c,lyqae HeH3MeHHbIl,t.
EC,tri t<zix.i.oe ua6"rroleHr.{eBbipaxe}to uexcrtcpoti aennulIItoii, to 06nqil<t olr;.r
r i r ' 1 e € r , r , p o 6 u i ' ' rqoa c r b , H o ! , f i r l a K C B b r3er I a q r e H f i a( a n e n o c . r I e - i o B z l ;e,'rbHbre
r o q K H c o A H I I a K O B L T Mx H
a p a K T e p H C T r 4 K a MlUp )a i i r i l , t e c i i i . r
(Ha,ta"'to)
i
-NPOAFIAJIH3HPOBATb MCTOAOM CKAIIXOB BBEPX I,IBHII3,
.Crpe:or ABC nsolpaxaer cKaqoK BBepx, TaK KaK Kax(:1oe
Hi,i6"'iroAeriue
trpeBocxoAur rrpeAbrAyulee;aHa,tcfnqHo orpezox GH I
r i . ; o d p a ; r < a e cr K a r r o K B H r l s . O r p e s o x C D E F n s o 6 p a x a e r c K a l i o K
Blrrrs, r.recMorpsHa ro, r{ro pasHocrb r,rexAy D w E paBua Hy"{}o.
Hnrepaa.n DE pacno,ro)Keu Mex(Ay AByNrfl orpe3,Jeiicra_Hre.nbHo,
x^r,ttr CD N EF, xaxAufi u_sxoiopux aso6pax<aei cxiuox unnis,
C.rtirag
neprrtri
HydTb MLIHycol,I, Mbi no!'iyqael{ IIg.rb cKa,rKoB: Tplt
t99
Ta6auqa 4.10
Ta6nsua 4.9
cnaHqa
{xcro paAro,nrpnfina I cmzutauQaKpeMH[croro
(Ocnorauue paspesa)
I
2
3
2
(
7
9
9
ll
10
t2
7
A
3
2
o
I
0
2
0
3
3
4
9
IO
l0
B
9
12
10
t2
l4
22
t7
19
l4
4
2
I
0
0
8
t4
16
27
(Bepxpaspesa)
oT IIJIIOCaK MUHyCyr{ ABa OT MHHyCaK n,'Iiocy (qEc,'Io cKaqKoBHe
SaBlICIlr OT TOfO, Ha3OBeMJIH ML'I BTOpOfiHyJllbir!'IlocoM I{!'II{ MI'{HycoM). Te[epb MbI MoxeM rIpI4MeHI{rbIIpoIIeAypbI,paccMorpeHHble
BbIllle Afl'I cryqafl [ocJIeAoBareJlbHocrefi c AByMf 83a,I'IMOHCKJIIOqarcurLtMaApyr Apyra cocroqnl.IsMli- cM. $oprrly.nsr (4.8)- (4' 10) .
.u,,rn roro r{ro6br annpoKcLIMauHfl HopMa!'IbHbIMpacnpeAeJIeHHeM
6 u n a o n p a B A a H a ,H e o 6 x o A H M oL I M e r b 6 o . l s r i r y n n u 6 o p x y , o A H a K o
B 6o,'IbtiluHcrBe reoJlofuqecKax 3aAaq raKIle o6:beMbl nu6opoti
BrroJrHeAocryIIHbr.
flpu nsyueuul{ KpeMHI.ICrbrx
c,raHlles s CxarHcrux ropax 6lt.uo
o l M e q e H o , q r o 3 r a n c p o A a c o A e p x { H r H e o 6 b t r { H oM H o r o x o p o u o c o xpaHuBrxuxcfl ocrarKoB paAl.IoJlflpuit.kIx npHcyrcrBlle B cJlallqax
cKopee Bcelo He fBJIflerctl c,'IyqauHbIM,TaK KaK IIOC,leIOBareJlbpa
oBHblx pac]tocrb o6pasUoe 6u.la co6paHa Ha rlpH6"'IH3HreJIbH
cloflHl.lrx rro pa3pe3y. Vls o6pauros 6bt.llt,tcreltaHbl ur,rtlQu, n xoTopr,rx Ha IlJroulaAxe 10X l0 uu2 6lt.no no,r,cql'IraHoLlHC,ropaAlror'Iflp n r i . . ( a u g u e A J l g 5 0 o 6 p a s q o B n p u B e A e u b lB r a 6 J I . 4 . 9 . M o x s o , r r r
cqr{Tarb, r{To pacnpocrpaHeHHocrb paA}lo,'Iflprit u:ueunercfl B lx,'illQe c.lyuafiHo? Bno.tse peaJlbHo cocraBurb npofpaMMy, Koropari
BbrnoJIHI,IJIa6bI ece Heo6xoAI.riralte BbIqHcJIetll'1fl,oAHaKo ycIiJII'Ifl,
Koropbre tpe6yetca npu groM 3arparl4rb rla npofpaMMnpoBaHue,
rlpeBblcflr rpyAHocrH, Koropble npxAercfl npeoAo"Ierro-BfiAHMOMy,
B:lrb rrpu pacqerax BpyqHylo.
B erou c,rryqaeAvxoroMLI3aql'Isua6.ltoAeulariAocrllfaercfl c IIoMorrlblo cpaBHeHHfiIlX Be"IllqHH c npeALIAyxII'IMHHa6IIOAeHUflMII.
B Aeticrellre!'rbHocru xplzrepui't cKaqKoB Mo]Ker 6url nprlteHeH K
KoropbIX ocyxlecrBJlflercfl no npol',I3Bod]IbAaHHbtM,AITXOTOMA3aqHtI
uoft cxeue [pil vcJIoBI{[, qro flpoBepfleMar ruilore3a Irloxer 6urr
n p e A c r a B J r e H aA r { x o r o M Z q e c K H H
. a n p u u e p , I r 3 B e c r H a f ln p o u e A y p a
200
3HaqeHHq yAeJrbHoro Beca o6paeqon,co6pannux npfl nepeceqeH[[
M A T H E T I T O B O TTOE J A (xpe6er Jlapaun, urar Bafiounnr)
( 3 a n a 4 H auaa c t )
3,57
3 ,6 3
teA
2,94
3,42
2, 8 5
3,67
3,78
3,8ti
4,02
4,56
4,62
4,31
4,58
5,02
4,68
4 :17
4,88
4,52
I,B0
4,5ir
4,6i
4,93
4,60
L"
a(o
tal
3,87
2
EO
3,77
3,84
?oo
4()q
3,86
4,13
+,')l
?oo
3.98
3.54
(Bocroqttaq qacrL)
tiuxoloMl{3arlux pflAa ga6,uroAeHuiicocroar B BblquraHHr.rKa)KAofo
na6,rrorleuuf r.i3 MeAHaHbr,BbrlIlIc.nesgofirro BceM Ha6rioAeHHfM,
ilocJre qero npoBoAr4TctrnpoBepKa rlirrore3br o cnyuafiuocru IIocJIe-1OB:ITCJIbHOCTU
MEAHAHbI C NOMOIqbIO KPH..
CKAI{KOB OTHOC}iTCJIbHO
repnfl BHaKoB.
I
H a 6 o n r r u o r i n n o u l a A u p a c [ p o c r p a H e H H r 4 o r e u 6 p n f i c K r . r xa H o p lo3uroB e ,rlapanruficrolr xpe6re B rrrrare Bar?ovtuHrua6JlpAaercq
riecr{oJrbKoMarHerLiroBbIXTeJI. OAHo us Hux 6u"ro BcKpbITo,n nopo:la Apo6[Jlacb A/Ifl lrcnor'ib3oBaHur{
B KaqecTBe4o6aara x 6yponony pacrBopy. B Naplepe 6u"ln oro6paulr o6pasqu B roqKax,
ilatsHoMepHo pacflo,ro)KeHHbix Ha riepeceqeHHr{ MafHeTLIToBOf0
r e . r a . C o 6 p a H l r b r eo 6 p a s u u p a 3 ! ' r u q a r a c b M e x A y c o 6 o f i ; o A H H c o ]1eplKa,'1rinpetrMyuIecTBeHHoIrJIaf[oKJIa3, Apyfae - oJil4BLIH, HeKoTopble noqTlr IIeJInKoMcocToflr'tHH3 MafHeTizTa,a Apyfle IlpeAcTaB,rs"la co6ofi cMecb rix Tpex MaHepaJroB.HecoorsercTBHe psAa rureHOB 3aCTaBJlfleT
itpeAIIOJIOlKlrTb,
q:IO B I,IafHeTHTOBOM
TeJIe I,rMerOT
M e c r o c i l c r e M a r r r q e c K r . rue3 M e H e H x f l .t l r o 6 u l p o B e p a r b g r o r r p e A rro,'rolr(eHue,6uJrn npoBeAeHbrH3MepeHlrrryAeJrbHofo neca o6pasuoB, pe3yJrbrarr,r Koropbrx npHBeAeHbre ra6r. 4. 10. Moxuo JIu
cqHTaTb, qTo [3MeHeHIreyAeJlbHofo Beca BAoJib lepeceqeHHfl cooTBercrByer roMy rr3MeHeHrlKJ,
Koroporo Mo)KHo 6u.ilo 6u olKi{Aarb
B npeArlo,'rolKeHua,rtro cocraB o6pasqoa H3MeHfJrcflcny,laflno otI l o c t t r e d T b Hi o{ c l l r p a ; b H o r o : u a q e u a s ?
Mu uoxeu raK)Ke npoBecru npoBepKy furiore3bi o c.nyvariuocrrr cKar{KoBrro orHolrreHr.i}oK cpe,4geMy gHarreHr.rro.
Pesynsraru
erofi npoaepxa Syayr lrclloJlbsoBaHlre erofi rJraBe B pa3AeJre,rocBfluleHHoMrpeHA-aHaJ'raay.I(plrrepuu cKaqKoB irp14HaAJre>r{aT
K
slHpoKoMy Kd'raccyHenapaMeTpr{qecKHX
npoqeAyp, paccMorpeHHbrx
a rn.2.
14Mercrcq MHoroq[cJreHHbrepa3HoBHAHoerHKpHrepr.reBa^ron*,
paccMoTpeHHbrxBbrue. I4uQoprraauHroo Hr.rx ql{trareJrbMoxer IIo201
T a 6'rn u a 4.1I
B.naxnocrs coBpeMeHHbrx HJtor B flpo6ax Ke]Hat B3trblx
3aJt[Bar Jlynouaua
ua no6epexre i{excuxascxoro
qeprlHyrb
CTarHcrr.rqecKr.rM
I pyxonoacrB_axIro HenapaMerpl.IqecKr.rM
M e r o A a MB p a a . r r r [r 8 ] , K o H o e e p a
[i0],3rre.rr
[
5
0
J. llp;4uepgHcno,'lbsoBa_Hl'lfl
Kp_arepl{flcKaqKoBB reororHr.r uMenTcg s rufire'MHrJlepa Ii Kaua [36]. Hexoropue u3 orux aBropoB csnraror
AJTHHy
caMOfO 60.rluroro cKaqKa [Or{a3areJrerranec.rryualiH0,CT}r,
apya""
nonb3yror qricJro rorreK rrnBepcnrr, T. e. ToqeK, s roropsix
"a3HaKLr
nocJreAoBareJrbHL'rx
Ha6.nrcAeHuiiueHsrcrcq. B Hexoropsix c,uyuaax
9rrr Kpurepnr.r Moryr oKa3arbcl 6o,ree roAxoAquIHMH, qeM
npo_
ue.{ypbr, ofitcaHHbre Bbr[re. Boo6ue foBopq, npoqeAypa trccJreAoBa_
H u f l c K a q K o BB B e p x r . tB H H 3c q u T a e r c f l H a v 6 o , n e eM o u I H b r M
npr.reMoM
H 3 K p ' I T e p t l e Bc K a q K o B ,T a K r ( a K o H a r { c r o , r r b 3 y e rH 3 M e H e H r r e
BeJrHIII,IHbI
B
TAXAOT? TOqKC
I]O OTHO''CHIZIO I( NPIIJ'ICIA,.,,ITIM
fry6lxa,
U
5
1L\
t5
TOIIKAM.
I,IJ'I}I C,]IHIXKON{ MAJIOIO qIIC,TIA CI{AqKOB
n03BO,'irrerBbrflBrrrb rrecra HapyueHlit c.uyuafiHocu{ Ir
He oro)KI I x c T p e H A o u . H e o 6 x o A l t M o o T M e T H T bq, T o c a l r n o
AecTB,rriTb
ce6e
Q a x r c . n y v a r i u o c r i zn e u o x e r 6 n r r A o K a 3 a H , r a K K a K y c J r o B r . r e
cnyuafiuocrti co!,eplKHrcfl B H)/reBorl runorese. Mu Mo)KeM
roJrbKo
y T B e p ) K A a r b n p H H e K o r o p o M 3 a A a H H O My p o B H e 3 H a q u M o c r H ,r { r o
H V J r e B a frir r i l ( ) r e 3 aH e B e p H a1 1q r o n o e r o f i n p H u H H en o c " r e A o B a r e J r b _
HOCTbHe riB,'Iqercn c.uyuafiuori. tr4ttultz croBaN,{H,ec,Tu I{aiflH
IIO_
I I b r r K t r I I p o B e p H T bu e c , u y u a i i i t o c T bo K o H q H J r H Cnbp o B a ! 1 0 M ,
ro HaM
HHrIero He ocraerca 60,'truIe, KpoMe rrpt4HfrJTfHynenofi rHlrore3bl
B , [ a ; r r H e l i r r ] € MM r r r p a c c M o r p r r Mn p o u e 4 y p o r o 6 u i p v ; x e u r i f l
rpeHAa
I.rJrr.r
cricrer\{arHqecKrrx
cpeAHero ssaqerlas. XIu 6yA""
_HaueHeHuii
lIMerb Bo3Mo)Ki{ocrt y6e4urncr B ToM, rrro Kpr.rrepHr.r
cKaqKoB B co_
IIETAHHII
i
rl
i
C 3'TIIN{IZ MCTOAAMH OKA3bIBAIOTC,I BCCbM
t24
78
20
J+
30
35
J:)
BraxHocrb (rpaMMbr
so!.u/100 r cyxoro
ocaAKa,
30
2l
22
l8
IIOC.IiCAOBATC,IbHOCTI,I,
ATfl NOTYI]CHIIq BbIBOAOB O BJiH'IHU]'ITPEHAA
ir.[t! J,IItI IIo,']yqeHilfl OqeHOK xapaKTepHCTHK' KOTOpbIe iuOnyr 6Url
oTHocHTe"llbHo pacnpeAe"teHl'lfl coBol.rftrci)ecHbr feoJlofaM. Eclu
B3qrbl nu6opru, Moxno cAeJlarb HeKoropbie
i(yrlrocrr4, ue roropoli
0a)cfiroBartHLre npe,il.IloJloxleHliff, To K HI]M MO)KHO IIpI.IMeHI'ITbCTar lrc i ir,{ecri.rtit MeroA, H &3ltBo0},{btri perpeccuoHilblM aH a,1lH3oM.
l npoA a n H u e r a 6 n . 4 . 1 I l p e 4 c r a B r ' t t { l o r 3 H a q e H H q t s J I a > N H o c r lB
Mexcnrau6ax xepna coBpe\{eHHbrx MopcKIlx l'lJIoB no6epexl.'t
cKor-0 3ir,ttisa e llocrouHoit "rlyttsttatle. I,lsl'{epeHlig rIOIyqeHbI B peJv,iir,,iiTc cptiBriellllq I'taccbi tl1ro6 ttel*el"IeHHo nocJle B3flTI'lg Hx H3
',i1;o(ttr...,:'i:o',lurti,r
BblcyultlBaFIHg. Ecnu IvIbI
lt ilocJre ril{artJIb}Iofo
(-oiir/1r'l:ilstIi\,i cj€.iiilllllLie Ii3i\4eilelltltl i'l cooT'BeTcTByIOUll{e I{M rJIy'
( - i i : . 1 , : ,l i o K f : . ' T oc . i e J d l r o H a p i l c . r i . 1 3 , r o , v B I I A I i M , q I o c o A e p x a H l l e
qacrflx cflofl I{JIa II
B,riii,ir i,uci1;o Itriil.er' c rny5niroii e nepxnux
\ i e . i . , , i c t i l { oi ; ( r r i n a e r , n o q I 1 4 c l ' e 6 H , 1 l r 3 I 1 p ! ' t l c b ,B o c a A K e s 6 1 1 I t : l t r - ] c cll0cc5bl IlccJIeio'
r t i , i r : r n l r r {c , ' r o f l . ! } a c . c l { o 1 p H \ { ' r e n e p b p a : l . r 1 4 r { H b l e
' , ,',1i:, lI :lillllJCli HetiBllbIx COOIHOilleHllllMelKAy sTHMi{ riaO.[IOAe-
Apyrne Ar'IxoroMrrqecKr.re
cxeMbl orpalKaroT ToJIbKo H3MeHeHr.Ifl
Iro
o T H o l x e H r { r cK o a H o M y 3 H a s e H H r OH, a n p H M e pK M e A r r a H eH J | H
CpeA_
HeMy3HaqeHlilo.
I ( p u r e p r r n c K a q K o B q e , r e c o o 6 p a 3 H on p r . r M e H r r r B
b Tex cryr{arx,
Kofna rpebyercr BbirlcHHrbnpr.iqr.rHy
HapyrxeHr.rflc.nyuariuocrir. gaJI}IIIHC CJII]IIII{OM 6O,rIrUOrO
fny6rHJ,o)nbl
$yruI
,lna,rcuircr .+7,75, yKa3ilHHoe tia pl{c. lt.13, - cpe:lHee coAepxaco60it T0t{ry, oTHocHTer'lbl{o
iiric F,'Iafil e ripo5ax -rpelcriiBnner
rl e.
cy}lM-aKBa.{,roropoii AHciiepcIifliu.llIri)'{arbHn,
ryllt:tl13i:Ia
So
T O I {T O q K H .
i r a T o B o r x . n o u e i l t t n c o , I , e p l K a I l l l HB J a r i l o T H O C a T e , i l b H
illilare,'il, .'r.o.1)i(!'ir
lioltuirrl (crl. r.n. 2), uro eciilt IleKoropble np0aLl ablgr,rserorcoMHel{ue,To llx Mox(Ho 3aMeHllrb HecMeqcHHol{ lI
}Iau1$Qr:urulroii oqeiiroli nlt6opouuorc cpejlgero, fl B,rlfiIolr1efocff
N{On^pO6,KOTOpbie
irPe;icl:a3:lH}leM
,[,OI]O,'IHHTeJInUUX
A.IIfl
"i)glurll,{
ri"r (rrtlr, r:-rc,ir€HglrlM3 roii >re coBoKynllocru. OAHaKo flcHo, qro
IIOJIC3HbIM,I.
II{ETOA HAI,IMEHbIU HX KBAAPATOB I{ PEf PECCI,IOH
HbIH AHAJII,I3
B o u g o r u x 3 a A a q a x H a c M o r y r n H T e p e c o B a r bH e r o r T b K oH M e r o I u u e c t B l l o c , ' l e r . o B a l ' e " t b H o cH
rH
3 M e H e H } l .H
' ro, r a K x e T e T o r r K HB
, KoTopbrx 3rir li3MeHcHr.trrlrpoHcxoAflT. A,,rq peueHr.r, srr.rx
3aAaq
H y ) K H o r r i l { e ' b u a O o p u s r , r e p e u u r ui s y u a e r a o r ln e p e M e H H o f ia,
rax>xe
3 H a T b r ) i l c - ' l o , r o l K e H rTeO r { e KS T H XH 3 M e p e g a r ?K. a x H 3 M e p f l e M a f f
ne_
p e M e H H a f lr, z l r { H [ r K a r a , n r o r o p o i i B C O o r B e r c r n y r o u r u e
i AHHrruax
Bblpa)KeHbr3d'teMeHl'br
nocJreAoBaTe.rtbHocTr.r,
AoJilKHbIHMeTbonpeAe_
.neHuufi pa3Max. oxagblsaerc.fl, HaM HeAocraroquo npocrofi ruri40pMarrr'r o flopflAKe c,'reAoBaH'fl roqeK. B 60.rnruurrciee npuuepoa,
xoropbre nrlr ceftqac paccMorpilM, nac 6yAer HHrepecoBar^lo6urnii
-erorur
xapaKrep r{3MeHeHr.rfl
AaHHbrx. l{u0opvaqas o6
6vaer uc_
IIoJIb3oBaHanpH HHTcpnoJIfluHrrMe)KAy naHHbIMH ,roqxiull
n ilfl,
gKcrpanonfiuHr{ 3HaqeHufr,pacno.no}KeHHbrx
sa [peAenaun 4aHHoft
202
. :Jt.l,iiCC 3H:'q3rlite
lle
MOil(CT
:ljieKts:r iIIO
rlileACl aB.[qTb
Aai{H'5Ie
p t ; c . 4 . r 3 . l l p o d t r c r 5 i r p a ; i u l l n o c . [ t ] A o B a ' r e , ' I b uIcI .I I o r o M y o H H H e
Eue 60.nee, qeM TorieqHag o]leHKa' HaM
!:.ii)ilcrcg lte3aBIiCUP[bitau.
Korollag Bblila3H,'Ia6bt csg:l MexAy
,tH!Iufl,
ii()i(ouJ,'Ia6irt npiil,lan
r t O t i e p ; i 1 a H r i eRl i! ' t a r t i U r n y 6 t t l O i i r t l r e C e l t N { i l O ) l ( e C T BHe3 M e H e H n q
:ua.l'eir.iiil repeMe:lHbix. I'llryltrllBHr,ie coo6paxeullg n.oAcKa3bIBa'
IO',fHaM, qro B l(aqecrBe rairofi JIuHHII Mo)KllO 6uno 5u ru6pars
KoTOpOfior AaHHblx sHa,IeHnfi Md>KHOCBeCTII
npsMyro, oTKJToHeHI{fl
20c
:
rl r
I
II
Braxxocru, r
r50
100
JII{IIrb 3a'
afloco6oB LI3MepeHI{qorK,lloHeIlI.Ifi,Ho MbI orpaHHt{I'rMCff
c[oco60B. ECIU Harua sano noBoAy Ka)KAOfoH3 3TL,r,x
NlerraHr.rflMn
orKJroHeHHiiCoAepxaiiaqa 6yAer 3aK,rroqarbcfl B MlrHLIMA3ar\HE
IrHii B,'raflr, To MbI noIyI{I.{M [pfMylo, [peAcTaB!'IflIouylo HaHIyquyrc oqeHKy BJraxHocrr{ npfi 3aAaHrHblxr,ry6uuax. Hao6opor, ecln
OrK,'IOHeflr4fl
tily1:.1.H,TOMbI
3alaqa 6yaer co,croflTb B MIIHHMI,I3aIIHH
rroJryqr{MHarrJryquryrcoueHKy 3aB}rcHMocrl.rfJIy6HHbI or coAepx(aHHr?Braffl. Tperu a,'IbrepHarl]Ba IIo3Bo.IIter BbIpa3HTbcBfl3bMelKMa 6 o p e 3 a A a q , p a c c M a T A y A B y M q n e p e M e H H b I M HB. C n e ( I { a , i l b H o 'H
pHBaeMbrx B sTotl rd'raBe,BpeMeHHile ilJIIr [pocrpaHcrBeHHble nHa BTOpaq nepeMeHHaflHMeeTHe'
TepBaJrbrcqr.ITalorct LI3BeCTHbIMH,
IIpepbrBHoe pacnpeAeJIeHHe.floarolty [IepBafl aJIbrepHarHBa KarioAxoAflu{efr,I.ns Ha[Iux ue,'Iefi. I4ultuv cJIOBaMIi,
xercs Har.r6oJlee
c o A e p l K a H H eB J r a f H Y p a c c u a r p l l B a e r c f l K a K c r y r l a l i H a f l [ e p e M e H '
Hafl, a rny6HHa X Surcupyercq. flooroMy 3aAaIIa cocrol{T B [peA,cKa3a{r,tH3HarreHHrlY no suaqeuusv X. fipyrue cflyIIaH 6yayr pac'
rJIaBax 3TOriKHI-Irll.
cMoTpeHbrB CJIeAyI,OUIHX
o xapaKTepllcrllKax npflMoft
floc,re rofo KaK MbI ycJIoBI.ir'ILIcb
rpeHAa, Koropylo MbI xorHM nocrpolirb, onpeAeJII'IMHeKoropble
r e p M n H b r . 1 4 : y u a e u a r I r e p e M e H H a r tf f B , l t i e r c q 3 a B H C H M O i i( r . _ 9 .
pefpeccyoHHoit a o6o3HarIaercq Y;. Orx,roHeHuq Y;
Qynxuaeli) 1a,'I1a
tnlar'lbHblMll.
6ltrl ntu'Hl]
oT npflMori JTHHHH
flpyral nepeN{e,HAOJIjKHbI
Hafl flBJrflercqHe3aBr]cHMOiI(14[IAapryMeHroM) n o6osnaqaeTcs Xi.
l l y c r r , a l n p o K c n M l 4 p y l o q a s n p f i M a r n e p e c e K a e ro c r Y B r o e K e b 6
J.raMeer yr,roeoir Ko3$Ququeur br. Toraa ee ypaBHeHlteHMeer BI'IJ,
50
i
,ln
)
&
ru
o
^^ a
ZU S
o
i
I
C
o
)
'
q
L
o
i
o
o
30
o
o
X = 47.75
40
Puc. 4.13. 3aerrculroct BraxHocru
ocaAKa or r,ry6lrHn (r rpauuax nolu
na 100 r cyxoro ocalxa).
Puc.4.1,1. Paa;raqsoreBapr.raHrbr
KpHrepueB MHHHMIl3atrHu
orK,'roteHufi or
JlHHltEaflnpoKcuMaqufi:
,{,auulte co6paHu B cKBaxrrHe, npo6ypevuoir
B c o B D e M e H H b I xH n a x H a u o 6 e p e x s e M e x c l EaHcnofo saJuBa. OTMeTHM, qro opuerrrautrr
rpa$nra He coorBercrByer opuesraquu, o6HqHo l{ctro.rtbgyeMofiB rrareMarnKe
,{ B -
uxxxuxsaqgfl
frxJoH€Htrfl BJaxHocrH;
M u H r M H 3 a r I H qo 6 o 6 u e s s r r x o r x l o H e g u f , ;
fnv6uH!,r
C - lruHuuusaquq oruoseanll
?, :
KBAAPATOB
OTKJIO-
EeHLIII,rBJrflerc.s HaHMeHbrxefi).Mu MoxeM rrocrpor.trb eAr{HcrBeHHyI.OIIpqMyIO, oTHOCHTeJTbHO
KOrOpOftAHCIrepCriflMr.rHHMaJIbHa.
EctH sHaqeHr.rrr
sroii rvHeriHori Syuxuuu B AaHHbrx ror{Kax BbrqecTb H3 cooTBeTcTByrouI[XHa6rroAaeMbrx 3HaqeHHft,ro no.nyueuqHcer'r6yler fiMeTb cpeAHee 3HaqeHOe B pe3yJrbTaTeNrHolKecTBo
paBHoe
HyJrro,
rr
Hr.re,
MeHbrrrynAHcnepculo, qeM Ha6op oTKJroHeHLrr?
or rro6ori Apyroft nprrMori, [ocrpoeHHor? no AairnuM roqKaM.
Hveercr, oAHaKo, HecKor'tbKocno,co6oBotpeAeneHug I.t I,r3MepeU fTi n o l 6 u p a e M o i t i l H H n H . H a n p z n r e p , M b r M o x ( e M
H H f l O T K J T O H e HO
paccMoTpeTb oTKJroHeHr.rr
3HaqeHHrisraxHocTu, oTKJroHeHHflfJry6utt tuut HeKoropyp Iix KoM6r.rHauzro.Ha puc. 4.14 orpe3oK A
coAep)KaHHfiBraxHocrti or floAo6paHHofi
H3o6pa)Kaer orKJIoHe_HI'Ie
flpsMori, a oTpe3OKC-OTx.rtOHeHrie 3HaqeHr.rsfJry6aHbr or ior? xe
flprrMoil. Orx.nosesue B LI3MepeHo tto nepneHAr.rKynspy K Heft.
Moxuo 6nlo 6u nocrpourb npflMble, Hc[oJrb3ys nrc6ori r.r3 srHX
(4.11)
. l e ? , - o I { e H K a I . J f r Y i t l P t r j I a H H o M3 H a q e H r l I X i . P a c c u a T p H B a e qa X O ; K M O eO T K , ' r O l r e Hp
r raeB H OY i _ l ' t , L I H a l u a 3 a A a q a C t s O A I . T TKCH
,[,eHrrr'oraKoir npflMoil, ]1"'If xoropoli cyMMa IiBaApaToB orK"'Io-
AO MHHrrMyMa.ECJII,IpaccyxAaTb no aHaJroflrH co cpeAHr.rM,To
oAI.tH Lr3 CTiOCO6OB
COCTOI.IT
B MriHHMr.r3arlnH
CyMMbtKBaApaTOBOTKnoHeHrr
ft or IIpqMort. (CpeAHee- gro 3HaqeHHe, orHocHreJrbHo
KOTOPOTO AI,ICNCPCHfl I,I, CJICAOBATEJIbHO, CYMMA
b o* b r X t ,
TICHIIiI
n
s \Y i
^-Y
i\2
:
MIIHHNIVM.
\4.12)
pe3v,'tbrara rpe6yer ltpHMeHeHIttt
flolyveune oKoHqare,.rbHoro
u
c
q
u
c
;
l
e
H
l
i
f
l ,r l o 3 r o M y M b I H e 6 y a e u p a c c M a r lHOQepeHuriaJrbHoro
lFil
.i|
p H B a T b A O K a 3 a T e r ' l b C T B Oa' O f p a H I { q l ' I N { C fTl e M ' q T O I I p l l B e A e M T a K
IOUIHe H a IiTl{ 3Ha qeHa3btBaeMble HOpMa,'IbHble yp aBlleHI'Ig, IIO3BO,'Ifl
unR b6 u bt Lnfl annpoKcl.IMl.{pyrcUeli npqMoii. OHa HNaercr euA
sr"
Z] t:
i_r
' \ rz.
0 o t l+ O t Z
Ati
( 4 .l 3 )
;-l
nnn
Z x r v r : b o> x s * b r X x i .
l=l
l=l
(4.141
r'=l
204
205
i
I
#_
Peruag cucreMy ypanHeHi'tfi,norvrll'iM
jtx, v,+l'ii.r, >lv,':f n
4'u
hwl
-
l:l
\ r:l
i:l
t7
Xr',,-[
'
4
\
\
t-l
n
Sl v.
Z)"t
i-l
-t)l-
"-
,
n
Pnc. 4.15. Ha6;rrcAaeuale 3HaqeHI{fl
U UX OqeHK-I{,nOJryqeHHbIe
B,'Ia)KHOCTr.t
a3 ,'rHrreirHoroypaBHeHHfl pefpeccul{, IIocrpoeHHolo no MeToIy IIauMeHb[rHx
KBaApaTOB
( + .l5}
5Sr
,4*'')'
l'
S1 rz
4'L
h-
Sp x.!r
i I
1 - t'r,u.
Bl a x H o c l u , r
100
50
150
(4.16)
Mbt Mor.rru 6br lictto,rlsoBarb alu QopuyJILI AJfl lloJlyqeHIlfl i(o3(pypaB]IeH!If
rfltqneuror
Ilpr]Moit, oAttitKo JIetKo 3t!!lerllTb,'lro
(4. l3) rr (4.14) IIpeAcraBJIflIor c06otl cuc'teN{\i vp.rEHeHI{li, Korof"'i. 3'
-pyI{J MO)i{i{O pelllUTb, IiCllO,{b3yu MelOJ.bl' OllltCaHHbie B
0 6 a 3 r u y p a B H e H I i r M o l K H o 3 a n H c a r b t s I ! 1 a ' t p l l L l H o tri l o p v e :
rtL
i' r4l1,t
)X\.6"r
t 1yr r / \ l ' . ' J t /
4
, f/
\:J'r
14.fi)
y:
o 6 w a s c y M M a r { B a A p a r o B(SSr) IIepeMeHHor?
t i i l i l i : J , : 1 b . l c B : t i l l ; 3 r \ ' { : l lp l l L t i i c f o l v i e ' l o A a
c'ryq:ie
ci1R3Ktle-au6o ttlreali,vllJ.eclilil,:-r itl,rce croxlH5ix
M
!
l
b
l
i
,
1
V
I
:
F
i
l
l
j
t
l
e
f
l
r
a
;
C
O
I
i
p
a
D
.
i
t
:
i
i
H
O
.
I
t
p
l
t
M
e
H
e
H
H
e
TVarill,<Ix ero
( ) 3 a B H C t l M O { - : T i . l C g l i L i p } l i i l l l ^ r t l B i I : i l - i i O T l ' , r : t ,a ) l l l l b l
Z
i
r
t
I
{
3
a
,
lieiUeHlie
,ielo;
e.'rie.6Dr,l II 0),.la.u llcliL\.rIb:;CBat:bl.rOi
\ie';gJal.,ill Iiaii)llqHoi';
;3 3rort
Xorg
0,q.sa,rv;xaer
;(;iii"'lee
Iipocrolvl
b HacT0tlili'ii
rrriise.
3;le:"leuri,t
ir{ilTillrl.
,1
ssr: Tl i,,,_ l
lJ
\
!l
140
- ? 5 C i )i r ; t l
r']ti7rl
206
n
t2
T'll',) : F, r)',*1,.
Hlbt
/
,.-.t
l=l
I'lK'3BI}}: rt7=8,
(,1.18)
;-r
r r o J r y q y l yA r . r c n e p c u r on e -
nn
,t-:
.q'
,
, . r c r l r i ' : ri'lT{ i . : . r . r i b u bl:--2,66.,i{.i,1
i i e s r i n e e , n o . r i \ - , 1 ! t e Mr 0 : 9 4 , 6 7
i
:
'
i i . ' , H OcI (u ; i r - : ; ) ] K a B
b
i
r
j
l
l
,
j
,
i
l
c
l
l
l
i
t
i
, l o B a T b i i r ) J l Y 1 1 € l I i I b l 3€ i l a . I C i i i l t j : r , r i . t t
(jlllri{l(}:
l l i r r i B J a l , r r B o i a i K e i i a i l a : l J i r { q } { L r i ri , n y i r i t l : l t { . f i 0 . i l ' i . l C l l i l b I e
ll.lr,lepli li', HiiCliO,,TbKOtI1.)111.{4t],
OirDCSOBarir'i'tIl TOqI{ali IIo3BOJ'I;lIO''"'
: : O C T I I O e F I I I : il li O
i l . 1 e ' ! O l l yH l l l l ' l C i l 5 i j j l i X l i t l i l , i i l l i - , 0 t s ,C C O l E e r ' : i l ) ' I
g C I O j I i q , l i \ i t j t ) i 6 C i ) O r t l { t , i t , t . ' t : t H i t t )El tC
t .. i l l t , - i l t i i { : ! T p r J { l } I 1 1 3 U : l i l t - l , f : : l l t
'.llirlcc't
'f
:1epe3
llL'iaiorioilil!'io .1'oLIKlr, :r; )'r
Ka)5A.vx-i
I:l
ll
Il),1.,-.J.1iiiii]
1 l i / i c ' i ) l l l l . i . l r H 6 i , l ; i t ) ' M x { a K B 2 l A j - r a r o i to r i ( ' 1 u i { i ' H l l ' 1 o l ' I l I t l l ! 1 1 ) I t
6sr,rl 6t't irt 3i{1 H}'.rIIo' i(cuc'rtto, B ilpllileAe}iI{rlr'1 rp}lNiepe 3 i() Lie
' r a K . S H r r I I c l l L ' ! fY" i i l Y i i l 3 o 6 p L i i i ( € i i l : l i I a i l l l c . 4 . 1 5 .
ii'in LrC:iret"tOnpe!,elllTb rpli x;paKTepllcTIlKH, KOTopble oflI{ctst- 3TO
t s a r o r r { 3 N r e r i e H u e3 a B H c l { M o i i I i e p e M e H I { o i i . I l e p c a a 1 1 3 H ! l x
n
fl
P a e 4 e n a e 3 r o y p a B H e H H eH a ( n - I ) ,
p e M e H H o i y' r:
: , I : l - 1 0 ,- 1 , / - 3 8 2 , : I ? - - 3 8 ; 0 u : . { 2 : 3 5 U U . l r i , : ' : ' r r . B r \ ' 1 : - r ' i p r r e {rr{eerBI'IA
rroii .'j)0pMc
.!
i J O ' 1 1 l ,- oi : |\ _ t 3 E 2 .
r
!
,
-.l)T
l[
n Q t- 1 ) L
:
rt-l
,)']
5li,'-iTlr'
H
\ 'di = l
(+.re)
i:l
Bropax xapaKrepH'cr'trKa r{:'}MeHq].rBocrl.r
3aBHcr.rMorlnepeMeHrtoii-3ro
c y M M a r ( B a A l ) a r o so r K J r o H e t i H foi q e H e H H b r x3 H a ! € u H i r Y i
o T c p e A H e f o3 H a q e H r . Iys:
.iltr
I
t
T
il
i
.,1'
irl
t.
Li
'I
f
4r
+
ll^
_
n
,
,
S S p : l ; , t , '' : l - { F
n \\ U
A
;.-t
;-l
i,)
:r
4r!
ti, - i')'
(4,201
i-l
(ar< c,re,l,yer il3 rrpaBoii qacrll oroto paBeHcrBa, or{eHKHHMex).i ro iKe cpeAr,tee3HaqeHHe, qro Lt [cxoAHbre AaHHbre. Cynaua
K B a r I p a T o B3 r l { x O q e H o l { f i X a p a K T e p H 3 y e M
T e p y H 3 M e H q H R o c rf lHH HHH pefpeccltu orHocrn'er'rbuocpeAlrero 3HaqeHI.Ir. Ecnu Yt rr Yi
coBnaAalor AJrfl Bcex sa6.lroAeHrrl, ro cyltuL,r KBaAparoB, BbrrrHcr r e i { u b r et r o S o p M y n a H r ( 4 . 1 8 ) w $ . 2 0 ) , 6 y l y r o a l r H a r { o B b r r * lH
r .a o6opor, ec,Tn cyMMa r{BaAparoB (4.20) 6yaer MeHbIIIe,ro pa3Hocrb
.SS2:SSr-SSR,
(4.2t)
207
Ha3brBaeMarrocraroqHorl cyuuofi KBaAparoB, 6yaer orrrllarbcfl or
uy.nn. I(ax JrefKo V6eAnrlcs, Ber'ilIquHySSo MoxiHo raKxe BbrqHCJrlrrb no Qopuy"re
SJD:
;ffi
^"';;11;
xo'IOpbll'l
IL
rr 1)
Z\Y i-
) i)",
r4 )9\
qTo AaHHble
t'
reprrH, npIrMeHqeMble Ar'In l!:,"..:f.i."-:l:l: oeauur
" "'
:i:ff
ur pe6
;." n.notop bIM 3aAaHHbIIr'r
;;;;;';fi -y;-
Han, xoropoit t o:l ut::l " {:j.,,X;
nepeoaeu
n'p'*'nnort. x" ro MbI MolKeM
;;;;;,{;"
;;'";;;;"';;;;";;;"
l'lHleptJaJl
flJlvrsnLnn/r
" " v ' " ' ' " ' . - : - , , ,n, ^, , - n^ .r.i ol r u q n r .
q
n .nncenn,v l o i l l e i i
nDe.u'noJIox(HTb'qTo]IMeIoUtHecqAaHHbIenoAqllHfl}oTcgcJteAyloiuell
r e o p e r l l q e c K o I M o A e r u:
(4.26)
Y;:PolptXi*ei,
npfMor?, [ocrpoeHHoii no uerAe ssD HB,rrflercffuepofi orKJroHeHrrrr
1 O ! . ) ' H a U N l e H b r r r r rKxB a A p a T o B o
, T pe3y!'rbTaToB
H a 6 , ' r t o A e H H rIi(. a r { e c r B oi l p u 6 . n u ; x e H r r n p n n t o f i x a p a r ( r e p r r 3 y e T c rorr H o r x e H H e M
p2-
ss^
"
(4.23)
"-ssr
E c " r u r " r q L l M e r o u { r 4 x cAr a H H b r xn p f l M a r r x o p o r i l o n o g o 6 p a H a , T o
3TO orltoueilue 6yAer 6"ri.igro K eAur{xqe; Hrr}r(e MbI pac:cMolpI.rM
KphTepllH,
IIO3BOJIflOilllle
CyAI'lTb O 1OM,
HSCKOr'lbKO XOpOUIO 3TO
orHorreHilc xaparirepil3yer riaqecTBo oqeHriH. Be"ruuuHy R2 Hepe4KO Bbrpax{a}or B npolleHTax. Ta iKe repMltHo,rofutl npHHflra B
TpeHA-aHaJrH3eK
, O T o p b r t i ,x a x M b r y B H A I . { M ,f l B , ' l f e r c f l n p a u u u o 6 o 6 x{eHHeM 3TOfO MeTOAa. HeO6xOAuuO oTN{erHTb, qro KBaAparHbIft
KopeHb u: R2 paBeH MHOxecrBeHiIoMy Ko3Qq)[IUHeHry KOppeJIfl-
ul.iu R:
R: lrP{ : I sS^l-sS..
1a.24)
A;rre6pauuecxr{ri :xeusaJieHr sroro coorHotrle}t}t.Ro[peAeileH B
r,u. 2 xax xoerfQHrrlieHTKopped'IqrllrIi
f _
ss,,,
l,/ss,.ss,/
(4.251
T a x i i H t o 6 p a 3 o v , n p r t T I a x o x { A e H H Hy p a B H e H } l r i t t p s M o l l , x i ] p a K TepH3yrolllcii sasucuN{ocrb B!'la)KHocrli ocaAKa ol' fry6xHbl, Il0 }leT O A y H a U M e H b U I { X K B a A p a T O B M b l B b l q l { c , ' I I L ' l Hp a 3 r [ q H b I e B e J l 1 4 ' ] H Hbr, Heo6xoAuMbre npn oitpeAe,'reHHH c)IN{M I(BaAparoB, Kar{ecTBa
lprr6,rrrxcuuH H nosQSalureHla Kopper'IflIUrn.Butquc,rure Ber'tuqHu t r S S r , S S H , S S o , R 2 H R . q , r q A a H H b r xr a 6 n . 4 . 1 1 .
ConepruettHo oqeBuAHo, qro lil)flMafl J'i]iHun He BCerAa xopouo
a r r n p o K C r . r M i l p y e TJ , a H H b r e ; 1 a x { e B c J r y q a f l x B b l c o K o i i K o p p e J I f l u H H .
rrpr.i6"nttx<enlle Bo3HrrKaer KaK c,'IeAcrBHe paAa IIpt{qltH,
llroxoe
cpeArr Ko'fopbrx c"rre.nye'forMerrlfb Br'rcoKyro AHCIIepcHlo 3aBI4cHN'lofi
nepeureuuoli (upe:uepHr,rtl pas6poc ,lauHotx), a raKlKe nu6op uenoAxo,t,fluleii vroAe"ru. B sror4 npflNIepe Mbr cK!'roHHbI noAo3peBarr'
t I O C J ' I e A r l e eT,a K K a K p a C I O J I O ) K e H H eI I C X O A H b I XA a U H t l x H a B O A I I T H a
r \ ' l b r c , r r bq, r o A J f l a n n p o K c H M a l { H H 6 0 , I I e e n p H f o A H a K p H B a g , a H e
MbI paccMorpuM HeJlaueriHyto annpoKcaManprr\,rafl iluHrtr. Hsxe
qlrxt. OrriaKo npexAe HaM nplrAercr i43yqurb crarzcrtrqecKue KpH203
Be'nizqusa e ff'BnocJIeAoBaTeJIbHbIx na6'nrc!'egufi'
rte i-HoMepa
r ' r f l € r c f l c ' r 1 ' ' u a r i H O i i H O p M a J I b H o p a c l p e ( e r e H l l o i i B e J I { q H H o f i co H
y"Iea2' He 3aBl'tcfluel"l r BeB b r M C l ) e A H H Ml r H e h 3 B e c r H O I ?4 U C n e p c u e f i
riro Ha6rl'oAael{ble
ru,rriu )'i. 14rtutrtlt croBaMH' rlpeAnoJlafaercq'
csgaaHHoii
Ay l ' , ' l u a v n n o c r o t H H O i i B e ' l I H q H H b l '
3 r r a r l e H l l t ) ' ; f l B , r l f l I O T CC
or cBoHx
o
r
c
q
H
r
b
I
B
a
l
o
r
c
f
l
co cpe-IHHM 3HarieHHeM^ittll--{'.-:-Y;
or x;
JII'IHefiHoiI
HyJIIo)'
po
syuxuuu
paBHo
cpc;\ilHx 3HaqeHllll' ro
uso6paxeHoua
xounoneriioiu. 3ro- coorHoueHrre
il-,,rl..I:i"ir"fi
'4.i6.
JtLr*tttl pefpec-
qro AJIfl xax<Aoit loqKH
flpe4no;raraercr'
;";.
CI'IHCyUeCTByeTHOpMa"IbHOepacnpeAe!'IeHIIerlaC'IOTBO3MO)KHbIX
IIilHMeHb[II]x KBar'pasuaqeilrir nepeueHnbit Yi. flpnuesfla.MeroA
pef peccHl'I' Bblqlli'roB r.{ HcIIoJIb3yfl au6opouu.ire. -xoeQQuuHeHrbl
OUeHllrb IIapaMerpbl
MO)KeM
MbI
(4'17),
t{oae,""
lus
HCxoAf
J,'reHlrbre
oqHbrM
'b
'Inapainerpu(4'26)l
Ii. e' nrpauerprtp-n'$opuv"re
;;;p;;il
"o--u-Mof
(4'17)]
'
Mo'r'e'Irl
B
roegQuqueHranpJtp;;;;;
BbInoJIHeHbI' To rIero;l HavEc.nu cAe,laHHbIe HaMI'l ofpaHI{r{eHnf
MeHbUllxKBaApaToBAacTHaMoueHl(uMaKcllMa"lbHofoIIpaB,Iono.
b1 u.bs' II ilocrpoeHHafl HaMH nHHlrfl
IO6flq rapaMeTpOB pefpeccHl'I
qem
'rrc6as
6vaei 6.nnxe x ncrHnnofr npnuofi pbrpeccr'tn'
f
l
B"Isery
p
a
B
H
e
H
u
e
n p " * o " . E c , r u n o c r -p o e H H o e" r r r n e i i u o e
ro AHcrepcI'Ir c'ryuafr'ori
Mo'qe'Ilblo,
l;t;;;";;;"[.rp"..ronnofi
KoMIloHetITblpaBHaAI,ICnepclIHoTHoclITe,'IbHo.IIHHI'l}Ipe|peccu11.
l"rn"."r,
.r;";;;
Yi: Fo*FrXfer'
MoAer'lli
perpeccnonnofi
P n c . 4 . 1 6KolrnosetirEt
.
[ I p e n n o r a r a e r c r ,u r o
cnyqafiHaa
KoMnoHeHTa
8,
HopManbHo
pacnPeaeneHa
orHocllreJlbllo
Jt t-
HHH perpeccllH
209
Ta6aaua 4.13
A.rr9 onpeAeneHH9
npoBeAeBHOro
PeryJlbraru AilcfiepcfioHHoroaHarn3a' ganucumocrr coAepxaHut BOAbI
perpeccuEr xapaKrepn3ylolllefi
Ta6nuua 4.12
,[,xcnepcrouur,rfi
aHa.lllsAJq cnyqasnpocrofi,rrsefinofi perpeccHH
,niu"oroa"*t
B ocaAKeor nJly6tlHbt
f lcroq HIrK ll3rteHqHBocrI.l
H c r o q H r x 1 3\ t c r r t H B o c r H
Jlauelinaq pefpcccuff
Cpe,r,ulre
KBAIDATbI
Cyuua xaaA' I rlacao creneparoa
I neii ceo6oP.lt
3hlcctrttc
/'-xDHrepu r
MSN
l'
23,07
7546,88
ilrrueftrtasPerpeccut
SS^
3Ha,teuge
F-KD u rep trt
CDtr\u ue
KBA,TPT TbI
MSnlMSo
327,10
Jlir lltle
I
C 1 ' vn a p l t a . R A t l c l l e p c l l r
I
-4rrcncpcIlt
i
H a o 6 o p o r , e c , ' r n M o r e / r b B b r 6 p a - H aH e y A a q n o ,
r o A n c f i e p c u r ro r H o clrre,'rbHoii llprr{ofi pefpeccHn 6yaer "6oltll]e, rieM
Aricnepcufl Be-
"rlur{Iilit t €.
I.,{ONIIO
o
paaeucrBe
AlicnepcHit
K O M B E V I I I { K AI J I ' I
TOIO,
IITO6bI
CAC.IIATb HA.IIEiKHbIC BL-IBOJbI, ,TIIOO
ecJiH nocTyr'rr.rpoBaHHar
rraMI] ]!roAe,,rbHeBepHa.B ra6,r. aJ2 n1r-tiB e . q e g ac x e M a A H C [ e p c u o ] r H o r oa H a . r r i l 3 a .
I(ax yxa:ar{o B iJ. 2, cperritie xBaAparoB
Iaior Ar{cnepcrrrr,
oueHKI.t KOTOpt
rx no/'rYrraIoTc, B pe3)',rblat.e Je"rjeHiIfl
cooTBeTCTlYiotullx ci'MM KBaApal0B Ha o'fBeqalouae HM rrilcra crenelrer:rcBo6 o A r , l .B e . n r r q u g eM 5 a o r n e u a e T O I H a c T € I r € t J rc,B o 6 o l b r ,
Tar{ r{ilriee
3 H a - q e H l r iel o r ' I y r i e H oH i t - o c H o B e . l B y x < ( r J a 6 J I i o A e u i i i t > >
3 H a q e r i h i iI i o _
()iu1aa _1,rcn.pc,la
f i l t { e e rr r _ l c r e n e H e i i c B o _
]QQuulreHroBb6 tr bi.
6oAgr. floatolry BeJlrzsuHaMSo .ron>xHzrrir",ierbriiic,rro
crencrtericeouoil',,n'lttoi^lot.l:ttH
M e ) r ( A ) ' ' t B y i l r t) - K i i J r r r r i rM
r rH , r . e . ( r r - r ) -t=-,-2.
/ v l b r M o x e M n p r . i M c F ; H r bA N o v A
K paccMorpe'rroii
B b r ' ' r es a A a q e , K a K 3 r O C A e r r a r { oe i a 6 " n . 4 . 1 3 . I - l p n
rionn npou*po.rcfl c"neAyrot{af fHnoTe3a:
He:p, :g
orKnonterct
npu
50/o-nou ,r-po!He 3HaqHMocru
(c-
npH ailbTepHaTlIBe
Hr:Fr*0.
I J C J I O J I I , 3 O B A T F ,N O J I Y q C H H b I C C Y I I M I , I
KBAAPATOB AJIfi BbI.
tlrc'Ter{}rr oilerio^
Arrc[epcufi, Koropbre B CBOiOoqepe,{b
' 5 s rr{eo6xo,tii-rrcno.ll_
M b r r r i t r . rf l i ) o B e p K eA B y x a , , r b r e p t r a i l r B B
. ,tacrHocTir,
3Jrerc'i Iial{ oueHKa AHcnepcl'rnorHocnTe,rrbH(J
r'ri4Hiir.r
perpeccnu. i4br
MO)l{eN{no,lytlHTb aAeKBaTHyioor{eHKy
LJrs,
To,,,rbrio
02
a rou c,ry_
qae, CC"lrn
Hl l o B e A e Ml , I 3 M e p e H n f] l, ; e x a x < 4 O f ir o q x e
Xi, .rar-xiiKet.O
EAI,'HCTBeHTII,I]i
nyTb, Ko'IopbI]i IIo3Bo!,IfleToiIeHHTb 3HaqeHIIe
JIiCnepcrr )' Heeas'c'i4o or-AacrepcLrr x.
oa'ar<o ;;;;;;;,"
5s^
AaeT ouerrr(y Ar.{criep^cHl.r
02 B TOM cJryqae, ecJrrrHarua MoAeJibilira_
B H J b H a ; e c J I H) K e H a u l a M o A e J I bH e n p a B I z J I b H a
g ,r o 3 H a r { e H H e[ p e BOCXOAI{T
02 Ha HeKOTOpO^e_
iro,'o)K'TerbHoe rr}IcJIO, Ha3brBaeMoe
c M e q e r { H e N 1L. l c r o r b 3 y x s s a , M O } x H o I r p o B e c T H
Ancnepcuonrruri,l
aHa,'[r3' IrpHBO.4guuIriK OTK,'IOHeHHTO
l{ydreBouffinore3br ts d,I}o60]\,1
II3 rtsvx cJiyqaeB, Jrrr60 xofAa H3DfeHq;iBOCTrr
Ha6JliolleHeii crlirii-
210
I-t1loTc3a
,.Irirrlrq perpeccltIt Iloilqr{Fiefla
HHe .]t{,qeH i1fl A H )'' Ec.rrlr
'l O 3l0
Ol "ltili.re aCjI fJT HyJItl,
jlclrhi0: pziccefirlire 3HarleHtlfr
t{€P€3 cPeiiyc,'ioBrlio: t,Hil iip(rio]irT
l{e:rtll i!{}"i0
I
(
O
r
{
l
r
l
r
l
l
l
i
l
i
e
l
l
r
!
i
)i','nosci'i
:l-KB!iB:i''ieIITliS C'ile-i'l'i)lll'el'iy y'f lllpiKHe
.ii'iill:l iiefpecillli
)' cluocti're.lbllc
\I€;!li,tilgyrlCMl'1XI)aCCetlHneOTi{0/'llli€ilhii0t'i)'-'r''ti)::rr50i1:liL'lii
^li':-oll""t"tn
(cr:0,CI).
Ec"rit l/n ;''-1'g;1'
),'l,ijiretlb 3Harlui{oc'rlr
,| t ' 1' '. \ ' z : b
ieile:
i
v
;
=
'
'
.
F
p
a
c
j
r
p
e
i
i
e
i
;
e
l
i
1
1
l
'
J
cTii, iicll!Ka iioi(qliHjleTcfl
"
i I COcTCi'lT pl:J :lflai
)
'
)
J
;
)
c
.
'
B
o
6
o
A
b
r
,
I
i
p
l
l
'
i
i
i
q
c
c
l
i
2
l
'
r
f
I
l
0
3
T
'
o
l
,
{
'
J
I
.
t
H 1 1i ( i i
qtririj?,iipeBLiularcil{HX,F:5,99.8r,i'lilc'riiill|1oe:liI:ltieH14eKplircpllu
-lc.:1x'HbI 0',ir,rI()ir(jiii,AiteI il KplTIIrlecKyIO O6,tacTb, Ilo3lOir{V.\r1},1
qTO AHC1lep'iiiti Clii(jr-liie']il ii() JlftHlllI pefilCr-'l
O
i
t
{
'
o
f
I
l
l
i
O
'
l
e
3
y
rlllib
'i'i0
fla6J]lOACiiiitiil'
C i j t i t i e r l ' f , t l t t I a C T C t tO I I l a C r r 0 l ) C I i l l , r . O i i ] q f t l r l r . '
'J)'Uje'j1B)'31 :JHx'iille'rii'iif ili iilJq
'
r
O
I
O
'
H
a
O;1ltaii,t .I:iltie He,CMOTpti
-ii-.li'll:l .{ lic3irc"[fleT
fipe,l.c.faBJl.-'iill:
Tp.JitA, fpa(FuqecRoe
lleiiur,lii
TOrl]lce'
liill;liI:l
t
i
l
o
I
l
p
o
t
s
s
r
l
f
l
'
1
MbI B COCTOfi]lHli
ilD
' C.tiIlo.[c)Ki.tTb,
i
.
'
i
0
}
l
(
c
l
l
}
1 g x v ( - " fb s
L
I
X
O
B
i
l
.
r
l
l
i
c
l
c
K
B
a
x
{
I
.
1
H
b
t
I
l
e
p
B
O
i
.
r
15 lr or
il
B
pervi 6LL[a npoS,vpeua BTopat cl,'Bzl]Kilua. Co,r,ep;xan'rn Bc'rlLi
11-llvteDeb
bil'JC'l
il'rQ,Il
€IOB
IloC.;r
,' p oOax il3 :rt Oil CxeaNuUH o6p :ls^)-iOT
'i'1,
no:jBornrci{ltx oIleHI{Ib o2. B pe:1';It'T;:',i? '\1Ll MOilteM oilpet'r',tit
, : . e , 1 ; 1 T br,r S J I t i e . r c r Ji l I . t c J i 1 6 a f l x o p p e J I 1 L , . : ; : I 1 1 e ) 1 { - i v c c ! . e p ) K r i i l l e i \ I
j:rOJhl R oCaAKe tI fn)/6nHOii CIeACrBllel{ citJlbllCar) pe,lSpOCi.i !ailB
Hbrli r.r.rlti pe3ynbrzlroM Henp14roAiiocTll y.ilaRfieiiltt, BbiSp-auHoro
rpllBellei{bI
no tsit)poi'{ L:]iBa)KfiIie
KarlecrBc MoAenIl. ,[l auHue
B ra6r.4,14. HauecHTe 3rH TOqKltHa fparlHK il cpasllri'Ie lloJiyqel{AaHHOe pacnpeAeJieHI.re e pacnpeAe,rleHHeM, coorBercrByioillltM
r i b r Mr a 6 n . 4 . I l .
I ,l'
ill
Ta6rHaa
3HaqeHrs BJlaxnocrr{ ocaAKoBue nropofi cxBaxlubr
B,naxsocrr {fpaMMbl
B o A b r / 1 0 0r c y x o r o
o c a ! . K a)
4.14
B.rraxgocrl (rpalrMhI
Boltbl/I00 | cyxoto
ocalxa)
f,nv6rsa,Oyrsl
Ta6nuua 4.15
aHa,'rH3B cnyqae npocrofi ,nunefiHofiperpecc[ll c IIoBTopeHleM.
oHHt'tfi
,lI,rcnePcr'r
{uc.ro sa6,nrcAesuftYr paBHo n; qHcJroToqeK'
cAeJraHHnoBTopHblensMepeHfig'paBHo P
B KOTOpbrx
Hcrorrllr
Jlnneiinag Perpeccut
Orxnogegge
He.(ocrarox rorlHocrl'l
Llucrag cnyaaituan
M o x H o o 6 a ' e . u , u H l i r bB M e c r e c . { a H H b l M H
Lauuue ta6n. 4.ll
ra6n. 4.14, fiocd'reqefo nocrpor4Tb ypaBHeHrIe perpeccfiH II() BceM
Ha6,'Irc,r,eHIrqN{.
Bnt,rzc,'ieHHflBeJruqHHSS1, SSa u SSp npono!,ttrcfl
TaK )Ke, Kar{ a paHbure, ToJrbKoTenepb qr.IcJroHa6,'IIoAeHHiiyAaouJocb. TaK KaK ceiiqac y Hac B pacnopnlKeHullItMelorcfl HoBbIe
HA6TIOACHHfl,
MbI
N{O}KCM IIO.].CqItTATb CYMMY
KBAAPATOB, BO3H[I-
K a r o u y m r r 3 - 3 a H e A o c r a r o q H o f ir o q H o c r H a n n p o K c l l M a [ u u ( s s r n ) ,
cJlyqal?HoliKoMn cyMM)' KBaAparoB, coorBercrByloulyp <<ql'Icroii>>
l o H e H r e ( S S e r ) , K o r o p b l e p a 3 6 l { B a } o r c y M M y K B a A p a r o Bo r K J i o H e MbI N{OHA6,IrcAEHHI'I
IIAP TIOBTOPHbIX
HUii HA ABC qACTI.{.B C.NYUAC
no QopMyJle
xeM HaiirH Beflr.iqr.rHy
n
S S p 6: l l 2 > \ Y r - Y * ) " .
14 D7 l
KOMNOHCgTA
O6uraq Alcnepcgs
a
6
({lrc.lo cteneHefi cso6oarr
tr3]leHqHBocrH
SSn
SSp
SSrr
SSpe
SSr
4pur"pHr
KarlecrBa npu6,ruxenlrq.
Kp,,r"p"n
coorBercrB's MoreJIIr,
I
n-2
(n-2\-k
h
F-r$HreDnfi
MSn
MSo
MSl,'
MSpa
TAHHfl, TAK )KE KAK I,I CC I]ACJIO CTEIICHCIi CBO6OAbI
SSrF:SSo-SSpe.
(4.28)
C o e c e M H e o 6 f l 3 a r e J l b H o , q r o 6 b t M b l n p o B o A I ' I J I HA y 6 r l l p \ ' ! o u { n e
I.r3MepeHHf B KaxAoIi Tor{Ke, Ho ecJIH 3To cJ,e,rlarb' To aHa.rlH3
TaKlKe HcIloJIb3OBaTb
y,x,acTcr ocyxlecTBuTb 6o,'Iee roqHo. Moxuo
6o.nee aByx noBropeHlat:t Yt EJls I(a)KAOfO 3HaqeHtlfi X;, IIpH 3TOM
6O,lee CJIO]KBbIr{[CdIeHHe BeIHrruHbr SSpr. CTaHOBiITCfl HeCKO!'IL,KO
HbrM. 3rH r.r Apyflre ycoBepileHcTBoBaHHff ol]ucaHbl B KHI4faX flO
p e r p e c c f i o H H o MayH a , l i r s yJ I u [ 3 5 ] , f i p e i i r e p a r r C u n r a [ 1 7 ] , u n a u r
H e 6 y A e r { o c r a H a B J l u B a r b c fHl a H H x 6 o J l e e[ o A p o 6 H o .
aHailH3a nptiBe'
C x e n a u o 4 u Q a q t l p o B a H H o r oA L I c n e p c H o H H o r o
A e H a B r a 6 n . 4 . 1 5 . I 4 c n o . n t s y a o 6 t e 4 u H e u H b l e A a H H b I e[ o A B y M
ss pr
cHoHHbIfi a Ha"Ipl3 H BbIql'lcJIIITe
AHCnep
cKBaxL{Ha M, BbI,TIOJIHI.{Te
u s s r r . c p e a n e e 3 H a q e H l l ec y M ] 4 b l K B a A p a r o B s s " u f B ! ' I t l e r c f
perpeccl{t'f.
OTHOCHTeIbHO
IIII'HPIL7
O[eHKOri gilf| 62y.x,T. e. AHCnepCHH
n
o
OHo naxoAllrct
QoPuY,re
MSou: SSpu/ft,
212
(4.2e)
MSe'.lMSpe6
n-l
fAc R - qrrcd'roToqeK, B KoTopblx npoBeAeHbl lroBTopHbrer.r3MepeHHr{. B HarrreMcJryqae Mbr cAeJraJrH3To AJrg Bcex ToqeK, H [o3Tou1- ft paeHo nf2, rax KaK rroJroBriHaHa6JlroAeHr.rii
Yt Ay6nupoBaHa.
BoA'1urorNre,iaJrlr,qro BeJrr{qr.rHa
SS2 annxerct Mepoii Ar.rcnepcur.r
KPi/f pefpecclta [Jrloc HeKoropoe cMerrleHae,Koropoe Mo)Ker Bo3HrrKlryrb H3-3a Bbr6opa HerroAxoAqrqer?MoAe'rrH,n rrosToMy cpeAHee 3HaqeHHeKBaApaToBssrF fBJrfleTcs orleHKofi ToJrbKo 3Toro
cMeuteHflfl. MbI nox<eu npoBecTrr rrpoBepr(y [prrroAHocTK MoAe,'rH,
BbIrrHcJInq 3HaqeHHe
F : MSul(I4Srr).
3ra senlt.{ilHa nMeer oAHy creneHb cBo6oAbI Arfl Kax(Aoi'tro'iIIyTeM Bblql{CyMMa KBaAparOBSSrr HaxO.U,llTCfl
KI{, a OCTaTOqHafl
MSa/MSo'
(4.30)
Ec.[a ssrq[c,'renHoe 3HaqeHr.IeKpHTepaq flortaAaer B Kpnrr.rqecKylo o6Jracrb, To Mbr AodrrxHbrcAeJraTbBbrBoA,qTo flocTpoeHHafl
MOAeJrbHe OrBerraeTAeftcTBuTeJrbHocTlr.
Ecnn nponepKa He npHBoMOACJIPI,
TO O6E OUCHKI{AH,CNCDC}Ift
AAT K OTKJIOHCHI,Irc
MO)KHOCJIO.
)KHrb (I4Sz rl MS ou:7y1So) re orreHr.rrbKaqecrBo arfipoKcr.{Mauur{,
KaK Mbr lelaJrri 3TO paHbule. Bltqfic,rure .F-oTHoUeHHew Aono,rrHltr e i a 6 J r . 4 . 1 5 , a 3 a r e M o n p e A e n r i r e ,t B J i t e r c f l J r I { s r a n p o c r a s J r n Heiir{ar MoAe,rrbAocraroqHo xopouer?. Ha pr-rc.4.lZ wio6pa)r(eHbr
qerblpe Bo3MoxHbIe curyalrl4l'I
Arq AByx xapaKreplzcrl{K, oAHa LI3
K o r o p b r x - c o o T B e T c T B H eM o A e J r [ , a B r o p a f l - K a q e c T B o a n f l p o K c l i Mauar.
He;ltHeftnafl perpeccfis
lloc,ue Bbrr{HcreHarr^F-rprzrepua 4.nn npoBepKr,r coorBercrBufl
MoAera Bbr6oporrHbrM
AaHHbrMBbI Moxere npalirn K BbrBoAy, qTo
nptMafl Ju.rHr.rfl
HeaAeKBarHonpeAcraBnrer ;br6opry. rlro AeJrarb
nOCl1e 3TOnO, 3aBI,lCIiT OT IIpeAMeTa
HCCJIeAOBAHVfl t4 OT BaIIIlrx 3Ha-
HHii H,'tHAofaroK o coorHoueHalr MexAy
[epeMeHHbrMH X
H y.
213
a
c'
-;---:-
"
L KOpOcrb
P1c. 1.18. Teopern_uecxatrpaeKropHtl
oroan,,t 6ortl6u, c6poueHIIoftc caMo-
t
a
J
JIETA
b
o
f
o
p
o
\f,
?
.
ocl
c)
ao
r
o
ll
aat-
j
g
-!---:-t
.Vpanllerrue,B KoropoM Bce nepeMeHHblecyMMupylorcg, IIa3bIBa'
T a, K K a K C o o r H o [ I e H I ] sM e x A y B c e M Hr I a p a M HH M e '
ercr JtrrHerir{blM
rpaqlIzKaMH
IIpqMbIe iltrHLtH. Pacuupeuue nepBoHaro1 .'BorlMrr
qaJ'rbrJo|oypaBHeHI{t]c IloMolqbl,o Ao6aBJIeHHflcJIeAyrcqHX Crene'
P u c . 1 . 1 7 .B o s N { o r x H scrrey r r a l r, ' r H H e f i Hpoei ir p e c c H n[ 1 7 ] :
perpecctlt
lI TOrlllocTb atrnPoKa;tlraqxH yAoBneTBopilrrnbHilB:
.t-cylqgcTBeHilat
JdHcillrar
y;loBncrBopHTeJbHofi
orc)''r013He ,ruHciiHolt
T0r:ttocrH
atrnpoKCItiirl{HH:
DerpeccHtr nplr
TocllocrB
antrpoKfts\r-:llHIl;
cy!qecrBegitafl
ll 3Lattn;lhl11 fleAocraroK
llrHel'iHag pcrpeccll'
p
e
f
p
e
c
c
u
H
H
:
;
.
o
c
r
a
r
o
K
T
o
,
i
l
t
o
c
r
I
t
S
n
n
poilcnM:l:'ii'
crcryrcrBlle
H
3
H
o
'
i
l
i
:
j
t
r
l
i
i
l!leiiuoij
dI z-
tr'Iuoi',ta ilonilro nI,Ierb Bno.rIHe ojll)ere,rieiilloe l'lIieFille g q'r;r-tli ilepeirclilrrnx. Il:lrrpiruep, ec,xr{ ciil\tore'r c6iiiict,rGaer 6oM5)" ,' . IIpeIic6pcf eri cotii,rilTijiJJleHliel,lBe'Iijtll \1bl l,fr).,iri:rt{ ltire.icl'ia3e : i-, 'r: jeCp e l l i t i S C l t l r i O T p a e i i l O i r u l O , I i O l C p e t I O f i p C . r . e J l t i e T CCt li i o p O ' J ' i L ' i . ' . f i r i ' l ,teia rJ HZirpilB,'r€iiitoii{ ilHIt3 ycKopeHireM cDoSoAtlcfo f,rrr cHii.
( p l c . 4 . 1 8 ) ; - r e, . c r e h r e , T i t i o , I l a p a 6 o , ' I a o q e H b x o p o r u o o r t t l ' . , i B : l e ' i
TpaeKropHio naAeHr.{fl 6oLt6st. c apyrori crop0}Ibl, \IbI }I(}xieil ilrlqei'O He 3li[l'i'I) O i]:lBilCIlMOCTit l!{eiKAy ;lUyIIti IIepeMeHHbl}'Itt -i' il y
(ee l,tc;rxe'r lr {ie c}'[iec'r I]oBa ib) tt ltpoc'ro .)io'rI1]{ Iiorriyql{'lb, IJrJlpa) r i e r i l l e o J . i i o i i r i 3 H u \ q e p e 3 A p y l - y ' 1 , 3c. c ' b i t l H o I I l u r l i 3 a A t q ' i H a r o A t T C > 1M e ; j i . l ) ' 3 ' i i l M I l " l ' q v l I f l l i p l r l H l l l ' i u C J l t l n n ' t , , : M I d I l i l e J I l o J a l a erlt IIa,:llrriire uDr.irtlrilHoir cBff3H, HO IIe 3lineX,I ee QollNlbI. B tloc.leAe J)'I!rt,!1X \.{i,] \{oxieM rlo;io6iJil'ib 3llilp(rl(cl'lrTlrD)10u{ce
llrrr IByx
rliO OHO il0-,1O)KeT
)''pilBl{ellIle K rll'lCiCii{lillCti IallIlLINl B ii:i;(e}l{/le'
tl:rr'I npCflCHrI'Ib Cyl]{eCTByIOUIIe COOTITOlxeHI{lluJIi{}Ke TO'IFtO OtI]lca'ib Oopr\4y:ji:stict.tliocrir IreperlcHHbIX,{ I1 }". TaKIle yireBHeI{iIti
B i i 6 : t l t a r o l ' c ' l I l 1 1 ' I C M y ,q T o c l l - \ i . i o i r l c l ] i i , t { -.r\ ' - i i l e T c r ia i l f l p o l ! a l t M I I p o Bii',rL \iHCi'ire l(":iilaei,l rf y tniilttii, il IICllc.[b3)']OTCtl B Tex e ,jl\''].itix,
liorAzl I4cjilFtiIblli BlrA tf ;'rititililr Heil3BCc'ieH.
BosvorxHr'r p a3,rri lrllbre r rin bI aufi p oKCuMIipyKru-(ux SyH KIlfl ii, fi o
qaule Bcefo H(rllo,lb3yefcH iio.rllilloMllnflbHi]fl annpoKcHMeullfi, 3aKJiloqarcularrcfl B TOM, qlC fJ liaqeclBe IlpH6"'lll)Kalouleii r!yurultll
B.br6HIlaercfl cyNlN{a Ue!'Iblx crenetleli He3aoilcl.{Moii nepeltcn'xot'i:
Y i : b o ) r b J i a b 2 X i 2* b s X i s+ . . . ' + b * X i ^ .
214
(4.31)
H C i i r ] P I I B O A I i TK T O M Y , I . I T OI P A O I ] K H A q H H A E TI ' C K P I ' I B N f l T b C AO. A I ' I H
jloiro.iir{lrrerbHblft gJIeH 3acraBJIfleT npflMyI.o l'I3MeHIiTbHzKJIOH,BTO'
poii jiono,[Hured'tbHbtit t]fle]l npl.lBoALIT K Bo3HHI(HoBeHI'IIoAByx roqreK nepeili6a u r. A. vse.uHqaBaloulatlcf
HCKpI.IBJIeHHOCTb
IO3BOIjoAxoAHTb
K
I{CXOAHbIM
roqHo
6o,ree
AaHHbIM.
.ll]rrilil
Aefi/'rrrtr
CTBHT€I'II,IIO, CC,{E ITi,]CTO AOIIOJIHHTCJIbHbIXTITCHOB AOCTIIIHET
(n-i),
ro JrHHIis fipoilAer rotrHo qepe3 Kax(Ay]o AaHHyIo rorlKy.
O A r r a x o B n o c r p o e H l . t r { T a K o i i J I l . i H u HM a J I o c M b t c i l a , T a K K a K o H a H e
flBrrrercrr 6o,ree eoQexrnauofi, I{eM caMLl }tc)loilHble AaHHbIe. I(poue
'foro, Hafi6oJlee BalKHyr.o HHQopMaqHIo o
AaIIHoM MaccLIBe MoxHo
qJIeHOB B nOJILIcoxp aHHTb c IIcilo,lb3oBaIII{eM JILiIIIb HeCKO,.'lbKI,lX
HoMHaJTbHOMypaBHeHr.rH. Ha p14c. 4j l9 r.r3o6paxeHbr pa3rr.lrrHbre
pa3JIIlqTLIIIbI fIOJII{HOlt{IiaJIbHbIXSaBHCI4MOCTeII,
COOTBeTCTByIOUIHX
HHM CrerreHffM 2pfyMeHTa. MaI{cHMa,'ibHaq cTe[eHb, Hc[oJIb3oBaHHar B noJlHHOMfiaJrbr{oM
y p a B H e r { u [ , H a 3 b r B a e T c f lc T e r r e H b l o y p a B H e Ht{f, T. e.
Yi:
bo *
bdr
-l bzXi2 *
bsXis
-- IroJilrHor,rua,'rbHoeypaBHeHHe TpeTbeii cTeneHlr. Tarosa )Ke cTeneHb ypaBrreHliff Y;:bXi3,
rax KaK oHo flBrqercff qacrHbrr{ cJlyqaeNi npexblAyqefo [pr{ be, b1 u b2, paBHbIx Hynlo. florusouHa"rbHoe
ypilBHeHire crpot.rrcf Ilo Ha6Jr]oAeHHfM c noMotrlbro MeToAa HaliMelrbIUux KBaApaToB, a npo(ecc STofo [ocTpoeHHq Ha3brBaeTcg
r0a6opoM Kpr.rBofi.
llprr eurno,rHeHur.r HeKoroDbrx crarucrr.IqecKllx vcJroBufr KacecrB O a l l l p o r i c r r M a r l i r H H e e 3 H a r r H M o c T bM o f y T 6 u T b n p o e e p e H b r c I I o MOUlbrc pefpeccHoHHbrx MeToAoB, aHaJrorHirHbrx y)Ke paccMoTpeH-
HbrM.3rrr crarHcrr.rqecKnenpoqeAypbr gBnqrorcfl cocTaBHoriqacrblo
T a K H a 3 b r B a e M o f oH e n a H e f i H o r op e r p e c c n o H H o t o allails3a.
tlro6sr alnpoKcnMupoBarb
AaHHbre r{pHBori Bropofo rropflAKa
,
(HnH r.(BaAparr.rqHori
ypaBKpHBofi), Hy)KHo cocraBr.rrbHOpMaJrbHbre
2t5
Y=-1,0+1,0x
9 = 2 , 8 + 5 , 3x - 0 . 4X ' - 0 . 0 1
3 r o u a r p u q H o e ) : p a B H e H I I eM o } l { H o p e u H T b , I . { c r o ! ' l b 3 - Ynqp o B r J ' l .3 . , 3 a u e r u v , u r o
u e A ) ' p y . r , r a r p u u H o iai , r r e 6 p u , n p H B e A e H H y l o
C
r
e
I
l
e
H
I
l
H
e
s
a B H S H M Oniei p e v e H g o l i .
B
b
l
c
o
x
u
e
B
X
o
A
t
l
r
a siu"grcreMy
B
M
a
T p I { q e ,p a B H a y , l B o e H H
c
n
o
r
.
'
l
b
3
)
I
e
M
a
f
l
c
T
e
I
I
e
H
b
,
B
b
t
c
o
x
a
r
r
cartan
u o i i c r e r r e H I In o r l l H o M a , x o r o p u t i l l ! { b l x o r r l } ' l n o l o 6 p a r l K H . l y q a e \IbtM JlirHHIJIv.3ro o6croqre,'llcrBo f B,'lteTcq lJIaBHblMHcToqHlzKoM
lpOfpaMMaX llO.l.iHllOylta,rlUOia
i n11pOo r u r . r ( ; O xB B b t q H C , l I l T e d ' l b H b Il X
' r ' a K K a l ( 3 J I e M e H T F ,nl p a B O f o H H ) K H e | O
)r"Ia MaTptlllbl KoKCilt\,riiitiltr,
Bc'llltlllH-l/
;rll{rrruric'HroB Mof}'T Ha MHofo nopflAKoB IlpeBbluarb
.r.i,.-ti,reu'ic,e
nl}llBeCT}l
y
r
J
I
a
M
O
)
K
e
T
M
a
T
p
H
r
{
U
.
3
r
O
B
e
p
x
H
e
f
O
"{eBOfO
I1 C]U{eCT, rr u t l 6 X a U O K p Y f , r e H x f I l [ O T e p e 3 H a T I H M O C TB
x i , l r i . r i - . i 1 t r rO
r l e f O 6 1 r ; 1 1 ' rU e y C r O f i U A n b l eU J t l { H e L l e i t i i L n - \l r r r { t p a x , l ) C 3 \ ' " r l b T a T O M
i 1 l . ' l c ; t i i l l ) l Lp
. etrreHUflcrlcreMbl ypanueuHii. floAo_6noe paCCMOlpClille
J l r i x i i , . ' 1 u qc o j l e p l K l l r c t l B K H I { f e v e c r , ' r e l i r < a [ 5 9 ] .
Y = 2 4 , 1- 7 . 7x + 1 , 2x
- 0 , 0 7X " + 0 , 0 0 x1"
( . i p . .x r r ' 1 t a M a r p t l u b t x o a Q Q u u u e H r o Bc r a H e r O I ] C B I I A H O I I , C C . I I H
\ 1 1 , irl c l o , - r b 3 ) ' c \ {I i e p e M e H H y I oX 0 , x o r o p a R p a B H a I .4,rq BCex lia6, , ' t K ) . itr(r r i i - \ i . M u l l , t o x e l t : J a H ) ' M e p o i a r b B C e c r r p o K H u c ' r o r 6 t l t t l t a t p i l r i l { | i r , \ ' p a B H e H I , l f lC r ' I e A Y I O U I I ' IOMO p a 3 O M :
b
i:I
i:I
*,"1_
Prtc. 4.19' Kpi,norsfio,'rrrr{oMrrarbHoii
perpeccln rJrfl Bo3pacrarcunxcreneueiinepeuerinori X:
4-npt\ra!
n I H H f l , c o o T B e T c T B y r o u a qM H o f O q J I e H yn e p B O l i
cTetret]n;6_ KBa.[DarHqecK:it KpBRafl u;lt (prBafl Bropofi creneir; a _
if,iri'n, nnn ng^"u, TpeTbefi cTeseHe: ?o xq veer iBr iei ,p r o f i c r e n c s x
K p i l B"ay q
HerlIrfl c BK!'IrOr{eH}{eM
qJIeHoB.,II,ea nopnaaJlbHbrx
AOno,'iHrireJrbHbrx
ypaBHeHHs (4.13) H (4.14) rpeBparqarcrcfl B coBoKyruocrb
rpex
ypaBHeHr.rfi:
2Y:bon*bDXtbz2X2,
lXY : boZX + bt2X2 * bz1Xa,
2X2r' : bo2X2* bDXs *.bz2Xa.
(4.32)
qro cyMM14
poBaHHeBL,riroJ,rHsercn
tro BceM
-flo4pasyrvreBaercs,
Ha6rroreHuffrvr
or I no n. llepenuiae ux B rvrarpuqHoft
tto_
SopMe,
nyrlaeM
r .
f#::':,lfr:l-t;hl
(4.33)
L>X22X'2X'J L A
916
Y
ll Il
(4.34)
3 . r c ' , r e u r u rM a r l l x u b r l < o s r p S i r u u e H r o Ba, r a K i r i e c r o , ' I 6 u o B t i o l t p r f u u r r e H i o n b u t r l r a e n x q a c r e i r Y r g , ' l R r o r c qc y M l I a M r I c M e t t r a H H b t x
n p o r r : r n e i t e H l l ie " r e r a e H r o Bc r p o K I r c r o " r 6 r l o s c 3 a A a H H b t l I I .Hi o M C p a v r r . I l u e r r B B r r A Vc H a q e H u e. X 0 , M b r o i l p e r e , r f l e M 3 , r I e N I c H A
T t,
| .l:
r t , A p y f r r e s d r e r , l e H r bele p x u e r i c r p o K x n o , I ) / q a l o r c f l) * N I -
t t o ; i i e l r r €r r I u a c o o r B e r c r B y l o u r u i r c r o " r 6 e q . H a n p n u e p , s " r e I t c r n . . l. - ,I r a ' f p H u b p
t aBeH:f3'X2,::X5. HanouHrlu, qro Irpn yMHoi r ( c r r u l r i r o K a 3 a r e , r l uc r e n e l l f i c K , l a A b I B a r c T c f'l1, . e . . X o . X b : X " + 0 .
- i . . r r i r . ' r , ' r r o c r p a q u rerb r u H c , r e H r n ir,r c n o r b 3 y e M b r xn p l r n o c r p o e H l . u ri . J ) ;B H e H u f lH e , r [ H e i i H o l ip e f p e c c u l , n p o a ] t a l r u 3 H p y e Mc o B N { e c r I I ( ) - l r r l i r i , r c' r a 6 a u u 4 . 1 1 u 4 . 1 4 . f l o c r p o u M K B a A p a r u , r r r ) ' racn n p o ticu\Iaur4lo, qro no3Bo!'ruITHaM y6e.qurtca ts ToM, riro IroBbrureHIIe
cTellelrlr ilpHBo;IIrTK 3HalIi4Te,lbHOMy
yr'tyq[ieHHlo KaqeCTBaallnpoKclrr'lii u Hu. Ilo;ulHol,rna ilbras. KpriBafl nlopoir crefl eHrr, nog,o6paHuan
K 3 r u M J . a H H b r Ml ,r : o 6 p a x e u a u a p u c . 4 . 2 0 . B A a H l t o M c " l y t { l t e
y p a B H L - l r Jpr ee f p e c c r r l rH r r e e r c , r e l y r c u r u r i n u g , :
Yi : Po* prX; * 9zXi2:
122,9-7,9Xi * 0,1X,2.
2t7
Puc. 4.20. Kpunan no.nuuollnanlHoir
perpeccriu nropofi creneHu,nor'ryrreHHaH
no
3aMepaMBJ'laxuocrn,B3flTbIM
n3 Ta6nHq
4.ll u 4.14
Ta6nsua 4.16
onpeAexenlllt 3HarlHMocrtl
flHcr;epcnoHultfi auanfis Anc
perpeccg[
rloflo,'IHt4TelLHblx rt,leHoB s nerHHefiHoii
:n.-...,,,,-Fl, lr"^,
I
|
c
2
I
rr u4oS
Ro
z,
lllsn'"1lSp'"')
i:r oe^o r o,,- i SS,- , I
t
I
us,-,
| /vts,-,i,\I.s,,toi
- ^e f-p.c' c^-' I
, , : r-a-f l p
I
rll
cS( n^ r^
S
|
I
itl
_____t_l
ittl
! " '- '
l 'r ts '- 'i 'tts '
'll
ltl
_----i-
B sroxa rrpIi Mepe HeoSxoAIIx'rIie A,rff BbrnourHeHlr
fl .ar,raclreD
cli o HHorO aIIaJI[3a CTa'r.IrCTI]I{Lr
tipHHLIivIarOT
C,{elyrcil{He 3HaqeHHr:
ssr : 21363,0;
5S' : 689,8;
R2 := 0,97;
SSR: 20673,2;
S S P E: 1 2 6 , 0 ;
R : 0,9B.
.rlerxo y6eAHrbcrr,r{ro 3rraqerrusssz fi sSpr raKire l,Ke,Liilri!i B
cryqae rliueiruofi arrl]pOKCANrar-\riH,
TaK K:1ricrr]{ He coAepiKarorleHOr(Be"rr4r{}tu
}'. ](ax x,{ox<Ho
5sr,toorr<rz1arb,
60"reerlt6rar KBaI\l)a-
TUqHafl Iipi{Bafl 6.tri;r<e noAxojlfi.r r Ha6,rrc,laeMbrN{
Ar.lH}rbtM, rlgy
ilprr}ieri Jrt|Htlfl. cymlrit Ktsar,p:iroB ott<,togesirii orHocI|r.t,'ibHo
.lrrHirrr pefpeocufi ylreHbuH,L:.rcb c blT7,8 Ao 699,8. Oio t-trtli,ruoe
yh{eHbueH]le, IiO 3ra pa3Hitr,a ire tscefAa 6bt}laer. cro.li;
:Jr;lrrfi_
' fe i i b H a ,
1 ' a 6 n r r q y t l H C i t e p c i i o l I l I o fo a H a , ' i t I 3 a ] r i o ) t i H o c H o t s ; r i ) a i _r , t r { p r . i r b , A r r an p o t e p r ( r r : i o i i . r a p l x r e p r r c r t i K u ( r a 6 " , i . 4 . 1 6 ) .
I(ax i',to;xtrc; ),,BriAeTb lr:: liofi Ta6,,ti.iIlbr, cy,\{1,{a riBrr,-{p.,tIofl
lio"tyqaeTcn B pe3yJIbTaT€ Br:irtxT3HIifi cylitIL,i KIlztilpliToB ;l,ri)r Jrrii{eii_
uoii tityHxilriu s5a1 i13 ai{r.rcfr.{'lrroir cyrrtulr r(Baip.lro3 _.i.i!fi
KBaJ.paTuuuoir tfyrrrrrirIi ss,"z. 3rl
Hor]afl cyillMa r{Ba!,paroil ;m,1fl€.fcJ{
l'repoti yr'ryrruetrirn KaqecrBa 2rrpoI{ctrivaqlnt
ts pe3y!,Ib't.lle Bile_leH I { f l A O i l O J H A T e J r F r r r o fror r . i e t i aB ) ' p a B H e H L I ep e i p e c c r l { . g i . , ; t r i r - c p l l l r
(cra. ra6,rr. -1.16) rr,u B€r.rrieHH:rK
, o i o p a a o 6 o s H a q e u ) r q e D-e
el
16?
ssz-r, rrcrro!'r-b3yercn
itlrtr oqeHKr. Aono,'rHrrre,rbHoriaucnepclrii
p e f p e c c f i I i . E e g H a t l l r N ' rrobe n p o B e p fe r c f l r o q H o r a K H M X e _ o 6 p a 3 0 M , r { a K U A J l ' . C a M O f Oy p a B H e H r z rpr e r p e c c H r i .E c n u o x o u , r a r , e . n u H O e 3 I I a q e H a e. F - x p l r r e p f l r l r o n a A a e r B K p I l T U r { e c K y I o 6 , r a , , : f , -T
.o
2lB
lina,rp lr i
]icHIte
,lroc or'n"no
i
fi
n-J
h4Snz
I
i.rirrt:lr ,'r'r'':rcpct,rtl
'
ssr:
, r 1 r r r r ,1 , , , i i f , i i l l l t , i l J ' r 1 l L! n t
SSr
l"-ri
LIli,ilfaf]iillloio
npoBel)ittr
rr'.r;,jrnii
3Harr{riocrll
xrt
.,.. ,, i r.
l . t , t c l , i l l Oc l n t , t i i r t u i i .
liplli irrriert6tj'
ytscrliccil}ltl
KaqectBa
KBaApartrqHoit
annDoKcH-
II ef o
B pefpeccHio
. t r Jj l i r : r ; , , i r i , i i i q , r e n A : i e r c y r i i c c ' l ' B c l i l l b l i l B K r a ' A
I
l
e
c
)
/
i
1
i
e
C
TBSH.
,
.
O
X
l
l
z
l
H
r
1
r
'
r
)
.
3
H
a
t
l
C
H
X
e
EC.ttt,t X<e IIOJl\iilelll{Oe
t,[e-i\.{] t't
B 1 ) e fp C C q
.
X
e
H
B
K
,
l
a
A
a
3
F
I
a
q
l
i
\
l
O
i
O
I
i
e
A
e
i
e
T
i.tO, ti .ri.()itOJI'itttTC.rII'lli,li'i
c\'tI'to I{pIlrepIlii
<(ii)) Mo)l(er 6uru
or\'lcrllTL,,
ilcr,(,'xorrttuio
1,,,,,
qB!'IfleTCf'
H
e
<
6
>
T
a
l
i
l
'
l
M
trictlili'llllbll\1, R 10 Birer"{u I(alx Kpl'iTepur}
A'IIfl
<(a>) IlpeLHa:JIlaqell
jT6
rip{)1CXO.t\it'i'llOl'OMy, u'lO XpltrepHii
I'I
t ' l l ( r r r , : . i r , . r i l - l t t t O ' fC ' i t t , t O p i i B e H a T B e I I y . r i l O I i O l l 6 l ' l H a l . ( ! I 1 l r ' l l i H e i i H b I l i
r
l
a
c
r
b
o
}
:
:
l
'
N
I
o
N
i
e
r
j
t
i
,
i
l
e
l
l
o
B
.
r
i
l
l
l
i
x
n
u
H
e
j
i
l
{
r
f
:
'
r
o
l
t
1,llr.r i,,! i i
llpil
'fO BpeMtl I{al{ BX.IlaA I{Ba'IlpaTtlqllOf O
i r ' lL r ' , 1 ! l i l C O l i O 3 I i a r l l i N l O i i ' B
'iorta
l l t { a r t e H I i e K p t l T e i i n t l < < a > >6 ) r ; l 3 T
;,,ielit f,\.'ic.r (rrletlb lrir3ritlM.
a
r
O
;
1
a
p
l
3
f
l
a
q
i
i
T
e
r
'ibHLrNIJ' Br'1}ltlIliliO OX.}iOrO 'n}lL'\'tilrc; rrCitiibtX{ 6,f
, : . 1 e Hj : " I i t l o u l
r{o)l(eT oliil32'li:'lE. qio 3Haql1tr'ibI\ill tlB'rItlr:l:li:Ii1r
: ) ' i( ' r i l r i ' r r o i l t i H l l : l A B y x , n u 6 o a 6 a r i , q e l I a , . r l l r 6 o I l l l o A I I F I I i : l ; i B Y x
, r , ' r ( ' l i I r i l i i t i 1 l B a ' l f ] € ' t c l l3 I I i l t I I N { b l M .
3aBIICIl1l:ilr:c.qb
y){c
Mor, 33irle'fllTb, qTo lioppe.[rlur]oH]Iaf
rl'lIeFIoil roH
o
E
l
'
l
x
1,1(ri,'tl :1{.LiAa }'ijer'ilirluBaeTctl npli Ao6SB,rlcHI'1ll
To xo(tt-1)'
. r r r r l i ( ) \ i1i E c n l r r r H c J r o q . t e H o B n o J I I 4 H o M a A o c r l l r a e r
or
paBIlbIM 1,00 tlesaellcltMo
3qlqrltii.ileHr KoppcJ'tflUl.lli cralloBl{Tcfl
i i : c i t c u u p a : 6 p o c a . u . a i { H b r xr o q e K . O A n a x o [ p I i B e A e H H b I e B b l l l r e K p l l reptiit itor(zl3btBalor, rITo yBe.rtuqeH[e Kogqb0uulleHra Koppe'[flul{l{ IJe
H N { e e TC r a T r . i c T u q e c K } t Xo C H o B a H H f i .f l p H 3 T O M e C J I HC p e . ( I I H e 3 H a q e HHfl iirr?,np3ToB o1 K,'loHeHHii yBeJii'iqH;alorcff, ro 'F-orsotuenue, xa-
219
paKTepI'r3yloulee3Har{uMocrb aIInpoKcliMar{LrH,
yMeHb[raercrr.oteHKa ALrctlepcIiIrqacrHqHo saBHcIIT or qlc,,ta ira6.trcneHrrii, ucrrt.r,,tl_
3oBaHHblx,(,1q ee Bblqucd'IeHIIf
, vrJrrlor qr.rcJlacrenetreri ceo6o!.1t.
lloc"re4uee nocroqHHo yMeHbIUaercfl ro Mepe yBeirHrrertfirrq!rcr,ra
x o a Q Q a q u e H r o BB y p a B H e H r r r p
r e r p e c c r . r HH
. inoi.lnl,u (cu r.rr.2),
q T O M b I T e p s e M B T o q H O , c TH
r ra K a ) K A O Mo U e H H B a e M o lrvi ra p a M e T p e
oAHy creneur cno60gH Ir qro xoeQ$uqaeHru b rroJruHoNifta.rrbHoro
ypaBHeHr.rEqB,'rflrorcffoueHKar,rHxoeQSrqueHroB pefpeccau p.
rlpu nlrno,'IHeHr.i'uonpeAer'reHHbrxcrarHcraqecxux' ipe6oeaHari
IlpolleAypy npoBepKli rHrrore3bro He3Haqr.rMocru
406an,rsenauxq,reIroB MOX{r'ropacnpocrpal{j.rrb Ha r{.rreHbl60,ree BbICOKLIX
CreneHet?s
) ' i p a B H e H H rf r o d ' r H H O M u a , r l u opiei f p e c c I I l I . E c , r z n o , r y q e H r l ei i o r r o J r IIIITeJIbt{brxna6,rrc,qeaufi pea"ruuo, ro or? KptrrepHH Nrui.{(ltc)
Hc_
X I O J I b 3 O B A T b A X O N T 6 H H A U U HC K P I I T C P i l E M N P O B E P K I i
O T C V T C T B I - ' fIii P i i -
6nnx<euun, unu KpHreprreM rrlrcro c,rryuaiiuoii xo.urnorreursr.
.
I ' T a O J ' ]4 . l / n p I l B e A e H al o n o , r H f i T e r , t b H acqx e M a
AItCireDCr.{oHHoto
a H a J u r 3 aA. ., ' r f K B a A p a r H , + i o r p
i erpeccau H O6reruueuHoii nu60pxi.r
sgaqeul.rir B,'ralKHocrlr ocaAKa.
B u e x o r o p u x c J r y q a r x H a c M o x ( e r a H T e p e c o B a r bH e r o J r b K o r r o -
TYqEHI]E OIICHOK B 3AAAHHbIX TOqKAX HTI,I OTKJIOHCHI,Ifl
OT JII|HHH
pefpeccHll' Ho 14 ee HaKr'loH I.I 3HaqeHae, npH KoropoM 3Tor
HaKJIOH
H3MeHflercf. B xaqecrBe npHMepa 3aAaqH raKoro rrifla Mbr pac-
Ta6nsua 4.17
Pery,tlraru AHcnepcnoHHoro
aHaJlx3aArc onpeAereHrs3HaqrMocrfi
KBaAparli,rHofiperpeccr,r,coAepxaHnn BoAbrB ocaAKer r,ry6ntrrr
Hcroquux Ir3\teHquBocra
Cyrrlra xta4
PATOB
CpeluHc
KBallpaTbI
I-rDqrenall
,rlunefisas perpeccfiq
:277 .83a
:98.96
O6uraq AHC11epcfiq
alra,qpararH,aa
perpeccHr Bbrcoxo 3HaquMa.
pefpeccHr n-pHBoArir x 3HaqHreJrbHoMy yryqneHHro
c^,,^.-.1.{":ao":lrqHae
gMalulr no cpaBHcHHpc .nuseilsofi perpeccuerl.
220
xaqecri};r aflrDoK-
n oT b C K B a X { u H e '
CMOrpriM crparurpa$tlqecKyIO 11OCJIeAOBaTe,'lbHOC
'tacttl
noo6vpeHuori n nopo,qax HI'I)KHefo naJleo3ofl B BocroqHofi
gB;1fl,locb BoCHccd'teAoBaHI.{g
feo,'IofHqe.cKoro
I_le"rrurc
Oxnaionu.
c T a H o B ! ' r e H H ey c l O e u f t , c y x I e C T B O B a B U H X B O B p e M f l $ O p n , 1 H p o e a u l t r
H
or,lo;r<eirnir. LI:y,leHHat roJllua cocroltr ll:J c,'IocB aJ'leEi"o"lurIl
t
I
T
o
I
I
N
I
e
I
oT
o
l
l
l
l
K
o
T
o
p
b
l
x
AonycKanocb,
riecqaHLrKa,oTHOCI-ITeJ'lbHo
IIp€AIlortO}KeCAe"raHO
feOJIOfaMH
6u,rO
IlpOHCxox{AeHHe.
),.loDCKOe
Mepe
H11a,qro ocaAoqgrtii 6accelig 11ocrerleHHo IIano,'IHflJIcg, 11, no
KMecrro
HarrpaBJreHLrIO
ilLr]ginfl,
npoABlrfa,'racb
TOfo KaK 6eperonat
TOIroatO)r(et{t{toCKBaXUHbI, MOUIHOCTb1OCJIeAOBaTeIbHOO6pa:OeanTbItUItXCrl Ci-'IOeBIIeCllaHHKa yBe!'IUqUBaJIaCl. TO,rUa HaCql'ITbIBa,'Ia
H3Mepflrb
Ka>KAbIfI
ariue
o6peueHttreJlbHo
Nf
6r,I
.51un anoau u 6st,rO
C"IOR
i r : : i H H X . B r t e C r O 3 T O I O 6 b l , l a X 3 M e p e H a M O U I H O C T bK a i K A O T O
n3MepeHHfi
(3 Nr). 3ru
irecrr:rritjKaqepe3 HHrepBa!'I B 10 Qyron
I.lHrepecHo 3Harb, c-VulecrByer
feonory
rf)riBeJCHbi n ra6.l.4.18.
OTAe,YIbHOTOCJIOfl I'I O6qeft
3aBtiCtiMOCTb MelKAy MO,XIHOCTbIO
"lir
t{TO CyMMapHag
rroulnoCTbtO HaKol,rteHHOrO OCaAKa. OrlterHV,
a MOilIHOCTb
roql{ax'
rfgrcuponauHblx
B
l",lollHocrb X usueptergg
rrHAirBrJAya,'tbtlblXCr'tOeBpaCCMaTpl4BaeTcq I(aK CJyr{afiHatl BeJIIIqHTa6.nnrra
4.18
M o u l u o c r s c r ' l o e n n e c q a H [ K a B K J I a c r H q e c K i l xo r l o x e H l t t x
HqlxHero nareo3oc n Ox,naxotue
HHreDBa,r.\, $Yrut
l0
20
30
40
50
60
70
80
90
100
ll0
120
130
140
150
160
170
180
190
200
210
220
230
240
250
I l o u r H o c r b Y . . u r o r ' l u nl l t t u r " o o u n . { , $ v r n
ll
qt
7,1
5,9
6,2
4,1
3.9
5,0
44
6R
50
6,I
7,7
7,0
5,t,
9,8
6q
5,2
6,8
8,5
7,1
10,4
6,7
8,6
A4
260
270
280
290
300
310
320
33(-)
340
350
360
370
380
390
400
410
420
430
440
450
460
470
480
490
500
M o u r H o c r b} ' . g o i l r m t
8,5
8,9
10,7
144
tE o
1 2, l
15,3
9,0
ll ,2
8,9
9,0
65
11,0
t? o
ol
lt ,2
t 7, 3
15,8
ll,l
ilI
l8,9
9,6
t 7, 9
12,8
15,0
221
rI
tr4ttutr'tl'l
Ha, qro rro3BO,rrrieTHCIrOJrb3OBaTbperpecclloHHyIO MOAeJIb.
B
3aKJlnqarculyrcctl
fHrIOTe3y'
rlpoBepl'ITb
c,rroBar{I4,feoror loJIX{eH
oTHyJItl.
o
T
,
'
l
l
{
q
a
e
T
c
f
3
H
a
e
l
z
M
o
i
r
l
q
r
o
p
e
f
p
e
c
c
H
r
{
x
o
a
t
}
s
H
u
r
r
c
r
{
r
TOil{,
r o n i l c a H H b r M B b r u e N { e T o A o Mn o f l } ' q e r l o y p a B H e f l o c . n e r o f o r ( aH
l v l o l K r l o o U e H l l T b A H c l l e p c ] 4 l ' oo T H o c l i Hue perpeccvu Y;:bc-lbrXi'
BeJIHTIHI{)IflfSo. flOc.leA}Iioio
IlCIIoJlb3yf
Te,,rbHo JrlrFrrru llerfecCuu,
t-cTa'IllB CBOIo oqelleAb I\{O)KHOUCIIOT'lb3oBaTbA'[tl BblIIllcJIe]l]',Iff
C'III KH:
(4.35)
(MSn),
c n e a u e e 3 r i a q e H l i t r i B a A p a r o B c, B r 3 a H H o ec o r K I C I I e H u e u
3
r
o yKa'
I
i
a
K
c
B
o
6
o
t
b
l
,
c
r
e
i
i
e
H
e
i
?
n
2
H
a
pie'o SSl, .lcnelr'oN{y
H
a
xorurS
S
x
r
{
B
a
I
l
:
l
r
o
B
c
v
i
l
r
M
a
I
4
c
i
p
a
B
r
'
i
e
r
r
r
r
a
r
4
.
1
2
.
r
a
6
t
.
;;;;-"
cfl n0 $opvy.ne
tl
5:y :
tE-t,."
#,'
3r'a
tsertrqill{r
I
91,\i----{2Xrf
n
.
(4.36)
IicnoJIL,3yercfl n!'Ifl IIpoBepKI'l o-rHoil H 3 f u l l o r e 3 :
l) Ho: pr:0,
2 ) i l o : P r( 0 '
3) tlo:pr>-0
rl p 0 i r i B c o o 1'B'l T il T Lr,\'I J tli IJ )i a "qb T e p Ii a T l'l B :
H1:'P'SQ,
p1>0,
Ht:
Fr < 0 .
Kpl{I l e l ) B o r 1 i ' l ' . r i c r l l o rf li l l l o r e j L l 1 p € 5 ' 1 ' e r
Ilpoeelxii
" i B ) ' c f o i r o H IIIali,'IoHbl
{efo
TCIt.tji.-Tari KaK I.t ItoJox{HTe,l1bltbIi.i, 1i oTpHu,lTe/'IbHblii
tlB'IIfiioTcfl oAiltHBtrj.flT Ii et) of li.ioHei{tl:()' /ii:'l Spyrlrx KpliTepnf
o
TBeTa II:t c'[eI
l
I
l
o
d
'
i
y
q
e
I
I
I
i
l
t
(
'
i
)
.
'
,
O
t
.
3
i
i
l
l
l
l
T
C
p
(
,
'
C
O
B
a
H
I
uLc;c;noHHui\itl.
c
J
t
o
f
l, T. e. iroJIo. l y r o t j i t . i i l B O I l l ) O C .\ . B C . r i I l q t . i B l e r c r . - i i l N { O i l I ] i o c r b
l
\
'
1
e
;
K
:
1
)
'
l
'
{
o
u
{
H
o c T b looT ' r ' c i i b ) i l . i T e J t e Hi I H l l e l i , ! . : ) l l . ' I l l H l l i l f e l 1 3 . ' ^ ' - - '
u.ea'lcil
ritiul'lx
quo.cTblo?
nJIfl
no3Toiri]
uo
rr
c\:]5li;il)iroii
Irofo c.[ol
o
L
H
O
C
T
O
p
o
H
H i I \ ' lC
IloAxoArJT ncpBat ftiirore3a' Iillrlrepuu.. 61r5er
C
n
p
a
B
l
'
H
O
I
l
p
S
c
l
l
o
.
'
1
0
)
K
e
H
r i'nAH, 1' ilri,tri c c K o f i o 6 ; ' l e - t L l o ,
j\loliieir 6r,tcrpo BbtljlrcJillTb Iieo6xoAliI'11'le i{"Ii.q KpliTi'irllt
3HaqeHl.lfl, I.lclloltb3yeMble B 3TOM Iiplt'l cll) il i i'
,.i-.i| i rjilltbI. Hexoropue
nililBeAeHbI HlIxie.
J''
e;rlic pcrpcccllli: \' =- 4'25 A'02AX
l-1-'al:l
S S , = ' 7 3 09 4
9Q'i:a25,18
S S r : 1 0 , 11 2 5 0 . 0 0
SSr-,3,t5,;O
p2.:n i.i
R-:0,76
,rq
HcxoAssle AaHHbrecoAepx{ar 50 Ha6.nioleH}rir, iro3ToMy Be,r}rquna SSo coorBercrByer 48 creneHflM cBo6oAbr. .[lpn 50/s-HoM
y p o B H e 3 H a q I { M o c r H( a : 0 , 0 5 ) o A H o c r o p o H H e eK p H r r 4 q e c K o 3
crraqeHile t-crau4crr{Kt't npn v:46 creneHflx cBo6oAbr paBuo 1,68. 3naqCHHC t :
CTATHCTHKH PABHO
0,02
&:
-ROq
l/6 ntoNN,oo
flo,ryueuuoe qItcJIo ,lexl.rr B Kprirlr{ecKoii o6racrn, r{ nogroMy ML,r
fltrroTe3y o ToM, qTo Har(JIOHnpgMOr?pefpec,(oJrlr(HbrOTKJIOHI.TTb
paBeH HyJrro.floc,reAoeaTeJrbHocrHfipucyua
cHir orpxr{aTe,IeH r.rr'rl1l
He6orbuaq, Ho BnoJrHe onpeAeJreHHaa reHAeH(trfl yBe,tuqeHltfl
} I O U I H C C T T - IO T A C d ' I b H b I X C J I O C B .
J-llrlree.lerrnbrilro,'rbKo qro KpHreptrr?fl B,tflercrr qacrHbIM crryqaE}I KDIITEPH'
,, : -
br-Ft
(4.:l7J
l,,,izs;_]sq
IlpoBepliH iHltole3bI,
3aKr'lIOqltloueltcfl
peri)ecclrrr llrieet HeKoTopoe 3apallee
Lr To],{, 11o IIaKJIOH !'Irt3a.lairili-e tlraueurre 1i1.
r l I a c c l v l o ' r p e l i r r ocl r, r ) ' q a e ( x p l l r e p l r i r 4 . 3 5 ) . j l r : i ' t c H l i ep 1 p a B r r o
H \ ' , : ! i ' I 3. r o r r < p r r r e p r r i ir,o u H e e , l r e i i c r o p i i r i e r o ' J a . i l r o B r i , ] , H o crrIb[ i,e CT' 3,11;ii.liul Illill,r!leHetlile
B
aHa-'lli.lrl lDe..,leuur.t:i pafoB
Iii)e:,ieHllblli
lrtl.lOB. .&lerOit t
ociIOB:iti,r IIil I]pe.Iiio,itoi,t(eHIIil c6 o-r'r.
I . l r V L i a l e ] , i i , l. : f : l i { i . i i , l - \ : ,
e . L { ' fO i i ; l l { J l O i l J - l l l f i i l i l
C ) ' - iC l ' ! i l i l
1'llell;1.ii 3
pci l-jir'-)iii {ro crircueHt!ic
paBerr H\'"1io. Fc,i[t rperijl
:tlIaIii3e
or:r (ii;tri cr:ir llaccio;l]iltii)
cyr{cci Bye'f, To ef o rr!';t(Ho '{cri]aHlrrb,
l i l l . . ' l L i J l l a . ! l t J U p e : , t t t t U i ' i X l ; l - l O L l , o i , i C ' t \ 'j , ) l U \ ' l l , ' l ) . P l t : r , t , I i e
I ' l N { e i C i l 1 i ' i e : } H a q l i T C , l i L , H O l O , r y t l i - i e i , 1 } i U i t ) I p e H l . z l , H i l . j b i B r j l l O ' lC f i c T a U H O HairHLil,Il.t. hc,rlt
e;1i]IIHLI]i
I{ Bij.J}iciiiloi;
it:\'lee'fct
\:c'foiiqli$!rii
lt.'tit ilailpall.iletf-
lluit TpeHI, To prjX Hii3brrJaeTCti 3U-:llilu!ttliiili,:t{. ir"'Tti HecTat.tirolt:l l)HLi I,t.
rlioii perpecciit! )il1i--),lrllrt;rr:J ]rilelllioJr))KeHUil B t irr)l);iti
"riitii.
. l l i C l C t l I i p e J i l O J I O I ( e H l l eO ' 1 O l l I , i l I 0 - r l l C I l e i l r i , : i O f H O r J l l ' f e , [ b l I O , r ] l l I i r i i r i r a i ' p e c c i r r r i r o c T o r t . t H a . 3 T o - \ , , r o l i { Hi0j p { - , r e i } i l fb c I l o i l { c l i i L r c u c e " l e . i O B i . l l l i lL
t l) C l a T I { O B\ 1 e ) l ( i l VJ . : t t l i i i r. \i 1 1 li l r . - r r r i ; , i t t i . : . l t l F
. lC.'itl:lliCi l ' J 0 i : U f l i i i ) c - r ' C i ' t J r l aT, 0 O C ' f i : t j . . i .C
I i -1l t a : . , ' ; i r i ; 0 . - l e . - : ; t . ! i {I ' i € l t € e l ) i ! i t i t O i : . ) i i ) L I ; r i O , { O C r) , K O . i C. r l l l : l l t t J - ; ; , - , g 1 ' 1 1 t, ,' -. , ' , r . : . I i \ t , . et C ) r r . ' lC i
l , i ; i r l l o B I I : 1 _ . 1 Ci !l tl e
t e u l r i l ) i i i l i , i r i o , : i i i u i : to ' i I ( , i o ij c ^ i i j , t j u - i l i t l l e p c i l r l H e
I ' i i r ; , . er i t u i r l l o c l c t l l i l o i i .
(.BoH
Sili 1t:.t vcitoLlltl .llt,lir-' :,,J"tvrtit,rIH
i i t i ' , i ) " t b t { oy c l p a u a i o u l H e i { : i 3 u J : i t : a : f o } { o c c . , i . i . T i ; u i i o c T t lA , l r { n o c l o t i r r ] { o i r j { H C f i e p c r i l t H f e ] ' c i r c } , _ c I i L L ' , i ' ; l i i H o c t I l . i , l i rr i . ; } i € H } r } o u e i i c a
, I i i c t ; i l l l c l i r i . E i , t c r p i , r r : i H H e r l o , r l i { e . ro r r n b i i j i ] l o c o ( j o l 1 ) e A e . { c r r r r t
l r i i i i r u 3 t l e H e H u f l A r 4 c i I e p c I U o T t i o c I l t e J I b F l od r r U H i i l i ) c r . p e c c l r u c o c l o l ( r 8 ! i i ) c t p c e H r { r . i , ' r n H e i i } t o i i p e f p e c c } i f i J l " r i r ra i ) c o . t i o ' i } r L . r x3 H i l r l c } l r j i l
O'ii(J'-IoilcHlrii.tr4s\,tegeulle Aucnepcrrr.r B rrOc;eAou;l't €,:tbltocTr.r6\':leT
II 1)ol B,t1t.bc1 liaK 3HaqtireJrbHbrii Ii lr K,rloH.
zJ3
, [ , p y r o e A o r r v u { e H u ep e r p e c c u o H n o r o a H a J I [ 3 a c o c r o l ] r B r o M ,
qTo oTKr'roHeHHfl
o1' ,'rHHur.rpefpeccHH He KoppeJIHpylorcfl Mex{A"v
c o 6 o l i . f l o A a e r o x o p p e n n r l n e f i B A a H H o Mc ! ' I y q a e n o A p a 3 y M e B a e r c q
crpeMr'reHneocrarr(oB r o6pasoaaHl.{}ofpynn 6,rHsxttx orx,loueultit
B o A H y H T y x { e c r o p o H y r l o o r H o u e H H l o K , t H H I t Hp e f p e c c u n . f l p " c v r c r B r . r e p f l A a n o c , r e A o B a r e . n n g o c r e iai B r o K o p p e J I H p o B a H H boI xc TaTKOBMO)KCTyKa3btBaTb Ha TO, qTO perpeCclloHHaf MOAe,'lL'He
coorBercrByer l.{cxo,rnbrMAaHHbIM.Moxer raK)Ke cryr{HTbcs, qro
pOBaHIlble OTK,roHeHH
a BrOI{oppeJII'l
tl CBllAeTe"IbCrByIOT
O CyUIeCTBoBaHHu rereHHli, npeAcraBJrfltorr1uxreonornqecxtit I.IHTepec.Srtt
rronpocbr6yl1'r pacc\,rorpeHu no4po,6uee B r,'IaBe o rpeH,r,-aHa/III3e,
ffe aBroKoppe,'rrrpoBaHHbre
no,'Io)KIireJIbHbte
ocrarxH ast6uparcrca
r ] K a r { e c r B e n o K a 3 a r e J I e i r a x o H o l u r q e c K o f o n o r e H u I 4 a J ' t a3 a t r a c o B
ueQru r{ x,pyfrrx IroJre3HbrxrrcKolaeMbrx. flponcpr<a Ha,'rrqlifl aBToNPHMC.
C TIOMOUIbIO
KPIITCPI{'ICKATIKOB,
IiOPPCflflIIHHNPOBOAI'ITCfl
i T r ' l l i H I I Hp e H t e M O f O K n O C " r e , [ O B a T e , l b H O3CHTa] lI i O BO t x , r O H e U u fO
rpeccHH, t'Ltli ox.Hofo LI3 MeroAoB, paccMorpeHHblx n paag.e,reo6
i l B r o K o p p e n fu H i l .
b I l c n e p c H L ra a B r o K o p l ) e , r f l 4 l t I or c r a r 1 4 H r e p e c u a3 a B I r c t . r M o c rA
r { o B , B b r r B , r e H r { a fnl p r x 3 y q e H I l H f o p H b l x p a : p a 6 o r o x B c e B e p H o M
Kee6exe. Ha necropoll{AeHllll 3oJlora 6ynt.r,osepou 6ut,ta npoAe-
0106paHbr npobbr, B Koropbrx o,rrpeAeJIslrocb
cogepxaHlre so.rrora.
Tpcue noryqegubrx sHa,regrzfi6lr.u oueouqHbrM,a Ha oAHoM Kor{ue
rpaHrxes 6trnH oTueqenlr 3HaqrzreJrbHbreorKJroHeHlrfl or JrrlHLtu
perpeccHr.r.O6uqso gro [peABeulaer 6oraroe Mecropo>KAeHr.re
30ilora. VIMeHHoTaKIIe MecTopox4eHr.rflqacro o6.rra4arci xpaiiHe ua:KHMH 3HaqeHrrrMr4COAep)KaHr.rft
Sorora n 60nrrueft qacru Mr.rHepa,rH:OSaHHOfiSOHbI,HO HapflAy C gTI,rM Iro[aAarOTCg H 6Orair,re
)r{ri,ribt.Kpoue rofo, B HLIX rpynflaMv LtntrlcKarrKaMll BcTperra]orcri
6o,rruNe [oa'Io)KIIT€JIbHbIe
orKJ]oHeH]tfl,Koropbre TaKxe yKa3brBaIor IIa To' tITo TpaHlxea [epeceKaeT soHy Ml4HePaJIIi3oBaHHbIx
x{ri.]].
llo Aauusru ra6n. 4.19 rpoBepbre HarHqHe rpeuAa B 3HaseHusx
coAep)KaHr.rfiso,'rora u uccne4l'fire noBeAeH?reAr{cnepcuH BAo.rrb
ililoQH,rIA.
I.lcnolreya xpurepafi 3HaKOB,oTBeTbTeHa Bonpocbr, I\ro)KHO.rrrr
t q i r r a r b , r r r o o r K r o H e H I i s p a c n p e L e j r e H b rC . r i y q 2 g r , tcor t . i o c i i r e r r r H o
r ' t n r i r { r ip e r p e c c a n ? B s l r e r a e r , r u
? r 3 p e s y . n t r a r o B a H r r T r i ? ? 1q, T o
rpilHrues fiepecel(Jla yqac'I'Ktr MHHepa,rrr3auul.t?
Mox(Ho .]ili [o.[yrreHlrbtecBe-4eHH-fl
o6 orxnogeHrflX OT JTI]HIiIIperpeccti]r rici;o.'rb3osarb 4Jlrr pasyuuorl sKCTpano"'rg[nH
C O A e p ] K a H r rsfor r o r . a B t j e i i p e i e , . , r o Br p a n r u e a ?
OprorcHa,lnHaq noJ!r.tnoMilaJrbHaflperpcccn{
! ' I A H A J . J ' I H H H A f T P A H I I I C ' . B A O . T T I H C C C H C K O T O P b I M H H T C P B A , ' I O M6 H T f i
Ta6ruua 4.19
3oJlorae npo6ax ue llpocnexr Tpenc, CenepHuIfi
Keedex
Co4eprxaunn
1lJ(rrorHlrc, Olabl
3rrrrpHre concpxrl l r i i t t n 1 , 5 5 5r r )
il
I'
1l
^
.
Parcrotllllc. Q\ /Ll
3ua'rcrlre co:lepxas r i l i r n . 1 . 5 5 5i / r )
( C e n e p i r l t i i ri,rHcrirpanrueu)
3 ,( )
q9
l3,0
18,9
qoa
2 3 ,I
ttq
2 8, 6
3 0 ,i
30,9
-?3,0
3ii,4
39,3
4 2, 9
4 6, 0
5 0 ,l
53,9
55,8
60,0
64,9
224
0,9
1'
0,5
t,7
1,4
I 'J
I,0
I,l
r2,0
ql
4,9
q
,l
4
,7
,,
0,9
1,3
i,3
6 6, 0
67,0
6 8 ,r
7t,r
73,0
74,1
7 6, 0
7 6 ,l
8 0, 4
(l.r2
8 4, 0
8 6, 6
8 7 ,6
90,ir
92,5
9 3, 9
q1
/"
9,0
12,0
10,1
(o
| , ' L
I,4
1,2
I,t
1,0
6,5
1 1, 9
l5,6
6,9
l,t
t,l
15,9
qa
3,8
1,6
9 6 ,3
9'7
98,7
1 0 0l,
0,8
(lONrrurixose[ rpanueu)
I-Io4rouxa l'roJrr.tHoMr{a,rEsoii
xpHeofi etrcoxoii crefienrr ti A:tHi-ibrr,1 MeroAot\,{ HaHnreHbLrrrix KBa!,paToB TpedyeT pcrfi3r,rirjt
So.lturoro Ko,lIigecrBa coBMecrHbrxypanHeHrtii, qro-.uo t;li,;n.,leltr.Ui
3BM npeacraBJrrJ'ro
c o 6 o f i o 6 p e u e H i l r e J r r r H osea g f l r r i e . I ( r r i c , r e : r c r B H e 3 T o r o , H a 6 o n e e p a H H r . | i 3 T a I I a x I i c c J l e A o B a r e . n il .i t . - ; 6 c r a n n
ito!lb3oBarbcq o6xrHNIIi a,IeroAaLrrrpefiieccHoilHOfOaI{a,rij:.,.rr
1i, ricf .
,4a 3TO TO.iTL,KO
6br.nOSogllo)KHo, ircnl,:oea,'iricl 60.ree iri)oc].ilr,{ B
ilLiqUCJIHTe"{bHOM |IJIaHe MeTO.{OM, tiil3t,tBIeML,rM
OpTO|OHa"'ii,riOi! i:O-
itHlioMHaJrbrrofi
perpeccueti. !,,un IIpuMeircrruq3Toro Merota ra]iubrn
noJrlKH_r,r
6urr co6pauu c paBHblMtr fiHrepBaiji.tNr14
npupaq:ilriii
no x- Heo6xoArrMo orMernrb, r{To K ynpoilIeHuro nurquc.leuuii norrEO;lur ro, qro xoar|$uuuelrrbl oproroHaJrbHbrxMHofor{J'retioil
iB.r1flI O T C fH
l e 3 a B I { C H M b r M3Hr o, o s H a , r a e r ,q r o 4 0 6 a n r e u n e H o B o f o q , , ] e i{a I{ CTpOsI]{eMycgypaBHeHHio r,re HsilleHfleT\rx<e BbrqrJ('.rerrr.rblx
- Ji,e H c B .
O_ptg,aojaJ'IbHbre
no,ruuoMbr BrepBbre rroJrBrl,'rlicbn puJc.rax
.,
r r . J l . H e O b I U e B aB A e B q T H a A I I a T OC
{ ,O T f l C O B i l i . t , t g H n r i e
t {T O , t e T I t I X
i l p o ( e q ) ' p b i H x B b r r r r r c r e ufri 4 n p r . r H a r r e ) K a r p . @ a u r ep y ( t O : S r . ; .
j l o A p o 6 H o e H 3 J r o x { e H n er e o p r r H
o p r o f o H a J r b H b r xl t o n r { H o M o B, q a H o
ttyljg* P. @Hruepa f l8l, flpefinepa H Cuura
ll7] u Moppirco:n a
. olq noqsreuue OBM cAel J / J , a r a K ) K e B A p y f l r x H 3 A a H H s xX
Jla,lo lrcro,tbsoBaHr.{eoproroHsr'rbHblX MHoroqreHou He cronl o6q3aTeJIbHbtM,
oHI.r MOfyT OKa3aTbCyUIeCTBeHHyTO
nOMOulb B aHaJrrr3e AaHHbrx, co6upaeuux c pefynrpHbrM r.rHrepBaJroM.Mu pac-
r5-201
225
otteefiue ra6n. 4.20
Ta6aHua 4.2tr
rIJreHHcreneuefi or I A o 4
Oprorouaarnue noJrHHoM[aJtbHHe
or 3 Ao 12
ri aJtfl qncJrana6.nrcAennfi
9aeHu
-l
-4
-7
-3
-5
-2
-3
0-l-l-3-2-5-3-7-4
110-l-l-3-2-5-3
3ll0-l-l-3-2
23110-l-l
523110
35231
7352
-9
l9
-5
-i I
-9
-7
-17
-24
28
rperbeii
creneiltr
_-3
I
I
t11
J
t
-l
7
l4
I
i
-7
-1
1-5
I
55
ll
-l
-l
-6
-3
-9
-+
-10
-4
-9
-3
-6
-l
2-l
66
qR
-t7
-29
I
-35
*29
-17
I
25
(t<y6HqHlte)
l0
-5
-1
2715
0417
-2-403
t-7-l-3
-42
-14
7146
35
13
31
I
01214
9-120
-31
-13
_
-t4
|
J
-17
-22
_.tD
-22
42
tl
t2
-30
-33
3
21
25
l9
7
-7
_19
22
23
-14
-zJ
-25
-6
30
-21
e2
(4.38)
\tt))ri('T5i,rrt tpe.u,cTtBr'I€Ho
B Brlrl,e
q
o
Yi:
(4.39)
i ... + drrE^i * E,
* a r € r ; * a z E z+
qJreHF,r
.'jit 8,,,
oprorollarr,Hbrx N.iHororrJreHoB,
a d.- xoeOSilqH-
eIlTln NleToAa HaHNleHbIXIi]l KB:tjlpaTOB. qI.icJIeHHbte 3HaqeHnfl I]e(t tr'
: , r\ r- r. rvrrrLu -utr: dr b
w r ^t
I l 3 n O C , I e 4 0 B a l C , fb l i O C T H
S ' r , \ 1 u t) l ' O b l I b O i i p C i C . l e H h I
. r ; r 5 . i i , o l ] e H r { i \X t
rr3 crereHH riciioMoro ypaBHeHlts perpeccrrn.
Cdi,i.iHo, oAI'IaKo, q,reHLI oprorollad'Iburrrx MHofor{J'IeI{oB HaxorlflTcfl
!roil iroirry I{3 Ta6fi riU, aHaJrorHriHLrx ra6,r. 4.20. [7o tiltHotrrfiaJrbi]bre
in0ribi BceiAa l{e"rrbreH AJLF t{aiKAo|o HaorroAeHHfl B noAfoHfe}iori
iolilcAoBaTe,lbllocTi] Tpe6yeTct oAtiIr rrJlell. 3ro HanoALtT Ha N,tbrcr'tb
') )rco6xoAIlMoc:TI,t peulet{il'I Bit)t{Hoit 3a;Ttrqu: ec,,Tr.iIIocJ'IeAoBeTe.rrb:r{.)fib cocTor.rT r13 MHorr.{x Ha6,/lio.t.etrrili, ;1onx<ua 6r,rrt nocrpoeua
r,relil, 6oJrbruafl. Ta6fiItr{a roJuHo}rHaJrbHr,rx rrJreHoB. (Ta6"ruqa g"nn
;'5 ira6.nrcAenuri
@ruepoM14Eiircorr ll9]).
npr.rBo4nrcfl
I(os$0uufie]rrbrcc HaxoArrcfl H3 cJreAyrorqux
ypanueHuli:
"o:
*-2'''
sl'.
a^:
i:/,
E
-lJ*I.
-tlzi
:m
(4.40)
&.4r)
i4s'vepeHua BJraxnocrt{ B HeKoropbrx npo6ax, npHBeAeHHbreB
;a6n. 4.11, oueut noAxoAflT Lnrfl. ucc,reAoBanuq c [p]rMeHeHHeM
sprofoHaJrbHbrxMHotoqJreHoB,TaK KaK ua6.urc4enHflpacinoJroxeHbl
c paBHbn{ HHTepBanoMB npocrpancrBe Hrzxe Kepna. I,IsuepeHnR,
BMecTec qJIeHaMI4f1 OpTOrOHaJrbHbrx
MHOTOTUIeHoB
AJIS JIrrHefiHOI c.
226
18
IB
633
-27
-6
-6
-33
-l
-13
4t2
628
428
-l
t2
-13
-6
-6
--33
-27
6
33
-}{orpHr"{ IrexoTopbrelr3 3TItx [p]rao]KeHHfi a pa:4e,ne, flocBgrqeHT O Mr p r J r b T p a d r l rBr p e r v r e H H bpi xq A o B .
O 6 br,rHoe y p a BIt eHu e rror'rHHo MHanbHo ii p ef p eccli tr
ll
26
LLlcHbt
1'73
18
-22
-17
lfJ
7
I
II
IJ
a
3
t4
-31
-11
I
l8
I
-l I
-21
l4
Y ; : 9 o* p r X ;* F z X i 2+ . . . + g n X i n* e
o
77
l9
t-7-3
I
3
l0
-1
621-3
*4269
r-3
nrODOfi CTetrel-.i (KBa,qpaTHtrlble,
-5
-4
-4
-5
-3
-l
50-3-17
5l-B
-rJ
-l
h
11255728
-2-l-l-1017
l-l-2-4-3-3-B
-l
I
2
, D
e
94
t]lc:;lr
rl37
ll
473
(xsapruxx)
t2
rlreHbr nepBofi creneHH (JluHeilHbte)
t0
vernepiofr creners
227
I]o BocbMHHa6nroAeHI'IsM'B3srbIM w3 Ta6n. 4.20,
ro nDH6nr{}KeHHq
nplrne,u,euuHHxe. VxasaHH TaKxe rpol{3BeAenws'Y u Er.
Yt
E;
!iE,
e
78
124
:-7-5-3-ll3
-868
-390
:
54
35
30
2l
22
18
D'
-162
-35
30
63
ll0
126
KoaQQHuueHrcr,ganrpoKcHMllpyn_qefinpflMoftecrl nonpocry cpeAHee5naqeuseY;: 6r,s:!$218: 47,75.
KaxAoro Ha6nloAeKoa$Qnunegr ct1 HaxoAnrcsyMHo)KeHueM
qneH' cyMMI'IpOBanus. Yi Ha coorsercrsylouHft [oJII'IHOMIza.nlHntft
Ha cyMMyKBaAparoBIUIeHOB:
HHeMsareM AeneHI.IeM
a t : 2 Y i E r l ) € t ' : - l 1 2 6 / 1 6 8: - 6 , 7 0 .
Vpaoueuue .nuseliuofi perpeccnrl coAepx(aHI1flBJIafl'l ua r.uy6uue
no3ro,MyecTb
t t: 47,75- 6,708rr.
Hcnolrsyl
o6uuuyro perpeccllrc, MbI [oryqnM
coorHolleHue
? ,: 9 4 ,6-2 2 ,6 8x,.
I\{HoIOTOMy, r{TO-OpTOTOHaJIbHbIe
3rH Asa ypaBHeHHflOTJIUqaIOTCfl
roqJIeHbIBbIpa)KeHbIuepes f,1i, a He qepe3 Xi' OAsaro ecJII{ I\IbI
srltMIt AByMfl ypaBHeHlIsMIr' To ollH o6a AaAyr
BocrroJlb3yeN'tcs
rlro hlbi
oAHy rr ry xe oI{eHKy gnn Yi, Hanpultep, iIpeAnoJIo}KIdM'
r,ly6UUa
B
I(epHe
BJIarIr
CoAepX{aHHe
rH11OTSTI1qeCKoe
Bbrql1CJItrJir{
He I M, coorBercrByloueti ceMHaAll,aroMyIi3l\{epeHHloB nocJleAoB a r e J r b H O C T t9i .n e t t o p T O r O H a . t 1 b t l o rMCH O f O q J r e H ac,O O T B e T C T B y I o urufi ceugaAqaroMy Ii3MepeHlllo, ecrb {-5, rax qro .r'Ba a.rbrepHa'r"r.rBHbrx
ypaBHeHHfl 6yeyr I'iMerb BI{A
i : 9 4 , 6 7 - 2 , G 8g q :
A,27
K
t :4 7 ,7 5 -6 ,-0 {5 ): 14,25.
C roqnOCri,tO AO OrUlt6Ot< OKpyrneHIig 3TlI ypaBHeHIrf 3KBI1Ba.teHTItbr.
npeI.rMyu{ecrBo oprofoua,'lbIIblx MHoroq,leHoB craHer
Lpyroe
oqeBtl,D.IIbII{,ecJIH Mbl 3axoTHM nocTpol{Tb anIIpoKc}INIaIIHIO C llOcreIieHLI. !,nn eroro rpec)'ercr
lroulbro ypaBHeHHq 6o,ree rltcoxoii
froBTOpHTb BCe BbIr{ucJIHTer'IbHblenpoIIeAypbIJ TO,llbKO IiOA_CTaBJIflf
aJibHr,le q!'IeHbI 6olee ebtcOrOii CTeneIIOJII.IHOMII
coornerCrUyrcQue
Ha'
ocralorcq Heu3N{eunuuu.
rru. Vxe n'aiileggue xOeS$r.rUneHrbl
npr.rMep,Ans noflyrleHnqypaBHeHHtrpefpeccul'IAJIfl co4epxaunft
qJIeHoBBToporo ropgAKa, MbIa
BJrafil Ha fflV6HHe c ToqHocrblo Ao
228
nu6epeu
qJIeHL'Inropofi
"ra6n.4.20:
Yt
E"7l
yiE, :
124
78
s68
78
crerreHr.t AJrfl BocbMn ua6rrcAeHufi Hs
54
35
-3-5-5-3r7
- I 62 -t75
2t
22
l8
- 150 -63
22
126
30
Cyruua rpou3BeAennft. panna 2YiEz:544, raK qro roe$Snrlnenr
qJIeHe paBeH dz:544l.168:3,24.
Perpeccun
npLI KBaAparHqHOM
Broporo lopflAKa BJlaxuocrr.r Ha rny6uHe rrosroMy ecrb
f ,:47,7s-6,7081i
{
3,24g,,.
A u a n o r n q n o M o x H o a [ n p o K c u M u p o B a r b A a H H b r en o c J r e A o B a r e J l b H o
no,rr{Hor,laMu6olee BbrcoKr{xcreneueft, BnJrorb 4o xpunofi ceMHaAuarori crerreHa, r(oropar Ao,'IxHa npoirra B TolrHocrti qepe3 Ka)I(.loe 3HaqeHue. KoaSSITIIHeHTbIoprofoHanbHoii perpeccLtwd, Moryr
6lrrs npeo6pasooaHbr B xoaQSHqueurul o6srquofi perpeccur p
npocroil noAcraHoBKor?n ypaoHeHue, Koropoe acnoJrb3yercx Anttr
onpeAeJIeHprfrrreHoB oprofoHaJrbHoil perpeccHr{. flera.nn cM. B
r{Hr.rfaxAper?nepa n CuHra llTl u Ocr.na H MeHCHHTa[39], xo'ropbre TaKX<e npfiBoAflT ypaBHeHHq
Lilfl, fipsMoro onpeAeneHr.tfl
pa3fiur{Hbrx cyMM KBaAparoB, Heo6xoAnuux np}r AHc[epcHoHHoM
irHaJiu3eI.i rrpu npoBepl{e sHaqqMocrr{ rrorfirroMna,rtgori perpeccnlr
rlrrrcrutlxcrenegefi.
lIpuneleHHaq rraBHas ocb
PaccvorpeHHbre Bbrrrre perpeccuoHHbreMeroAbr no3Bo.rrrror IIo'rrroarb llrueriuyro anflpoKcirl{aqr]ro
;i,rfl coBoKynHocrrrAByIvlepn[,rx
ira6,un4elrnr?,Tax qro KBaApar orr{,rcHeHHiio4nor"l I.i3 nepeMeHHbrx
1)r nllrrMofi Mr4HLrMaJreH.
Ec,u orK,'roHeHl{sB HarrpaBd'ieuu*tY uulir.IMrr3r.ipoBaHbr,
To noflyrlaercf oArIo MHo)Kecrno xoeQSuqueuron
.ttrueiisoft pefpeccnr.r,Ho ecJru orKroueHriq MuHrlMrl3llpylorcn B Ha,
J p a B r e H n r r X , r o n o r y q a e r c f f A p y r o e M H o x ( e c r B ox o e Q Q u u n e u r o n "
L:c,rrLr
3rH ABe rrpflMbteu:o6pasurt ua rpa$axe (pr.rc.4.21), ro oHrr
ilelJcceKyl'crrB ToqKe -F, Y.'KoclrHyc yrna Me)KAy 3rrrMr.rnpflMbrMri
,ri)r{,\IocBfl3aH C NOarpQUUt.reHTOr{
Koppe.lqquu [.{e)KAyx u Y.
bbrsaer raK, qro Qr.lsnuecxueycJroBrir AHKTyror Hau ueo6xoAirr,Iocrb cqnrarb oAHy rrepeMeunyroQyuxuueii Ap1,roli, HJrHx(e ueJrb
irbtllclilHgel{OroHCcJIeAOBaHUfl
yKa3LIBaeT,KaKafl HS ABYX repeMeHill,lx AO,rr)KHa
6url 3aBi.rcrzMoitB ypaBHeHHH pefpeccHr.r. oAnaro
i l r l o f A a o K a 3 b r B a e r c fH e B o 3 M o l r ( HLot 3 p a 3 y M n b r x c o o 6 p a x e H n f i p e rnl]rb, KaKafl [epeMeHnarl AoJr]r(Ha6uru X, a KaKafl Y. 9ro cnyqacrcs, HairpnMep, B 6nouerpnu, rAe 6brBaer noJre3Ho3Harb coorHoIUefiae MexAy AByMfl MHo>KecrBaMaH3MepeHuft,raKux, KaK AJIHHa
]r ukpllHa paKoBIlH,oAHaKo coBeprreHHoHegcHo,KaKoe MHoxecrBo
l'tsltepeHaii Aonlr(Ho 6uru
Qyuxqueft or Apyrux. AHa.[ornqHue o6229
1a_it2
I
I
-l
o_
G
I
I
Pnc.4.22.Kpurepuuannpor{crr{auuu
llfO u fO:
I
I
I
-1
I
I
*t
i
|
nl
/,;
lA_
10
x
12
14
13
-J
18
2A
B:jflrlix I43 Ta6"Ifir' 6-19
P n c . 4 . 2 1 . . i i l l r p l r r : , i a l j i i c c e t l H r I I , ' ' { $ y M e p H b l x; i a H H b l x '
Y'
rpuee'uennafl rJrrBHse oci:
t.r;11,"{
rirH;rtr
o"ift"at6'itt"
tr{:o6paxieurt rrrK)Ke
J."",aljl
c - trprBe.[edHrr rJraBrrat ocb MfisvlM3lipyer npou3BeneHile orKroteHnf{ X-.Yl n Y-Yt ot
t r o A 6 H p a e i l o i i n p a r o i r ; 3 T a n p o q e , u , y p a3 i i B H B a J l e H T Hrar H H M u 3 a u l l r n r o u , a , { e i l g a l x r p r r x o B r i r s b r , \ T p e y r o n b r j H K O B ;6 - f I a B H a n
O T K I O H e H n r i( . Y - X ' ) ' ,
o c b i l H r I H l r H 3 u p v e Tc y } l M y K B a . r . D a T o B
y (Y-Yt\2, B pe3yJrbrale rrHHilMH3rrpynrcsKBa;.parbr orKroHenlft tro nepncHAfiKynngy t12
K a t { B H a n p a B , r r e H l .xl l,r r a K r r e } r , l n p a B J r e H r , ry} r o r x H o B p e M e H H o .
B cu,ry reopeMbr flucparopa 3To gI{BriBa,[eHTHo
lt{uHliMrrsarlnr.r
KBaApaToB nepxeHAriKydlrrpoBorr{JroHerrrifi o'r rox6HpaeMor? rrpflMorl
( p u c . 4 . 2 2 ) . T a x a q l t p s r , r a f l H a 3 b r B a e r c f lr J i a B H o i i o c b r o r r r { o ) K e r
iiurr sarlileria KaK r"rraBHbrilco6crBeHubtrl ner<rop Marplrrbr AItcnepcali H KoBapriauufi X vt Y. llpoqerrypy BbrrrucJreHr'rs
rJraBHorZ
o c r { M b ro 6 c y , n , u m
s r r . 6 B p a 3 A e J r er,r o c B f l u l e H H o M e r o A y f . r r a B H b r x
KOMTIOHCHT.
npo6.lteMl
r.{,e O6uIaq
B nerpOOu3IlI{e'
BO3HiIIialor
t i T o S b I C 3 i 1 . l ? T b A B a ( C , 1 e , ' I i ] H i I t l X l l a 3 J ' l I t I I H b I M i ' IM e T ( ) CocToHl.R,l.o}I,
'taKlie' xal( Bp-eN{eHa3BVKCBbI'{ nePexoAoB
Il3irlepcHuli,
.lirMH) ptfa
06a rlllla lt3MepeHHfi nOABeptI li3Mepe}{Hfl trJroTHOCl'u iieiirpouoe.
II I-lilK:tiioe I'13 Hllx I]e N{oN<C'T paCcit'laTpllBaTbc:l
;i(ellbl oLLIrriirau,
ii:]'x pa3 oH€l{L IIOJIe:lllo
B sTHX c'[yrrrin"
r;aK i!,vHlitlllfl Al))riof0;
f
i
e
p
e
\
'
{
e
HiIblx' BbIpa3iIB HeKolo'
p
t
l
A
a
0
6
a
r
p
a
,
r
p
l
r
q
e
c
x
i
r
lLpeA&irBlrTb
cBa3b'
'l ) b r M O 6 p a 3 o M H X B 3 a l ' I M r I y I o
-
crOg.ie.,ibCrBa
3T9 rloA6op
flep'noe peuellse, Koropoe rplixcJ,llr B tolloBy'
OT gTilil
Ha6JIIOAeHI'Iii
oTKJIOHeHHfl
MI]HH\{H3rrpyer
KOTOpafl
npflMoii,
y
H
a
[
p
a
B
J
I
S
H
I
I I oI c v
I
.
r
B
.DflMoii r(aK B HanpaereHuri'oan X, raw
pacqennnTb pa3HOC'l'bMeilioluoepeuenHo. Tar{af r'triHHrr4O,rI)KHa
x, r{ro cooTBercrByer BliY
u
ro
Y
flo
x
perpeccfiv
Ay JrirHl.rflMn
IIOETOVY
BICqATJICHIiIOOT TPCHAA B HA6JIIOACHH9X'
3VAJIbHOMV
pacceqnulo
p
a
c
u
{
e
l
J
l
e
H
u
e
3
r
o
l
p
l
{
n
l
i
c
a
r
b
q
e
J
l
e
c
o
o
6
p
a
s
H
o
6llno 6ur
eAl.ll{c'la He oTI(JIOHeHpIflM
rlaHHbtx TOrleKno o6eHM IlepeMeHHbIM'
seHilotzrepeMeHHoii or rIoA6HpaeMoii[pqMol?'
OAHtt litl4ueercs ABa MeroAa oIIpeAeJIeHHflTaKofi rlpsMo.Il'
IIpqMoil
OT
oTKJIOIIeHI',Ift
KBaAparoB
B
MrrHI.{MI{salIIiH
TOJLCOCTOTTT
230
npousBeAeur.rfforKJro,[,pyroii N,{eroAcocrol.IT B Mr4Hr]MH3arII4H
HeHHft B HanpaBJreuusxX Lt Y. B AeiicrBurerbHocrr.r sror MeroA
rrpr.IBoAHTK MnHllMH3arlr.lnCyMMbrI]JrOlj],aAer?
rpeyro.llHr.iKoB, 06pa3oBaHHbrx Ha6rroAerrr4rrMrr rr no46r.rpaeMorl I]prMoft
(crrt.
p u c . 4 . 2 2 ) , q r o n p r { B o A u r K n p s M o r l , H a s b r B a e M o foi 6 u t q u o [ p l r B e EonrulrHcteo crarefi Ha
. i e u r i o ' i r r ' r a B l r o i io c b r o ( n p r M o i l n f O ) .
r r y l e M y 6 r , r , r oo n y 6 . n u K o B a H B
o )KypHanax <Biometrics> ll <<Biotttetrilla>>,qro orpalKaer roiryd'rrpHocrb 3Toro r'{eroAa cpeALr yqellLr..:,3aHHr\1aIor]IHXcf
BoIrpocaMHpocTa opfaHrr3MoB.Xorq cBoflcTB;r rDlBeAeHlior?fJraBHor?ocfl MaJroHHrepecoBaJ]Hcrarr.rcrrlKoB,Bce
i r { c o H r r 6 r r n u l . r c c , r e A o B a r rK
be
r puaNolr u Xa,rreuou [31] u Kpacrtnou [33.|.
Pe:nlre ir,,*
A",rt feoJrofoB Aaercfl Tn.n.nou 1521,
"a.r"AosaHlrrj
:t 6o.ree roApo6Hoe
H3Jrox(eHrieuMeercq y Mu.n.repa u KaHa [36].
flpxne4eHuarr rraBHat ocb onpeAellflercn c IloMourrrlo o6blquoro ,rnHefinoro ypaBHeHurr, r{Merour,eroABa roaQQuqneHra: oAtlH,
ilpeAcraBJrflroqnfiHaqanbHylo rotIKy, Apyrofi - Hr.K,rloH:
Y:bo*bd.
231
Ta6nsaa 4.21
Cyurvru KBaAparoBu Apyrxe crarncrnxu AJIII A a H H b t x r a 6 " r . 6 . 1 9 ( c r v r .x H . 2 )
rtTo A a e r y p a B H e H H eperpecculr
X:3,97+0,65 y.
i cu
H o t l r J I a B H o fo
I'!v:25
rLx:25
h - _ul
sV-9rl7
sY-97f)
x:10,88
r-- I 'J,68
sx2:20,3
sx:4,51
ssx:487,2
\ , 2: r 4 1
bo:T-
- /"-ss;
- T S ; : ; Z, / *tl:
Y
W,
.[,ln npnneaeu-
1,09,
b r x : 1 0 , 6 8 - 1 , 0 9 ( 1 0 , g:g )- l , l g
I'panrteuiienprlroli fIfO ar,reersprA Y:-1,18+1,09 X. CpaeHetirie r{aeT C,j]eAy}Ouiee:
nepnotfiCo6crBeHHr-Iii
nexrop KOBapLIaIII4OH';r;il ltalpuql.; X u Y ecrr,
Sv:4,91
SS r':578,4
COVxy: lD,O
S Px v : 3 7 4 , 4
'/ -- -
r:0,7l
Haxlotl
orpeAeJIgercfl
Kay, o f liotjjeHiie
craHAi'iprl{ij x orK'rlollei) l ri
x u Y, unv.
JByx nepeMeHHbrx
b1:
Sr,/Sx.
(4.12)
Tax xar n oAHo It ro xe Afl,q o6ollx cran.{,aprHblx orK,rloHeHii:,
ypaBlieHl.it
b1 Mo)Ker Srtrl nafiAeHo c Ilotr'loulblo3KBIlBa,rieHTHoro
,1: J/S&/S&'
(4'1r3r
I(oe$QuuHeHr b6 rIpI{BeAeHHoftf"lilBIIoli ocll Aaerctl $oprvry.nofi
bo: f-
b'x-
(4.41)
Bbr.{ilcreHr.IenpHBeAeHHofir.rlaBHoitoctt npo.l.eMoHcrpupyeM.li:l
Ha pllc. 4'2i.
; l a H H b r xr a 6 " r . 6 . 9 ( c r r . { x. H u r y 2 ) , r p e , l c r a B J I e l { I I b I X
npou,llJllocrpHpcBaHi)!
C nouotqrto AaHHbIx ra6r. 6.9 6y;ryli'axxe
I
l
ilblr{ncJIeHHg MeTOAa TJIaBHbIX KOMIiOHeHT (Urli, UCrO,'1b3}fl T€p}lj:lrioJrorriiO HaCTOqUIefO i1aparpaOa, Iie To;-ll HaxO]I(.qeHLIfl f JiaBriL,l):
cylt{MbI KBa.(parorl I'I ncrlapHble Iipol'l3BeIeHijti'
ocefi). Cyuurt,
c p e A H r ' l e , A L r c r e p c H I I I r K O B a p H a u H i l l l p l i B e I e H b I B r a 6 J I . 4 . 2 1. 1 4 c .
rioJIb3vf trx, MbI MOXieM CHaqaJIa Bbir{fic,IIITb O6blqHyIO peipcc-
perpeccr4ri
Y Ha X
cvroY HaX H X na Y.,[,.rrn
:0,77,
: 374,41487,2
br : SPxYISSx
O o: V - b r T - 1 0 , 6 -8 0 , 7 7( 1 0 , 8 8:) 2 , 4 3 .
perpeccnlr
ypaBHeHI,Ie
€crl Y:2,46+0,77 X. Ann
Taruu o6pasotvt,
perpeccurx sa Y
SPxv
'
-374,4:0.65.
ar - TSi
578,4
bo :7
232
- btl':
10,88-
0,65(10,68): 3,97,
/ 0 , 6 6 '\
\o,zsi
:jrr.r o.rHaqzrcr,qro co6crBelrill,rri nexrop HMeer HaK,'ioH,xapaKTe'lr;ycrrtrii i'{,r?rHoii0,75 e.r.nsarl ro ocu I rr 0,65 e.UrHr.tuuo ocu X,
, n o J K n J i B l , r e u r r { op a B c r l c r B y i , 1 4 x o e Q Q r r q r l e H r ab y . I ( O a Q Q H U H e l i r b o p a R c l r T - b t 7 , - - = 1 0 , 6 8 - 1 , 1 , 1 ( 1 0 , 8 8 :)- 1 , 7 2 .
Vpannegue
i ' . { a g H o i i o c } r N r o ) K e r6 b t f r r 3 a r r . r c a H o B B H A e Y : - 1 , 7 2 * 1 , 1 4
X.
F I a p H c . 4 . 2 v r e o 6 p a > x e H b r - { B e . r : { r Hp iei }i p
r e c c n u , r J r a B r i a qo c b l l n p u B e A e H I r [ r r|rJ I a B F I a qo c b . . j a M e ' I H M ,r l i g n p r . r B e A e H H arfrl' t a B H a go c b
ri iJrasrafl ocb oqeHb rroxox(llApyf Ha Apyra. flpuse4enuafl rJraBHarl OCblle.[H] irorrc),'ia\r]'ro"r Mex{Iy .rllluneii perpeccH].rY g,a x n
. ' ;: l } i r n c i 'pi e r p e c c n r {x n a ) ' ; f J a B r r a r o c b c o o r B e r c T B y e ]r' r e c K o J l b K o
6 o . n n r u e fIi r r c r r e p c u r {Y , u r o c o o l B e r c r B y e ' rn c e o p o r y H a q y r b 6 o . n e e
;'lryrOii yro,r.
orun6i<r xoaQ0r.iqaesron o6enx nprrBeAeHHbrx
Crau4apruue
r'.raBr{brxocefi MoryT 6r,rrr, .nerxo BErrtrrcJreHEi,
SaTeM MoxHo c0op:"lynapoBarb ltpH6Jrn]KeHHbreKpHrepun 3HaqilN{ocrr.r.O.(Haxo He
c lul€crB 1l€r 3 KBr.{BaJreuroB
xopotx o o6ocHosauHoro AncflepcHoHHorc
:lr{aJIn3aToMy aHan}r3y, KoTopbili c,reg,yer BbrnoJJHLITb
n yc,rcauori
pcrpeccurr. Crau4apruafl, owr46KaHaKJroHafIfO pauua
se,, t,{F)
(4.45)
lr.:sHnaJreHrHocrbyrnolux xoo$QI-IUrreHroBbt u bz AByx [pHBe.'ti'HrrL'tx
fJraBHbrxocetl Mo)KHorlpoBepirrb c rloNlou{bior(pHTep}rfi
br-b,
o
-r
i.-_
--;---q/
V sci,-sc"r,
i4.46r
r '..irrOpOM ,lIefKO ySiizlTb Bapl{aHT O{i{OrO I'13 3,[eMeHTapHbIX {{i,,'{i , , r i r c l , 0 6 c y l K A e H i i b r ; t H r ; . l . f i p c u e p s e t " r a x crarllcTllKa il y ;:'::.i '
: icilelta !l[]rI6;ii3l:Te,';bHo ]i0pMeirlbHo Il ee 3It aqE 11Oc'I'bMLI)ri:':
u i i r L olrpeAeJleHa nr 1'a6Jiaubr cTall.:,apTl{Lrlo HCTIJL{7r
JlbHCrI{} j) ;,:1'"
il i)eAeJjegHfl.
23ii
Crau4aprHan outu6waonpeAeJreHHaxoe$QHrllreHra bs paBHa
Ser": S"
\4.47)
)
iieeeircrno (4.47) Mo)KHo lrcro,'rb3oBarb AJirI nocrpoeHr.rr{npil6ru3H:]rie)iieHHbIx AoBepIiTeJIbHbIXlIHTepBaJIOBA,'iU BbIqI'tCJieHHOfO
trs,F^bs. AHa,rorN,rrrocrar{AaprHilr{ oIIIH6ria B orrpeAe,'reHIirl
JrfJoBor o r o e Q Q n q H e H T a M o M e r 6 H i ' r n c n o J ' r b 3 o B a r {iaj , , I f i o n p e , l e r e i l J i s
n p u 6 J n 3 r 4 r e J i b l i o r o! . o B e p l r r e J i b H o f ou H r c l ) i l a J a B o K p y r b r . B c ) ' u t IiCCTLI, BOO6IIle 6lt,lO
UenpaBOI,lCpl{0
IiCilC.r6'lC-qilTb KpLITepllll
Iil)o-
EepKri sHaqirMocrH xo:cp{lr.iuneuioe rprlBeIeHHoii r.IlaeHori oc]rr.
I l . r - : a o l c y r c r B r r r r e o l ) cr i ! r r c c J i o r oo 6 o c r r o a " l i r ; r 3 T r r x r r f o i J c , 1i \)
nprJBeAenIrarr,'raBHar ocir r,{oiiie'i 6l,trt uciro;ib3oBtIIt Ar'Ig ueJreji
till{CaH}ifl, a He A.rlt Ilpoll:pl(II CTiTTI'iCTliriCCI(Oii
3He qHMOCTH.
ci':JIAijiItbt
Hexoropue AaHHbIeyAo6Ho ilpeAcraB.nfirb ce6e KzK crp1ru61s
rrpocTpaHcrBerrap KoopAr.iHar,T. e. Ha6JrroAeHrircocroflT H3 H3MepeHHti AByx cBoficrB, coBoKyrrHocrb Koropblx MolKer paccMarpl{npocTpaHcrB a r b c r l r ( a K n o c J l e A o B a r e r ' r b H o crrobq e K B A B ) r M e p H o M
Be. Anq qeJrerl HafJrflAHoro npeAcraBJreHHflxeJrareJlbHo cBs3arb
3ro c IIo3Tr.rrorrKH rJraAKor?Fre[pepbrBHori.nuuuerl. Mu c.r,e.uaeM
MorrlbrocnnaftH-syHKuxH.
Cnnarinu ecrb orHH l{3 rrrupoKrr)iKJIaccoBKycoqno-onpeAeneHnux @yHruHfr, Koropr,re r{ofyr 6urr lrcno.lb3oBaIlblArq npeAcraBr'reHHt KpHBbrx B AByMepHbIXUr'rH B TpexMepHbIXnpocTpaHcTBax.
A{.arerrrarHqecruiicnrairH IIorytIIir cBoe LIN{fl6r'Iaro!,apfl Qt'tsHuecKoMy 4noriuury, ra6xonay rreprexHor\,lyr.rncrpyMellTy,cAe,IIaHHoMy
Irs yst<ofi rroJrocKlrAepeBa H,'IHnJIacrllKa, Koropblt?ltoxer AesopMlrpoBaTbcs, rlpHHriMaflnl,o6ylo Sopt'ty B coorBercrBHll c KaKI]M-JIIloo
o6beKroM HenpaBrlJlbtloriQopvru. t{eprexiiluii HHCrpyMeur 3aKpe[<yrKaMI4>>,
KOTOpbIesLrKtl'lprrMH,Ha3bIBaeMbiMI,I
rTeHCBUHTIOBbINIH
ctrpyror rroro)KeHtle IrHcrpyMeIITa B ToqKax ItpIIB13Kri. Mex,1y
<.:yrKaMrI>>
HHCTpyMeHTn:rn6aercg raK, qro6bI noJlyqI{,'lacbrJIaAr.:as HenpepbrBHaflKpr4Barl.Ana.rornqrro MareMariirlecKuii cnJIaiiH
o f p a r { i l q e H o n p e 4 e J r e H H b r MTno q K a M I { ,H o M e ) K A yH I I M T Io H t s r l t 6 a crcfi "raK, .rro6lr B pe3ynbrare IroJryqHJIacbrJIaAKo Il3Melttlrcu{aflcf
JIHHH'I.
HLI aHaJ'rIrruqecKI4MlI tpyuxultrutt,
Hn
Cn"riafr.Hu He qBrqlorcq
cTaTIlCTgrlecKuMI.I MOAe,'IflMII, TaI(IrMH, IlanptlMep, KaK IlOJTHItON'II{aJ'rbrrrr irc|peccLIfl, olIIIcaHHaf paHee. cxopce oHII tB"ritli]Tctl coi ; e p u e H I i o n p o H 3 B O J I b H b I M HO 6 b e K T a M E , J I I I I U e H H b i M I IX l l l t O r O - , t l l 6 O
'ieopeTi! ,iccxoro o6ocuoBaHHff,, IICK,'1iOqafl'ro. qr0 oiilrl oiipe]{e,rtioT
234
xapaKTepr{crriK[ caMoft nusww. OAuaxo oHr.r oqeHb [oJre3Hbr AJrfl
iiHreprroJ'rflrIHriH BaxHH s o6ecneqeHHu laqrr(oif crpyKrypbl AI{ciiJeeB 3BM. trlurepaxrzBHbre Bbr\rHcdrrr4reJrbno-rpaQnuecr<ne
cldcrer{br rro,rryqr4,rlu
6oree lxHpoKoe pacnpocrpaHeHHe npn [ocTpoeHnl.I
fco,rofrirrecr{r.rx11 reoQusnuccKr.rx\roAe,rrerl.flo,q6op KpHBbIXc ltorio[,\bro cuJralinoe rzrpaer Bax{}ryrc pod'rbB orax cl,IcreMax.
Cu.raftuu KycorIHo fl8,'IflIorcfi MHoror{JIeHaMa,ror,rlHHeHHbiMH
vc"'loBuio HelpepbrBHoc'fn trpon3BoAttoit e o6u{}1x roqKax coceAHLIX
KycxoB H,'rucerMeHros. Halz6o.ree o6qafi cn.,iatin cocroltr ns r<y6uqecKux MHOTOqJ'IeHOB,
KOTOpbleflBJIgIOTCfQyUrqUrnAU euga
Y:9t
tprXlltsX2
*p+X3.
l(punaa, onpeAeJreHHanry6uuecKHM MHofoqJreHoM,Ao!'I>KHarlpoxoAl.rrb poBHo qepe3 qerblpe roqKLI, Ho Arq annpoKclIMar(liu Oo"ree
geo6xoAuuo Hcnoirb3oB
arrr lrocJieAor "rllsHoii noc,'reAoBareJrbHocrri
NOJIHHOMHAJIbHbIX
B TOM,
CCfMEHTOB.T{TO6UY6C.qNTICA
B:ITC"IIbHOCTb
,rfo HeT pa3pbrBoBnpI.I I{3MeHeHIrH
HaKr'rOHar4JrHKpHBi.isHbr
MCi'IiAy
noJtrrHoMrIaJrbHa
fl t!5,uxuul ilo,[roHnercr i{e
coceAHnMLicef l,'reHTaMH,
lto qerbrpe\{ ToqKaM, a roJIbKo no AByN{. 3ro noesorffer Halyi }icKOTOpbICO6eCtte.ta't'
OrpaH14qeHI,Ifl,
|Io,'rb3oBaTbAOnO,'lHHTeJIbHbIe
iretrpepbrBHocrbnepBbrx trpor.i3BoAnbrxpe3vJlbrnpyrcuero cnflailHii
R r o q K a x c o r r r e l { e H n q ( u a r n o u J r u H r 4 ro. rA } r H a K o Bn o o 5 e c r o p o H r i
rrpofoe,rrer'r€Hnfl).Cnnafiu crenerru nt 6yler HMerb Herrpepr,rBilbre
I r s B O A I I b l eB T o q K a x C O q , ' I e H e H l B
l qI J I O T bA O n O p q A K a m - \ .
14:.noxesue reopHIl [ocrpoeullrr ypanueuul:r ctt"'Iatisr;]lltoipe6cila"'Io 6H LIcrroJIb3oBarlauQrpepeHl{I4aJIbHoe
IicrJLtcd'teHLIe,
BitaA€':tigc
r{oropbIM He cqfiTaercq o6g:ale,rrbHL,IiuAJrtI qr.ITare,n;i..ritlit i.iliiii vi,
f l o a r o u y M b r n p o c r o y K a ) K e \ { u e o 6 i o ; 1 a u u e } ' p a B H e t i r ; ; re & o 1 : l u i e ,
llo6noft AJIrr Bblqlrcreuati, Ii oclanoBfirICg IIa rrx Trprl,roii{cirir}r.\.
iHiepecynuirxcq Teopueft cn,r;ririroB r"rbr o'fctrl"tar--l,I
K o'l,ilr,i\iiIL,il\
3o;IHcMy K)'pcy PoAxepca H A.qaltca [45 !, rccne[deiirr,oi,4]'irf,r)i ) . r e l , r a Mr p a $ z u e c r o r o a s o 6 p a x e u u f l c r o . ' v r o r r i h r3oB l i , r r r ( \ 4 o n n .
'r:rr!ali Tunlepa
f 5 3 ] , r < a c a r o t r l e i i c frlc o J r o r l r , r e c K i r xr p l r i r o ) r * ; : i :
, l e r o x o B r r o c r p o e H H r ra n r p o r ( c H M L i p v r o l l I I ]nx 0 i ; e p x n o c ' r e i t .
e Tecilinr aii,,i.r,i
M a r e M a r r { , { e c K r r eo 6 o s g a q e n u f l ,I l c l o . [ b : ] y e ] , i r , r B
ilOl,i(ilirrrit.,
:i.,-tr, HeCI{OJIbl{O HeOXil.iAIlHHbl, OHii
lIOtCHiliOTCtl
C
'','. 4.23, Ha KoropoM
Lrcrblpex ii-:rC,'illlpr.lcraB.rleHo
Nlitolxecrut
rlrrrir, cnfl3etIHbtx K)'cortHo-oirperle"rieHlrori c:..r1;;il-(;3';rrrri ile,l. i]lL6';
P;, Ilpiilici,i iio!,i,e1{tiii npeIcTtlB,leHbl TOrll(li,iii, o5o:glqtiirlLihlil
'!:t1\'l,icli:::Tcg,
riTo r'-i Il IleilcTll:'t':.trrllcc'ill
rlB ifr.tcit
iifti'io;ja,-,,{ B jte-
. n ; t r o r . l i i c i r c T ' c r i eK o o i i i i i I I I a l "r . c . P i - - [ - ' , ) , i . I i r r r c l t n r . ' i r , lrr e x < i' il()rt,iiel.giltre,'rbrlbrxiii
roqritir..,iir,',rolr{rio
rr3r{epr.{Tb xopAoii (HJII,I
. r 1 - i r i t 5 o . ! r i L l e i i i roi ,rnpre s x o u , c o e 4 t r H f l t o r ] { u Mg , e e r o u x z ) , N o r o p o l i
.,r();riTro
IrpHffi.caTbqllcrro ti, r'Ae.I - Hor,tepnropOli TOIIIir{.Ky6rt,le..
' i i r : r c n r r a f i u - c p y u t t q u cr tr p o l l r c r l x o r t a p e r o r i e K ; l t a p l i c y H l ( e y K a 3 a :lrr|ipu
l l o c J l e l l o R a ' l ' e J r l b H b I Xc n , l a l i n a .
o;iilll
Il3 TOrll(li P1 B TouK}/ P2,
, t r ' . r o i it r : t P 2 a P 3 u r p e r H r i u z P 3 v P a .
!3f
KflIoqaf AHatoHanbHbreSJIeMeHTbI
I.r SJreMeHTbr,
cTOqUIrleHeflOCpeAcrBeHHo BbrrrleH HrllKe Auaroua.nu. !,.t1 o6paqeHnfl TaKHx MarpHrI
'I{gBecreHcltellpraJrbHbrrinreroA. flpra pe;laxcaqr.ioHHbrxrpaHHqr{brx
y c J I o B I 4 t xM a r p u q a f i 4 ] u u e e r p a 3 M e p n x n u B b r r r q A l r r r a K
f)
0,l,
0
l-1,0
l, 2(t,lt,l
t
"
0
I
'' t_t 1: | t , , : , t , ) t "
I
r, t'
|t ,
I (r
,'
,)
lr
i,
t::::: o
o
I
l,lii -- |
I
rr
0
0
0
:(1,-l-1.1 tn
tn
2(Bf-t6\
... 00
... 0
0
t)
l0
l_o
i)
o
Puc. 4.23.9erupe roqKrl,cBr3aHHtre
$yurqtlefi xy6uuecxorocnnafisa.
HcxoA[bre sa6aoAeuHs o6ogsaqessl cepe3 Pr. PaccrotHut no xopaaM MexAy roqraM[
Hu l;, Kacare;lrnaa r cnlafiury eo eHyrpenuefi TocKe P2 o6osHaqera lepes Pz'
B o6qervr BHAe ypaBHeHI4ec[nafiHa MoxeT 6ltrr
QoprrreMHoroqreHa rperbefi creIIeHI{ or [apaMerpa l:
paB-
''
.
u
3TO
Ay AByMfl TOqKaMI{.,[l,.nllonpe4eJleHHflKosQorqreHroB sroroypaBHeHLrsrpe6yercfl 3HaTb KoopAHHarbITolleK, onpeAerqoil{llx KoHI{bl
npflMblx B STHX TOqKaX.B AOcrrJrafiHa,Lr HaKJIOHbIKaCareJIbHbIX
6asreHlie K oroMy MbI Mo)KeM yKa3arb fpaHurlHble ycJIoBHr, ollpeAenqrcuue [oBeAeHIie a[[poKcHMHpyloueft ilLl:,J'rrnHa [epBoM H
NOCJIEAHEM
YTIACTKAX.
KOTTCqUO,
3AAAHbI
KOOPAI{HATbI
TOiICK.
IIo eruu AaHHbIM Tpe6yercn onpeAenl'Irb HaKJIoHbIKacareJlbHblx
BeKropoB. fpanvvuue ycnoBllfl Moryr 6urs nu6paHHbIMIl [o-pasHOMy B 3aBIICHMOCTIIOT BHAa JIprHr4HB ee y3nOBbIX TOqKax.
MEr paccuorpuM Tonbxo rpaHfiqnble ycJIoBHt, Ha3blBaeMbtepeJIaKKacacarIHoHHblMv!,vlltv! HaTypanbHbIMH; oHH He Tpe6yl,or 3aEa:Hl/lfl.
B KOHqeBbIX
TOqKaX.
TeJIbHbrxBeKTOpOB
.[I,aa naxoxAennt KacareJlbHblx BeKropoB Bo BHyrpeHHux ror{Rax (P2 Lr Ps Ha puc. 4.23) MF,IAoJIIKHbIpeullrb pnA coBMecrubIx
ypaBHeHHfiBHAa
lMllP'l: [B],
(4.,19)
rAe Herr3Becrnuft BeKrop Ko3QQI'IuHeHrosP' onpeAeJlfier pIcI(oMbIe
MaTpnqa B neBofi Itacrlr ypaBHeHlifi tBJlflercg TpII'
KacaTeJrbHbre.
HyneBbIMW,:l1.Ct
AHaroHaJIbHofi,T. e. B Heft BCe gJIeMeHTbITIBJIEIOTCfl
a
ql
.,2
3 - t , , 1 P , - P , ) + t 3 (2P ' - P L \
(4.48)
IPCACTABNCHI-iC B BHAE KY6I{qCCKOTO MHOTOqJICHA KOOPAIIHaT CrrJraftHa Ha HeKOTOpOM paCCTOtHI{x / eAOJn HHrepBa,'la Me)K-
236
Bexrop npanofi qacrn [.8] uueer nrla
ganucaHo B
F, : fi, * fr,ti F,t'* Fnt'
-
2 4
(4.50)
123456
rar_
rr, (P*-_ P,) *t," (P, - pr)
3-t", (p6- p,) + t.,z(pn- p,)
lul-
I
J-to,,o, -:,,
(4.5r
)
-lt2u(P5
- p^)
i
It- * , r , - - P n , r \
!irrrjru,riroeypaBHeHHe
peuaercq o6paqeuueMMarpr.rrlbr
lMl Lr
rareM yMHolKeHrreM
eroii o6parHoilMarpr.rubrHa Marpnqy lB].
JaMeTLtM, qTO TaK KaK KOOpAr.rHaTbrroqeK P; onpe!,eJlflrorcfl 3Ha-
'i.,rrir.taMtr
X u Y, To Marpr4ua
nlreer nopsAoK ttX2, rne n'i].rc.[o roqeK, lto KoropbrMfB]
crpoI.ITcfl cn.laiig-annpoKcHr{auug.
ll (4.51) yxasan arA .ureHoenra.rpuquf B]. flepnuii cro.rr6eq
naarrlluir,r l-B] HaxoAr.rrcfl
noAcraHoeNoiiBMecro ArrHH xopA 3naqe::tri lt, ll suaqeHzfi KoopAHHarX ua6nrc4enur1.Broporl cro.ri6eq
3'r'ponrcxaHaJrorEqHo,
To,'rbKorroAcraBJrrrrorcg
KoopAuHarbrY.
&larpr,rqapeuenufi P' raw>xer.rMeerpa3MepbrnX2. Kaxla.t{
'i)rpoxaP' xapaxrepr.rsyerHaKlroHKacareJIbHoli
x cn,taliny B TogKe
iraoflioAer{ug,
saAaHHofiKoopArrHarauu
x w y.
Puc. 4.24, rlerupe rorrrr.r,no Koro.
pbIMcrpor.rrcrxy6uuecxnficnrafis.
yKa3alrhr lnHHbr xopd, xre)'(Ay rorrKa)r!i9
il..nusnxopA patsHbrtz:2,0i 13:3,0 H ta:),296. 3ro nce, qro rpe.
oyeTcl-Ans nocrpoeHur MarpHrlbr
ro QopMy[M] onpeaeneHHor?
ne (4.50)
:Ii,:';1,,
,2,,0*,1,.
I
()
Lo
:,0
4 , 0I
olparHafl, K Heri, paBHa
I I
!,.un HaxoxrAenfifl qerbrpex rio3Q$riqueHroB p, onpe.lc,rlf,t,-'!ri{.,:
'i-l,tii cir,lariH (T. e. JruHHlo,cBfl3brBarou{yroroLu{i.i P2 [ P y;'
), \ibri NIeeN{
9r: Pe;
P2: P'ni
,l (Pp ' 1 ---P1r'l
r-,
it.----J
-
---:-'--;
t, l . - : L
{h -:
,.., I
I t
I lft.,r
f,.----i"
'iri. I
t;
Pi,,
2P;
-
'ok'
-re
i
.kll
- r|
ec,{il
: ),i J,'1t,5 il,3l 39 - 0,0I0,+'
I
ir, !';-:i'1 -_ i),0279
0,')2Cf' I '
ii, ).?li
il,| 18,1 - 0,0SS; |
0,,115ij -0,0592
0,2944J
i ;io,'l;liHbl reKlKe oripeAeJ'rnrbMarpnqy npaeoii qacTr.r
He_
.ionr\'rari lrgrlopr,laqufl )j.iln HaxoxiAeHHs b,renreuroB [B]..c.rotB']
ri:, A"{rrHxopA H xoopA}rHar roqe K. Tax xar Ka>KI\afr.
ioqra znae_
rioopnrrr{arr,r,
ilBe
ro Ber(rop fB] H;vreerAsa cro.n6qa, nepauli
x X, nropofi - nnn I
"
i' >
. ;' r . i
2'2
; + 2 , G _ 3 ) + 3 , ( B - r- ;
3'?i
3- 4)-f'2,2'36'(4_-l)l --+- t311-3)+2,236'(3-3)
J
3.2,235'
z'J
rrerbrpe
;"r^i
6
o
, ; l , i l r H O I , l i l C l l O " r I O ) { ( C l l l l L i : ' ; l l j ) 0 a " i r ) : r i l i - . ' i ' i l : ' ' i O i r L i i ( , C B , : i ' . 1 : i l i ; i l . l - li , i i " r l t . ' - 1
ai.iri, rlfo iio,rj\llzle.l'cI i;,):;liril cij,rlliiii-:]iliif c!,c]l.rli,.ii'f; :i'i'..;'
i r t r i j r ' . e ' ^ - I i O I I T O p f i C ' i C l , ! . 1 . a . \i i : l i : ( . : l . O l ' Oa ' i ' ; ' \ i t l : l ! ' i a i i l ' C O : i 1 l C l C . . i l e j C " r l C i l tilrr 0 l]lt.:ii1.iua, llllliut'ir,t HciIo,il,i.r'icTCtr lii.,ti !f.ricBbre iiDJil;Li)i/rtr.iitlt'ii,l.
l O t I l r : l ; , i l : Z ! I { , , 1 . . Ql . l r )
CB_ti:lLI}li:i(;ill}.lXUiI\/lrlt'HIiile
oll;'lrriIori>l ToqeK c {e./'iblo Itaxoi'l{Jl,eliI{5{ lIOBoro },{Ho;l(ec--tsa Iir)9ii,''
ij!ilir.rerrrciB AJIti Kai'I(l].oro yqacl I(a cil,tlarIlI:1.
t
i
n
-- |
- l
5
0
6
2,633
I __ () AS'?
iil.ii t{,:i.":l:.ljbt lioij,l,
[ - I p c u . l . : ; o c r p t r p y e' \JIr o r ] t e r c . ' iI r a n l r i t \ 4 e p eh ) ' i t t t ' .c l i oj u ' i r . l . r i : ?'loM
6yAelI
IlcIc.7It, joB3T5
r l ( ] ' ib r p c
I
Ha,
I
KoTopLir LI\leror BlrA
pil('. 4.2,tr,rioopALrIIa'iLr
[-
l'
', r r
rlati
r
_. !
r
-l
tl
'|i
I
i4:"i
L,:j I _.1
:l
23t3
r
f otlKll,
yKa3xi{irtifl
li;-r
d o ^
fl-g,
ztzJO
t r:.,t:t
lrl)ll
(3- l)
l i f 3 ' z t-l t ) j
tJk- - l l
'.-i{) :ji1eK03Q(pr{li.r.reHTai -'.i:iH'l
l.'ti
L r a , I l O l i { i : 0 O I p e l e . , l } i T b T r ) r i i \ r I D , - i i l . : i l ,l i - j i 1 l J i J i r . l ; } l O i l : . . l C - 1 r r . . 1 : ; : i
' i . L ' r l l i : , i r r l u i : t i i t .- ' !
:)roio
irriT*tlla,1a,
xopir.iri :,leli{ ii.\,
...ri.::?KA;tgga
;i :;'lii t;i)U a d b t ' r ' b p a l 3 , l { e ! r e H a H a i ' . o c ' j ' i r c ' i ' c :I : ; i ; 1 i " ' ^ a ' q i l i " r t o t i i i : i t i i
, r . 1 , l-f
IIC,,ic'l.6ii"]i: ii,l
rJieAclr;lrer i,Hbie paccT011lllifl
.liO"[;,;iir1,' 6ii'i..
.
.
r
,
:
i
i
(ito / Lr ypaBHelilie
i
.
i
(4.48).
iJlio)Kf
3t'ro i;;'iit.-il,iLIIil ii:t
l,:lrl,'
Haroxeq,
| ,f'f tt |
-{1,:J7,{$
-'
i.1,1j -- I
{J,t9,3.{ -i
-0,0':fl7
L
Y l'{ilOiir..1t
1.5 I
el
-B,o5o
l'
*
5,367_l
' IIOJI!rlaC)''i
l- - o,eosz
1,2{)26
I
0 , 6 1 e 7 0,6750
|
I
E 0,3723 - 0 , 6 1 6 0 |
j
I - 0,3.;52- 1.0328
Ilenef,; i.{br IIr{eeh{ Bce, qro ireo6xoArtro
Arrr Bbrr{Hcrenit:lrtosdtbir_
riicHron cn.rafiga Arfl Kax(Aofo 3geHaB HaueM npnMepe.
ll.nl no_
239
JryqeHHsypaBHeHHfl [epBofo I.r3 HIlX HaAO nOACTaBHTb COOTBeTCTByroque 3Haqenlrr t, P u P' B ypaBHeHrae
$.52). llo"ryulru
AJrfl r(OopAr.ruarux
P 1: l ;
9z: - 0,3097'
3(r- I )
0
trs:--S-
2 ( - - 0 , 3 0 9 7-) 0 , 6 1 8 7:
,
2
(
0
,
3
0
9
7
)
'
r 0'6187
2(l-l)
o
Puc. 4.25. flaAras cnnariu-Qyttxtlurr, cocroqlraq Hg 30 cerMeHroB
il.ri,ov xaxAoft roqrofi Pnc. 4.24'
TocKH Kcx(Aoro
To'l,,po:rexyroqllbl\
yKa3ullo
cn-', r'.r'r, BblcffcJeHHhle haK
NlaJIeHbKItr{H
3 T C K i t rc , 1 1 3 g f p a ; x e H l t
ToqraMu
of
I
t II
II
2i
0,0004;
I
,l--
0,0773;
2l'22'22
I
I
I
AJrfl KOOpAHsa',ruY
I
0
Pr:l;
Fz: 1,2026;
a
2 ( 1 , 2 0 2 6_) 0 , 6 7 5 0
2t
2
2
2 ( l - - 3 ) -ft 1 , 2 0 2 6
0
,
6750
-r|
'2,
2J
z-
3(3rt
r-.r
t)
--0,0401;
---0,0306,
WTI4
r
I
[I
IBI: I
I
D a B H i t0 , 5 ; 1 , 0 n 1 , 5 .
B c r a s f l s s H x B y p a B H e H H e( 4 . 4 8 ) , c H a q a J r aA i l f l X , a r o l o M A i r t
IrLrryqaevi
: 6,3549'
Ps.*: I - 0,3097(0,5)+ 0,0004(0,5')'+4,A77310,5';
tl
I
I qr..A i
0,ilii97
{1,00,14 - n- r r)4nl
I
"-'
I
.0,177:.1
0,c3c6
_!
- 0,04C1
(0,5'1':1,5374.
Fu' : I + 1,202
(C,5)
(0,5')- 0,0306
!l
i
l''iOiIItlHO
i\'lLI N!Oll{e\{ BblqliC"IIHlb
i ) ; - r u c r o f l n r l.:r1l i, 0
8,u,ro
l,r,r, -3,u'uo
l- l,n,o,
I l--0,5506
I
o,+eu -0,2447
-p,1872
||
0,0066
I L
0,0323
|
0,02g0
I
Haroueq, xoeQ{rnquenTbr 3BeHbeB cr-uraiiga MoxHo HcrroJrb:JoBarb A,rfl onpeAeiielitrn Kcop.{Iiler npoMe}KyrorrHbrxroqeK Ha cn,naii_
Ire ruexAy rax40ri napofi sa6l;oAeHuii. Ei.nu Mbr BbrqrrcJrlrM
KoopAEHarbl 6O.nrruoro qHcJIaraKr{x roqeK H cBrr)I(eMfix SareM l]pfir.rbrMH JIH}II.IflI\.,IH, BIISYAJIbHO IVIbI NOJIYqIIII
HETIPCPbIBHYIO Id'IAAKYIO KP}I.
eyru.3ro.Jlty prs ror MeroA,na ocHoeexoropbrorpa$i.ruecxar
ct.Icrettzl 3BM esrqHcJIfleTIr Bhrrrep(rHBaerfJran,r(ilelicripus.neunlre
Ji?r[t:t:;"J'l"'ln H.n.nr.-rcTpaunll
&Tbiorprlirriqfthicfi pa:cvorpilrpieNr rpir\
l l p O M t l i l \ ' i l J t { H b I X ' I Oq e K l ( a X { ! ( . ' i O c n . l : r ; j r t ; l ,
,/-l.rl:i:ra.{O)Kil"lt{ltg IIilO,l,ieiiiV'ICrtti;:tX,ICrLOi{.\,lLl aHAqa.ti:l pe-3Xt.
ti[lCTn;
.i1I{M Kaii(.llIO
XOpXy i{a llerblp8
a
l _ ) ; t C C T O f l H r i r r3 t 7 " 1 4 , 2 l t l 4
240
2
3t1,14 onpegeJlflior 3HaqeHI.Ifl I, KOTOpbre
AOIX<HbI6Urr nOACran,re3TLr paccloqHus
r r b l B y p a B H e H H e C n n a l i u a , A n g rrepBoro crrJlat:rHa
AHarorir,iirur,r o6pa.:ou r\{br Moir(eM onpeAeJrHTb xo3qbLlrrruleHrbr
cti"rrariua
A " ' r rB
r T o p o f o H T p e r b e r o 3 n e H a .O u n p a n u r , r
I
l_- 0,1l2l
1
I(OOp:{llilaTbl
IIel]BOrO
CllJIallHa
n t:1,5. Oun pasHu
!,ns, tr,o10,7679 2, 1319],
A ; t x t t , s[ 0 , 7 9 6 9 2 , 6 1 0 4 ] .
3ror npoqeccrroBropffercrAJrr BTopororr rperbero cnraunon.a s
p e3\/-.rh'r'aTe rro,tvrr a L.\/r c.l eJ.ytoqce
A,'lli cl,rairua
2
l",rs cn,raiiua 3
M il ox{ccTBo KoopAI,tHaT
u,677,+
12,5924
[3,i612
[4,050
[3,8431
13,3442
3,37141
3,4841
l
3,35481
2,6020]
2,11631
|,57221
3rir pe:y,'r_ararl[ fipeAcraBJIeHbI Ha pHc. 4.25. Tarc>x.enoKa3aH r,rraAliiirt crltatlii, rrop0)KAenusrii ettquCJIeHI.{e}t 30 npor,re>xyToLrHbtx,foqcK :"iexry xari<Aoii napori
y3JIou. Xorn nponeAypri tsLr!rrc.irr.illiir
:ii,i)(p-lrIltt}teltTOe c.n.{;,iirU:l SairirraHHag, OB;'lt,[,€HIt€ ei,) n()3i]O,rj.!ii)
].
(lilloiliTe,{Llio fipocTo lonyqaTb cTojlbKo Tor]eK rta xpilll;;, (,r{rJi]l,.
r<ororpeOyerca.
241
CETMEHTHPOtsAH
Hb!E [IOCJIENOBATEJI
bHOCTII
3ounponaHue
3onapooanue-gro
pagAeJre'He nocteAoBareJlbHocrrrB orHocrrC,'IbHOOAHOPOAHbIC
CCIMCHTbI,rAX<AUfi I.I3 KOTOPbIXOTJI[I!IE}IOT
, r p f i , ' r e r a n r r u x c e r M e H T o B .l I a . r I e o H r o n o r u , H a n p u M e p , n p u 6 e r a : c r
;{ 30HUl,\OBar{uro
crparHrpaQuvecnofi noc,reAoBrrerbHCCTri Ha ocI{OBe.COOTBercTByroqefi
us6brroqHocrH }rcKorraer{bTxMtrKp03,'reMeHi ' c r . { a n n u e o n p o 6 o n a H H f lM o r y r 6 n r s p a s , q e J r e H iBr r o r g o c r { T e , , i b Ho o_T.r{opolrrrrie
I.rHTepBaJrbr
tr 6lrlyr jt0G;-lcr?B,rIflTb
3oHbr Itocro-riir_
HOii
coorBe'lcTn1,rcuieii
crparHrpa$fiqecriirN{ errlrir.iu:I\.r.
"rriro,!oirrri,
'r
iiorvqennLre no;;lrrnrioii pirrror{ery}rrrccri(.;ri
"(,1;tttlte laBepcoB,
pa:se;lnoil, Iloil,paeAer'irroTCf
Ha 3oHLI, rioropi,re :"roryr 6r,iir, riHrcl,_
Ilpcl lipcBarlbl IiaI( Iloqca oA]{opoAIir\ix ci(aJrbilbrx crpyxryp ri.irir
u ; i n e pz r ; u ra: q l l i i .
H u e e r c s A B a o c n o B r { b r xr r o A x o A a K 3 o r { i r p o B a u l r r of .l p o c r e i i r u r i i l
143 lul;( I{a3bIBaercrI <(uroIiaJIbI{brM
ltoucI{or{ tpaHIIu>>.Oll ocHoor,u
H a I l o l l c l i e B H e 3 a I ] H o r ou 3 M e H e H r i t Ic p e A H I i x s H a q e H u t i , r i J t H , r ] T o
3r{BHBadrcl'trFro,
Ha IrollcKe naH50.ueec}i.ribljoro Ir3i'leHeHeqfpeAire:i
Tir TIocJic.iaR:lrc;iirHocru.finn oirpc.{e",jeHIIfl
t-paHHu l\{ctr(jlv frogBeirH b r D i H3 0 H a M } rB A O J Trbp a B e p c a v l 6 c r c p [ 5 6 ] - p a s a u , r u e T b 4 c K o J r b ,
Stlu{efo cPeAgero. PsA sHaqelrrrii rr3),qaercs ricc.qeJ.oBlireJrbHrrrr,{
.4BIl)KeHIleM
K.o. p o r K o r o H H T e p B a J i a B A o / I b r l o c J I e A o B a r e , ' I b H o c T ' i r .
L K o J r b 3 n u l l r i i.liH T e p B a " H
T a 3 b r B a e r c foi K F r o MC
. u pacnaAaercfiHaALe
sacru: cefN'reHT
o r r o g K a i * / z n o c l e A o B a r e J r b H o c r rrro r o q x H i u
Apyroii cerMeHr or rorrKr.ri Eo ro\xu i-11..
Mepa, HasbrBaeMarro6o6ueHHsir,{ paccror{Hr.ieM,Bbr!rrIcJrflercg
J.r;t pa3Hocreli ltex4y cerMeHTaMriBHyrplI AByx no,'roBHHoKoKHa.
o6o6utessoe paccrosHHeecrb orsouesxe, o6iasoeauHoe AeJreurrex{ KBanpaTa,pa3HocTa Mex{Ay cpeAHr.rMH3HaqeHr.IsMHAByX c{ti_
MerrroB sa o6teAuueHHyio Alrcllepcurc [ocJreAoBare.nr,rrocrer?
B cciM e H T a x .O 6 o s H a q H t r3 r o c p e A H e ec e f l , { e H T ao r . r i A o J i - p r e e p e 3 X 1
s efo, Ar.rcilepcHroqepe3 sl2; cpeAHee cefMeHTa oT Ji AO xr_r, .re0e: ,\2 ri Atrclepcurc qepe3 s22. TorTia o6o6u{eugafl pa3riocTr, Ccri)
p. - (T, -7r)t
(4.53)
s , 2* . , r r
3luerirna, qro o6teArueHHafl Aucnepcnfl ecrb npocro cyliMa Arrcr e p c l r r ? I B y x c e r M e H T o BT, a K r a n o 6 a c e r M e H T ac o A e p x { i r o ! . } i r ) l i
T O ) K e q I i : J I OH a 6 n n A e g H f i .T a x N < e3 a M c l i r M , v r o t i . i ; c l , r e ] J i i o i , r i l r ; I nlre 1r 'torrcK tIoc,'ieAoBareJ'IbHocrli
He Moryr rlortacrb B pa3.nHqi{l-le 3tlHI:i.
, flpe,r.cran,leHuena rpa$zre h xax QJrnxrluu D2 npuno1ur K r]peo5p:i:tonanuro rrcxoAHoto rpaBepca B HoByio irocJieir,oBare,'rbHocrb,
i r . ; r c p o i i r i r a l r n i i b r 3 o H H r , r e r o rB H A o c l p L r x i r i i x o B . I - { a p i t c . 4 . 2 . 5 , a
IipCrIC'l
i.l3.4eHO
iIepBOHaqaJIbHOe
Ifi€CTTII(iLTOI{eTpODOe
CeqeHlleB.ItC,r1b
242
OJ
l-
In
a
aa
,4
'ig
:!,)0
tl
,l oi
4
.)
,,]
r:tlleu;te
)il:
ti.l
C':'let:li:.
i.26.
U
- . 1!,, l r l
'
l'.i)roiii)ii
r,li,if, :liti;I,,T
. : i . i i i r i l D.:pr;ia,l
rll i irSiiatri no lleplali f.-l ti:ioii
''':. ."'!lll l:
i . i i ) ; ; l i a , l: . 1 . : i i t i r l
OI
;l
r-lciirJll iIii
. l : 1i ' l l i
'f
l:o:jlclj'HTe:
.rllr. .liailii
I it
cD0ilcrts IloriBL{ i]rl!
'l-
il i(11
c i i ] ! c l J 3 . l . ' l ; i i - r \ | f . l l i t : , 1:
5 - 3rta'rclrr': D? l:-rr"
l,i lt: rp;rr!l'ile e
i 1 r . ' f! i
, r ' r - ' " ' ' " i, i i ' 1 1
ji,lt;r,il rrif l-iil:c,,
r,., i:
i.i !B ro,leK.
'j:rIl;i(li;r
.iro tst-ino,[]icHlle ?'{cii f I-tcile-I:/l):l
ll''rticrqi; r ;ilic'iiiici,
' ) i j 1 : ! . \ i et j , i t . i D ( r ; 1 l l l . i t t X O : l t t O t : ' l i 1 O C . r i e i ' l O ] : ] a T C " . r l L I i C i l Til{l ; 1 . r l 1 l l l l , i t ' i ' . O ' r [ i - ' ilUlCf{)
r_rriia-. [lUtiHCC
O l l t t ( ] J . C , l i l i l l O ] ' C i ] e ; i i l : r ' : L B i 3 . ' i r r 1 \ 1 i l " i l , lr{ : l O H
OllO (;\r;i.Cr
,t tl0)*i€i.;i;iotiyC.rri.rb
t{OpOIIitte HIiTellBaJlbl. OAriarlO
. t ) , i l C T D H T C j l b g O K O U t i t 6 t < i r l t i i 3 . ' ! l e l t ( l l l B O C T I l , B O 3 H I I K U I 3 ' r 1 { l ' l M" ' . ' 1 ( r i i { ! ' l
t
l
x
t
l
c
I
(
.
o
p
o
r
i
t
c
e
Llitc lillN{otl)lx
110\{e}i B :lulIIIicii HCXOIHLiX Aa.IlHbIX'
llo },ic'
oo,ree qyBc1.SnTe.rrbHo ll 5.v. le'r o'roll{AecTR,'lflTi, }1:rJII'1e 3oIIbl,
thll li'r'
;lie f lipuRer: I1i ii I:i1)pel'yiItlpHolvlV HellHTepnpeTI{Dye\{orlv
-fl:
D 2 . V j 6 c r e p o i ; , v 6 n H n o B a "IiI p o f p a M I \ { Yt i a s : b r x e S O P T P A [ ] '
'tolirr:r peeij;l3J1e'io'i'or MeroA [Iaxox{Aeullt{ fpi]Hllt\ son [1"'7I
rio
.:A2
Ibr
oluo
r'{3 Bo3paxeHr.rrl nporHn MeroAoB JroKaJrbHororroHcKa
upaHllll cocroHT B ToM' tITo oHH Mofyr npl{BecrH K noJ'ryqeHrrro
Heo6uquoro q+cila rpaHarr, s qacruocra, i uau6o,ree lis^{eiiqasorr
qacrH IIocneAoBareJrbHocrI].fro6a,rsHoe
S0HHpoBaHHeocHoBaHo
na 4pyrori HAee, a HMeHHoHa pas6aeHun [ocJreAoBareJrbHocri.tB
3 a p a H e e 3 a A a H H o eq t c J l o c e f M e H T o B 'K o r o p b l e B H y T p e H H eH a c r o J l b Ko oAHopoAHbI'HacKoJIbKo3To Bo3Mo)KlIo,lI orJIilqHbIor IrDHJIerarcilILrX CeTMeHTOB
HaCTOJIbKO,
HacKoJrbKo3TO BO3MOXHO.
OAHa us nepBbrx H san6o.nee rtpaKri.rqHbrx npor{eAyp raKofo
po;1a 6u"ua peKoMeHAoBaHa
!,xul.nol,r f2l], xoropr,rfr uino,rrgosa,,r
H r e p a q H o H H y r oB e p c l r l o A l l c n e p c H o H H 0 r oa H a d l u s a .c u a q a J r a I l o c d r r e A o B a r e r b H o c r b A e J i I I T c f lH
' a IBa cerMeIITa,oqeHb KoporKyro HaIIAJIbHYIO qACTb H OCTATOK
IIOCJICAOBATCIIbHOCTA. CYUNAA KBAAPATOB
BIryrpLr cerMeHToBssw Bbrr{acJrrreTcrr
no Qopuyne "
mni
SSr:
lm
) l Z)_lJt, . r, ,r , - A ' . ri ) . ,I 4\. '_ .l r r , - , n .
Z_J
i:l
i:l
I
(4.54)
i=t
rAe ,rrr- l-a roqra BHyrpHi-ro cerueHra,-r,.- cpeAHee
i_ro cer_
M e H T a ' n 1 - g H C l r O T o q e K a i - U C e r U e H T e ,r n - q l r c J l o c e r M e H T O B .
C ) ' n r n r a K B a A p a r o B M e ) K A y c e r M e H T a M aS S a s B , r y q e r c nv e p o f t z s _
NreHEr.rB_ocrtr
cpeAHHx cerMeHToB orHocprre,,rbHo-l .., o6qero cpe4nero o6teAaueHgofi nocJreAoBaTeJrbuocru
HJrri
srs,,
"
'
n-t
m
TI (k.,-X
"-'
U
:'
(4.55)
i -1
P a a 6 u e u n e r r a A B a c e f M e H T aA B u x e r c r B A o J r bn o c J r e n o B a r e J { b _
r{ocru, ri B Ka)KAoM noJIo)KeHlIi BbrqllcJlrrlorcflABe ee,,IaqrrHtlSSuz
rr SSo. A.tq KaxAofo Bo3Mo>KHoroIroJro)KeHr.is
rpanr.rubrBbrrrr.tcJrflETCfl OTHOII]EHI,IE
ssa-- ss,
^
{ .: -....---.
D,);
(1.56)
flo.rioxesue, coorBercrByror.r(eeMaKcIrMaJIbHoMy
3riaLieHirroR, Bi,r6 u p a e r c R B K a q e c r B en e p n o l i s o n a r s u o r l f p a r r r u i b r "
,[,a,riee, noBTcpeHHe]{npoqccca BcraBKU AonoJrr{iire,'rbHofirpirriuqrJ, Kor'opat cnoBa AoJril{na aaBarb r,rar{crlMyMR, erlr ABe sogbl
CHOBarrc.tpa3,{errrrotcs. 30snpoBaHrie rioBTopf;ercrr Ac rex I1o;-..
IloKa ECtI ]Iocr'ierloBare,'ibllocrbHe pa3Ae,TLitcr{B 3ai)tHce 3:tAaHHoe
qrtc.[o 3oII Il.rI.I rloKa BeJitrquna R He nepecTaHer yBerHrJrrBarbcg
n p r a o S a n l e H r . r rHr o B b r xr p-6nra
aHrrrl.
Ilpoueaypa fixur.na
Hcrro,rrb3oBar{a
.uJrs ocvlrecrBJreHi.rfl
aGtoMari.rqecnorouH4tpoBoro 3clrirpoBalfrs AaHHbix ci<naxns. FIer a S H O O q e H br r c x o l K a r n p o l e l y p a 6 t r l a o n y 6 , r r r K o B a H a
Xoyxnurou
rr Xtepplrsuov 127), [28]. Olur HcrioJib3oBa.rru
r,ro6a,rir"yro bnr,,v,r244
npOfpaMMIrpo3aAtrIO, OcHoBaIIHyIOHa MeTOAax AI'IHaMI'IqeCKOrO
I'{repaIBJIflercs
aJlropIlrM
3ror
aJItopHTM
n
,[[xu.rt.la,
BaHHs.Kax
rrrBHbrM, HO B Cl'lJIyefo peKypcHBHocrll oH I{MeeT npeI',IMyUIeCrBo
EeJIJIMaHaB TOM, qro B KoHIle
nepeA npHHrIr.InoMonTuMaJIbHOCTH
s
o
H
f
p
a
H
I
'
I
q
A
a
e
r c a M o e n y q u e e p a s 6 u e H u en s
n
s
t
6
o
p
a
npbu.avbot
IpoIIeAyp
He peKypcI4BHbIX
ucex s63[ao)K;IbIx.flpu ucno.nb3oBaHHI'I
BCerAa Bo3MoxHo raKoe TBJIeHI{e:no3alut' nnt6paHHan KaK Han'
Jryquafl fpaHl{qa MexAy AByMs 3oHaM[' He 6yaer naa.nyuilefi,
rpaHI{qa.
ei.rri.re oAHy I.r3son 6yAer BcraBJIeHaAottoJIHIITeJIbHatI
Xoyrunr a Meppua*t Bblqllc,rlflIorBeJIHqtlHy'Koropafl^ecrr, cyMBe"lliquHess1r e aJAacnepcufi, SKBI{BaJIeHTHatl
Ma BHyTpr43OHHblx
r Oprarltae'Axu.lt.na.EC.Upt3Ta BeJII'IqI.iHaBbIqlICJIfleTCtl11ttt BCex
B ABa CefMeHTa.To
no-s,MOXUHrpas6lleHait nocJIeAoBaTeJrbHOCTH
eosMoxpe3yJrbrar 6vaer HeKoropblM ra6nltqguu SSv AJrs n-l
iroli nororrennfi nepnot? rpauuqu. A.trq KalKAoro Bo3Mo)KHoronepeoro pa:6aeHfifl 3areNl BblqqcJ'IflerctlHoBoe 3Haqeglie SSrv A,rlflscex
nOCJIeAOBanosltt(fifi aropoii rpaHH[bI' Koropaq AeJII',IT
BO3MOII(HbIX
T e J r b H o c r bH a r p l r s o H H . B s l 6 u p a t u a u u e H b r x e eg H a q e H l . rSe S ' z A n n
Broporo pa36ueT4fl,,nonyqaeM onrHMa.rlbHoecoorBercrByloqee nonepAOtl rpaHAUbI H OHO OCTaeTCtHaxJtyqtuuM, CI(o,'IbKO
JIO)KeHr.ie
5u AonolHtlreJlbnblx rpaHHIr MbI HH BcraBJItJIl{.
Ilpouecc firepupyercfl [o rperbeMy uHKJIy' w AJrnxax4ofr rolr'6usa\uu orrrllMaJlbuofi nepnoii fpaHI'IubI co BceBo3Mo)KHbIMH
BTorperbx rpaHllllbl H BblJrbrMnrpaHHqaMH HaxoAgTcs BceBo3MolKHbie
q[c.rrrrorcfl coorBercrByloque ].rM 3Haitegun SSy'. Bu6op HaIIMeHb'
nOJIO]KeHHe
ixero 3rraqeufiq sSv 3aTeM OrIpeAeJIfeToIITHMa,'IbHOe
nropoft rpaHI.IIrbI.llpouecc noBropsercfl cHoBa II cHoBa Ao rex ttop,
rroKa He 6y4er HattAeso saAaHHoeqHcJIorpaHLIu.
B crry peKypcuBuoi'i npupo4t't aJlfopnrMa oKoHllarerbHoeMHoeoslaoxHotl Azcnepczer?cpeAII
)r(ecrBo son o6,'raaaer Har.iMeHbrueft
,'r06oto Bo3MoxHofo MHox{ecrBa c reM xe qI4cJIoM 3OH, [OKpblBarournx Becb HHTepear. K co)KareHr.rrc,3ror MeroA HeIIpaKTHqetl
H3-3A BbICOKOI,IqCHbI
NPH OqCHb AJII,IHHbIX NOCJICAOBATCJIbHOCTflX
BbIuucJrl.rreJrbHbtx pa6or,
BL,IIioJIHfeMbIX !,Itn
Aocrl.{xeHI.{q onTHMVMA.
i(naccu$urir rir{,qno cxo-x,crBy
B erou pa3Aer'reMbr ocraHoBirncfl Ha NreroAax yIIoprIAorieHIrl
'raf.t"rlIoAesLlii
ua ocHoee HX orHocHTeJIbHorocxo.u.crBaro rteKoro;)o)vIV)lpH3naxy. Ec.nH Ha6.nroAeHuflxapaKTepLsyioTcfi Hclioropbl)vl
I I I I o ) K e c r B o Mn e p e M e u u b r x ,T o g r o B c y r u H o c r x r p e 6 y e r i { x n p o e x r n p o B a n l r f l H e K o r o p b r Mo 6 p a s o u H a e A H H c r B e H H y rror p f l M y l o ,I { a K o -
.IODOI{
} I X N O J I O ) K C H I { C J I O I I , I q C C K I ' I C O O T B C T C ' I ' B Y E TH X P A C I I O J I O ) K C H I { K )
:l HCXOI.ti0r{MHoxecrBe AaHHbrx. 3ro uoxer 6url OCyU{eCrBJiello
: ) j i l l u N {l t 3 M H O T H X
, a n p r . i M e pr,i a K M e r o l f , r l a B I l b l } i
IUeTOAOT
B a, K L I X H
I ( o M I I o n e H Tu , r u S a x r o p H u l i a u a . r u 3 , K o r o p r r r ep a c c M a r p l i B a l o r c t tB
245
[ocJreAHe]ir!'raBe.Tat<oit r.naccrQnraquefi Mo]Ker 6urn xpoHororuqecKoe ynopfiAorregfle,rrrfipoKo HcloJlb3yeMoe
B apxeo,rorlru. K co>KaJTeHHIO'
HeT f apaHTuti toro, qrro rrocJreAoBare,rlbHocrrga6,rrcp,euufr, yltopffAoqenuafl rro cxoAcrBy, 6yaer xpoHoJrofnqecKu ynoplAorleHa Her{oropbrMocMbrcJreHHsru
o6pasolr. floHqrras yltoprAoqeHafl no cxoAcrBy rr fipocroro ynoprrAoqeHHs
paHee ulrpoKo He
ucIIoJIb3oBaJIHcbB reoJlofHH, HcKd'ttoqaqIIpHMeHeH].rflqtc.reHHoli
r a K c o H o M r . r rB{ [ a J r e o u T o J r o r r 4 ] r
[bl]. OAsaxo HMeercfl o6Jracrl,
r N o r o p o f i n o H s r a e y f l o p r A o q e H u s n o c x o A c r B y o r ( a 3 b r B a e r c ,n o _
dle3HbIM,a HMeHHo,I.TCcJIeAOBaHHe
reoJlorliqecxoir Koppe,'ItrIHlInBvx
c rp aru rp a QHqecKHXrrocJreAoB
are.nlHo creri.
Asa nerporpaSnqecKHX psAa AaHHbrx Mo)Krro uccJrenoBarb
c o B M e c r H oH a o c H o B ec x o A c r B a H x s a n H c e f te 6 y p o e u x c K B a x H H a x .
flpu arou r'{x fieperacoBbrBaror,noAo6'o KoJroAeKapr, c ror{olubro
n p o . i e A y p A i r H a M u q e c x o r or p o r p a M M l i p o B a n r z n
l2}l. Kax.{al ro.r-Haii6o;ree
xll olHolt flocdreilouare"r]bHocrli
cp anriHnaercs c
6u1lr:roli
To'l;<orir.lpyroli noc.rleAoBarerblrocrrr,IIprrr]eh{ co6,rrogziercl Jrirurr
y c . l o B r r e ,q r o c r p a r H r p a r b f i . r e c x i l rlio p r l 0 x A o J r x e I { 6 0 r r r c o x p a u e H
n o6enx rocfleroBareJrbHoc'frrx.Tarlzu rryrer"t jlocrlfae.rcn HCTHHl i o e v n o p J l n o q e H H er l o c x o A c r R l r ,T a K K a K o K o H q a r e / ' I b l t o e
Pa3),.Ieuei r l r e i i ! i e e r C M b I c . lK
I a K J I I { T o r T o r l t u e c x t t If iJ, K I I - \ p o t i o J l o t ' t t r t e c i < 1 i l i "
^A4o>xgoBi-rcc'iuAono/rH_r.rre,rlbHiJe
ofpzrHHrreirr{11,
riolopbre npHBeAyr
r oote-ltilterrHro cnellti$nuecxrrx roqeK ABv:{ fr(lc.{(-.,toeare,tllgocreri,
I t t 6 o . . o S y r . ' a c s l r l O 6 r , c . l H l t e n u el , i t < o r c - r t t , l ( , 3 u.ti a j i i r { J f o C ? r - r , { e H T i
(r.'r.ticirricu.re4cJBllre,'lrrri0crt..t
c H3KOl'OpOitrOqrcr'i ;i1r\,'roii. T.rr:lry
o51ril:ol.re
, r " r r r io c r r o r i r: r i r ? \ l r p K e p o g i r p e t r e . [ a x l r i i
cp,,u:iHai,i]_
i . ' n ; I Xi l 0 C , r t l t . i l , o B i t r e J I L H OO
Crrter ; -t <
t 1 e ( T B , r l t t o t c.ut ,t ) . j 1 ' h o c t i o B a l i l i . r
itai)KeDOB /{or'IitigbI 6tttu
L]
0i
ca x:o
i
}'ur,
,,,r-.,i:1
| + . ; ) iI
rAe #ir -- orK..rli.rK
KapoTalr(Hoiine;tel,reiruoiiI ua r,ly6une / rr rrep_
- O'fK,,lliXir-rii l.t{e nelteMeHHOAIIa r;r\'6lrHe'A
BOfi Cliila>KItHe,a Uy,q
246
124t4
313i3
4
1 2l ?.
--1 - - - - F - - '
7l ?(PruluJ
4l 41
crlr[.]:l-pa(;lr.lecxrte pa3pe3bl, rt:c6palieurri'tc BMecre.
Ha
XiIDaKTCpHcTHKa' b3ritpeHH!t
lprr HsTrlpDana, a paepe:,i/-qeruOe.
l, c.,,ct|il:T
co;1ep)Kul nDocrLls nlcDbl Da':ii-iiireor I ltc 6. i{arDHi'.n
i,: t,,'rep",r,ie. tt-irtcHsctcl
l
'
{
"
f
i
IitilCi)U::JlO:l D Ua3pe3:lK
fitj! il!)Kil)' taClill n03MrJX!lrJ:11{ F rll:'1li
tJ,
u2
^l
i-'l
i-.i
I
r*-J
ij
'',:,:t --,'-,,.)
;'ii.
ii
t;!11:A
.itJ"
U: i , ' / . , ''
,L-)
U: It .
7::il
Lr:
Jt
vl
L2
.
t/
f
L*-/l
-;9- (r.rrapi)2f
r
?u!-6
crai,,tzlz_1c
I!
1,6-(Crap:i i --4-9-l!
n'C
2'2;
oio 2 4iA
; iI ; i :
l*
3
2t2o'tiL
-l t-+
2 .1 7 0 2
E'-37
xgl,ittl,r{1.tDfi3111161.
P
Dj, --
a? I
u3 3
4
I r , _l__.L_l_._1._i
56
01234
t-,r I l ,l
! b
234
P t t c . 4 .!7. llciiycc:uriiirble
. i . , r i ' r p i l ' r r , {o, , i . i6 . 1 r u r { o ; } l r t tilir I - o ; - , 1 o u o r ;, :r p e i i r r i , l i r , t r , i
i 2 3 J, i l l r
L r ) . ' , , i l i i i l . l ':l l , I f O i ) i i : i r { 3 O H I l p O B a l t t t ,X. .Ct ; ' r l r : r r ; t t t , v l . . ] 9 p ; 1 1 . 1f12r8. rl .
t-lli.ii:1,': I iiil)Ii.{ilrl rot,it{;i iica"rie,aoB;l'le,nLiliicrii, ra(,,ol,-rarc'iu,ii,;itt,'_il
; " _ ' . ) a K : t i : l { I l i i i . . r ; ) i : L i i l ; 5 l c t c , l l l I i . i , { i . r . , r i it , ; , l t i r l 1 i
;tct,.tt...u5
'r.-'_j,LlIi)C'iU,
C ( l 1 r ' . i , , : t : itt ) ' j O i j l , : . - . j i e ; l 1 t r ; i l r , ! i , r . t : ; i J , : j r \ . I j - , t f . l : . , : r l ; t j t : : C .
rt:: eropoii, pcitlr,tLill r f
"ircScHitfr tr:r itt'11:oli ciillrliifliulrt v ml)l.1ir.
p::r:jl.1cpa n'.,(rn. lIp:l lio],I \,to;,Kito iiciio.:tbjoB.r ji;
Heuri:t *- tl6,;itii\:i
M r : { c ) K ec ' I B r l i j t t : } . n l l I I l I b l , ' { c t ) : i r J i l } l T e . i t b H b t x l , , t c i l , r i o i o p l i o i i
tt ]jeii!etr ;
IIClC.l:r r!li)'r ir tlo'i'r)'io \t Lrty Hecxoi.cTBa :
(t %ut
( c r a p r )2 l - -2- - 4- r - 6- 1 6
ul 2 2 4 5 1 6
-3
u2
ut
-iO,'1)l'lii.i (lC1)'ftst'lCTiJ()B:jTb .iipj/f j.pyi)/.
,l,,ti:1hl r{Oil COt'l:-i.lts;.re
ltlirON-rlil-l l{:l (Jairr}il€t fl.litif:;tiUief0
C t i O { C i i i i t , i i O ^ 1 r r 1 r , 1 | 5 ' - r :i i l i _ r 1 r :
,l.Ii)f"ii,'lliiill
Oiiiilii]IrtClir:ril"I:.riiilititi
KOfpe,'1iI{litI
r r c 1 , , r { - . } i . i .ItC. I : r C r , r .
iia:-i'Cfi it cCI{Cilltinu
Paspet
U
Pa3pe3
V
2'r2-f, 6t,6
o13 2*:t4
ri, ' j-s
I
ti
2i2 a 2t?
--i- -i+ -
!($rr;ru)2l?
?',? 4 616
Lio 2 4t,4
i1 ,l r
1 3i3
- r-
2t2 0 2i2
-i'-l-- ---t---
1C
) .- Z a 2
A 2 1 ? - 1 ; ; : n l u u1' ti >
L=?.6
E=16
(Qrir;r:r)
Frrc. 4.28. Peey,rlrarsI, no,'IyqenHbleo6teAlrHeultelrnoc,leAoBarelrgocrefi U v V.
Crpeaxn
B:darp;JIi:yl
ra,Ka3;i;l3rcr nca.rr:rcBar?rbi;ccrb il:,'rlli'l or oclJoBaEltt Ao nepulglibl.
O 6 u r e c p a c x o ; t < : i e s l t eo 6 o g : t a q e s o l e p e s )
ilo uropoir cKBaxrlHe. Ecru yroAHo, pa3JILIqHbIMnepeMeHiil,lM
\,ro)riHoIrprrnHcaTbBeca ol.
A , a r o p l i r i l ; l x H a M r { q e c K o r on p o r p a l { M u p o B a I I H nI i o 3 B o J l n e rI I af i: Ii cjrirrcTBruHsrfi nyTb B 3Tofi Ta6nurle II3 JIeRoro BepxHero )'i,'Ia
' , r t p : r n u i i H t r x { H H i iy f o J r r a K r . r Mo 6 p a 3 o } J , t l r o 6 t I c y M M a M e p I { e (l;io^icrBa 5ll,ra l,rilrIrIMaJrbHoft.crparurpa$irqecKlili nopfAoK co:"plll{tleTctl 6,rarOAaPt TO},{y'qro HCCiIeAOBaTeJIb
Mo)I(eTABHfarbcfl
T O . ; l b l ( ioj j ' r 3 ; ; 1 1 2 i 1 i r ; 1 , I11' rl ' . 1 : i r c ., i . 2 7 u s o 6 p a ) K e r I{l c c ' [ o ) i { H r ] l fnI p I l KllpOTa'
\iep, B I;OlOilolvlIrpoBoII]rCfl cpaBHel{i4eTpex ilIIrellBa.IIOB-3avc'i tt::.
,li:^ r.,.riiic-'ii
cirna>xlrgl,lc qelblpblrq uIITepBajtnN{:i.t11lyicl:t.
r r o i , r i . r r , u a r q a c r b c r p o l ( I I c r o J 6 u o B l l f a r p H u b ln o B T c p t e r c u ; 3 T o
oA'l
rro3B0rfleT anropr.rrMy c[ycr]4rb BHH3 ry rrnr-HHyro
KaporaxHyro
A a a f p a M M y K H a r r a r y ^r - t 3 a K o H q n r b f l p o i e c c . H e x o r o p u d
rpuuepbr
nyreli B MarpHL{e BMecre c coorBercinyroqauu
HM pe3y!,rbrar.i}Jr1
crpararpa$u,recroi
KoppeJrsrtnx npaBeAeHbr ttu puc. 4.bg.
.[,.nn naxoxAen,r.IfforlruMaJrbHoro nyrn HcnoJlb3yercs peKypcnB_
Hafl npoueAypa. HaunHafl c JreBoro n-epxuero yr.ni
(uau'aao; nu_
6upaerrane_pnuft r.ruTepBar,r
paBHbrM u1 rrJrv af Mepa HecxoAcrBa
BAonbrio6oro ryr' oArHaKosa
H paaHaZ+i'. iiii uo,?puro,,,,
c.ue4ynquriH^HTe-pBaJr
Mo)Ker6trrt "rru6ou, c ilrleli na"epo;
cxoAcrBa
2+2+0:4, HlrHn1 c o6rqefi*epo;r-n..il1.r"r'Z+Zi"e_
+2:6. Apyroli Bapr{aurMoxer 6Hru raruu_:ec/rnol
Bbr6parl4
Ha rrepBoM
rrrare, Ha BTopoM [rafe Mo]KHo nu6parl nu6'o
uz, aa6a
02 leer BKJIaAa o6uyro rapy naaroAcrBa, paaHyrc
2,t
H3 3rI'Ix seyx c.TyuaeBror, B KoropoMn,vrb
l.?l?:.,6..9o16-1pu"
(HaqaJro)-+ur+uz uMeeT MHHuMar,IbHyro
Mepy uec"o4cre,ar IIo,[1,_
qaeM, qro co6crseHuo neprui?
ruar ocyqecre,naerca n zr1.
Bu6pan B KaqecrBe uaqa,rrgoti TorrKr.r,1 c
,lB|lrfi Bo3l,{oir(}rr}1ri
BapuaHTaMHBTOpOforuara lu6o B Lr2,JrLr6oe u,,
r1cc,rel]relaeo:r_
M O ) < H b r eB a p [ a ' T b i r p e r b e f o r r ] a r a . c H O e a H M e e r c r
uerrlpe nc_rM O I K H O C TH
U3
: u z B ^ t 4 ^ c o 6 u { e r ?r r l e p o f iH e c x o r . c r B a2 + 2 * 0 * l : 5 ;
a1' ilycrr
H 3 L t 2B ^ u 1( 2 - t 2 * 0 + . 0 : f ) i H 3 a 1n a z
e + d , + 2 + q : 1 0 1 i r r u - ,u ,
\ uz Q+2-12+0:6). HauuenturaflcyMMacooreercrever
rvrr_r
( uaua"ro)
* tt ;-+,2-->e
1, ra K qt o on""r rnLniiii ;;,;i;;' ; ;i : ;.i,;f
xorr.B roqKyu2.p,aneelpoBoAr{rcff
cxeAyroru,af
uieparlun,B xo.ro-
poit tzcc.ne,lyerctrpe3yariar ccyulecrB,reggrr qel.bipe-\
Bo3Mo)Klrr,r{
[epexoAoB H3 U2.rlyrr c Mrr'riMaJIbHbrM
3 H a q e ' l r e r , ru e p u H e c x o A .
crBa onpeAeJlfler onruMaJrbHbrrluar iiocJle ,rz. flljoucc'c
t,onrn,roe r c f l A o r e x n o p , n o x a H H ) K H n a( , r e n a n ) r o q K a ( r b u e u )
6yler lc
crrirHyra. B npuee4eurro-\'npr.{Mepeorrrr{r\rr,[o"n,ii rryro'
aaio
(Hava.no) + u t -> tt 2 --+-7t, --.>Itt + u z -->4s** (rr __>
(xoHeq)
c o 6 u e i i l t e p o f i H e c x o I C T B a1 0 . M a r p r u a 1 4 g o . i t \ . : q e l r H b r e
c1pirrrr.
r p a Q u u e c x u e f l o c J r e A o B a r e J r b H o c rursr b 6 p a x e u r i u a p i r c .
4.2g.
u3
U ; 4 .VJ
C r a p r 2 l ?- - - 4- t - 6- t B
. {-+
u,.2ri? 4 6 i0
.,2019 2 414
r r .I I i * l 3 l 3
! ' .- -2 1I -2- . - ' J 0- - r2- 9 -i ?
U^
I
vl
V.,t;a.:'^.
Ya'tt;ri
uz t l
F*_*r
r. - i0
: . ' . : , 4. . 2 i . O n l i r u : t , ' i i ' r i o ec O'jre;1uuc it ll e tr c;,:l r,i .,rt.rf.i)"tAg{.)cte
ii U ll
crptri',,'.:lTrrlrlex
O6llre,rar:,-:xAriltre
] : i e 3 b r S i r F r ii!-iJtnox nyra{
B cjrtri,;ti,LtaFHi*l
0*(J!(',!l,j:!
p a B t 0 l i i , ? , e. l:altlicil)ne.,j.,D03lC)r-iJouy
gnqcel,irn
nocJe,qoB
9A.A
aT eJj h Hioc TII
EJIflU}I fi
AB'TOKOPP
qaHa pHc. 4.30 npeacraBJleHblpe3ynbra'rbl raMMa-Kaporaliia
,l.fH cKBaxHHbr B pa3pe3e fleHcHnlealrcKnx or.loxenufi B 3anaAilov Kangace. Pa3pe3 cocroHT Ii3 H3MeHeHIIbIxI'I3BecrHsKoB Ll
c,taHrIeB. Vls-ea pap.ila11:rlnKaJIufl,-4} B f,'IlIHIIcTbIx I{nIIepaJIax cJIaHBbiOTHOCIII'€r'Ib}{0
Ubl xai)alirepli3yloTct
coKIiM (lonol't, B To BpeMtl I{aK Il3BeCT'
HqKaM cBol'icTBeHHa Hli3Kafl paArloaK'
lriBnocrb. B aroM qacrnoM pa3pe3e
5bt.no sal\,IeqeHoHa.rl{que u[l{JloreM' T.e.
Sonee r.rJIIIMeHee peryJlflpHblx noBropegrrii JitiroJiofuqecKIIX pa3HoBIIAHocreii.
Eernoro B3i,'rflAa IIa pe3yJlbrarbl KaporaiKa AOCraroqHo, qro6st y6e;Ii'irrca r
TOlr{, tlTO H3BCCTHfili nepeCJIaHBaeTCfl CO
c,tLlHIIaMIl, KoTopble I{MeIor npH6"nuslle"lbHO Ty )I(e NIoU{Hocrb.
raK )Ke KaK Lr Apyrue
flooropeHIlfl,
cnoftctsa nocJle.(oBareJlbHocrl'I, ycraHaBBblql{c,lleH}1fl
noMou{blo
,'iltBaloTcg , c
McpbI cxoAcrBa Melr(Ay qr'reHaMrr 3Toft
irccJIe,tl,oBaTeJIbHocTH,
T. e. nocJIeAoBare.rrbHocTb cpaBHr{Baercfl c caMorc co60fi
B JIOCJIC.&OB
ATCJIbHbiX NO.IO)KCHI]fl X I] BbIqliCJlfleTCfC
l T e I I e H b C X O I . C T B aM e X A y C O orBercrB)'ioiulrMH
rrHTepBaJiaN,rri. Ec.rlu
Krx(Aaq Toqria cpaBHUBaercfl locJre!,oBareJIbHo co BCrl(ofi Apyrofi TouNori, Tcr
o6HapylKuBarorcfl Bce flo3uqr.rfi xopoue-
ro cooTBeTCTBIrtI{ Tar{)Ke OnpeAerliteTcn creiler{b HecxoAcrBa B Apyrux no3iluttxx. .[,,rr ocyiqecrBr'IeHEflsToir onepaur.rrrBpeMeHnofi pn4 AoJr)KeHLrr\{erbHeKoropbic xaparrepucruNrr. on Ao,rxer{
7 1 2 L)-2 -r--Z's
ut i
B cu,'ry cBoeft fI'I6KocrH STor MeroA c,'Ie)KeHxflKaxercr noreHKoppeng,IHaJrbHOoqeHb srlQeNrunHblM cpeAcrBOM LICC,'leAOBaHI'lg
altnapara
MolqHoro
npr,t
I'Icnorb3oBaHI{Ii
coxaJIeHI{i,o,
Aaxe
urrrr. K
{ t r H a r { n r r e c K o r on p o r p a M M I l p o B a I I u fof H r p e 6 y e r 6 O n U o r O I u a [ I H H OTCJIe>KHBaHHe
Ar'lI{HHbIXIIOC,'IeAOBaHOfo BpeNIeHli,H COBMeCTHOe
IIccJleBblnOJIHeHIlH
peKOMeHAoBaTb
!'IIzllib
nplr
MO>KHO
Te,'rbHOCTeii
qnrer'IbHoliBa)KIlocrH'
IioB:lrrlr ti ttc t<,1rc
cocrotlrb
V.
tI,l
1 ,t t . c T t
,trJ'.ho60i
I
Ii3 fiociteAoBareJlbHocrlr
ua6-
E
jcO
J35l[---_'_i'-----1
i
i
i
4000|
i
I
i
4f :01
,
l
'-.,
ii
2a0
5-
--<
>
/
>
<=
j
a-'"'
*-->-
:.
: 4100
>
*--->
___.-=
t
rrriC
(.
4z0a
4250
*-'
><.
Puc. 4.30. Peaynr,raru rau-
y, usuepeHHor?
noAeuriirnepernreHuoir
e iT;#|f##, ;"J;3#rJ"Tffff;
IlocJIeAoBarerbHi,re
BpeMeHI.t
,t.tr'IltB
TOqKax
N'roMeHTbr
npocrpaHcrBa.
KaxAoe
ouoxeHsfi rue$raHoiicxnaxuHe B 3anaanbruKaHsace
249
Ha6nroAeHr.te
6urr orAe.ueHoor npeArxecrByroulero
Aodrrx(Ho
na6JIIOACHHfl HCKOTOPbIM IIHTCPBANOM
NO
BPCMCHI,I HJIIT, HCKOTOPbIMI
paccroqHueM' Koropbie flBJltlorcfl nocrosHHbtMLlr.Jtfl
AaHHotopqAa.
llo.uoxeune ua6.npAeuus B prAe uu 6yaena o6osuaqart Hra)KHrrM
rzHAeKcoM,Ha[pHMep fr. Iloerouy ueo6isarer]rbHo ffBHo yKasbrBarb
BpeMfl I'Ir'IHpaccrofl'Hue Ailtt nepeueHnotl X, "raw rax ono Bno,yHe
xapaKTepH3yercrrHHAeKCOM
rr Molrier 6Hrs g c!,iyqae Heo6xo4rauoc r l r o l p e A e . n e u o6 . u a r o A a p f lr o M y , u r o X : A l ,
t4-e A_paccrosuze
M e ) K A yc o c e A n u M l rr o , r x a l a u . _ B e c bB p e M e H H o lpi a 4 c o A e p x ( H Tn r o _
qeKr.r HMeer o6utylo
A J T H H yT : L ( n - l ) .
PaccroflHr.reMex(Ay IByMt
yt u yt+, Ha3br_
"np6ulru roqKalrH
BaeTcf JIafoM AJtI.rHbr
T, tAe X - qI,ICJIO
trHTepBaIoB Mex(Ay AByM.E
TOr{KaMLr.3ro - cMeureFruenpeueuH6ro pr,u,a orHocrrre,rluo c-e6g
caMofo B npeArrrecreyrcquil MoMeHr BpeMeHriuJrlr B npeAuecrByro_
IueM noJro)KegHa.Mexny BpeMeHHdruapalaux H qelrfl\rr.r N{ox(Ho
rrpoBecrr.raHaJror[o. Kaxaoli cBrrsHB qenr{ coorBercrByer Ha6,rroAeHIIe B ptAe. Ec,ut l,llt IIplI.rox{}iM ABa oAI.tHaKoBbrxcefN{eHTa
qertu Apyr I( Apyry lr cpaBHnM HX Me)KAyco6ofi, ro rroryrrirr{ noilapHoe cpaBHeHltec JraroM 0. Ec,ur Mbr c.qBliHeMoAHy u,enb Ha o;lHo
3 B e H Or a x , u r o 6 u n e p B o e 3 B e H On e p o o i i n o c . r e 4 0 n a i e r ' r b H o c ,cf H
peBHlrBa,'rocbco BTopbrM3BeHoMBropoi:r,To BCe ApyfHe 3BeHb, Tar(x{e
cllBI'{HyrctI' il TaKoe IIoJlo)KeHIIecpaBHI.IBaeMbtx
IIocJIe;loBareJIbHoc'ieil Haslrsaercrr r.rMelotrliiM,rar l. Ilenlr lrorvr 6i,rrr, c4atruyru
6oree qeM Ha or,Ho sBeHo, ri nonapHoe cpaBHeHrie ror;l,n 6yuer
- fig\{erbnar 2 n raK AaJree.
Aeroroeapllaqllf c ,TafolvlT-oro
r(oBapuai{Hfl Me}K.itv BCeMri
ga6,rrcAegust'/.wYt lt ua6,rroAelrr.rfM14
Yt+,, T.e. r{oBapHaqrrgnuqLICJIfleTCfl
MeXAy lrJreHaMHcaMoro pflIa n TO|O Xe pqAa, CMeX-(eHHofo Ha Jrar AJurHbrr. Onpe4e.nsroqee ypaBHeHJ{eaBroKoBapnar{tar6
ecTb
cov
(4.58)
Aaroxonapuauurc J'iaroM0-ero npocro .u.Irclepcr.js
Bper.reHHord ptla. Ec.nupa4 orreHbA.lmlrulrri,
a.rraf r xoporr<ari,
To cpeA-
H C e A a H H O f Op f A a r r _ c A B r 4 H y T o fpor A o B B c y u I H O C r HT O X ( A e C T B e H _
H b r x y p a B H e H H e( 4 . 5 8 ) x r o l K e r 6 l r r l y u p o u l e H o . O A s a x o e c J r a T
rB.lrrercfl suaqaN.roft4po6Hoft qacrbro AJfl.rubrnpeueHH6ro pflAa, To
pa3.rlHr{HeMe)KAy cpeAH}IMHcraHoBurcfl CyUeCTBeHHbrM.
BbrqUCJnr e , i r s i l u r j o K B r B a J r e Hyr p a B H e H H r ( 4 . 5 8 ) e c i l
tn
L --sr
covr
250
s
/)
t:l +a
v' t v' t _ _ -
+
a
1:l+r
(n-")(n-r-t)
vr t . S
a
/:l+r
v, , _ ,
(4.5e)
l
C
f-i
"f
I,
I
r
l-
L
l
r 'rt n l
u f
tL
\r/ v
t-_-l-.j-rrlJ
rr
53
1 o' 1
,:_.t r
c' !-yptut xcl .l u a r i M ' \ l a - K a p o r a N a , u a o 6 p a N e H H o r o H a
4.30.
J I a r 4 8 c o o r B e r c r ! ] a r c , t r B t r rlyo r ' r y 6 x t t eu a 4 8 $ y r o e
Puc. 4.31. Aeroroppe"rlqllortl{a,l
14lreerCg COr,'IaUeHHe O TOM, qTO aBTOI{OBapllaUI'tflBbIqHC,lqeTCtl
n,rfl r'rafoB or 0 AO nilHMepHo ttl4. TTonyueHHble 3HaqeHIIfl N{ox(Ho
ilpe.lcTaBHrb r{aK aBroKoBap14oIpaMMy I.IJIU allTolioBap}lauHoHHyIO
rrpeAcraBJrfier saBHCuMocrb aBToKoB.apHauliu
Q1,uriurrrc, Koropafl
aBroI(oBapi.IaItHoHHyIo QyHKrillrc
or Jrltia. Pllc. 4.31 npelcraBJltler
't,.rrri
tr.ant{brx KaporaX{a CKBa}KI.tH, llsO6paXeHrlbIX -Ha pllc. 4.30'
J(nusaa r{aqnHaeTctr c MaKci.t},,lairbHofo :JHaqeHr1rr 672 A,'ItL'lara
i : ( , 1 ,s a r e l r . r r 6 u n a e r L I f t o A H I l l { a e r c f l c H o B a A O d Y I a r a4 8 , x o r o p s t i t
l l o o r B e r c I B y e T p a C C T O q H H I OB r I p O C r p a H C T B e ,n p l l 6 ' l H 3 I i T e J I b H o p a B ,ic,M--v48 $,vrar,i, TaK KaK AaHHLIe fal!1Ma-I{aporax(a 6bIJII{ orll'l(bDoBaubr C lrilrepBalroM A I Qyr. 3rO eCrl npiiS,rllsareJlbl{O BC"'IIl'jllHa
B C p r l r r i l r . ' i b r i o f o p a c c T o f l H u q M e x A y n o C J I e I O B a T e J I b H b I M HI I O J i o > i i e I t t l t l t ' i l i I l 3 B e c r H t l K o B B I I O C J I O A O B a T e J I b H O C TnIpI 'e r c r a s r e H H O t ? H a
ptic.4.30.
- 3TO KBIIAE1l.rHr.i[r,i, B KOTOpbTXr.r3Mepflercrr aBroKoBaprrarlHrr
parbi e,ilruru H3MepeHlii epeuenHoro psAa; B Hllue-M [puMel]e3ro K3aApaTbl eAriHrl{ 3"'IeI(TpOABHx{yqeii cu,rst E. 3rO OsuauaeT,
qrO anroxoBaprraUrifl qyBcrBHTe,IbHa K H3MeHeHLltlMMaCIxTa6a Bpe'
ueHU6rO pgAa, qTO AocraBi]fler 3aTpyAIIeHIlq npH cpaBHeHI'IllAByx
anroxonapuorpaMM. OAsaxo ecJIH BpeMensoii pflA craHAaprn3oBan
tsblqllTaHl|eM I{3 KaXAOTO ga6'rrcneHufl cpeAHero u Aer'IeHHeMHa CTaH,taprHoe orKJIoHeHHe, PflA 6yeer [peAcraBJteH B eAHHHllax craHAaprlloro orKJroHeHI'Ifl II aBroKoBapgauutl 6yaer llMerb craHAapTl1'
.:osaHHuii Bnn. KaK orMeqaJlocb B rlr. 2, KoBapllaql{fl craHAaprl{'
25r
r
II
I
I
3oBaHHoft[epeMeHHorl ecrb Koppeilfl]\rrfl, ro xe BepHo H
Alrfl aBTOKOBapHarIHft.
llpexae rreM cranAaprr.r3upoBarb Harx npeueuuor? pflA, Mbt MoxeM BbrrrucJrHTb
cpa3y aBToKoppeJrsq[rc,pa3Ae,'II'lBaBTOKOBaprIarlr{ro Ha Ancnepcurc pflAa, [.. e.
n
'r -
cov u
----17
var I
,
t? .
Y , Yi - r, _ l ,.r
i'_r
(4.60}
n
S
l r t 'I ,- v)w
T.J\
Anroroppe,rqqufl BpeMeHH6ropa.qa xoHeuuori A,rrrrlrbrn c Jrar_oMT, xoropufi flBrsercq sua.rr.rj\4ori.qpo6Hoii qacrbro n, MolKer
6Hrr' slt.I[cJleHa KaK orHorueHae AByx Be,Iaq]rrl: qricJrureJb- Bbr- oi{eHKa
pax(eHHe (4.59), 3HaMeHareJrb
y, \,ar y;.
IlocNo,rr,_.
fir
Ky rIpeAeJIbIcyMMI'IpoBaHHqB qllcd'IlilTe,'Ie
I{ 3HaMeHare.rre
o.rHHaKoB b I ' T O E H C U I H I { I 1 B I . I A P C - 3 . Y J I b T A T AM O } K H O
YNPOCTUTb, COKPAT].IB I]I]C-
.no ua6.nrc4esnitn-r.- Kax H n $opuy,re (+ SSl npe4e,,,or
cvh{}.rfi_
poBaHHfl
6yayr or l: l*"r tro n.
:y | 7,
t_a-tY,>Y
I
i-3
l ' ; : r 7 - ( i ] 't 1 2l ' , ' : Y 2 - , - ( x r ' , _ , 1 z j
(4.61)
H a p a c . 4 . 3 2 n p e 4 c r a B J r e H aa B r o K o p p e J , r o r p a M vial a H H L , r xf a M M a - K a p o r a x { a , [ p e A c r a B J l e H H b r xH a p 1 4 c .4 . 8 0 . 3 a u e r ] t n r , q r o o H a
rrAeHrr'{qHano Qopue aBToKOBapHaquoHsoli
syHxrluH, HCK.r}Oqari
rr.irrrbro, rrro oHa npuurlMaer 3HarieHaflMe>KAy* 1,0 rz _i,0.
Heo6xoAunao orMerlrrb, r{To B TepMI,iHo,ror.rir{
TeopHr Bpe}1eHrrfix pa4on r'rMerorcflHeKoropbre pa3HorJracrrn.Hexordplre aBropL,r
cqr]raror aBTor(oppeJrqrlr.lrc
IIapaMerpoM coBoKvrrijccrr] r.t ]rcl]o.rrb3vrc'l repl\{ltH cepliarbHaq KoppeJIfiIIxfl KaK gKBlrBarrrerrr
crarflcrlrKti.
nbrlr],Ic,'rfleN{oii
no nu60pxe. !,pyrue Hclorb3yror rep\I].irr cepfia.[bilafl KOppe"IflULIqB 3HaqeHLIfiKoppeJIflULrH
Nrelr(iy ID)',\.,if{BpexieHurirnau pa4arrau. Hexoropbre aBTopbr noc,'ielliroio r(oppeJrrrilrrloHar s t n a l o r .x p o c c - x o p p c . n s u u e iM
i . s r 6 y : e r i H C r l o d t b S o B rxr b
a K ' r e r ) \ t4r H
rBroKoppeJltrr\uw,TaK ir repMr.iH83aHMilafl Koppe"qrrutuu ue dvAerra
.'leJlnrb paeluulrii MelKAy crarucrrrKaMr.rri ilapa\rerilaMri.
3alreraM, rITo KoppeJiorpaMMa e 4elicrnuranonoarr., rlts,rrrercii
- l , B y C T O p O H H eCf i O
, r p u q a r e n l u o f i q a c r b r O - 3 e p K a , r i r ) F r b r Mo r p a ) r ( e qacrtl Mu noncut.tM 3To -qBJreHHe,
HtleM TIOJIO>XnTe,rluor?
nepuyntrrr4cbK uamefi auaJorrlu c AB)'Mfl uensr{a. Ecrru ogHy ris rielret-l
o 6 o : H a . r H r r q e p e 3 . 4 , a 4 p y r y n - q e p e 3 B u n o c ; r y e A o e i r e , , r r Hnoe peABufarb qenr .4 BnepeA tlo UenE .8, ro no.tryqarcxlfiecflr<oo$QracocraBttr no,ro)KIiTer'rbir]'rc
uueHTbl aBT_o_KoppeJItIri'lI{
qacrb Kopper ' r o r p a l r M b rH
. o e c . t r . rA B H r a r b u e t r B B [ e p e A n o i t e l u , 4 r s r , r q r . r c _
t\\
JIflTb
ABTOKOPPCJISI,IIrc, TO JIAIH
6YAYT
OTPITIIATE,']bIII,]MH, T?]Ii KAK
orHocHTeJIbHoeABI,IxeHHe AByx noc,'IeAoBare"rlHocrefi IroMeHflr,tG.
252
Itlltltttt'
50
0
r00
uso6paxeuuoroHa puc' 4'30
raMMa-Kapora)Ka,
P uc. 4.32.Anroroppe.lorpaMMa
na o6parsoe. I{enu A
HarrpaBJreHlre
n B uAeHrHqHbr,nosrorry
o'rI,l3 HIIX CABI.iraeTCq
B KaKOM HaIIpaBJIeHI.It4
6espaS.nUuHO,
_OAHa
Ha npamnKe MbI He paccMzl'rlloc[TeJlbHo apyroft, TaK KaK f-':r"'
priBaeM oTpIrI{aTenbHyIOqacrb aBroKoppenofpaMMbl' Ho oHa IlrpaB px4 @yple
cr HeKoropyto poJlb rlptl pa3JIo>KeFII'III
Koppe.rorpaMMbI HanoMI'{HaIorxapaKrepucriiKlr Bpel\{eHHblxpt1AOn. cpanurrBar KoppenorpaMMbrBpeNreHHoroprlAa c KoppeJrofpi.ltvlMoAeJefi, retxo y6e4llrlcx B To\{, tlro
,\,,ra\,ru
uAeanH3I.rpoBaHHbix
fo
r\lole"rrb BpeMeHH(r
corJracyioTct. llpocrefiuaf
or.ru xopouo
pac'
-3TO
HOpMa'ribHo
Il
He3aBI'icliIvILI::
pfl,I,a
IOCJIeAOBaTe,IIbHOCTb
npe.r.e,'reunrtxsa6,uoAeuIlfi. 3ro SHaqHT'-qro lle)KAy Ha6,'IIOAeHITII'
r,tu s i{eXoroputir uOueHT BpeMeHsI Iz ua6;ic",1ellI{tlM}In 4pyroii r'roM e H r B p e M e i u t * T H e r I t u K a K o i i c e q g n . T a x o e y c " I o B l i ee c r e c r B c r l lio B roM cJlyqae, KorAa eperr'IeuHolipff,4 rlopo)KAeH cJlyu2;"ott
npoqeccoM. OxuAaeltaan aBroKoppentlrne AJIF erofi uoAellz ecrb
p,:0 a.[q Bcex JIafoB t, 6onrunx uy.nx' TeopernqecKat Iioppero'
ilI4Hllfl' npOXOASI{at qepe3 'I'OqiT)ahiMa B sTOM cflyqae-IIpflMafl
,,'r'f:0.
eagucltvoHeKo-f_opoii
!,pyrue Mon,eJrlrflpeAno,'rararor HaJir]rrr4e
ga6,rio.u,enuauu.H anpuMep' xpeArrr.r MexAy rroc,IIeAoBareJlbHbIMII
qTO HeKOTOpliii np OqeCC[Op OX<AaeTcfiC,'Iyqa itHu rrauUop11
o.r'rO)KtrM,
fi
MII' KOrOpbleycpeAHf IOTC
\\ aJ,rbHop aclpeAeneHHbIMHI{a6JiroAegr.ifl
rorqac >Ke,KaK 6u.ln nopoxAeHbl' T. e.
L
r-
Y ", :
7,
$1. "r
,kA i')
t;,t
253
.:I
\+
JTO MoAeJrb cKoJrb3glueto cpeAHefo lr oHa HMeer KoppeJrofpaMMy Br{Aa
(4.62\
P":l-.l@.
t'_
I4ueercs utrpoxnfi cleKTp rtloAeleir nospacrarcueri cJrolKHocrn, KoropbreMoxno 6u.no 6u npeAJ'ioxurs.XopoureeBBeAeHHe
B
sry reMy npuBoArr IOn Kenae.l [63], n rpuMeHeHur{
K rr.rAporro"
fnri-Plesnesllq [64]. Pac.
4.33 u"rr.nrocrpupyer
rrocrpoen]recJroxHoro BpeMelrnoropqAa, eBrflrou1eroce
"ruHeirsoiirou6ugauHeii6oJree rpocrbrx pqAoB. Ha puc. 4.33,a [peAcraBJreHapefynspHafl
npaBrrJrbHar
cr-tHycorAaJrbHafl
BoJrHaH ee KoppeJrofilaMMa.
flo uepe
roro KaK peA cABr.rraerctno Qa:e oruoclrreJrbHo
caMoro ce6er.rrrr
B CJI)rqae,eC,lH IIIiKII CnapHBalOTCfl
C BIaAI]HaMLI,KoppenorpaivIilIa
r i 3 M e H q e r c ror r + l A o 0 u s a r e M a o - 1 . 3 a r e l r x o e Q Q H r l n e H rr i o p j)e,'rflr{HucHoBa pacrer, noKa He Aocrlrruer gHaqeHtrfi*l s ror l',roi\{eHT,KOrAa CE|HaJI CABI{HeTC' poBHO Ha OAHV
-c A,'IIIHV BOr'iHbI.
Ha pr.rc.4.33,6 uso6paxeu cHrHaJr,no.rryqeHHbrri nououtbro rrepnori I.r3 paccMorpeHHbrx BbrrIIe lro4eneft,- nocJreAoBareJlblrocrb
c , r r 1 ' u a i i H u xr r n c e J r .K o p p e l o r p a u u a 6 u c r p o y 6 u n a e r o r I c H y .rreBbrM
J r a r o M ,n o r o M c l a 6 o K o n e 6 r e r c q o K o J r oH y a a . O 6 a 3 r H p r i A a
rB.rtgrorcg cral{uoHapHbIMLI,T. e. g FIa6fl}oAet{HRX
Her 3Haqrrre.lbIroro rpeH.u.a.Hecraqaouapuufi clrfHa,,'iu:o6paxeil Ha pr.{c.4.33, a,
rre sa6.nloAeHHfl,o6pasyrcqae riocJreAoBareJrbHocrb,HeyKJroFrIlo
pacryr rro BeJrliqlrHe.CoorsercrByrourafl r{oppeJrofpaMN{anor(isbrB z r e r , q r o K o p p e r f l r l n q H e y K n o H H oy 6 u n a e r . H a p l r c . 4 . 3 3 ,e y z o 5 n a ; x e s a x o r r a 6 u u a q u qc r y q a e B 4 . 3 3 , a u 4 . 3 3 , 6 , r . e . c r r l l _ \ . ' c o rr:r.a,rrbHori
BoJrHbrtr HaJrox(eHHofoHa Hee IUyMa. llo,rsas aercxoppe,'ItUHfl BO3MO)KHa
TOJIbKonpil HydreBolvt
r'Iafe, OAHaIiOO neplrOAII,recriotl KoMrIoHeHTenpelrenuoro pflJ,a Harro]vnruaer[IrK Koppe,rror p a M M b r , u r a e r c q e i l A B a n e p e c e q e n u r c H y , ' r e B L , ryMp o B H e M . f p a -133, d npe4cran,rner co6oii riou6i.inauun rpatpuxoe 4.33, a,
$rrx
4 . 3 3 , 6 1 r 4 . 3 3 ,B , T . e . c r r a y c o n A a J i b H a B
f l o J r H ac K J r a A b r B a e r ccs r p a Ha HHx lxyltol.r. .ia:'riKoM,rugefiHoro TpeHAa H c HaJiox{eHHriM
\'lETII\1, qTO TPEHA
010a
L--_--ffi-
z
{io
0 5 1 01 52 0 ? 5
dT6Eils
610o
I
;l>:^
3HAqHTEJIbHO CHI-I}KACT HAIilI,I BO3MO}KHOCTI{ BI)I-
aerrrrb neprroAuqecKyroKoM[oHeHry B cl{fHaJre.
Kax orMeqaJlocb Bbrlrre, N{areMaruqecKoeoxuAaHr.ie Hr'rlrcpeAHee 3HarIeHIle aBToKoppeJIflilnuIJIfl I]ocar€!,oBareJrbHocrH
c.riy'uafiHbrx rirlceJrpaBHo HyJIro. oxuAaeuat
TeopeTlrtecKarr AHcIIepcHs
aBroKoppeJrflrlrauc.nyvariuofi rocneAoBareJrbuocrrr rlptz .nio6ou
T paBHa
"Iafe
o2:
"
|
n-t-3
-
t,rl
_
ili r!-iilils
{-,a
(4 53)
Srlr Asa napaMerpa onpeAerqior coBoKynHocrb gJreMenroB c!'ryqar.isoro BpeMeriHoropflAa AaHHoii 4nuHu n
f63]. Kar< yxe oiMeqaJrocb B til. 2, Mo)KHooflpeAenr.rrbBepoqruocrb nogBJleH]rr HeKoTopofo cnyqaftHofo co6brrns AJrn HopMaJrbHoropacnpeAeneHr.rsc
254
ri-515.1!lols
106
0
Puc.433.
flpnlrepn
u trx aBroKoppeJlt{uullAear[3rtpoBailHblx.BpeMemblx pttAoB
ottnlte QYHxuutl:
- cHl,ycouAarb'aq
\Jjaaoi zv eAuHuu; "
";;fii;;-,y-Jrnooy,
BorHa-c..A13.""1^?9-:*1iT,l;.6;
<rpeEAt: 2d
a-cHlrycouAarbgaq-_B_orHa-c
,ff1":Io1?i"l""i
Hnil
'i;;;;;;;;;"
r dru qa r '1" l?:1'#,?",i;'lil"H:
so3pac
'rpeF
t;"t;:;;;;;&;;;i"";..
ll.t .t;v:-::-::':"*::"::ft":'1?"1:"0?1n^?'Tfl:
gors
rtrHchlbrlr
Mv^u_1t.1To-:Iilu^ln?t".",**brM
rrrvMoMH "i,::.1T*"{:""i:
BoJrHbr ru
HnH nyM;
d -
troc"'IeAoBareflbHocrb,
lviitt?'.ii"i"o"rursriirx
rocrb-
4
nJI rcc -nocJleaoBa'
a)
;:;ll,l.ii"'6i?'5T".i,"'li,,""J,"tl.?1";X'i'l"o'"""1i;"::,,ilji')*["'#3:'^J""i,i]'
'uocti 6): A - cyMMa cl,|,Hy^coH'll'anbHolt
"'"?^'it",iiir"-n'ocreAoBareJrbHocrb
I
",
d nrloc nocreaoBarcnbllocrb
ii"i'inJiir"iouu*JlbHocrb
I { 3 B e C T H b I M C p e A H H M 3 H a r J e H H e M I l 3 a A a H H O t i trficllepcHe]i, ecJIH BBe-
cTr.rcTaHAapTrr3oBaHHyIo
BeJIr.rqlrHy
Z:
r-p
T a 6 a u aa 4.22
paspe3e
B
Moqsocrr nocJreAoBarenbnocrttcJloeB
neQrenocuux cnanqeB fPnn PnrePt M M
(4.64)
(Bepx paspeea;
ll:s.rerat
r(BaAparHbrii
nopenr ri3 Br,rpaxeHr.rfl
(4.63), Mbr rro,rry-
L{I,IM CTAHAAPTHOC OTKJIOHCHI,IC ABTOI{OPPCJIgUITII.
fIOllCTzRUI}
CIrCI-
H e e 3 H a q e H n en c r a n A a p r H o e o r K J r o H e l r i l en Q o p u y , r y ( 4 . 6 4 ) , n o _
"IYtIHM
z":
,.- 0
I lI/ n -'t -15
r.ltn -,
1-3.
(4.65)
3ry ne,nuunHy Mo)KHo Hc[o,'rb3oBarb B KaqecrBe crarr.Icr'K' ,qJrfl
fipotsepKrrr[[oTe3br, 3aKr]oqaroiqeitcr B ToM, qTO aBToKoppeJriluis
rr paBHa HyJIIo IIpII ycJIoBI'i!I,Kou,a AJlirHa rloc,lleAoBareJlbHocrit
n
- TeDx,tL]HbI.KoroDbte
Be.rlaKa,a J'Iat T Ma"lt.<(MHoto>> H <<Ma.rto>>
rpyAHo orrpeAeJrHrbToqHo. O6r,rquo n vu6uparor u'e 6onee 50, a r -He npeBocxoAsxrliN{tzl4. (Tt'et<oropbleaBropbl ycraHaB,'ri.rBaiorclile
6o"neeHH3Krre[peAe,'rbr r]ltl -(, Hanpuhlep nll0 unu eure Mel{bure).
3rlt orpaullqeHiifl ocHoBlIBalorcfi Ha roM, rrro ecr'In Jraf yBelr.Iqrri::_lercf' To 3HarIeHHerr_ npfiXoAlirct Bblr{Iicrgrl, IIo Bce MeHb[IeNtvH
rv{errbuenryqric,ry Ha6"rrc4eHHii.3ro [ptrBoAHT He TO.rrbKO
K yBe.liirreirpuoAHcnepcriHrr, Ho TaKlKe X sce 6onee 3HarrHTenbHoMy
Hapy_
lreHliIo [peAnoJlox(eH[fl o ToM' r{To aBTol{oppentqllt Bblqfic,rgerct
{o Bbr6opKeH3 BpeMeHHoroprAa 6ecxoHeqHofiAJrHHbr.flo yxasaHirLrM IIparrHHaMBbTCOKHe
3HalreHuf aBToKoppe,rrfluHor]Hofi
Qyuiruirlr
npir 6onriuoM Jrare He Hrparor cyrqecrBeHHofiponu, rtoKa iaM Bpel r e l i H o f ip s A B o M H o r o p a 3 A r ' r H H H e e .
B ra6n. 4.22 npercTaBJreubr Heo6brqubreAJrs feo,'rora AaHlrbre,
a irMeHHoHa6IIOAaeMbIe3r{aqeHlrgi{cTHHHOroBpeMe}rHoroDfl.[a Ir.r
feoJrof[qecKofo npou,loro. To,'rbKo np14 orleH; peAr{oN,rcieqenrl,
obcToqTe.rlbcTB
yAaeTcff AaTfipoBaTb npomeArxl]e co6r,rTHFno pe_
3"v"{bTaTaNr
H3yqeHHqnopoA, qTo B cBoro oqepeAb no3BoJrteTO[peIxKar'iy Ar'Ifl nocJleAoBareJibHocrufeo,'roruqecr(ti]:
Ie.rurb Bpeil'leHHyIo
,[aHHbrx.S0ueHosble oSepHbleor,'rox(eHnq s cKarr{ctHx fopax cocrorrr tis roHKocr'ioltcrbrxAoJron{i'irH3upoBariHbtx
Heq)Taubrxi,rariuee
MOTqHOCTbiO
B COTTTH
Qyron. Eulo ycrauoBJreHo, qro cJlolrcrocrb
rrpeTepneBaeTr.r3MeHeHr{r,
T. e. fiB,rrseTct pe3vJrbTaToMce3oHrrbrx
K,rrr{Marr{qecKfix
H3MerreHHlia 6acceitse osepa. i4srraepeuur MoilrHoCTII gTIIX CNOCB NO3BO,IIIIJII] O[PCIlEJIriTb
TOAHqHbIE
IZ3MEHCIIHfl CKO-
po-clr ocaAKoHaKonreHnr 3a BpeMfl cyrqecrBoBaHufl o3epa. Ta6n.
4.22 cogep>xnT3HaqeHIIt{MolrHocrerl cioen, 3aMeperrHbtxB pa3pe3e
3TUX orroxeHfiri B6ri.{3lr 3a[aAHoro no6epexbfl oAHoro Hs caMHx
6onsruHx osep. Mu fiorrbrraeMcqorBeruTb Ha HecKo/'rbKoBonpocoB,
cBt3aHHblXC 3THMr.r
AaHHbIMlr.Haupurraep,cyuIecTBoBaJIr'rr.rTpeHA B
cKopocTu oTJrox{eHLIs
C TeqeHueM BpeMeHH,npHrrHHOft
AoJToMHTOB
256
6,0
.7 .'
7,r
7,1
7,4
8,0
8,6
10,0
1 l, 4
12,0
I1,0
9r6
8,7
7,6
7,2
7,2
7,8
8,1
7,8
7
,1
,? (,
7,1
7,0
7,0
8,6
9,0
12,0
13,7
14,0
13,6
t2,l
12,9
12,8
ll,l
on
7,5
7,5
8,4
8,4
7,9
7,0
6,7
6,8
I,O
/ 'o
7,2
8,1
9,8
1l,0
10,8
9,5
8,I
7,1
6,8
7,0
7,1
5,6
3,8
o,*
4,2
4,8
4,5
3,6
3,0
9R
4,1
6,8
8,1
7,8
A4
4,6
3,7
4,0
&9
Ad
7,3
7,3
6,7
6,0
5,8
6,5
e9
10,2
t2,3
l? t
13,2
I'L
o?
o9
9,3
8,3
6,0
5,7
6,I
6,3
6;3
(Ocnoaanne
PasPeaa)
l rl
sB[Tbcq nocTeneHHoe LrsMeHeHHeKnnMaTa? 14ueerKOTOpOfOMOTJTO
efr ila oqeBuAHafl I{I.IKJIHqHoCTbMouIHocrH c"IOeB' KOTOpaf' BO3MO)KIIpu HaJIHIIIIH
Ho, HMeeT cBg3b c acTpoHoMHqecKHMlt flBJIeHLISMII?
(cBfl'
nepHoAbl
MHOrO'terHHe
qHKJrnqHocrII MbI MoxeM onpeAeJIHTb
ll .rrer).
flocJleanne
3a
ngTHaME
coJrHerIHbrMH
c
SaHHbte, HailpriMep,
Eu.ro nponeAeHol0l ua6,rrclenue.
JII{ 3H29II'
LIMeIOTcf
Btrn6,ruure aHaJII{3AaHHbIxu O[peAe,'IHTe,
B ra6'
Mbifi TpeHA HnlI nepHoAl.IqHocrbB AaHHbIX'npeAcraBJIefiHbIX- tlTo
Jrrrqe,xapaKTepli3yloulefi H3MeHeHI'IflMOUIHOCTH'Ha[oMH[M'
rITo Ao BbInoJIHeHI'Ifl
AaHIlbIe ,ionxriu 6utl crau,uoHapHblMl.I' TaK
TpeHA HyxHo
3HaqI'IMbIfi
JIIO6Ofr
aHaJIH3a
aBroKoppeJIgUUOHHOto
ycrpaHHTb.
B reo.lornn LrMeeTcqoAHa 6or'rblxafl 06!'IacTb,B KOTOpOftI{CCJIeAoBaHHgnDoBoAflTcflIIocToqHHo,-sTonpeAcKa3aHne3eMJleTpflce.
utrit. 3ru Hcc,reAoeaHKflxopolxo cy6cI'IAHpylorcfl IIpaBI'ITeJlbcrBoM'
nepBble Aox!'IaAbIyKa3bIBaIoTHa HeKoropblftycflex B o6r'IacrH KpaTKocpoqHofo nporHosl'IpoBaHlis6oniluux 3eMJlerpsceHufi'9TO AeJIa'
BOJIH'IIpeA'
eTCfl C TToMOXIbIO
H3ytreHl'{tHeKoTopbIX ceficMHqecKI'IX
IO'
IIICCTBYIOI{HX
MY CO6bITI{
OCHOBHO
coBceM Apyraf,
.[,o,rrocpouHuir npoirro3 3eMJIerpqceHI'IiA 3To
p oOne"i.'f e peureuirerpe 6yer o6riapyxenufl nepuoAl.ItlnocreftIIJIII
"
257
r7-201
r
T a6nsta 4.2&
llorasare,m
aKTnBHocrn H3BecrHbIx 3eMJterpqceHnfi sa nepro4
1 7 7 0 - 1 8 6 9r n . [ 4 2 1
t770
lttl
1772
ll
l\)
t774
1775
I / /O
1777
1778
779
780
78r
782
783
784
785
786
t6t
788
t789
I 790
r7 9 1
1792
1793
1794
66
62
bt)
197
63
0
l2l
0
27
107
50
122
127
152
216
171
70
111
69
160
92
70
16
96
795
796
797
798
799
800
801
802
803
801
805
806
807
808
1809
l8l0
18ll
l8l2
lBl3
l8l4
l8l5
lBt6
1817
l8l8
l8l9
td
It0
79
85
l13
59
86
199
o..)
8l
81
roo
27
8l
107
152
99
t'7'7
48
70
r58
22
.lo
t02
lll
820
82t
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
B4l
842
843
844
90
86
ilg
82
79
lil
60
I 18
206
t22
i3+
l3l
84
100
99
99
69
67
26
106
108
155
40
75
99
1845
1846
1847
1848
1849
1850
l8bl
1852
1853
1854
1855
1856
i857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
186B
1869
86
127
20i
76,
64
3l
l3&
163,
98
7A
155
97
82
90
122
7C
96
lll
42
97
9r
64
8l
162
137
TpeHAa B rrcTopHqecKux petHcrpauuqx 3eM,'IerpflceHlift,Koropble
Mofyr 6strt excrpalo.nlipoBaHbl Ha 6yAylqee. Ue!'Ib raKlzx llccJieAoBa{],1.i'1-He npeAcKa3aHIleKoHKperHoro3eM,'IerpsceHl'ls,a npeAclia6yAer He3aHfie rex nepuoAoB, KorAa celicMllqecKafl aKTLIBHOCTb
BblcoKotl.
o6r,rKHoeegHo
B ra6n. 4.23 npueeAeHblnoKa3areJII{ceficMuqecKoii aIirHBHocrH
Ha e)KeroAHblxAaHHblx pefllBO BCeMMr.rpe3a 100 ,rrer,ocHoBaHHble_
crparlr{lr cx,'rbHbrxseMJrerpsceHufr142]. tr'lcc"leAosarb3T]I 3anllcll TpeHA,nepHo9TO 3HaqlrTonpeAeJIuTb,uMeeTcfl"'lH B Hl.lx3HaqllN'tbifi
EcJrfi
oreer noil,rrr{
c[eqr]QnqecKr.ie
oco6eHHocTll.
ApyfHe
AlrrrHocTrr
O, K a K 3 T a U H Q O p M a I I H f lM O ) K e T6 l i r S U C l O n b 3 O B a H a
! 1 O ) K H T e , ' r eTH
A.lfl nocTpoeHfifl rrporHo3HorlMoAe"'lu?
B3AHMHA' KOPPEJI'IUl,lfl
HJIHCABI'IrBO BpeMeHHHJIpIpaccTOfHHeMe)K,[ByMt ptAaMfi LI
llpo"Iaf
MaKcuMaJIbHoft oKBI.IBaJIeHTHOcTU.
B Hx nOJIOx{eHHII
gi'" HLINflT
noc'leAoBaTerrbHblx
pflAOB
q-ecc cpanHeHl'It AByx BpeMeIIHbIX
-(xpocc-xoppensuHefi
.np.Il
).
,{art_\ Ha3brBaercflssav MHOii Koppe!'iqrlrefi
HJv"rIeBOO6o3HaquTbnO,lO>1ieHile
BO lrsOrlix ilpxMepaX HeBO3MO;I1HS
geAyit{I.IMAJI'
fo Jafa, raK KaK JIIo6ofi H3 AByx psAoB MoxeT 6urr
TO
KpOcc-B3auMHafl
HAeHTI'IqHbI,
ptAa
He
flocxonlxy
ABa
Ap\/foro.
r i o p p e , t o l p a M M aH e c l I M M e T p l { q H ao T H o c l I T e J I b } I OC e p e A I I I I b IJ; I a r H '
c rioroprritu pffr. A BeAer peA B, o't,tlIuarcrct or JlaroB' c Koropblirlrr E seAer A (puc. 4.34).'Oc.noxuesl.rfl Bo3HHKarorB rex cflyqaflX,
qro I{ PflA n'
KofAa pnA A He o6s3are,IlbHoIlMeer ry >xe AJIHHy'
K0ppenfi'
<<aBTOMaTLIqecKoH
AeficrsnrerbHo, oAitH r.r3 noAXOAOBK
qun>> (no4 STLIMfloHuMaercfl ycranoBJleHue paBeucrBa AByx crpa.nocJIeAoBaTe,'Itgocrefi B reoJlor[ilecKoM cMblc.le)
i"rpu$"uecr""
qacTll OAHOIS
cocTorrT B cKoJIbxeHLIIiKOpOTKOI}lUelnuKrllBgoft
qeroro
cTp_arl.rfpa'
nocJle
raHTepBaJla
Apyrofo
crparurpaQnqecKofo
Hall6oJlbue'
no;o>xeH1ls
o[peAe"IeHuq
IIeJIbIo
c
pa3pe3a
4riuecxdro
fo corJIacoBaHHff.
onpe4e.neuue r<os$suqueHra B3auN{Hofir(oppe,'rsllul{raKoe )Ke,
o6blqHgro,xoaQQnUtteuTaKOppeJIflIIl{}I,H J'Il{lIIb
Kari li O[peAeJIeHLte
EcJn MbI
HeNIHO|OOrJrriqaercr or xoeQQr.rqxeHTaaBTOKoppengqHLI.
pt
n*
psAoB
H
OflpeAer.II'IM
Yii
Yri
Anfl AByx
BBeAeMo6o3HaqeHl.lfl
KaK qr.rcJronepeKpblBarculgxcqno3l1qufi B AByx qentx' To B3aHMHaff
KoppeJiflUHgniaa- $yur<qus AJIfl t71 cxOAHbIXno3llllsfi BbIqI.ICJIseTctl
no QopMyJIe
(4.66)
rm
[IJI It
,m-
covr,l
SrS,
'
(4.67)
- KOBapilallHt nepeKpblBaloulHxcqyqacrKOB AByx nocJle'
r[€ coV1,2
CTAHAAPTHbIC
I H 2, 51 N S: _ COOTBCTCTBYIOIIIHE
AOBATCJIbHOCTCft
crri.noHeHlrfl.3auetnttt, uro cyMMI'tpoBaHlltnpoucxoAflT ToJIbKono
TaKlrM oTpe3KaMAByx rlocreAoBaTe,llbHocreii,Koropble [epeKpbIBa'
Iorcfl B cnapeHHoft no3HqIIu. Cnapeuuue no3HIlHHHyMepylorcq rIo'
c ! ' r e r o B a r e J r b HK
o ,a r ( y r ( a 3 a H oH a p u c . 4 . 3 4 , u K p o c c - K o p p e J l o r p a M M a
e c r l r p a Q r r K c n a p e H H o f tn o g l r u n H B 3 a B I l c t i N I o c r H o r K p o c c - K o p p e '
!'If ILllII.
Ec.'iH il{oxso ltpoBecru cpaBHeHrreBpeMeHH6ro ptAa c caMI]rlr
r'taroB c ue,rblo o6Hapy]KeHIlfl3aBuco60fi Anfl troc,,ieAoBare.I]bHbIX
b Ba
c r r M o c T HB o B p e M e H HT, o , B e p o s T H o ,M o l K H oT a K ) I { e c p a B H I . I T A
prAa Apyr c ApyroM AJIr roro, qro6u olpeAeJII.ITbtto,'IonpenaeHHdrx
x{eHHs Harr6o,'rbillefocoorBercrnl]r. !,aa runa nusopMaufiH Bblxor - ? T H a n e p n r , i f if l " r a H r p r r r a K o \ r c p a B H e H i n l : c n . ' I a c B s 3 i t M e x A \ t
258
paclpocrpaHflrorct ror'rbKoHa nepeKpb['
Tar xax cyMMl.rpoBaHlrff
ruii orpe:oK, To BbrqHcJreHrre
rioaSQiruueHTa83aI{MHofiKoppe"'Itlrul{
ocHoBbrBaercH
f l a A r r c n e p c r r HB, b r q H c i l e H H onf to o 6 u u l t r o q x a u . H a '
o6opor, KoaQQitqHeHTaBroKopper'IsquuBblqucrqercs c rloMoll{blo
no ecefi qenu. !,ucnepcl.rfl HcrIoJIb3yeTcE
.r,Hcnepcrir{,BblqllcJreHHoft
lolllefo aBToKoppe!'Ifl
IllloHHofo ypaBHeHnflH
:l 3HaMeHarere onpeAe,/Ifl
259
,'ffi.
l'tr^r'flIk
''tf
l-
,o'f
a
sl
_t,0L
0
Jlar
n=35
n=f5
1lill]ililr,-*
illillltiltnnili|n-",\
0r0203040
tt!,,iclo cnapenxtrx
nosltlrfi
(n)
Pnc.4.34.Koppe"lorpauuu:
a - troryqeliHar npq BblcHcreHHH aBToKoppenru.uoHHo[ $yHrquu art noro]fiurerbHblx H orpl{(roppeaorpaMMa cuMMerpncHa orHocure,lbHo uyJleBoro 3Baq€sHB
q,arearuilx sHaqeiuil lara
p-asrHcHbrx n-ocJe!,oBareJrbHocrei (xopreaorpaMlla
acllrl'
lJra nsix
;;;;i;--6-noayveuaaa
Merpultsa, ecau o6e nocreAoBareJlbuocru He coana4arcr)
260
cqHTaercfl nocrossnofi Ar'lfl Bcex sHatleHufi ,rara. .Il,ucnepcufl, BbI'
quc,'reHgattArq ueroii locr'leAoBareJ']bHocru,
6o.nee yctotiut'taa, ueu
o u e H K a , n o , ' i y q e H H a qA " r q 6 o n e e K o p o T K o f o o r p e 3 K a 3 T O f o p g A a '
H rro3ToMy 6o.nee [peAnoqrure"lbHa. OAHaxo nplt Bblqltc"IIeHl{liKoaQQuuueHroB B3aI,tMHollxoppennutut He c,'IeAyeroxillAarb,,rITo AI'lc'
n e p u r l 6 y a y r [ o c r o q H H b I M I ]H a n p o r f i x e H l t t t o 6 e t t x u e n e i i , B o c o 6essocru B roM cJlyqae, KorAa oAHa Ii3 Ireneii Kopoqe apyroft.
3Haqitn,tocrl xoeQ$HuueHra esaultuofi KoppeJltullH MoxHo
ycr aHoBtirb c noMolrrblonp u6;luxeuHoto KpHTeplls
t
(4.68)
cteneuefi csoSoAH. Sror rpurepHfi BblBo.!,Hrcfl
rrMerourefo n* -2
i r 3 K p u r e p u t 3 H a q u M o c r r x o a $ Q t t u u e H T aK o p p e J l s u l l t tM e ) K A yA B y M q
an6opravu, B3qrbIMLrH3 HopMa.rbIrottconoryfiHocru. flpn arona uy'
.'reBarrfunore3a 3aKJlroqaercfiB ToM, qro lacruHustfi xoaQSttqueHr
xoppeJrflIr,firiMe)KAyAByMt noc.rleAoBareJlbHocrsMlls saAaHuofi
cnapeuHofi no3LIIIHHpaBeH Hy,'rrc,r. e. MbI HMeeMc"lyuaiiHltti plt4,
qro MoxiHo olKHAarb B cJryqae,ecJII ABe rIoc"{eAoBaTe.TIbHOCTH
He3atsIICHMbI.
Bsaar4uas Kopper'rflIrus- uatt6olee noAxoAsulufi npIIeM l.;lfl
3aBHCrlllOCTb
UMeIOT BpeMeHHylO
c p a B H e H L rA
s B y x p f f A o B ,K O T O p b l e
I r e l r i A y c o 6 o f i . B x a q e c r s e n p I I N I e p aN I o x H o [ p o a H a " ] H 3 u p o B a r bA a H .
> >C x a a l t c r u x t c p a x ra6,r. 4.24. <ApceHaJ'tB
H b r e ,r r p r . r B e A e H H bs r e
BO€H.
3TO 3aBOAIIO npor.t3BoAcrBypa3,'luqHblxflAoBHTbIX B€XICCTB
; paclo,roxeH B LeHnepe (urrar l(o.nopaAo),
H O r o H a 3 H a q e H r . r fol H
s6.[usH or nepnoii rpflAbr Cxa.rrrcrux rop. OrpoltHble Kofl]tiiecrBa
3 a f p f l 3 H e H H o rel o A n t B o 3 H I I K a I o r x a x n o 6 o q a u r i n p o 4 y x t n c e s t t o f i
BoAbI,
flnrascr
ti:6asrirrcq or etofi rptsuoil
npoMbrrx,rreHHocrH.
y ocHoBaHuir op.
e 1 9 6 1 r . n p o 6 y p H , ' r l iA , ' r r ie e 3 a r { a q x u c r { B a ) K H H B
I( coxa.rresuro, cKBaxHHa npoHHKJraB Beprnranluufi cpe: 6o,rluroli cx,raAKH BAo,'rbQpoura Cxa"rrtcrltx rop, H oqeBIIAHo,trro 3ariaqr(a noA 6o.rrur.{M AaBJreHrIevrpnsHoil xtIAKocr}I [oc.rly7K]lJla
lBe,r[qeur.r]o rroABux{HocrrrcK.rrafriu B pe3yr'rbrareee cuasxlt. O4liu
p s A , ( a H H b r xn
, p u B e A e H H n xs t a 6 " r . 4 . 2 4 , - s r o n o M e c q q H b l e3 a f l t l c l l
o6relros x{rrAKocru, BBeAeHHbix
B cKBax}rHy <<Apceua,ra>e Cxa.nHcTbrx ropax sa 4 roAa I{cno,'rb3oBaHr-fl
cr{Ba}I{rzHu.
,[,pyrofi pqa npelcraBJrfler co6ofi qficr'Io3eM,terpffceutiii, saperucrprpoBaHurtx e [euBepe B KaxAoM Mecrqe. flpu riayueHlrr crarr.rcrr.rqecxoilcBrI3HMeN{J.y 3rr.rMHAByMfl BpeMeHHbIr.{nptAa\{i{ Eagyo,u [4] npegcraeH,'r
Irx B KyMy,rsrnsHoii Qopue H cleJa"q BbrBoA o roM, rlro HMeercq
pe3Ko BbIpa>xessrtrl3-ti,tecqqHr,rr?
Jar Me)KAysaKaqKoii I.I IiHqHAeHrHbIM 3eM.rrerpfceHl.reM.K coxaureutlto, sror MeroA Bu3ya"rlbnofo
cpaBHeHrrsAByx KpHBbrx cKopee ecero ortru6ouHt'tii, raK KaIi [p]r
efo ficrroJb3oBaHHHycTaHaB,'rl,rBaeTcqcooTBeTcTBIIeMexAy .u,tsyMs
p f l r a M r i : a n n c e r i , r r M e r o [ I l r xp a s u s t i t u a c u r r a 6 .
2Cl
JO
Ta6nuaa 4.24
O6lem xnAxocrr{, saKaqaHnofir cxnaxnuy, npo6ypenHyro
r Crauucruxropax,
u quc,5o3aperHcTpr{poBaHHbrx
3eu,lerpnceuufi r ,l,euaepe(rurar Ko.uopaao)
[41
Bpelrl
roga
O6tey saxa'laHHofi
)l(llAKOcT, ( MHJIIfiogu raa;Io',og)
ulricIo
a
3ev-IeTpt'
ceHafi
6
o
I
o
o
L
r
1962r. llapr
&{ar?
Anpe;rs
[,lnnl
I.lo.nr
Annycr
CeHrx6pr
Or<ra6po
Hoa6pr
!era6po
49
ao
84
80
3,6
20
1963n. flnrapr
@enpa,ro
.Ilapr
Anpe,ru
trlaft
6,0
7,6
7,8
25
22
2I
42
2l
8
6
l0
ll
t2
4
2
llpnl
Hro,rr
.{erycr
CeHra6pt
Oxra6pl
Hon6pu
"f,era6pl
1964 r. fHeapr
<Deapanu
.Nlapr
Anpell
Maft
l}onr
I llo,'rb
Aarycr
Cenrx6pu
Oxra6pr
Hoa6pl
f er(a6pb
1 9 6 5r . l u n a p r
@eapa;rr
.\lapr
Arpe,rl
11aii
lftoHl
I.ln"rs
Aarycr
CeHra6pr
Orira6pu
262
tro
6,0
5,0
5,6
40
64
QA
40
J'*
qA
3,9
0
0
0
0
o
0
0
0
o
0
o
0,6
1,8
OA
2,0
9n
1,7
t,7
AA
40
6,4
8,9
54
6,4
3,8
>'
2
t2
35
23
29
24
8
t)
Puc.4.35.K o , r u q e c r s o
SHBapb
tsgapu
9HeaPu
1963
i964
1955
o r p a B , ' r e H H o i xr l A K o c r x , 3 a K a q a H H o f iB c K B a x l ' i H y B C K a n n '
crblx roDax
)s
s -^
r ou
o
F
e
F
o40
'o
o
o
o
2
I
I
2
4
4
5
2
l4
2
7
I
30
I
l9
ll
Jd
62
48
87
Dn
o
s
J
9 Haapb
1963
P s c . 4';;ti';;i;pfi
'""
.36. 9uc'ro
!.i
1l
lI
tu
fl uaaps
1964
I He a p b
aaperucrplrpoBaHtrHx B, TeqellHe Mectrla
3 € M a ' I € r p H C € H Ha- fni 'u -
(urrar Ko'ropaAo)
B6IH3H
.Il,ennepa
6urapacno,roxeH
3rz Aea peAa 3arlncefi npeAcraBJIeHbIB rpaQuqecKofi QopMe Ha
pHcyHKax 4.35 n 4.36. BsaliI{Has Koppen-orpaMMa3rllx .u,ByxBpe'
MeHHbIXpflAoB nOKa3aHa Ha pHc. 4.37. Tax KaK B sroM npl.IMepe
o6a pflAa Hrvleroro6uee HaqaJro rz BpeMeHHyIOUI(aJIy, To no3I.{qIIH
u
cnapIiBaHI.ISMOxlIo oXapaKTepIr3oBaTb KaK <<[oJIOX]',ITe''llbHble>
COBna'
HaqaJIbHOfO
noJlox{eHHfl
c
HaqHHafl
JIaflI,
<<oTpI4qaTeJIbHbIe>>
reHlig. flolox<esne HaH6o,'rbruerocoorBercrBrir Me)K.r.yAB-Y\ttlpfl-
+1
T a6anua 4.25
Co,nesocrr BoAbI B lllusanfir Eefi. Mecro or6opanPo6 Ansanonuc
1927r. [581
(urrar Mepu,neul) nta,lu or no6epexr,n,
s
5
J
Co.nesoctl. urr''r
o
rs
o^
TU
(l
o
o
F
I
s
I
s
a
o
o1
r
'-3624120122436
Jlar. mec
xapaKrepr.r3yrouar
Puc. 4.37. BsaHMHaqKoppenorpaMlra,
cBrsb qucJraseMnerpffceHHris reqeHre Mecflqau o6reMos orpaa"rennofixuAKocrlt, gseAeunoftB Teqeg[e
Mecrua B cKBaxHHy.
( q g u o B s r c o K H e( o p p e n q r l g x n D H o r r e H b
Max:uuarrHas KoppeJlsquflHMeer Mecro npn rare *l
t 3 - 3 a H t r 3 K o r oq u c J l a s a o a l o a e H n f i )
C c . r b n u x n a r a K c r a r t r c a t q e c K q H e 3 H a q H M bH
B AaHAaN{ricJyqaeTcfl npH Jrare +1, ror4a quc"ro 3eMJreTpsceHnfi
HOl,rMecflrl,ecpaBHr.rMoc o6bei'vtoMrpn3Hor? BoAbr, 3aKartaHHoftMecflueM paHbIUe. Koppe.nrqHq B 3roft no3HrlHr.rcnapHBaHufl ecTb r:
: 0,60. Bropal HauBbrc[rafl Kpocc-Koppe,'rflqr.rs
r :0,57 noJryqaercfl
npII .IIA|CO. 3TO yKA3bIBACTHA To, IITO TCKToHI,IqecKIiIi
oTKJIHKHa
o n e p a l { i l l o 3 a K a q K r {B o s H H K a e T
oqeHb 6ucrpo H pacflpocTpaHrreTcfi
H a n e p r r o Ao K o J r oM e c g q a .
I l n o r A a 6 b i s a e r H e o 6 x o A H M oc p a B H r r r bA B a n e p l o A n q e c K r . r xB p e N,reHHiixpflAa c oArHaKoBbrMrrnepnoAaMr. I4clorb3oBaB [peuMyrr{ecrBo nepnoAuqHocTlr, Bbrquc.rrrrM83alrMHyIo KoppeJlorpaMMy B
<<KpvroBori>>
Qoplre. !,eficrnure"rbno, Ka)KAbrftnpelteHHoftpoa BKJraA b r B a e r c r B o K p y x ( H o c T bH H a q a , l o p f l A a T a K H MO 6 p a 3 O MC B q s b r B a e T cq c ero KoHuoM. Buecro roro rITo6bI [peAcraBrqrb ce6e ABa prAa
ueIrr,ilr, IBHXiyuilMr.icff Apyf oTHocriTeJrbHo
Apyfa, r.rx MoxHo npeAcraBnrb ce6e B Qopue KoJrec.Kaxaoe KoJrecoHMeer oAHo r.rro xe
rtrjc.lo ,le.lesilfi Bor(pyr ero o6o1a, Kax{Aoe H3 KOTOpbTX
COOTBeTCTByet' ollirrMy H3 rrocr.reAoBaTeJ'rbHbrx
na6lrc4eHuft. Ec.nn oAHo KoJIeco
B p a u i a e T c qn o o T H o r x e H H r K
o A p ) ' f o M y , T o M O I K H On p O B e c T I K
. rp o c c cpaBHeHfieMex(Ay HHMH B n pa3rrrrqEbrx noJlolKeHlttx Ao HarIaJIa
noeropeuuft.
B LUusanrrr Eefi, xar H Bo MHorr{x ycrbqx peK, B reqeHr.reAHeBrIHKJraHa6.nrc4aercflKoMnteKcHo€ H3M€.
HOfO nprrJr{BHo-oTJrr.rBHoro
261
Ilpurttn Hrx orlus
Bpenq
a_
o
f
3 rto,rs 14.30
16.00
17.30
19.00
20.30
22.00
23.30
-1rirc,r.a 1.00
2.30
5.30
4.00
7.00
8.30
10.00
I 1.30
13.00
llll
OT.nllBd
,lz
Or,rus
>)
1/a npl.l,rlilBa
tlz
>
tlt
)
llpu,rue
I/l
OTnI{Ba
tlz
Or,'rus
Ha'ta,[o npHrrrrBa
-lB
tlt
31,
llDnnse
troBeDXH0ClHAq
6,97
6, 2 0
IIPHIOII:!:X
I i .lll
11,54
5,"Q3
l9
6, 3 2
6, 3 6
6,72
6,80
6,90
7, t 4
6,91
6, 7 6
6,74
6, 2 0
7, 4 5
7, 4 7
i3,52
13,35
12,83
13.31
13,t2
1 2 ,r +
12.1{
12.e0
7 1,7
to
! 2 7.'l
13.46
12,33
t2,4t1
l9
I I
HeHUecoJreHocr[ r.r3-3anepeMeuHBaHllfi npecHoft BoAbI c trlopcxoft.
Ifscras BoAa lllu3anuK PaBep reqer cxBo3b rrJlorHylo MopcKvr.sBo.r,y B 6accefiH; so BpeMfl oTJr.rBa3Ta BoAa ABLIxeTct AaJlbilre BHu3
rro ycTbro. oAnaxo [MeeTcs BcTperIHbIfinoToKBAoJIbAHa,KoTopblftBo
BpeMs MaJroft BoAbr [epeHocr]r [JroTHyIo MopcKyro BoAy BBepx no
6accefiuy. B ra6,r. 4.25 npusegeHbl pe3yr'rbrarbrH3MepeHur cor'reHon 1,5 u B TeqeHHe cyroK
cTr-rnpo6 BoAbr,B3flTbIx c r.rHTepBa,rroM
( c p e 4 H r r r , ' r y 6 r n a I I r r a ) .B r p a Q u u e c K o f i$ o p M e A a H H b r e[ p e A C r a B JeHbr Ha pr{c. 4.38.
K o p p e . r r r q u o H H a fQ
l y u x u u n n p e A c r a B l r e H aH a p u c . 4 . 3 9 t r , o q e BllAHO,yKa3brBaerHa Jlaf 2, npelcraurgrouHfi pa3HHuy B 3 q rlrelK,ny llHKoM noqBreHuq coJleHofiBoAbrB6JrH31r.
AHa ]r MaKcHMyMoMCOAep)KaHr.rrcoJrH B noBepxHocTHbrx BoAax. Tar xax 3anncn [peAcTaBJrgFoT
24-rtacosofi AHeBHofinoBToprioiquricr qnx.r, To B3axMHafl
rioppeJrflrlus Moxer 6url npe4craB,'reHa B KpyfoBoft Qopue. fio3roMy KogQonrlueHrbr B3aHMHofiKopper'rflrlufi MoxHo HafiTH !.nfl
.rro6brxJIaroB Bnr'rorblo 24 \.
BsanrvrHaK
q oppersUuc u reo!'roruqecKaK
c oppeilsquc
f eor our n ocrosHHo Aedrr
alor noltbrrKr.rnpr.rMeHl.rrb MeroAbI B3ar{MHoii Koppe,rfluur.rAJrs cpaBHeHHrrcrparuriaQilqecKr{x
nocJreAoBaTeJrbHocrefi,oAHaKo, craJrKHBaflcbc TpyAHoCrRrr,ru,
o6paqaroTcfl K
reo,lorr.iqecKoftKoppe,'Iflrlr{n.Hecuotpn Ha To qTo
aBTOMaTHqeCKorT
,rureparypa no 3TuM BonpocaM oqeHb o6rrlupua, vx ycvnufl Aocrr.rzoD
Ta6nura 4.26
1al
r
i3F
Mouluocru cJroeB B pa3pe3e HeSreHocHbIx cnauqeB CBHTH fplrH PfiBep.
( P a s p e r p a c n o f l o x e n B 1 0 M n , ' r r x c e B e p H e ep a 3 p e 3 a , n p u B e A e l t H o r o B 1 a 6 ; t ' 4 . 2 2 ' t
L
F
,' 4r1l
rl-
r11t
:l_
=tOl-
ll
c; ^T
iil
o
o
il'
9F
t-l
Pi3pe3 B
iBepx paspe:a)
fl ogepx x oct u
- v i
I F
(U rl
o
cl
<I
Ilprrrae
0tlr
fl or4euu
floax orrs
F s c . 4 . 3 8 . C o l e p x a H r r s c o J I H B n p H l o H H b I x B o l a x H n o B e p x H o c r H b r x B o A a x II LLII.
3anaK Eefi B6nn3ri Asuano,ruca (urar Mspu.neng)
i
2
sl
q
a
0,6r
I'ar 2
aal
n r, . L
w
I
o 0,0f
s ^" I
= u,4r
I ),t"
13,0
l0,:l
C)J
9,0
r 0 ,I
t0,3
r) .2
ql
9,0
at
10,7
1( ), ' l
R r-.1
q.1
10,6
t2,6
tr t
12,3
l1,l
1 l, 0
(OcHonarrire
o
Tenept 06partrMcr r( npo6r'reMereoJrorur{ecKoiirioppe!'rrrqrrrr, rAe cneqHaJrbHbie
yc.4oBilfl He ToJIbKO6,naronpHnrcTByroT
u,0-
Jlarr0
2
f.1:-ccr0 3
. O O 6 U , eH e B O 3 M O } K H
s T r r { T p e 6 o B a H H r MB
pO
a s M e c T r ' r TTbO q K I iO [ p O 6oeauuq raK, qro6bl oHIl pac[or'Iarar'ti]cb
p a B H o M e p H oB r e o J o f u r { e ctioM BpeMeHLl,u ecr'II{TorIKrrpacnoJtox{eHbIHa paBHbIXpaccToffH}tIITOCKOpOCTb
s.{, TO MbI MOX{eM,l(OnyCTI.iTb,
OCaAKOHaKOIId'IeHHfl
6bI.rranocTotHHoft B TeqeHHeBcefo BpeMeHHo6pa30BaHHflABI'-\ n0cd'reEc.rrn noo6pa3HTb ce6e, qTo crpaTr4rpaqrHqecKr.{e
AoBaTer'rbHocTer?.
pa3pe3br aHaJrorHqHbrsanHcsM, rrpo[3BoAHMbrMpefrcrpHpyroiitHMi.i
ycTpoficrBaMr{,To oHH SyAyT BbrrJrsAeTb TaK, KaK ecJrr{ 6ri grtr
ycTpoftcrBa pa6oTailu c pa3!'i[qHbrMr.r
H Heu3BecTHbtMr.r
cKopocrffM]r
B pa3rirrrHbreBpeMeHa H .qa)Ke6o,rtruyn qacTb BpeMeHr.r
pa6oTa,lrr
BCTIflTb.
I o.+f* o,oI4
6
5
9
I
12
10
15
12
18
16
21
Puc. 4.39. BgauuHaq KoppelorpaMMaMex.ly coAepxanfiflMllco'Iu B nplrronHblx
Bo.lar n luusanux 6eri.
tl [oBepxHocrHbtx
c o o r B e T a r B ! r f lH a o r o A a e r c g n p t t J I a r e 2 , n p c A c r a B n g n q e u
3-vacoaoe pacxoxAeHBe
raloT yclexa .rrrr[Ib rIpH lrcKflIoqHTerbHbrx o6cTogre,'IbcTBax.flpnqI.tHbI3TO|Or'refIio noHflTb.Mero4 B3aIIMHOfi
OCHOBaH
KOppeJIfIII.{I.I
Ha
TH
an p e A n o , ' r o x { e H H rqrr,o A B e c p a B H H B a e M b I en o c J I e A o B a r e J I b H o c H
6 n r c A a . n r r c sB A r { c K p e r H o MM H o } K e c r B er o r I e K , p a B H o M e p H op a c n p e C6Opa AaHHblx B O6eB npocrpaHcTBe,I{ tITO HHTepBa/'lbI
Ae,'reHHbrx
6buIII oArtHaKoBbLI( coxra.neHl.Ilo,
TpyAHo
Hx rrocJreAoBareJbHocTflx
co6parb crparrrrpaQltqecKl{e AaHHbte raK, qro6bl yAoBJlerBopl.rrb
266
15,6
i5 , 0
1 3+,
MM
B
fl o.nHo,ru
Marcuuyn
10,8
I1,7
il,0
-(r,ii
9,9
10,0
10,0
10,2
10,3
I1,3
12,0
13,5
ofO
MoqHocrb,
rrcnoJrbSoBaHllro83aHMHOfi KOppe,lgr{HH,HO lI BCeJTflIOTHaAeX{Ay Ha yc[ex. B ra6n. 4.26 [peAcraBJleHbr ri3MepeHrifl MoulHocr]i
gOrIeHOBbrx
cr'loeB,nor'ryqeHHbte
E3 Her{oTopoftnoc,'reAoBaTeJIbHocTI.I
o3epHbrx oTJrolKeHr.ti'{
B cKarKCTbrX ropax. 3ru ouoxeHlig, tBtttoI]lllecf qacTbl,ocBHTbrfpfin-Punep, cocTofT H3 ToHKIix cJ'roHcTbrx
HeQTflHbrxc,{aHueB MoulHocTbro B AecqTKI{ MeTpoB"
AOJIOMHTOBbTX
AHa,roruqnbrri pa3pe3 npeAcraBi'reHHa pr{c. 4.22. erot pa3pes yAa.leH OT nepBofo r'rr{ltrb}ra l6 xu, LI, no-BHAHMoMy,KopoTKat [oc,'re31{BHBar'r€HTH3
AOBare.rrbHocrb
HeKOTOpOiiqaCTIt 6o.nee AJILIHHOfi.
I(ax.ue-.lu6o x,rapr{Hpyroud}re
c,{ou }r,'rHoTrnqHTeJrbHbre
cBoficrBa B
3rotl MoHoroi{HorlqacTr{ oTcyTcTByroT,H no3ToMy Mbr
Aon>KHbIIIpoBOAIirb Bbrquc,'reHr.rr
Koppe"rruzrl npll nonapHoM cpaBHeHHlrMorlrHOCTIIIrHAr'rBrrAyaJrbHL,rx
riracroB B AByX pa3pe3ax. BHqHc.[ure ssaII N'lHyIoKoppe,'Iorpa MMy H o[peAed'rrrre [oJro)KeHHeHar4,'ryqile]i Koppe.Tf(riu r{exiAy AByMr pa3pe3aMrr.KaK sH o6tscHure Apyrne rro3lil\Hw C IvteHbIIJlIM, HO 3HaqHMbIN{ ITOnaDHbIM CDaBHeHHeM?
2t7
Pnc. 4.40, Cpanneuue ABy.l. HeqlrcnoSblr [locJleAoBarenbHocTeli c -no'
uouLblo ueroAa B3a[MocBfl3eH.
Ilre noorcIorarerbHocrH H3o6paxeHbtB
BsallnrHac accoquaqns
PacclrorpeuHsre Bbrure MeroAF,rnpeAHa3uar{eHbr
Arq cpaBueHr.rn
BareJrbHocreft, o6p asoBaHubrx 3HaqeHuqMn HeKoropbrx
,[Byx riocJreAo
f i 3 M e p s e M b r x[ e p e M e H u u x . K c o x a r ' r e H u r o ,M H o r H e c r p a r u r p a Q u u e cKr(e ilccJreloBaHrrflnpl.tBoAflTK nOCJTeAOBaTeJIbHOCTTM,
KOTOpbIe
COAeplKaT To,'IbKoHOI\IHHaJlbHbIe
IIDHMeHIITb
AaHHbre,H He no3BOr'Iflr,OT
M e r o , l b rn s a u N { H o fK
t o p p e n s u f i f i .3 a A a q a c o c r o H T B T o M , q r o 6 u H a f i Trr Mepy cxoAcrBa, Koropafl, B orJrnr{pteor roaQQuqr{eHTa KoppeJrflr{r4r,He ocHoBbrBailacb6ot ira pe3yJlbrarax H3MepeHHgItgyr{aeMblx
IrepeMeHHbrx.OAHrru ltg Hat6o,ree qacro HcrroJrbgyeMbrx
teoJroraMl{
IIICTOfOB 'BJTgCTCfl IIICTOA ESAUI,IHOII CBfl3I,I. I4CXOATTUCAAHHbIC TIPCA.
craBrrqloT co6oft pflA cocroqHafi (Hanpuuep, TaKr.rx,KaK JrHTo,ror u q e c x l l f t T l I n n o p o A b l ,T . e . H 3 B e c r H t K , r l e c q a H l r K c, J ' t a H e tH
l T, A.),
H a 6 " r y n A a e l r o r x B c r p a r r . r n p a Q r r u e c x o n rp a 3 p e 3 e . 9 r N c o c r o s H u q
B3ar.{M}ro
rrcKJrmqarorApyr Apyra H He Mofyr 6ura paHxr.rpoBaubi
H H K a K H Mo c M b r c J r e H H o o
r u6 p a s c l l r . B u e r o 4 e B 3 a x l r o c B r r 3 e fAt s e r a Kue noc,reAoBaTe/'rbHocTH
[epeABrtraroTcr oAHa oTHocHTe/'rbHo
Apyroil, a AJ'rr nepeKpbrBarorr{Hxcfi
orpe3KoB oqeur.{Baercflcrerrenb coorBercrBufl. Lnl xax4oro rroJro)Kenr.rq
[oAcqr.rrbrBaercf o6uee qrrc,'ro
cpaeueuuli H r{i{cr'rocoBnaAalouux cocrogHaft, a sarel\.tBblquc,'Iflercfl
orHoueHue qac,'ra coanaAeHflftx o6uer,ry qucny cpaoHeulft. 3ro orHoilreHlreMoxHo HcrroJ'rb3oBarb
B Kaqecrne xoaQQHqHeHTacxoAcrBa
4oyx qenefi B rroJrox(euunrrepeKpbrrrifl.
flpe4no.noxuN{, r{To Mbr rrplr H3yr{eHr.{Hpa3pe3a gaKoAHpoBa,'rrr
.rrHToJrofHqecK[re
rfirrbr nopoA I1o cxeMe: necqaHaK- 1, clane\-2,
- 3, yro.nr - 4, a,reepo"rrrr- 5. f ctto, qTo cnoco6 Korr3BecTHsK
ArrpoBaunt coBqprrrenHonpoa3Bo!.ren. Tarau o6pa3oM, ABa crparurp a QnuecKrrx p a3pe3a Mo)KHonpeAcraBr.rrbcJreAyroqulr o6p asorrl:
(a) 512125232425
(6)32t525121232
fl
C A e u H e Me r o p o f t p a 3 p e 3 o r H o c n r e J b H o f l e p B o r o ] r B K a ] K A o M
cr'IyqaenoAcquTae\,t qrIcJIocoa na4euarl:
flep noe rroJro)KeH
r{e:
512125232425
32t525t21232
9uc.llocpaeueuuit
panuol,
H H e- 0 .
Bropoe no.iioiKeH[te:
qlrcJroconna4enuft
- 0, orHorxe-
MaKCRMyMa
CXOjI'CTBa
\AI
&!rF
v\^A/
{is P
3 i zF
t'l
L
ir5r
.h
3f rl-
s,
,!
* 3 1F
:llt V
";l
I
il
AA
'il:
nf,
r 5-l
I
sii
iil
fi:.'
v !^.,4,
-7,/
AA
,JVV\^.^^--^-
f;Hl0 r 0 2 0
qncro
cnaPeBHb)x n03r14!;
(n,
Tperle rroJloxeni{e:
$
$
g2l525l
5t2125232425
2t232
- l,
tlxc.nocpauueuul'tpaBHo3, uucflo coenaAennfi
sse 0,33.
orHoure'
Ec,nn ua rpaQuxe Ka)KAoMynoJIo)KeHHIo cpaBHeHI'IqnocraBuTb
OTHOIIIeHI'Ie'TO MbI [O,'Iyql.IMJIHHI{K)'aHaJIOl[qCOOTBeTCTByIOqee
Tar<ofi rpaQnx AJIfl AByx ce'Ieuuft ltso6paxeH
m-vloKoppeJrorpaMN{e.
4
.
4
0
.
sa onc.
3Haquuoctr orno[ienttfi cxoAcrBa Mox(Ho ycraHoBaTb c noMo'
utrro 12-xpurep!rf. Liro6rt BbInoJIHIIrb oTy npoBepKy, MbI AoJI)KHrI
onpeAe,'rr{Tbr{r{c,'rocosnaAeHfift LI rIHcr'IoHecoBnaAeHnfin nepexpu'
Barol]Irrxct yqacTKax. A"rg erorO AocTaTorIHOBbIqHCJIIiTbBepOgT'
3aAaHHoroqHcJIacoaua4,euuftB AByx coBepIIreHHo
Hocrb rroflBJreHrrfl
3rn c,ryuafiHbIe nocJIeAoBST€JIb'
c.r-vuafi
uux rroc,'reAoBare,,lbHocrrx.
Hocrrr AoJr)KHbrcoAepxiarb -TaKoe xie quc,rio ua6,rpAeunft xaxAoro
TllIIa, KaK H ABe AaHHbIeBT,IOOpKH.
3rtz Aee fioc.rreAoBareJbnocrll6y4eu IIa3bIBarb coorBercrBeHl{o
I{enbro I n qensrc 2. llpelno,rrox{HNl,qro IIMeercn fft Kareropttii, Ha
r(oropble r,raccirQnqnpyrorcfl Ha6,rioAeHtts. Ecnn Irru o6osHaqHN,t
qr{cJrosa6,lrcAenufi, nonaAarcIq}rx B K.rraccc HoMepoM (a), A.ty uenn I uepes XrE, ro o6ulas EilHHa Uenn I 6y,4er paBna ftr:Z
512125232425
321525121232
tfuic.rro
- 0, oruouepaBHo 2, uircno cooua4eHuii
cpaeueurrii
Hue- 0.
268
[oJroxeHHU
...n-5
9Isr
B u,enu 2 urrleercs TaKlKe m xareropuii,
Xw"
Ka>KAafl.c Xzn na6nto1e-
tlto6n
I t t t r M H , u n o s r o i l r y o 6 u l a q . u , ' r H H at \ e n w 2 p a B H a , t :
A{ro.
onpeAe,'ItlTbBepofiTLiOCTb
COBrraAeHHfl
AaHHoro qr{cJla Ha6lrcleHtrft
B !,Byx IIOCJTeAOBaTei'ibHOCTflX,
Mbr AOJIXHbTpa3Aerr{Tb cyMMy npo-
i:{
tlx
IISBeIeIIIIIi
tlprrc
q ! ! r L i r
,
ii
rr
. l .
,.I ,Xrr,X:n IIC BCe]r riaTeroprrtM Ha rrporl3BeAeHrre
A"rIIfii
ffi
-cr
gTi.I BeJII{qfiHbl, no cr p ou tr't12 ar ucTI'IKy:
o
7.":!9=!t-+
D_
I
Xtt Xrt .
t \ n 2 LI
a-
(4.t)9)
I
B H a r u e r vn p l r M e p e - q u c J i oK a r e r o p [ i i p a B H o , b . l l e p n a a q e n b
coAep)KaT IBa rlecqaHnKa,ttflTb c,'raHr{eBI{ T.
A, r{nc.na Ha6",rIoAeH[F,Li,
KalKAofi Kareroplia B AByx qerrflx [pHBeAeHbrB ra6,r.
i.i|. nor,iit
HI.III CTOT6CI{TA6,'I[qbI COACP)KI,IT
IIHCJIAHAo,'IIOACHilfi
IPOI43BCACHIIC
Kax{Aori Kareropr'r' a noc,re4Una crpoKa - Co.TBercrByroirrrre,
:
_
cyMMbr IIo croJr6rrana.Bepoaruocrb rroflBJieHfir
xors 6u o4rroro coBITaAeHI{fl
B flIO60M noJro)KeHHH
AByx c,'ryqafiuux nocne4ouur"nono_
creft [D]r HX CDaBHeHrrr{
[p].IMeHHre,rrHoK HaUI]rMpa3pe3aN{paBHa
$
*
pr
g=-,
oe qHc'
, r e O - u a 6 . r r c J , a a t o au u a r " o c o n n a 4 e u u f i - ;O ' - t t a 6 n n \ a e M
- cpe4nee qllcJlo cosnaAeHllfi; E' - cpe!'Hee
E
6""i.o"nu!euHfi;
u it'
qIIC,'IOuecoanag.eH
o c J l y q a f i u o c r l t c o s u a ' ( e H n f iB e p H a 'T o 3 r a c r a r
l
t
n
o
r
e
3
a
Ecnu
Ec;;;;;-*z-pacnpeAe,teHlle c oAHoft crerleHb'o cso6oAut.
,n.ini*
c"Iyqae coenaAeHI'II't
KaK
B
NIa"IO,
llfic,Io
cosnaAelruri
ntr cpeAHee
KoHuoB ueflell, To - Kpllrep Hir ltoxno y'ryqullrb' Ilcno"'lb3y-fl
96 Jrr4'gLr
tl2
fi;fir"u .*"tlBl. b"u't-uoA'rcnI{ BblqnraHl.rc rrc a6'
;;il;;^t
3Haqepasnocrttsa6'rroAaeuorotr cpeAHero
3HaqeHltff
co.,riorsoro
uufi:
(o'-E'-112)2
Q-E-ll2)2
I
(1.71)
"
,_-::-
:OlZz. aepo"t'uocri----*.1r.r"""conna4euuft
1,00_
0191J12:g)
,27:0,73.
E'
Llrrc,iiocreneueii ceo6oAH npll sroM OCTaeTct HeIt3MeHHbIM,v : 1.
[o3ToMY IIPIIE':8,8,
B r t a r u e ui l P l l r l e P eO : 2 , O ' : 1 0 , E : 3 , 2 ,
p
a
n
e
u
repuii 12
MH sHqI,IcrI{JrirBepo.srHocrb[or,ryrieHugxors 6u
oAHoro coBnil_
ACHIIS B ABYX qC[rX CO C,TYUAftUO
3J'ICMCHTAMI,I,
PACIOJIO}KCHHbIM}I
oAHoMy H roMy )Ke pacrpeAeJieHr.rrc Ha6nrole_
:-o-_o"1":1:l:yrcxluMri
KaK r.r B paccMoTpeHHbrx HaMH AByx irocJreAoBaTeJrbHocrflx.
\H_:r:,
qricJra conna4enrr?
\-peAHee 3Har{eHr.re
Ad'If HHTepBa,'IaflepeKpbrrrrs
OTIPCACJI.ECTCS
KAK NPON3BCACHI,IC
BEJIHqUHIT
P HA qTICJIO
CdAEHCIrrrIl.
AH anorH qu o cp eAHee q ri crro HecoBr a AeH,r.,t-p
;
r;;;";;;;
u ro Be_
J r u l r r { H b(rl - P )
H a q u c J r o c p a o H e u a r ?f.r p e 4 n";;
onoxuM, qro ABe no_
cJeaoBarerbHocrH B HaIrIeM[pr.rMepe [o,tHocrbro IIepeKpL,]BaK]Tcfl.
B pe3y,'rbrare qero noJyrraercfl 12 noeu\ufi
4;ra cpanueuHa. Cpea_
Hee qHcr'roconna4euuft B noc/,reAoBareJrbHocru
paerio l2X0,2T:Bj,
a c p e A H e er r r . t c , ' ruoe c o n n a 4 e u u l i p a B H o 1 2 X 0 , 7 3 : g , 8 .
14cno.irssvg
,.:
-
( l o : q ' 8 ) ' z:
(2-.3.2)z
0,G1,
+'
3,2
8,8
H gBJ'lteTcqHe3itarIIIubtU,MO>xHOcJ,e,taTbBbIBOA'VfO Ua6"rtO4aeNloe
B AaIIHOii
qIICIo COsnaAeultl'l\lex,u,y AB]'Nlfl IIOC.rleAOBaTe,'ibHocTflMI.t
rro3riutifi cpaBHeHItfltte 6ourtrue, qeN{ cpelHee 3HaqeHHeAJII AB]"x
clyuariuori noc.reJ,oBare.rllsocreitc aHaJIofIIqHoficrpyxrypofi. flo'
l'Ieirrca r.rlfl ]larrblx ni'l6opox He Il3MeHser 3Toro BbIBoAa'
ripaBKa
'
Tar< Kar{ Nrn II}re.rrl AeJIoc Alrcl(perHbIMpgAoNl co6blTlift (cosna'
r e c o B i l a ; l c l t t t e )T, o l a c n p e J , e , ' I e H Hqea c T o Tc o s n a A e u l { t is
A e H r { er r r ' I r H
3aKOHy.
yc,rroBrr
fl x Hl;-r€eoli rrrnore3br noJ,tIllHfercn 6u:g.ow.anbHoNly
/\,peAHee
- ^ ^ , . , , ^ ^ qilc.'ro Bo3]rolt(IlbrxcotsilatreHlli.IAJls
AByx cJlyqaliHbix noIIO'
c,'leAoBareJ'Ilrrocleli,
IicTopble cpaBHIIBaloTcflrIpII nx CUapeHHbIX
3riur!9xp
, aBHo
Ta6;rt:i.-a4.27
{nclo na6toAennri xaxAoro H3 nfiToJIoruqecKux
cocroqHl,lri
B AByx crpartrpa{uuecrux ,IIOCreAOBaTenbHocTrx
E : P(n*).
Kareropxx
I
l. llecqaHux
2. C.'raneq
3. I4ssecrHsx
4. Vro,'rr
5. Anenponlrr
Llenr I
Uenb2
yv
''
Ih"2k
5
25
2
0
2
I
I
J
c_
nr:12
nz:12
(4.i3)
K coxa;ryeuulo,rlrbrHe i\{oxe}I Bbrqrrc,'rnTbBepotrHocrb llo,uytlgHtiq Ha6"rtroAeutiff,
or cpeJ.Ililetoiriefo croJb 6o,ltruoe orri!'roHeHLIe
H e r o 3 H : l q e H r r r6 i r r r o r r r r a i r b H o r op a c [ p e A e , r e H r { t ,e c J r } r H e 6 y 4 e r t
Illierb u pacttol)r]rieiitril ero noxpo6Hulx ra6.nur{. floc.ueJHle ue
Bfro,tlie nptrfojlitbi nrtu 6o.rturrr.\ sHaqeHrrfixt?, Koropble KaK pa3 r.l
IlvlKHbt B saAaqax rr3\'qeHrrrrB3arrlrocBs3eii.O.u.uaxoMbr Mo)KeMHc-
o
nl
:
.D
tt-L
E(l-P)
I
Cyurrlsl
(1.72)
P a c c r o s H t t e u a 6 ; r o J , a e r r o f oq t r c . r r ac o e n a A e u i l f io r g T o r o c p e A H e f oB
eAIrHIiUax cTaHAapTilofo oTK;'roHeHilrr
BbrpalKaeTcflIIO QOptrly,re
f)
0
2
e.7o)
XleXrr:39
270
271
qt{,t ,
ii,
nod'rbscBarb HopMaJlblloe npt46Jlt4xeHl'ie K 6uHoit'tua,rlHoMy pacfipe-
Ae.renuro[40], nr'rpaxaeMoe
$oprvrynoir(4.74), u Haftru Beposr-
OT CpeAHefo.
HOCrb rroflB,'reH[f 3aAaHHOfO 3HaqeHHfl OTI(.[oHeHIIfl
C eroft ue"rbro MolKHo rrcnoJlb3oBarsra6,'rnUrt cTaHAapTHoroHopMaJrbHoropacIIpeAeJIeHHs.
Z -f
n* (2arcsin{O-lt-2arcsinlP).
$7ay
bHocreli
flo,qcran.naarpe6yeusle gHaqeHLIfAJIfl AByx loc"{eAoBare,'I
n Qopuy,ry (4.74), rrorryqllM
Z :\i
HJIU
12(arcsin/-zln- 2arcsin
1/W),
Z :3,46 (2 arcsin0,41- 2 arcsin0,53): - 0,97"
CpaoHaoaa 4oe cnyuafiHble [oc,'IeAoBare,lbHocrlt,MbI Mo>KeMox(]iAarb rpri coBnaAeHut, a ua6ltoAaeM ABa, qro Ha oAHo craHAaprHoe
orKJIoHeHr.{e
orruq aercq or oxnAaeMoro quc!'ta conna4eHuil. H a 5.nrcAaeMoe qricJrocoenaAeuufi e sroft no3I{IrHIlBrtorne Mo}Ker 6uru clyqafiuurra.
3Toro KoppeJltlluoHgoro rteroB r<a.recrae[pnMepa ttpIiMeHeHIzg
Aa paccMoTpnM 3aAaqy cotlocTaB,'IeHuflMHoxecTB Hao"rMAeHlll'l B
paspesax yfoJlbHoro 6acceftsa lleHrpaJIbHofiAnrnuu. Xopourrre o6HaxeHr.rs flopoA 3Aecb peAKI{, a sJleKrpoKapora)K He Aaer ratioft. n u 6 o u H $ o p M a r r f i u ,n o s r o M y 6 o r r n a q q a c r b A a H H b I xo c r p a r t t r p a no!'IyqeHaus r,ry6onttx eupa6oror,
QHuecxoft nocJleAoBarer'rbHocrll
pa3TaKlIx, KaK Kapbepbl Lr uaxrbl. 3aro4npyeru
nK;2aJIeBpo"IHr;
H o B u A H o c r l rn o p o A T a K I z Mo 6 p a s o u : I - n e c q a H"turo,'tofuqecKlte
3 - cnaHerl, He coAep>xauluit QayHu; 4 - no4cru,'larcqas r,rtulla;
5 - yro,rr; 6 - c.naueu, coAep)KauruftQayuy; 7 - Hssectnax, llepslifi paspes r{3yqaJlct B BaronJlenuofiyroltnoft uaxte. Bropofi, tr.teHee MorqHbritpaspes o6saxes B creHe orKpblroro yroJlbnoro Kapbe'
pa n l0 KM or nepBoro. HaiiAare [oJIox{eHHqHallJtyqtuero coBnaAeHrlfl KoporKofi u A,luuHoti uoc.neAoBareJlbHocreft.,[,aHnuenptlBeAe'
Hlr e ra6r. 4.28.
I4a npegu4ylqefo rlpuMepa ncHo, qro N{eroA H3yqeHnfl B3aHMoMeroAy ssaulvlHoftKoppeJlscsqseft ue o6ssareltbHo oKBLIBaJIeHTeH
Ta6lsua4.2&
crpatrrpaOuqecxuxpagpeoag qeHrpamuofiAHrJrsn
Ana saroAupoeaHHHx
(OcuonaHr.re)
24563453145345
34545324534531
45456345634521
345353245352
(OcHosaHI.Ie)
P a a p e s n a p b e p a4 5 3 4 5 4
Paspea uaxrrt
5
3
2
1
2
(BePx)
4 5
3
Be coAepxal{ltil OayHbl.
O 6 os a a qe HIr e: I -necqaHHK, 2- ateBPonnr, 3-caaueu,
,l-no.u,crnnaouaq rJrHHa,5-yroal,0-cnaHe4,
coAepxaulufi OayHy, T-ilgBecrHeK.
272
flpeAno'rauw. VMeg Ae,'Io c apelteuudtnaIzpgAaMH, MbI Aor'IxHbI
uexoropo.ft
BAoJIb
B
roqKax
pacnorlaral'orcfl
Hab.trc4eunfl
;;
;;;,
oTcyTcTByeT B aHaJlH3es:anltocssaeii.
nOslrOil: sTo OrpaHl.rqeHl,le
cococroflTb II3 noc,lleAoBare'tbHocrl4
npocro
Moryr
Fiaurr.rAaHHble
BCTpeqaB
KOTOpOM
OHll
n6pflAKe,
TOM
B
[epeqUCJIeHHbIx
CTOaHuft,
rorcs. Kar li s rOltxo tITo [pI{BeAeHHbIXcrpararpaQnrlecKllx pa3ToI{KaMII B 3ToM
pe3ax' paccToflHng MexAy nocJIeAoBaTeJ'IbHbIMI,I
cflvqae Hecyx{ecrBeHHbI'
"Asa,rOr.irqHstlrO6paSOMHeqHCJIOBbIe
MOlknOC,'leAOBaTe"rlbHOCTII
a
B
TOaCH
a
3
b
I
B
a
e
T
C
t
S
T
O
T
n
p
O
q
e
C
C
C
O
6
O
f
i
;
c
C
a
i
U
I
I
u
l
l
HO cpaBH1iBarb
nepIiOAsrOacCOqltaUHflno"rle3Ha 11pn ICCJIeAOBaH]lIl
COU1iaUlrefi.
I{c4uvHocrefi B noprAKe cJreAoBaHrrflcocrogsHii II OqeHblxllpoKo
v
IruKJIore
aHI'lH
Ilcc,IIeAoB
]'
npu
a JIacb
noJrb3oB
la7
B eroNa cJlyqae cpaBHI'lBalorcq He ABe [ocJleAoBare.rlbHocrl'
CaMa C CO6Oli.Vraxeirl BepOflTHOCTi!
a O1;HarrOcJIeAoBaTeJIbHOcTb
BepoB
C
O
B
n
a
A
e
H
r
l
f l s T O MC , l y q a e . E u H o n a z a . n l H a q
6
u
o
A
H
O
r
o
xorg
rrrnocrb [ofiyqeHl.If AaHHoro qlIcJIa cosnag,eHuftB cJlyqafiHofinoc.neAoBareJrbHocrunpn cpaBHeHuHee cauoft c co6oft cocraBl'Ir
,:( fxu,-,\fru,-nt.
$.7S',;
\e:r
) |
qro nocreAoBareJlbHocrb
npeAcTaBJrfleTcoMu upe4uoJlaraeM,
r{eN{
6ofi c,'ryvafiHoepa3Melrlervem cocrosuuft tltrtrtKJlaccoB, rIp14
KaxAoe cocrorHue Bcrpeqaercn Xp pas. O6nree qlicd'Ioua6,'Irc4eHuft
n
paBHo 2 Xh:n.
3ry aeponrnocm
HaAo npqMo
[oAcraBJlflrb B.
k:l
(4.72) H r{crroJrb3oBarb
npH BbItIprcJreHuta
H craH12-pacnpe4e,rreHlrg
AaprHoro orKJroHeHHfl.Kpurepuii [peAHa3Har]enAr'rr npoBepKu Hy,renofi farlore3bl, 3aKrloqarcxleftcq s roM, rrro qucJro cosnaAeHvrl ue
orJrr{lraercfl cylr,ecrBeHHo or ox{aAaeMoro q-vcila coenaAeHaft L"'rR
c.nyuafinorl nocJreAoBareJrbuocrrz
npu cpaBHeHHrlee c cauofi co6oft.
.[,,rx u,rr.rfiocrpaunnnp]tMeHeHl{fll\reroAa aBToaccouHaufiri Mo]KH o u c n o J r b 3 o B a r bA a H H b r er r 3 p a 3 p e 3 a [ r a x r b r ( c u . r a 6 , u . 4 . 2 7 ) .
Ec,r[ s pa3pe3e uaxrbr 6y4er co4epxartctr MHoro rroBroprrculuxcfi
3JreMeHToB,
To 3To npnBeAer x ueo6uxuoBeHno BbIcoKnMgHaqeHr{RM
orgoueuuji, xaparreptl3yloul'Ix coBnaAeHlIt, H K 3HaqlITe"IbHbIM
orK!'roHeHuflMor ox<rrAaeMof0CpeAHeroqHcJra cosnaneHr.rfi. I4grepf l p e r a r r H n r p a r f r H r o n ,x a p a K T e p r r 3 y ] o u r u X8 3 a r r M o c B f l 3 un,p o n o 4 r r r i a
a H a , ' r o r r r ( r Hror H r e p n p e r a u r r rK
r o p p e r , r o r p a M MO
. 4Haro r<oeQ$ilqueur
B3aHMocBs3H
Bblqllc,{flercqHa ocHoBaHIIIrHoMHHaJIbHbIX
AaHHbrx,I.t B
cHJiy sToro uuSopuaqHt, coAepxauaflcfl B rrocJreAoBaTeJrbHocTH,
sHar{HTer'rbHo
6e.u,uee,rreM B oKB[BaJreHTHoM
BpeMenH6u pngy. Tar
MbI llcrloJlb3yeMKaqecTBeHHbre
IlK
AaHHbre,To He Mo>KeMoxr{AaTb
Toro r(e pe3y"Ibrara, xoropufi MoxHo
6st.no 6lr no,,ryqHTbnpr.r aHanll3e Hacroexrrrx Bper,leuudrxpflAoB.
Oror Qarrop neo6xoaui,lo yuanptl llHrepnperau[u pesy,rtraroB
ro B3aHMocBssrMH aBrol:t^u^1lo
accoquauHtM.
r8-201
273
NOJIYBAPI{OTPAMMbI
Tepir,tlu reocrarucrr.ira ceiiqac rxupoKo npr{Meuflercfl K clreqlr.ar'rbHbrM
BerBflM nprrK,'IaAHoficrarHcruKlr, HarIaJIo pa3Brrrufl Koroporl 6n.no [o,'ro)KeHo f. Marepouor,r n lJ,eurpe lrareuarrrqecrofi
rrroptlo,rornlr s @oHteH6,ro,tDpaHqHq. Uerr reocrarncrr{Krr cocroflJIa B trccJIeAoBaHuitnpo6,renr, noropbie Bo3HIlKarcT TorAa, KorAa
o 6 u i q s a g c r a r r r c r u r { e c K a r r e o p f i t l r c r r o J r b 3 y e r c gB o q e H K e H 3 M e H e Hrrfi cc4epNaHufi pyAbr B pyAHoNrrene. O4HaKo raK r(aK reocrarr{^ 'o<c, l. -p' a- .K' 'T H a f l T e o p u f l c T a T H c T l r q e c I t oof I I o B e A e H I { f l , o H a
cTutia (,crb a
q ) r r r l e H I i t v t a K o \ ' l H o f t z M o 6 c t o g r e u r t c T B a M B p a 3 , T I I r I H b t . ro 6 r r a c r g x
feoJ-offirr r.i Ap)'rirx ecTecTBeHHbrxHayK.
- NOHflTfiC
i\,'I}OtICBOCIIOHfTIIE IEOCTATIICTIII{H
PEIIIOHATII3OBA}IN'rexAy
uoii nepel"reuuofr, rioropafl HN{eer cnofi craa, [polrexyroqHble
ceoiicrnaMii no.!Hocrbto c,ryuariHur Be.rluqrrHII lto,'t]{ocrbFo Aerepr'rIIH r r p o B a l i H b r x n e p e N { e H H u r x .T r r n n . r H n r e p e f } i o H a , r r r r 3 o B a H H b l e l t e p e I{euHbre gBlrfl rcTcf c!yuxuunurr, onrrc btBaIourn\,IIr ecrecrtseHHbre gtspactrpe,4e,reHHe, TaKire, KaK
,'reHrifl ir HMeroilr,rrMrrreorpaSnqecrioe
Bbrcora HaA ypoBHeM rioBepxHocTH, lr3MeHeHHfl coAep)KaHrrH B pyAIIOTeHrIria!'r,USUepenHSrft
HON{Te,[e I{JrH CnOHTaHHbIfi3r'reKTpr.iUeCXUfi
B c'ne4yrcB oAHoM'AByx H Tpex E3MepeHHtx'
BaHHbIxnepeMeHHblx
npoueAypy--ol{eHl{u'
paccrtlorpllll
ufuf inu"d MbI 6oJleenoApo6Ho
JIIzlIlboAHoit us
ilur"ur"*yro xparir'uforr.'Cefiqac MbI r<o6nertlcq
a H11eH
f eocTaTI]CTJ'iXII,
I.ISTHK
crarucrnqecKrrxxapaKTep
saxHeri111fix
Bblpaxie'
HO rOHrrTr.rs no,'jyAllcnepclIH, KOTOpoe IIcIIOJIb3yeTcf AJIS
B,[.c.rib
nepeMeHHblx
perHOHaJIH3OBaHHbrx
H3MeHeHlin
Htig cKopocTr.r
nDoc
o
A
e
p
x
l
l
r
3aAaHHoro HanpaBneHHs. Oqeuxa nonyAucnepcnH
pflAoB',
BpeMeHHblx
aHaJIH3a
IIeAypbI, aHaJIOrUqHble npolleAyp_aM
npI.IBOAHTK HeO6X6AHMOCTIiIICIIOJIb3OBaHIIgIeOCTaSJIeAOBaTeJIbHO,
THCTI'lKLI.
f l o . r y A u c n e p'npo6arran
c l i t e c r b M e p a c r e f l e H f i . .n p - o c r p a H c r e e H H o i t 3 z B I l ' " l i eeo,'rl saAaHHoft 6aztt. !,nn flpocrorbl 1\'1bI
Mocrr{ tiuxay
r{TO
npo6lr flBJIfl}oTcs ToqeqHbIMIt U3MepeHuflMrl HenpeAnoJro)KuM,
, a K o r o , x a r r , r y _ 6 3 n a[ o ^ r l o B e p x H o c T H o r or o p f i x 6 r o p o r o c B o f i c T B aT
soHri. ,[,,rrr o6.rrerqelllfl BbIqHc"reHHil uu 6yAevr Aa,rleeflpeArio'lar a r b , q r o 6 a s a p e r y . i t f l p H a f lT, . e . [ p o 6 b l p a B H o M e p H op a c [ o n o x e H b i
B npocrpaHcrBe BAoJIbnpqMblx .ltltntlft. Ec.nu paccroflHue Me;*'Ay
A, to no'n5''paBHo uexoropofi Be,'Illq_HHe
npo6arraano nprrvofi JtrtHLtLt
4ircnepcux rnrox<er6Hrr sr{q1rcilera Anr paccroaHuft, xpatultx A:
^(
n:
pefr{oB criBax{uHervrero:loM
Kaporax{a.B orurnqueor c.uyuaiiubrx,
Ilar'Irr3oBaHHbIe nepelleHHble He[pepbrBHbl oT Tor{KLI K-TorlKe, Ho I{3ilteHeHl4fl UX HaCTO,lbI{OCr'tOXiHbr,qTO OHII He I\{OfyT ObrTb OnilCaHbI
I
I
i
I
Sl rx, - x,rh:,2.
/
M
l \
(4.76\
T o r r o J o i i i e H u i is p y 4 u u x e . O A H a x o t o r $ a x r , q r o o 6 b e M r , rn p o 6 n
orHoI'r \'rHolr{ecrBer3MepflnTcfl e x5'6rruecxlrx caHTHI\rerpax,a B
Ha
Ap)'ic:'1- n x5'6liuecrirrx \,reTpax, aeil:6ex<go AoJix(eHB,'tr:rflTb
CXelly tl3lJel{qllBOcrll coprHocrll pyAbl, KOTopy}o lvtbI KapTItpyeI{ B
p)'.{,rrn(e. f,raeuaJi gaAaI{a reocrarllcrr{Kn - cBr3arb pe3}r,'IbrarbI,
[ o r ) / q e H H b r en o o A s o i i 6 a : e ( u a n p u r t e p , o 6 p a s q u r i e p n a ) , c p € i s L p l , r o f i 6 a s l r ( n a n p r r M e p ,3 r ( c [ , { y a 3 ) ' . q b T a T a N rrrri o
, J ] q e H H b r M rA. n
TarlrroHr{Iie6noiitt ) .
feocrarlrcrrrKa no3Bo,rrterAarb or{eHKHQopuu pefuolra,'rIr3IIpo-
[€peMeHB srilx o6o3HaqeHu.gxxi - 3HaqeHHeperHoHa,'IIl3OnaHnot?
3HarIeHIte, B3qroe uepe: &
HOfi, nSRrOft s roqxe i; xi+n-Apyroe
n H r e p B a J r o BM
. m noeroMy HaIIJII{ cyMMy KBaAparoB pasuocrei?
Mex<Ay3HaqeHtrqMHpefvoHar'r.r3oeaHuoiinepenteuriofiB rtape roqeK,
qro qncpaccroflHueu Ah. t{rrc.noroqeK
pa3Ae,reHHbrx..
_paBHon, TaK
Jro cpaBHeHuliruex4y rrapaN{r{ToqeK ecrn n-h.
Ec,rr uu Bbrqucd'raM
rroJryAricnepcwuAJrtlpa3d'rr.rqHblx
sHaqeHnlilr,
To Mbr MolKeM HaHecrn pe3yJ'rbrarbrria rpaQun B Br.rAenorrlBapitorpaMMbr, se,'rsFourericraHaJroroM r{opper'rorpaMMbI. Ha plrc. 4.41
npeACTaB,rreHa
rror'lyBapr.iorpaMMa,
coorBercrByrcuafl r,ry6lrue ceiicM I I T I e C KO
HT p a ) K a l o u l . e ffoo p t i 3 o H T aH [ o c T p o e H H a t n o H 3 i l l e p e H f i f M
B A o J I bc e i r c , u r q e c x o r on p o q b r r . n rn, p r r B e A e H n o r os a p u c . 4 . 4 2 . 3 a u e T H M , r r r o K o f A a p a c c r o f l H r i eN , r e x { Aryo q K a M r r o n p o 6 o n a u u f l p a B H c
{ } t . r i o , T o 3 r r a q e r { L iee x a N A o r ' rT o r { K ec p a B H r i B a e T c cg c a M H Mc o 6 o i i .
Cure4onareabHo,BCe pa3HOCTilpaBHbr HyJrrO,H noJryAHcIIepCHR
Aj1fi
Je ecrb Iry"lr. Ec,'rr.rAft - ualo6 paccroiruue, TorrKr.rrrpH cpaBHeHril.i
oKa3brBarorcfloqeHb rIoxoiKrrMt4,ri ilonyAr.rcnepcI4fl6y4er MaJra. llo
Mepe yBe!'rr{qeHfifl
paccroffHufl Aft CpanuunaeNrbre
ror{KH craHoBrrcfi
cr'r?o€ecBrr3aHHbtrvrH
Apyr c ApyfoM H paccroflHr.rflMe)KAyHHMr.r
yBe_
JIIIrIHBalorctr,rtTo rptrBoAUT K 6Onlrurlrr.r
3HaqeHHnM1r,. flpeAnono) l { H M ' q T O H a H e l ( O T O p OpMa C C T O 9 H I I I I
cpaBHI{BaeMbT
l eO i t K I t H a X O ral{ Aa,'Ie,Ko,
r{ro oHtr He cBfl3aHbr
{11."
Apyf c ApyroM, H ux KBa.q6yayr paBHbr ro BeJrHqHHe
Aricrepcurr orHocnre.4r,l:l:t
^p_1t_""crefi
Hofo cpeAHero
3Har{eHHi.no,ry4Hclepcuq 6o.ree H^epacrer }r [od'iyBapuofpaMMa nepexoArir
n n,rocryrc^ o6,uacrr, uasoioaeuyrc ttopo-
q1A
lg*
n a r i o i i - . n u 6 op e r l , r x p u o r i A e r e p M H H H p o e a H H oQi ry u x r l H e r l .
nepeNreHHafl
l,aixe Hecllorpfl Ha ro rrro periroHaru3ripoBaHHaq
H e r r p e p b r B uB
a n p o c r p a H c r B e ,o 6 b r q H oH e B o 3 M o x H o3 H a r b e e 3 u a q e Hrie B ,qro6oii Toqrie. Biuecro ororo ee 3HarreHuqlr3BecrHbrroJrl'rio
6,naro4apr npodalr, Koropbre 6epyrcr B oripe.qeJeHHblx r\{ecrax.
P a s v e p , B l r A , o p r r e H T a r l u fH
l l p o c r p a i r c r B e H H o e p a 3 M e q e H r r eg ' l r r x
n p o 6 c o c r a B , r r f i l o r6 a s y p e n r o H a . r u g o s a n H o r l n e p e l r e n u o f i . 3 r a n e p e M e H H a fnl p i r n 3 \ r e H e r { } r xuo r f l 6 u o g u o r o l r 3 a r r { x n a p a v e r p o n 6 y A e r i r M e r b p a 3 J n q u b r ex a p a K T e p r i c r u x r r .H a n p u N r e p ,n p e A n o J r o ) K r i N { ,
q]'o t\4btxoTrrrt onpele,r[rTb il3\reHqiiBocTbcopTa BIipan,leHHblxp]rA
e Hro";rLr6AeHoBo\r
ilrecropolKAeHlur.BepoRrno, pe3yJrbrar aHa!'Irr3a
5 - c aH r l r , . , r e r p o B o rKoe pu a , [ o . q , v q e H H o f n
o p H a / ' r \ { a 3 H o N6{y p e uu r r , 6 y [poo H3 pyAr{brx oTBe[€T OTr'tr{aTbcgOr pe3yJrbTaTarr3Nle.r]brreHr.rfl
cn)'qaflx
Mof,'ilr
6rtssqrl
Bo6oux
Mbr
BTor{HocrH
To }Ke ca\,roe
"rr.,e.
TIIICJ]C ilPO6,
II OHII MOIJIII 6IT 6ITTI
ilO,'IYqCHbI Ii3 I,IACHTIIIiHbIX I\IEC.
2I?
Pnc. 4.41. floaynapnorpaulta a6coarcrHbIXorMeroK KpoBnHMe,rogoir$opuaBAonbuopcxonoceiicrIHH,rr3MepeHHoir
Inrqecr(ofo pa3pe3a s MarerraHoson
nporHBe.9n,rn [38] .
1i
:
,rlfiHHq, u3o6paxeHHaq
roqKalrn,
IpeAcraBnfler ropor.
HnK trtrcnepcHm, Bo3BhrueHHil H
prBsa
yKa3aHHhrfr crDenPaur,
8380 lre.
HHxe Koroporo
Koil, - paccroqHHe,
Da3flocrb
trexay,uHcneDcHr)lH
H noporon
cqHTaeTcfl
llanofi (3,5 KM)
nDeue6pexulro
ou
T. e. noJIyAIrcah Apyr or Apyra, Ho Il Allcnepcul{srnx pa3HocTefi'
no
onpegeneHa
6strs
QopMyn
nepgra MolKer
.tl,
'n
:
-
2n
E{r
Xr- X*o)-
I
n
>(x, - X r * r )
)'
.
(4.77)
pefnoHaJrri3oBaHHofiIIepeMeHHoft
3anaeruM, tITo cpe.!.Hee3HalreHire
perIiOHaJlIl3oBaHHol?
IIepeMeHHoftXi+n, TAK
cPe.]Hee
TaKXie
Xi ecrb
KaK 3TO-Te
ptAKe, T. e.
2
x i e c a \ l b l e Ha6,'IrorteHlrfi,ToJIbKo 83flTbIe B ApyfoM
lXi
tlo-
Xfi tn
nn
0
J
o
1600
s
6
I
;
18oo
Q
s o
2
a
L
l1
t
I
I
2000
Puc. 4.12. floAnoqeenHHe
crp)'KTypHbte a6co,rroruure orMerKtt
KpoB,'ru
Nre,rosori
Soplraquu,oueH e H H b tneo o r D a x e H H pc e i r c v r r qecKxx BoJrHBnonb 2l-KHnoMerpoBofo MopcKororpanepcan Marer'IltaHoBorrnpo":IlrBe.Ceirc,l.tuqecKue H3MepeHHrr
B3qrbl s 300MerpoBollrrHrepea;re[38]
[oM. PaccrogHlre, Ha KoropoM non-vAltcflepcllflIIpll6"1[xaercq K AIlcne{repcHr.r,
Ha3brBaercf paHfoM, HJriIpa3MaxoM peflioHaJili3oBaHHoft
peMeHHofi,oHo onpeAerrFeToKpecTHocrb, B rlpeAe,'Ia.\Koropoli Bce
cBf3aHbr Apyf c ApyfoM.
no,'rolKeHHrr
A"'ls Heroropoii npou3BoJlbHoft Toqt{H B rlpocrpaHcrBe I\{bI I{o'
x{eM npeAcTaBlrrb ce6e oKpecTHocTbKaK cHMMeTpI{qHbiilIiHrepBa"'I
(u"rn n.nouta.r,b,rl'III o6aeM, B 3aBlIctIMocrH or pa3MepHocrI'I) BoK p y r r o q K H . E c . n [ p e r u o H a , ' I I I 3 o B a H H a frlI e p e M e H H a gc r a l { H o H a p H a
rr.rrr.iBcioAy IIMeer o.],HoH To )Ke cpeAHee 3HaqeHIIe,To JIIO60enO'
OT UeHT'
BHe 3TOfo IIHTepBaJIacoBep[IeHHo He3aBHC]lMO
JIO)KeHr.{e
pa"{bHoriToqKn H He lvlox{er ,[aBarl lIHq]opMauIIIOBOl{pyr 3HaqeHIIfi
[epei\4eHHoitB 3roll roqr{e. B npe.{e.naxsroti
pefHoHa,'rr{sHpoBanHoir
o K p e c T H o c r u ,o A H a K o ,p e f l r o H a , , ' I I I 3 I I p O B a H Hnaeqp e M e H H a fB o B c e x
H a 6 r r o A a e N { b rrxo q K a x c B r 3 a H a c p e r H o H a J I H 3 o B a H H oIilie p e M e H H o f {
Mo)KeT6lttl ncno.ttb3oBaTOqlie I.I, CJIeAOBaTeJIbHo,
B IIeHTpadlbHOit
H& ,[Jf oueHKrr ee 3HaqeHr.is.Ecrrlt ML'IHcnoJIb3yeMMHoiKecTBoII3MepeHHfi,cAe,laHHbtxB TorrKax BHyrpi{ 3Toft oKpecrHocTllAJIfl oqeHTOI{B UEHTPAJIbHOft
NEPCMCHHOft
KII 3HAI{CHI,IS
PEI}1OHA,'IH3OBAHHOI"I
a 6 e c f l e q I I T c o 6 c T B e H H b l eB e c a , I ( o T o p b l e
Ke, TO nOJryBapHofpaMIlo
6url n p unticaHbI Ka)KAO)Iy LI3MepeHLIrc.
AO,'riKHbr
OcraHoelirrcfi Koporlio Ha QaKTe, Koropblft 6y4er HaDI IIoJIe3eH
KBaAno3x(e. ilo,ryAUcnepcllfl paBHa He To,tbKo cpeAHeMy3HaqeHLIIo
paToB pa3HocTeli A,'Ig nap TorIeK, pacnoJloxeHHblx Ha paccTogHllli
276
6Urs paeua uynrc
p
bO , ' l x { H a
' a 3 H O C TA
XXi,-rr - g.
2Xi nn
K o u 6 u u l t p y t c Y M r ! b I ,n o J l y q a e N I
floarouy
14 0 0
o
I
4nv
(2Xt-ZX*n) ln : lZ(X, - Xi+n)lln: 0.
tIfleHa p_afloAcraersn a (4.77), MbI BIIAI{M,qro r{IlcJIIlreJIbBToporo
qro
(4,76).
ypaBHeHHeM
c
ypaBHeHl'le
coBnaAaer
3ro
BeH HyJrio,TaK
3aueruu, rITo 3To coorHo[IeHIIe crporo cnpaBeAJIIrBoroJIbKo rofAa'
. cnH AaHHbIe
K O r A a p e r H o H a . q l I 3 o B a H H[aefpl e M e H H a qc T a u l { o H a p H aE
I',I3MeflOCJIeAOBaTeJIbHOCTI'I
To
cpeAHee
3Har{eHI'{e
He cTarluoHapHbI,
Hflercfl Blrecre c h, w (4.77) Ao.IIxHo 6rtrl uoAllQnqupoaauo.
o]K[Aarb, Itllenrcfl MareMarllqecKne coorHoKar u cJle,u.oBa,lo
TaKHMII,
rueHug Melr(Iy no.'ryAucnepcneitn ApyrIrMH CTaTI'ICTI{KaMH,
II,Hff
rrfl H aBTOKoppeJIff
. EC,rn pernoHa,'IHsoBaHHafl
Kari aBToKoBapr{ail
LIL
[epeMeHHaq cTaqlloHapHa, TO [O,IlyAHCnepCUtA"Ig paCCTOgHrIg.
paBHa pasHocTrr \rexAy 4ucnepcueii rr [pocTpaHcTBeHHofiaBroKoBapuaqfiefi A,rrRroro )Ke paccroflunx (puc. 4.43). Ec.nu perao[alrr4s O B a H H a f[ e p e N r e H H a sH e T o J r b K oc T a ( [ o H a p H a , H o 1 4c T a H A a p T H 3 o BaHa raK, qro6or cpeAHeepaBHsJ'rocbHy,'no, a Ancflepcnt eAHHHqe,
ro loryBapnorpa]rrra 6yler 3epKaJ'rbHbrM
orpa)KeHrreMaBToKoppe-
rsuaouuofiSyHxurur
{puc.4.44).
I( coxaneHriro, qacro pefnoHav'in3oBauHbre
nepeMeHHl,reHe craq H o H a p H b rc, K o p e eo H H o T p a x a r o T H 3 M e H e H I i H
f x c p e A H H Xs H a q e H r . r f t
or roqKu K ToqKe. EcnH uu [olibrraeMcfl rrocrporirb [oJryBapHorpaMMy 4"ra raxoir nepeivreuHofi,
ro o6HapyxaM, qro oua Molr{er He
uMerb onucaHnbix strrtre csoficre. O4Haro ecJrn nepecMorperb onpere"{eHIIe roJr!'r,rrcnepcrnr,npr{BeAeHHoe B QopMyJre (4.77), ro Mbr
3aMerr.rM,qro oHo cocrouT H3 AByx qacreft, nepBas coorBercrByer
p a 3 H o c r q M n e p e l r e u u o i i B n a p e r o q e K , a B T o p a r- c p e A H e M y3 T r { x
pa:Hocrefi. Ec.nu peruoHa,'rH3oBaHHaq nepeMeHHas crarlproHapHa,
T O , K a K M b r B I r A e J t r ,B T C p a r l t a c T b p a B H a H y J r r o ,a e c J I Ho H a H e c T a ulloHapHa,
lo 3ro cpeAHee6y4er air,rerrHeKoropoe He paBnoe Hynlo
3 H a I i e H H e[.e r i c r e r i i e , r b H o , p e f r i o n a J r H 3 o B a H H anfel p e M e H H a sM o x { e r
6utro paccuorpeHa Kar( cocroflrqas rr3
AByx uaciefi, Ha3brBaeMbrx
ocrarKoM Ii ApnSroM. Apu$r - 3To MareMarriilrecKoeolKr.rAaHr.ie
pefI{oHa.IIH3oBaHsoli
nepenreHHofiB ToqKe i, ntu c TogKH gpeur.rsBbr277
Puc. 4.43. CoorsoureHlreuexiAy nory.qucnep$reri1,rru aBToKOBaplrauraerl
rja
crarlHoHapHofiperrroHa.rrr:bnaHHofi
nepeMeHHoi.
yAo
"6Hbrft, Ho Bce*:. il:
1-:"""':u t ^: :*f :*f ":"J:1?;
i ; ; ; t ; ; peHHo-MoxeY".T:i::"i
'":#?
{::.'.pTff
^lll- Li'^oroft
::":T11
::1'.11?
qro T,npoll3Bor'IbHofi
B npeAerlax
o r 2- A u c n e p c n q s a 6 a n A e g H i l H r H l B T o K o B a pvat\trg Atrfl lara 0. Ils
3HaqcHnii BHa 9To.
ro lrHoxecTBa ?rr:Oo2
6ii..",io"iu
AYJ'
-
i;;i;i;.
^rt
Httelt, uanpliltep
(.luHetiurtii
Ph
7500
t
p
s0 0 0
2500
Prc. 4.44.CoorHOUeHlle
MelriAy
no"'ryArrcuepc,.refr
"[h n aBroKoppe-
0
.'rrrUueii 0/, A,,qq
cTa qn oHa pH.Il
perrloHSJl.t3o -
itrrrlrlrl,'rrl
1n
r.
B:rHrrofi rapeyesnorl
q f i c r e H r r i r ,B 3 B e u l e H H o cep e A H e eB c e X T O q e KB H y r p n o r i p e c r H o c r H
BOKpyr roqKH i. flpuQr 6yler riMerFJsnl_xpr.rnofi, annpoxcnMi.rpy_
loqer? perHoHa,'rn3oBaHHyro
nepeMeHHyr,o.
Ec,urr Aprror slr.recru rr:
p e r r 4 o H f l r r r 3 o B a H H onfer p e r v { e H H oT
f iO
, O C T a T K UR i : x i - X ;
caNiu aa.
' l y r p e f u o H a " l l { 3 o B a H H y Inoe p e M e l { H y I o , H M e t o u l - v r cop e A H H e3 r r a q e Htrfl, paBHbreHyJrro.Apyrulrrr cJ'roBaMIr,
ocraTKr.i65rgyr cTar{uoHap_
HbrN{uu N,ro}Krro
locTpor.rTbHx no,'iyBapHofpaMMy.
3ACCI
ilfT,I HCO)KIIAAHHO TIPIIXOAHM
K IIPO6J'ICMC
I{IiKJTHIIHOCTI.T.
ApHSr Mo)Ker 6urt oqeHeH,ec,rr[ Mbr 3HaeM pasMep oKpecrHocr* r.r
Beca, [pulrrcaHHr,re TorrKaMBHyTpH9TOftoKpecTHOCTr.r,
oAHaKO SeCa
Mofyr 6rrrl gstqHcreHblTor'IbKoB TOM Cd'iyqae,ec,lrll MbI 3HaeM nonyAucnepcrrrr, coorBercrBvroqrre paccroflHr.rfiM MelKAy roqxoi{ i,
qeHTpoM oKpecrHocrr.rLI p asJ'IlIqHbIIUI.r
ApyraMr.IToqKaM[ BH.]lrcreFrHbI[: oAHaxlsr 4przSr Bbrrrr.rraeM
H3 sHarr-eHriii,
nonyueHHbrxnpir Ha6;rrcrenHu. flo'ryueunyro craurropapuyro nepel{eHHyro B cBoro oqepeAb Mo)KHoI'{clloJlbsoBarbA,'It oqeHKHpa3Mepa or{pecrHocrrrB B}iAe noJyBapI,IorpaMMbr.
Tenepl oc.na6nnacrporocrb Haurfix onpeAeJreHlriiu neper?Aenrrc
r v r e r o A yn p o 6 l r o u r u 6 o r . C s a q a n a H y x u b n p u 3 H a r b , q r b H e " r r o s q
orIpeAeJI[TboKpecrHocrb B ToM cMblcdre,B KoropoM MbI IIc[oJb3oBa,IIH STOTTepMUH. BUeCTOgroro oKpecTHocTb orrpeAe.riseTct KaK
278
h;L4noro*"tr,
"
-,i,.^.',"^
rnnDGhL
nnn^Tllf,r
R
{ p>
- Ke'
BLbr nl ept a
.lplrQr MolKHoanrpoKcllMgpoBarbnpocrblM
Xo:Zb$i
xpll qlr ) ll"rll{JKe
x o : I ( b 1 X r+ b 2 X i 2 )
I cex
( x u a . a . p a r u u H r , ;i p
i i i l Q r ) . B : r i r Q o p v y , r _ r tB x o A f r K o o p A I { H a r b B
q
r
o
r
a
K
c
y
il{eO
K
p
e
c
T
H
o
c
T
I
l
'
n
p
o
l
l
3
B
o
.
l
b
H
o
l
l
, r l a H i r o r _ "r o q e t i B H . V r p H
II
oKpecrHocr}I,
pa3\{epoM
Ap}IQroN{
Ntex.qv
B3alt\rocBfi3u
.ii'yg
. c n t t o x p e c T H o c T bB e , l l I K a 'B b l r { l l c J l e i l o . r l v B a l ) l i o r p a \ t l l o foi c T a T K o B E
I a 6or'iblxoM qllc,te roqeK' H ApI'ISr
i i u o ' a p i ' 4 , t i o i r S ' t o c H o B a H bH
rlaAxoit xpHnoit. B erolt c.ryqae
oqeHb
np-egcranlrrb
6j':er
*or,i,u
a nO'
ocraTKtr Oyli,'r iaparirepHsoBaTbcfl -6O,rlruoliH3)1SHr{HBOCTbIO,
C
,
r
e
A
o
e
a
r
e
"'Isuo,
n
o
$
o
p
r
u
e
'
c
.
'
t
o
x
i
u
o
i
i
,rynapuorpariua oliaxeics
6oiibill]'to
Ha
6yAer
B.rluflrb
olipecrHocru
NIa,loIi
pa3]tepa
cneUircfruiia
O C T a T I { OuB I l a n p O r r 3 \ { e H r u t B o c TobU e H K l IA p I I S T a , H a } ' N { e H b u e H l i e
c T o T y B a p I I O i pa l l l t b I .
O n p e , r e , , i e i r uK
e o 3 Q Q l l q l l e n r o Bb l p u . Q r a r p e 6 y e r - p e u e H l z s H e x o T O p O f Oq u L t J a c o B M e c T H b l x. v p a B H e H l l H[ o B b I u e H H o I i c J I o ) K H o c T I I '
f lO p a 3 A e . [ a , n o c B g l l l e H H o t o
o n l r c a H r r eK o r o p b l l o T K . - I a J b l B a e T CA
x p a f i r H u r y . E x t t H c r s e H H b l en e p e \ I e H H b I e B 3 T I ' { xy p a B H e H H g x - 9 T o
paccTof Hl{fiN{_Me)KI,}'
pa3,'IHqHr'IM
no.rlyAltcne!rcllli,cooTBeTcTByFou{ile
r o . r K o i i c H o \ i e p o \ 1I l i l p y r l r u t I T o q K a M uB p a c c M a r p ] I B a e M o foi K p e . c r H o c r u . O A r r a l i o o u I I e u l e H e n a t o r n o , ' I y B a p t { o f p a M M buI s, x o r o p o t " t
c,rre,r.yer[o,I\rqilTb ]reo6xoArlNlbleno,'IyAI{c[epcHH. MoxHo AonycII\{eer raxoii-.nlt60 ecrecTBeHHbIit Lng'
Trrrb, rrro no.-rvBaprrorpaMMa
r{ee BtrA, il uc[o.lt,3oBaTb efo B KarIecTBe rlepBoro npu6.na\rreHltr.
K cqacrrto, ,refKo rrpeABurerb BIIA npocroii no,rynapaofpaMMbl,
I I 3 T O[ O 3 B O . - I R C
I IT
C I I O J I b 3 O B aOTKbp € C T H O CH
TabC T O / ' I b KMOa J I O | Op a 3 N{epa,Hacr(o.'lbtio3To B03Mo;.t{Ho.
3ricnepttrreHraJbHbreorreHKrrApri$Ta Bblrll,rratorcflH3 cooTBercr'
Bvlollllrx tra6,rn:.esrrii, a pe:y.lurare r{efo no,'Iyqaercf MHo)KecrBo
3 r i c n e p r r M e H T a . r b H ro, cr xr a r K o B . l l o e r u , v o c r a r K a M M o l K H oB b i q l i c '
" r l l l T bI I O , l y B a p r r o f p a N { \ 1r r} 3 3 T € r \ r c p a B H H T b e e c T o f i n o . r l y B a p I . r o r p a r t r t o r i , r i o r o j ) a r 6 u n a a u 6 p a H a B K a l r e c r B en e p B o f o n p u 6 J I H > K e ttttl. Ec"'1t c:.e.i"utttte npeg,no"'totxeHltq
To o6e
6br,'IiInpaBn.qbHbIr\4II,
OIIII COBIAAVT.II N,IO}KHO
CqIITATb,qTO OOPMA APfiQTA Ii IIOJIYBAp t t o f i ) a l r M b ro n p c l e , { e H b ry c 1 r e u H o . O g u a x o 6 o , r e e B e p o r r } r o , q r o
ollllnor.rIlqarorcf, rr cJleAyeTflpoAe,'raTbBbrqr{cJreHrifl
eqe pa3.
I lpouecc coB\recTHofoilocrpoeHr{f yAoBJleTBopuTe,'rbHbrx
BbIpanor:,'Baplrofpa\{Mbr^rr
rlr'In
cocraBBaxHori
aBJrflerc;
4plr$ri
]:,.-I'l]i
H o i i t l a c r b r o o c r p y r < r y p u o r o >a s a . n l i 3 a :B H e K o r o p o Mc M b r c , { eg r o IIcKycCTBo,rpe61'rcqee orbrra, TepneHgfl r'r r4qory,a yAaqrl ATOT
npouecc He BCerAa ttpr.rBoAtrrK npHeNtJreMbrMpe[reHasM, TaK KaK
279
OHIi HCOAHO3HAqHbI;
MHOIOKOM6HHAIIHfi4PZ@TA,
OKPECTHOCTCfi
U UO.
TIOJ'IYBAPIiOIP
AMM,\,IOIYTAATb TIPI{MCPHO
AC"TCfi
AKOBbIE
-C,ryuae, OAI-iH
PE3YJIbraru. og npuroAeH oco6eugo B TOM
KorAa perLIoHaJIrZ3oBaHHbrenepeMeHHbreHeycrofiu:,/.Bbt
LlJrkr)Ke Mbr pacflo,'IaraeM JIHuIb
xoporNofi nocJreAoBare"rbHocrbro.
B raxux o6crosre.nlcrBax rpyAHo
cKagarb, KofAa Mbr Aocrr.tfrier,taQQexra or Nou6uHaqnri ouenoK.
l l o . r y n a p a o r p a M M a o r p a x a e r - n p o c r p a H c r B e H H o en o B e A e H r c e
DerHoHarH3OBaHHbn
i Xe p e M e H H b r xl r J r Hu x o c r a r K o n . H e N o r o p u e u ! e 3r'rrr3r.rp
oB?Hu.u.eQ op nau noJ'ryBap rzorpa MM Aa Hbr tta puc. 4',48.
H a p r . r c .4 . 4 5 ,a n p H B e A e H an o , r y e a p a o r p a M M an a p a 6 o . n r z u e c K o r o
Tura, Kacaroqarcfl ocu x B Haqarre KoopAHHar. Oua u.l.rrrocrpnpyer oqeHb rr'raAKoeH3MeHeHr.ie
peflroHaJrH3OeauHoft
nepel,leuuoli. Ha
puc.. 4.45,6 npegcrawreHa noJryBapr.rofpaMMa,
uMeroqafl BrrA [ps_
M O r ?r H H r ' r a ;o H a y K a 3 b r B a e rH a y u e p e u i o e H H e n p e p b r B H oIer 3 M e H e HHe peraoHa,'iH30BaHHoft
nepeu.euHoft. Llcruuuai c.nyuafiuax nepeMeHHar ue 6yAer HelpepbrBHofi,u ee ttoJryBapaorparr,rir,ra
6y4er ropnloHrad'ilHoli .nHunefi, opAriHara xoropofi panna 4Hcnepcriu (puc.
4.45, a). B Hexoropbrx cflyr{aqx uo"rryaapnorpanruaue npbxo4ur ve_
pe3 HaqaJroKoopAnHar, a uMe_ernpa a6cqwcce, panuofi HyJrr,o,
HeHy_
JreBoe3HaqeHHe.3ror c,ryuafi c_oorsercrnyer <i64eKry
caMopoAxos>).OH uso6paxen
.10
I{? puc. 4.45, e. B reopuz se,,ru.{Hnbi Ao,rxHa
6lrrl panua HyJrro.SQSexr caMopoAKoBBosHr.rKaer
rofAa, KofAa pe_
raoHaJIH30BaHHaflrrepeMeHHaflHacro,rIbKo orua60qHo onDere.'leHa
q rT,o [ o J r y B a p H o f p a M M aB b r x o A H TH 3 H ] ' _
Ha KOpOTKOM
paCCTOflHHL
i l f l H a y p o B e H be Q Q e x r a c a M o p o A K o B H a p a c c r o r H l r x , M e H b r r e N { ,
q e M n H T e p B a ,o
r upo6onauuR.
Mo4elnponaHr.te noJryBapHorpaMM
B n p u H q u n e o K c n e p r r M e H T a J r b H anf lo , r y B a p H o r p a M M a N , r o x e r
obrTb npflMo [crroJ'rb3cBa[a Alrfl.troJryqeHr.rfloqeHoK, KOTODbTe
Mbr
p a c c M o r p u M B c , r e A y r o q e i i r , r a s e . O A s a x o n o . T y B a p u o r p a M M ra. r 3 B e _
c r H a r o , ' r b K oB. A r i c K p e r u o u H a 6 o p e r o q e K , p a c n o , q o x e H H b r H
x a pac_
c r o f f H n E x A / r ; u a r p a K T t r r \ e ,o A H a t i o ,n o ; t l B a p H o f p a M M b rM o f y r r r o -
"l'-l
lr
16"-l
npO6 n OIUUMeTOAOM
D r 4 o r p a N r Mfel p o B o A u T c f lO 6 u q n O H a r J I a 3 O K ,
;;;.'K;;o^
igl onr"otuaer rr ,naer rpl'rMepbl pyqHbIX Buulacreuuir,
B ro BpeMfl riax o"'rea [38] npueoAr{T npofpaMMy BllrIHjJIeHI{flJIHnefinOfi no,,tlrBapllorpaMMbl,Iauercirlefi TOT >l<eyr,lOnOfi XOoQQUutreHT B Haqa,'le KoopAI.IHaT, KaK Il SKCnepI'IMeHTaIbHaqnoJIyBap
' ilorpaMMa'
B uaeane r{oAer'tb,osl6pauual A,'Ig ttpeAcraBJleHvflnoJlyBapl'rorpaMMbr, HaqrrHaeTcf B HaIIa,'IeKoopAI{HaT,fJIaAKo Bo3pacTaeTAo
lieroroporo BepxHero npeAer'la, 3areM ocraercfl Ha oAHoM rlos a pnc'
. c r o q H n o My p o B H e . C Q e p u u e c x a g M o A e r ' l bn' p e A c r a B , ' I e H H aH
4.46, o6nai,aer eruul't csoiicleaMr' Oua onpeAe,rena no Qopuy,le
"{n:oo"
(+-#)
_h
i
-\
a - napa6oalvecxag
Ooptra, uoKa3brBaouIf,9 OrnHqHy0
HenpepbrBHocTb perHoHa.rH3oBaHHoii
ncpcueHHoii;
6 tusefiuas
noKaSbtBabtrIas
yMepeHHyro He_
QOpna,
npepbrBnocrb;
o-ropu3oHTaJrrual
dtoD_
\rr.. ypoBHs
(t02, cooraercreynuaa
iny,iaiiHori nepclreluor'r,
rre trlrcrotrteli trDoJBTOKOppc.ltuillr: aes_
rprKr cllroll0fKoB. IJtH tBHOe OI:(.toHcl(IIe
"nrop. .! ]i rl cBIaapcHHoi fl poaf i) { l l b t
oT ]laca,!a KoopaHHaT,
IroKa3LIBanrqee,
qTo pertroHaJIff3OBaHrrag
trepelreHHtq cHJbHo ff3tleHqfiBa npn pacqeu ]tHTeDBat onDocTotHttx,
IIeHb[Hx
608a HHq
(4.79\
).
Tr,:ootl.l-et
Ha puc. 4.47 cpaanuBarorcfl c$epuuecxafl Ir 3KcnouenufiaJlbnaq
MoAed'rx.SrcnoHesqvailbrafl KpiiBar HuKorAa He ,ttocrllfaer cBoefo
npeAe,'rbHoro3HaqeHut, a npu6lulKaercfl K HeMy acnMIITorl.IqecKIL
.3rra.IHr,no,'iyArrclepcuf 3KcnoHegqua,ruuoiiMoAe,IIlIHI,t)Ke,ueru cQeD I I q e c K a s ,A " I I qB c e X g H a . I e u H i i/ 1 , u e u g u u x , r { e M p a 3 M e p O 6 , r a C r l t
.B.xuflHr,ls.
,rllrHetiHaq MoAe,'rbnpoure, ueu cQepnuecKafl I,IJIIIaKcrloHeHllllar'lbHafl, TaK KaK OHa HMeeT TOr'lbKO OAHH [apaMeTp'
HaKJIOH.
M o A e a r i r M e e rB r 4 A
1n:ah
Pnc. 4.45. I4lea.luslrponaHHbre
no!'ryBapuof
paM\.rbr:
(4.78)
.q.'IflBcex paccronulfi Brlr'lorbAo o6,lacru BltllflHrlfl'[oJIyBapnofpaMMbr a. 3a npere.'iaua arofi rpaHHIrbI 7n:602. CQepnuecras MoAeJIb
o6uquo xapatirepll3yercfl KaK I'iAea,'IrJHasQopua noJlyBaplrorparInar,r.I4uorAa rrclo.nb3yercfl Apyf ag MoAeJIb- gKcrIoHeHt4HaIIbHag'
6
i,l---',1./280
' B,'IqeTH S 3 a B I i C H MOOT T O 1 O g
rpe6oearnCflA1fl.lp6ux paCCrOnHuii
3KcnpuutlHe
arOfi
Ai'lCKpeTHag
cfl, JrgOHo KpaTHbIUA u"ru Her. flo
n
p
e
4
c
T
a
B
JIeHa
6
u
r
l
A
6
J
I
)
K
H
a
n e D g M S H T a J , r b Hnagr ,r' t y B a p H o f p a M M . a
Mo)Ker6strl eutqucK
o
r
o
p
a
f
l
H
e
n
p
e
p
l
r
n
u
o
r
i
Q
y
H
n
u
n
e
f
i
'
rt.lotop"n
-neHa
f i o a 64,'ttt
o p N,lrc6oro
l o A e , ' l )Ke,'laeMolo
b H o f o y p a BpaccroqHnq'
HeHHsKoKcnepl'IMeHra'nluoft[oJIyBa-
(4.80)
ii npeACraB",rser co6oii npsNrylo, npoxoAflulyrc qepe3 Haqa,'ro KoopAIIIiar. OqeeuAHo,3Ta More,rib He NIo)Ker fiN{erb ntrKa, TaK KaK oHa
p a c r e r l r e o r p a r r l q e s s o . t r 4 H o r A a . { H H e i i u a q M o A e J r bn p o H 3 B o J I b H oM o , i l t t r p u u u p y e r c f l c n o ] , r o u l b l o B c r a B I i t I B H e 3 a n H o r o u 3 r ' t o M aB T o q K e n I { iiil, r(ali, Hanprr\rep,
1n: ah
_
riln h < a,
Apucrpourrr !,;xe#,:Jfi'noli]"rr:i:
(4.81)
rar{ueMoAerrr,
Tat( Kari rrcrro,:rb3oBaurre
"purrKeoIIeHoK npeAnoxpafirHHra A,,rflnod,tyrleHHfl
r'laraer HenpepbrBHocrbH r!'IaAKOeI.l3MeHeHLIe
paMMbI.
[Or'IyBapt{Of
:{J-fHaKo A,rtf paccrolHufi,
suaunre,rrbHo MeHFrtuttxrpaHHIIbI,.rIllHeft281
2
6o
i )
6s
Puc. 4.46. CQepuuecxanMoAe,'rb
ro,'IyBapI{orpaMMbI.
i
6-vxeofi a o6o:saqeua a6cqucca rouru,
B K o r o p o r i n o J y B a p f l o r p a M N r ac r a E o B i l T c t
paBHoil AHctrepcHr oo2
Plc. 4.47,3xcnosesuualruat u crfepuqecKaflMoAe,rHnolrr)-Baprrof
p ar\,IMbr.
O6e vole.na uyenr ortrru t4 Tor )r!e
Haqa,rr,ulrriHan.rou [9] :
J-3KcnoHegrlnanbHat yoJenb: 2-cde,
pHqecxaq MoleJb
Hafl MOAeJrbrBr'rqeTcfl rrAeaJlbHoxopouefi
anlpoKcfiMarlueii. 3re
xopotxo Br.rAHoHa puc. 4.47, rle o6e nro4enu, csepuqecKaq H 3Kc*
noHeHrlua,'rbHar,loqTr.r coBnaAaroTc nprrMofi JrnHr.reiis6nueu Heqa. c , r I , Ip e r H o H a r ' r H 3 o B a H Hnaef lp e M e H H a r6 u . n a o n p o . r a K o o p A r i H a TE
6oeaHa c AocraroqHofi nJrorHocrblo, orHocr{Te,rrbHo
o6,'racr[ BJirrflHrrfl, To 3Haqr.rMbixpa3,'rrrqHiiMe)KAy orIeHKaMu,[o,tyqeHHbrMri B
yc"rroBHsx"rruHetlHoil,
c+ep[qecKoit u;tu Apyroft MoAe,rruHeT.
CNEKTPAJIbHbIH AHAJIIN3
q H3MeHrri.tBocr}t
Crexrp a,rrH brr?a I{a JrH3- 3To MeroA p a3!'roxeHrr
BpeNreHHoropflAa Ha oTAe,rbHble KoM[oHeHTbr, cooTBeTcTByror{He
HJru LJrIrHeHHTepBaJroB, B npeAed'raxKoTopbtx
IrpoAo,rr)KrlTeJrbHocTr.i
3Ta rr3MeHqIrBOCTb
npoflB,'rfleTcX.!,nn ero ocyuecTBr'teHuffBpeltteHHofi psA paccMarpuBaercfl KaK cyMMa 6o.rrnroro qr{c,'ra6o;ree npocTbrx BpeMeHHbrxprrAoB, rrMerouIHX Br.iApefy,'rspHbrx cuHycorrJ,c
pa3,'IHqHbrMu
aivrn,'II.rTyA,aNlI.I,
TOqKa\tH.
AJIIIHaMUBO,'IHH HaqaJIbHbIMH
B e u t q u c , ' I e H n f lM
x o l I { H on p e A n o r a f a r b , q r o c u H y c o u A b lH e 3 a B n c u M b I
Apyf or Apyfa. Tar< rar< cyMMa Bcex srux cuHycoHAAaeT rrcxoAHbrft'
r O B C e XC x H y C O r r A aAXO . ] i K B p e M e H H Op
i i f l A , r O C y M M a u 3 M e H e H H iB
pflAa.
Ha 6brrb paBHa o6qeii r.r3MeHr{uBocru
i i a , ' i H 3H M e e r i l a 3 B p a s l H u l r l r x p y K o B o A c r B a xc n e K T p a d r r b H barH
J ' J I ] T i H b I CI I A 3 B A H I I f l ,
HANPHMCP
IAPMOH]iqCCKI'TIi
AHAJIH3,
AHA.IIIIS,
@ypoe urrrr qacrorurrri auaurrag.HassaHr.ieororo r\{eroAaBoc:icAur K
Teoprtl{ My3bn{n, H3yqarcil{erl 3aKot{oMepHocrtr,cBfl3aHHbIec Ko,{€*
6auusl,ru. B XVII BeKe KenJrep, irprilreHrfl coorHoueHufl rapN{oHHqecr(ofo aHaJrrl3a,HariAeHHbre
Hvr n apHsueTrrKe,reoMeTpHHr{ M.v3bIKe, oTKpbLII3aKOHbrrrJraHeTapHofo ABr.rxeHr.rfl.
oAgaNo xau Ear r r c r O y p r , e ( 1 7 6 8 - 1 8 3 0 r r . ) 4 o r < a 3 a ! 'or 6 r l y r , o r e o p e M y o r o M , q r o :
ilro6afl,oAHo3HarrHasHenpepblBHaffSyHKrrr.rflMolKer 6urr npe4cranJreHa B BuAe pflAa H3 CUHyCOI4A.Jra TeOpeMaTerrepb Hocr4r ero.
r]Mfl. npex{Ae qeM noApo6Ho u3J'rararbreopHro prAoB @yple, ltlt.
l l o . l ) . l i l r r Jo n p e A e , l u T bp f l I T e p M r r H o BB. o J b r [ u H c T B o3 T r ! x T e p \ l l t ] l o B :
282
U HCIIO,'Ib3yeTCfltIpU aHa,'ll{3e 3,'IeKTp[qeB3fiTO Ii3 3.qeKTpOlfeXHVKll
Ii,,* ."rnr,'IoB. Xorfl 3,'ieKTpuqecKufi clirHa,r npeAcraB,rfler co6oii
i , r , , r a n a , , u a 3 H e p f l i l i B o J I H b Ic r e q e H t t e M B p e M e H i l , I I H l K e H e p h I J l o 6 q r
B ocllli,llrotpaQe. flpu usflpeActr:!J rb ce6e efo <<3aMopox{eHrlblM>>
,rb;rieur;i reopilu pflAots @ypre IIHX{eHepbI BcefAa npeAno,'taralor,
qTo criiHa.[ Il3MeHfieTcf co BpeMeHeM, oAHaKo TOT QaI{T, qTo OI]II
g C C , [ e A Y I O TC H f H a , ' I K a I i n p O C T p a H C T B e H H Ofel B . r ] e H I I eH a 3 K p a H e O C qTO BpeMfl H npocTpaHcTBo cqllTaIoTcfl
uIl.']to|paQa, yKa3bIBaIoT,
HecoMHeHHo,
NlaTeMaTIlqecI{H 3TO I(OppeKTHO, 14 Ta
?BIibI"!iil.
!) irBHotll)
ItuN<euepbl [oJIb3y]orcfl TaKHN{
c
Koropofi
.[efKocrb,
ireoco::;-iauualt
tITo 3TI] ABa noHflTIiff, KaK
noIIyxleHIIe]I, [{o)i{er y6eLuTb Hac B ToNI,
Ha[Ie
]I3Jio)KeHI.IeTepI{HHO'
llOerOmy
B3aIlN{O3aMeHteMbI.
npaBlrro,
B 6or']blxHHcTBe pa0T"III{qaeTcfl
oT
TaKoBoro
HecKo"rlbKo
loiltqeciiu
6or rr.r aHaJILI3Ycl{fHaJIoB.
Ha puc. 4.48 ueo6paxeH roBropsrcuiliics cHrHaJI, Koropbni
Bo!'IHofi.PaccroqHlreor
\1O:xHoorrHcarbqlrcror?cHHycoHAaJIbHoft
O.IIHOIi TOTIKI{ BOJIHbI AO 3KBI1BAJ'ICHTHOftTOqKIt
HA CJIEAYIOUC'i BO"'I-
1,. Hacrora f -xapanreplIcTHKa,
lle lrzl3I,rBaercflA,quHofiBoJrHL,r
o6-
.t
- qIICdIIOBO,IH' yI(JIa.U,bIBaIOUIIIXCfi
l"
B eAUririily A,'rrrHbrlr"qH BpeMeHa. B 6O"riluHHCTBe LiH)KeHepHbIXpaC:reroB ciirHaJr xapaKTepll3yercs Ilacroroii. B reolorHqecKHx 3aAaqax
1)aTllAt A"'lIiHe BOr'jHbI't. e. I:
Tpe6yeMoe AJIfl
rlHrepecHee rrMeTb AeJro c AJir.rHofiBo,lHbI. Bpevl,
TOIO TJTO6bITIPABIIJIbHbIfiCHIHA,4 NOBTOPHJICS,HA3bIBACTCSCfO TIC.
puOAoM. lepNIHH IIepHOA fl8,'IfleTCf 3KBI']BaJIeHTOM
AJIHHbI BOJIHbI'HO
IIepTIOAll3N{epfeTcfl B eAIIHIIIIaX BpeMeHIl, HatIpHMep B MH,rl,lll4ceKyHIax, ii rie B eArrHr.ruax paccTorHr.rq, T. e. B caHTuMeTpax. fIpH onucaH r r r l T a x r r x E B , l e H l t f i , K a K M o p c K H e B o J I H b t ,y A o 6 H o n o , ] b 3 o B a r b c f l K a K
l.iilrrort tso.lrrbt, raK rr nepnoAoM. [.nHHa BoJlHbr B ST0M cJryqae I]3illeDrreTcfl r(ar{ paccTofHxe Me}KAy rpe6Hfl\,rIr coceAHlix BO,'IH, IIeplll).1-.h3ii
BpeMfl, Tpe6yeMoe AJ]q Toro rITo6bI ABe [ocr'IeAoBaTe,'Ibl l l r r e B C . r H b rn p o u . [ r r r p u x c l r p o n a u H y r o T o q K y o T c q e T a , H a I I p H M e p K o iieu B0"ltircpe3a. 3ro BpeMeHHoii [poMe)KyroK Me)KAy il,roMeHroM notir].reurr,eo,tHoir Bo,rrrrbrn MoMeHToN{rroflB,reHufl Apyroii. (BoaHltxHoIlet{ire repl{riHa flepnoAuqecKr]ii
c,'roBy [epuoA, Koropoe
o6fl3aHo
o_:l:lerlaeTcrrfHaJ't, IIoB'IopffIourlilcfl c IrpaBIl.rrbHbtMHuHTepBailaMIr.)
I t ( r . l o B l . r H ap a c c r o s H r r q o r B [ a A r r H b r B o . r H b r A o r p e 6 H r H a 3 b l B a e r c f l
:r.)i n"rlT\rIor:i (ll .
)
tla lrrc. 4.49 uso6pax(eHbr ABe oAxHaKoBbre cnHycor.rAaJibnbre
i i i r l i 1 3 l , i € c, \ r e u l e H t r b r e O T H O C H T e " r r b H
; t op l r A p y f a . C O O r s e r c r s y l o r q n e
i : r . 1i l l r r " r n r ) ' A r , t r r
A"rurlbI BoJH oAuIIaKoBbI. PasHocrr Me)KAy 3Hai'i ilill \.il
) r rr )': nptl AaHHoM 3HaqeHilIt Jf; ofip€!€rflercfl pa3r'rl{qr1eil s tltrt:e r,rex(Ay
Sro pas,raune Mox{Ho oltrcarb c
AByNrfl Bo.rrHaMr.r.
Il-o\i'llllbio c!a:onbro yr"lra
O, a ero onpeAerreHue yflcHurb ce6e c no!lollltrlo prrc. 4.50.
lloocroe MexaHuqeaKoe rptrcroco6reH[e
Ar'rfl no' - r \ : e H r r : :c l i r i ' c o 1 . 1 a . - r b H o i i
B o . t H b r c o C T o r r Tr 4 s n v c l a p a A H y c a r , B p a 'uiir iotr.eioctl
c nocroflHlrorl cKopocrblo.
Kapau4,aru,' saxpen,reHuuii
283
Vro.n d,i 6yAer
KoopAuHaraY roropofi paBua Asin(2nxilx*q).
X ecrt o6uar AJrwHa
sarucu;
t2rr'nlX*q). B arux BblpaxeHr.rffx
rITo
yro.n
HaqaJlbultti
orMeTHTb,
B
I.IcxOAHoM
[o,'lo]Keor:e
Baxgo
I
)^
-t-
l:
Puc. 4.48.Peryaapuoe
noBropeHue
crrl,-
HvLt flBilfleTcfl nOCToqHHbIM AJIfl BCeX IIOCJIeAyIOUIHX gHarleHzti
HycolrAa,lbHoir BoJtHbr
:
g l H u a r o n n u ; r 4- a M n t u T y A a
a&t-
KoopAIrHarbl
Y u yrna a. KoucraHra g Ha3brBaercflSan,rrrrryAbr
yfr'IoM,
LIJII.I
aofi, $asoruM
SasoBofixoucraHroii.Tpu napaMerpa-
Puc. 4.49. .[,ae criHl.coilla,rbHbre
Bo.,lHbr.
KoropbreH:eHrrrqHbt
no Qopue.
P . a l ; l u q u qv e x A y _ ) r n y t \ J t s c t r c U u 4 g q e c x o r o 3 H a q e u r r g. y - r a p a x r i p a : y r o rp i e i o c r e
e a g A B y x a s , r e o n u t xS o p u
Fl_r__J_l__J
2i1n0
Puc. 4.50. flpocroe MexaHlqecKoe ilplrcnoco6,,reHre
A , I f B H q e p q H B a H H t C l l H y c o u f a , t b H o i B O J r r H br r y T e M
Dpeo6p,a3o-BaHtB
i f lp a u { a T e J r b H o r o , l B H x ( e H HB
f l, , r u H e f r HOe (4r. Pa3.rrlrque Me)KAy yrJtoM g paAuycoM
AHCKA
u aMn,rrr.rryAori a_ Qasoaurlr
).rJov cr_ruyiolrAaJlbHofi
BoflHbr (6). lI:o6paxeHa qacrb BoJHbi coorBercrH3MeHeHHroyf!'ra (D or HyJ,rqAo 3HarreHur,
:ry51"
HeMHorliM 6o,lbuero 2n paguau, r. e. noqrr{
oAHoMy_
nojrHoMy noBopoTy .lucKa
rruHrrro,
::
:l:l^Ti.,_IIpHcoeArlIeHHoMK Kparo ahcKa,Bbrqepr{HBaer
Ha oyMafe'
ABlrrarcueficfl c IIOCTOflHHOT{cKOpOCTbIO rroA I{OH{OM,
crepxHr. era auuns, rBd'rrercfl cnHycor.rAaJibHoii
xpa-fr1i, rrMea: r u ArrrIHvBo'rHbI, npeAcraBrrrrouyrcco6ofi:
f.T.:i..i.Y":y:!!!QYHxtturocKopocrr'rBparqe'r'rflAricKa ri cKopocrri.ABrrxeHrrf
..'^ 6yuarH. 3HaqeHHe
Y s rrogoMroroxeHuil paBHo'y:A;i";.
Ec,ra uu xorrzMBblr{eprl.rrb
nor'iHyi BoJrHy,To roqKa 3aKpenJleHIrq crepxHs Ha lrrcKe Ao"[xHa c4e"rram nbaHru?
o6opor BoKpyr
UeHrpaAricKa,r. e. noBepHyrbcflHa g60oHiln Ha 2n paa:nin.
nplAqTO
NO,'IO)KHM' MbI HAqI.IHAEM
BbIqCPqI,IBAHI.IE
NPU [POiI3BOTbHOM
HAqaJrbHoMnoJrox{eH'r.r__Kapa'Aarxa
Ha 6yMare, KoTOpOeMbr Ha3oBeM
HyrreBbrM.vron cr *.T{I
r{eHrpoM Ar.rcKau fopr.r3oH^l1paHAaruoM,
raJrbnofi JrllHrlefi Ha 6yuare
r{Meer HeKoropoe snarreHr.re
g ap;;.
4'51).Ec.nuuu o npoleccepa6o*r c-np"6opolo-.a""".it."
un"r,
Ha paccroqH*e xi H ocraHoB,Mcfl' To KapaHAar[
oKa]Kercfl B Torr*e..
284
O[HcbrBaaMrrJlttryAa, IJtr4Ha BOJIHbIU QaeOOrtfi yf OJr- nOJTHOCTbIO
nr Qopuy BoJIHbI.@asoeHfi yroJl cnHycolrAarluoti Bo,'rHbIr{3Mepflercfl or ropH3oHra,/Ilsoli nHHnn, I]poxoAtulefi uepes IIeHTp.
Ec"rrul.rlr xoruM rrocrporirb ptA Bo,'rHpae,ruunoft $opurr, To A"'rR
sroro HyxHo I,t3MeHurb aMnJII{TyAy, AJIr.{HyBo,rrnbr u.nn Qasoanft
KpHByro,no rpop],ro,'r. Mo)KHo raKx{e on}rcarb Ko,cnHycouAaJrbHyro
\{e r.rAeHraqHyrocr.IHycoIr4a;rrttoil, Ho xapaKrep}I3ylorJrylocx QasooT BepTLiKaJIbHofi
npruor?, npoxo4nulefi
BbrMyriloM B, NslrepaenabrM
qepe3 ueHTp ycrpoftcrea. IZHIrtvmcfloBaMLI,KoclrHycouAaJrbuasBoJIno Sase ua 90o, u.nu ua nl2 paHa or"'l[qaercfl or cllHycor.rAaJrrHofi
,lnas. Ecnll K HaueMy ycrpoficrny [pncoeAuHr.nl 4pyrofi Kapar{Aail}
riaK aro yra3aHo Ha puc. 4.52, "to Mbr cMoxeM BbrqepruTboAHoBpegonHu. OqeTaK H KocrlHyconAa,'IbHyto
MeHHor{aK clrHycor.rAaJlbHyro,
BnAHo, rrro oHIt oTJrl{qalorcfloAHa or gpyrofi To,'rbKoQasoeuv yr:ro:,r. Mu MolKeM cyMMapoBarb ocHoBH[,rerpr,rroHoMerpnqecKuecoorHo[IeHlis c rroMourb]opuc. 4.53, npeAcraB"rqrcuero cllHycouAaltbluyro Kpr.rByo.3ro pasJroxeH[e AaHo B repMrrHax Qynxqnn Kooruypa3"roxeHr.Ie,BeAyulee K ToMy )Ke cooTHoueca, Ho sKBr'rBa,'reHTHoe
HtiIo, ocHoBaHoHa cunyce. ,[,onycruu, rrro Bo,'IHaHa paccroffunn X
Ir.rri 3a BpeMfl X yr,ra4unaercfl qeJruxorrr..IIp6a.E TosKa X n npe,reilax orofo uuTepBad'raMo>Ker 6url oupaxeua
B paAr.raHaxc norroulbro $op vy,rru o6pau{euun
(4.82)
0 : 2nxlX.
Tenepu xoopAuHarbrX uoxpunarcr r.rHrepBa!'r
or 0 p.o 2n papltan"
4na y4o6crBa Mbr npeAnor'roxtrM,irro aMnJruryAaxpunof.ipaBHa
eALIHHTIe.
Tor4a ypaBHeHrre
i<punoftrrMeerBltA
(4.83)
Y: cos0.
3ta al,rr"rrrryAa MoNier 6srrr saN{eueua
.1rc6ofi,lpyrori ann,rrry1oli
nlrocTo y\,rHo)tieHrreM
Ha xoa$QHrlueur
A:
(4.84)
Y : .4 cos0.
tItrc,tIo qrrK,toB,
I(oropoe B C T p e q a e T c f lB H y T p H o c H c B H o f o r r H T e p B a . q a
l u a c r o r a ) , l r o N e r 6 l r r l yBelrHqeHo rrr'ru yMeHb[IeHo yMHo)Ke.Hueu 0
ua riorQQlqueur ft:
I:
cosk0.
(4.85)
o,
K a r g 3 p 1 1 a o B a HNIar{crlMyM
BO,rrHbr
HaxoArrrc9 B HarraJIeKOOpAHtlaT, uo oH N,ro)Ker
6r,rrl c4nuHyr e ,trro6oerto,qoiiieHrleBbiqt{TaHtleNt
Q a 3 o B o f oy r r , r aq :
Y : c o s ( 0- O ) .
(4.86)
K o v 6 r a u u p y a n c e erlt
nrotru(lr.rKarrlrrr,
ur,r nafiAeu, qro !t106afl KpH2r.i
1L
z
n
37c
2
2m
ztt 1rr 0
Pnc. 4.52.Crnycou4alruaqu KocHHy- Pnc. 4.53. Cuuycou,la,rluasso,'rHa.06*
COrijl,a,'IbHafl BOr'IHbI, COOTBeTCTByIOUIIe
BPAUIEHHIO AI-iCKA.
u r B - coorBerc?BeHno <fasoeue yrnbr ,qns
c ri HycoH,qaJrbHoi Lr KocrJHycoI,Aa.IIbHorlBo,rlH.
l l 3 o 6 p a x e H u e c o q j : B e r c r B v e r H 3 M e H e H g l oy r ra (D or syrq ,4o 3HaqeHrg, neusortu
6olr,uero 2r paAuaH, r, e, oAHoMy noBopory
.!.ucKa
ulaq A"'lrrHaxpnnor"rpanwa2n pa.illraH
: r r c u l r r i r r H T e p B a JTr .a r r a x B c [ e K T p a , ' r b H o M
a H a J I u 3 eM o x H o c i i o M 6lrHupoearl MHofo pagJlnqHbrxtapMoHIrK AJIfl [oJr_yqenirflHcxoAuofo
n p e v e u u 6 r o p f l A a , T o r { H A e K cf t u e o 6 x o A l r MA r q o 6 o g n a q e u l r f lB o , r H o eori Qopuur qacrHoro BrrAa.
!,a,ree Mbr MoxeM r{cnoJlb3oBarbrprlronoMerpfirrecKoe paBeHCrBOArfl pasHocTrrAByx yrJroB:
cos(R-S) : cosScosR
+ sinSsinR.
llepenrrcao
paBeHcrBo
(4.87),no,ryqriM
Yn : ABcos(DncosftO* .4nsin Or sin &9.
(4.88)
3rc nulpax<eHue
Mox(er6urr ynpoqeHo,
ecr'r[ onpeAe,'r]trb
r<o:$,,.pH'flpt
Ulleilrbl ctn:AncosqA u pn:Aa sin cpp.
erolr noryoua*t
Yn : aocosftO* pesin &0.
(4 89)
.rlroSofr
rpelreuHofipng, xaxoil 6n cnoxsocrtr oH Hrr 6ol.n(rrcri"rotlaq Tor c.rty,lair,I{orAa oH HenpepbtBeHIJd'IlI
6es usr'IoN4oB
II .f,'IgI.:e;KAoro 3uaqeHLrflx Mo)Ker 6ltrt onpeAedrreHoroJIbKo onuo 3Haqeutte Y), \,ioxier 6url npe4craBd'reH
B Br{AecyMMbrprAoB r(oclluycorrAa"rrbllbB
t xo r T H o, [ p e A e , T e H H b trxa K f i M o 6 p a : o u , r a x t t : c 6 p a ; n e _
l l o H a p l c . 4 . 5 4 . 3 r o - B b r p a x { e H r r ce o o r H o [ r e H r r g( D v D l e :
'P;rc4.5!. nocreneHtroe
Qasonoroyrra or Haqa,'IbHoro
srlatlerruJi
C).
,4,rnror,re1onar"n.11:Itnt""
b H b l x 3 H a q e H H i ix i , Y i : A
sin(:nrri,t+(D)
Ir or:2;r.[rl.y+(D
Bar peryflflpHori cfir{ycorAa"lbrJori
Qopnrr,rMOX{er 6nrr
BIINE
euc,roft Has
rreaer." I:;J:d;
"
986
sanucarra B
(4.87)
lix ;,,-, ] lr'cr,roM
urrx.rroB
ua 6a-
y :
s 0 1 p us i n4 0 .
I a,,coh
(4.!r0)
t'-n
JalleruM, vro (4.90)-3ro ypaBHentre,rrrueiruoe,
?. e. BCetr"[enl,r
cli.la.\brBa
rorcfl BMecre.Ono u anouuuaer no Sop
lre iror,iilitoM
na.tb'pii,Hee
pefpeccuro,Koropyrc ML,rpaccMorpeJrrr
s sroft f,'raBe.
Sylo
u.-\'paBHeHrlu
q"o'euot
@ypuerprrrolroNrerprrrecKue
cosftO a sin F0
3l(BItBa,reHTHtt
clr-eneHubrll qvleHaM TaKI.rx Mgofoq/IeHoe, tiaK Xz u
,r
!\oe{yrh1ir.,:errr,r
c { ' r ,r I g r , S T r r x q , r e H o B M o f v r 6 u r r H a j i l e H b r M e i87
rhnDll\'.rl2Ml
n-l
o
v,l
'o
i
- -2! : ]rr; S t.,f l l
hlJ"\,ttj
i=o
/ 2ril; \
l,
(4.e1)
n-l
2 Tt )',cosI z"ift-\.
^-./,A--'
6
\-
v
',
\r^/
(4.e2)
k4J\n/
i=o
Kali N{oilieT[oKa3aTbcfl Ha nep'
cJIO)KHbI,
H
e
c
r
o
J
l
b
3rr 1'ltaeHetltlq
B
ur,tii e:;l.ln,'l; BI-,1
PalKeHufl B CKO6Kaxecrb npocro rIpeAcraBJIe[IHOe
npeueHHoro
ec"rlt
o6ulyto
TorrKrr,
l
l
O
.
l
O
>
t
t
e
t
t
t
l
e
l
f
i
A"rt{Hy
r)r liJAHaX
nfl.tir oIpei(e.iTrlrb xax 2r p a A H a H .B c r r . r r yr p I I r o H o N { e r p I I q e c I ( I ICXO '
r)'trr0 UieHIlil Iio3QipllqrlellT B0 ncerla paBeH HyJIIo,& ao 1'np61,u"t."
\nJ
I
-
_ -
n-l
o^: -J-I r,,
,TH
,tt
\nnr\n/\nn
\^"^"
Prc. 4.54. Pesyrorar c.roxeHrrfl
\^l^/
J
rapMoHuKKocrHycor.rAaJrb.
a - $ y ' t r a v e u r a n b ' a f l ' J r f f n c p B a s r a p"X"r.t#??ilr.rrr,Hbrx
' o H r x a - l : 0 , 5 . , A ^ : 1 . _( D 1 ^ 0 . : _
o p a nr a p M o H H K a
A : 0 . 3 , k = 2 . O : 0 , : a - 3 p e r j a _ r a o u t t s n x a A : 0 , 3 , t - C , O : l S " : ' r _ "6. ' o #Bi T
i
rapMoHrKa
4-0,25, k-7, O:180": a
rperbq
(')+i,;^"ffyi:i,Jfi,'"#1.'i"iiill"ixfuJ'i'],l,1ul;ria,l"t"
rapu6uuxa,
+"ix'f;
, n r r o c B r o p a q H r p e r b n r a p y o H H K H(,a r + ( 6 r + ( s l ; u _
Bropat' rperbg H
M a q r a p N t o H r x fA
l l*tulifll\iantloc
ceab'
ToroM HaaMeHburrx KBaAparoe. OAuaxo ecJrHMbI nonblTaeMcs oqe.
HIITb 3TI4XOEQSUqUCHTbI
MATPHI{HbIMI,I
MCTOAAMI.I
II CCJII{rPC6YCrCr
cnpeAe/'IIITbi\IHofo rapMoHI'tK,To MbI oqeHb cKopo croJlrueMcq
c
freII p eoAo,'rrr[,ibrN{ri Bbrq Hc druTeJrbHb]Mr.rTpyA HOCT' MI.I.
fapuoHlluecrufi aHarns
li
ll
E,c.lr epelreusor? pflA npeAcraB!,lffer4eficrnure,rbHo nepuonuqe_
c K o e q B . n e H H eN, r b rM o x < e Mi l c r o , ' r b 3 o B a r br e x H H K y r a x H a s t i e a e M o f o
rapMollilqecKoro aHafllt3a Ailfl,pas,'roxeHr.rg.
ptr!.a Ha ero cocraBHble
qacri.r. BpeueuHtre pflAbr,
_o6naAarcuIHeceoficrsoM neploAr.rlrHocrrr,
B c r p e , r a r o r c f lB n p r r p o n e . 3 r o , H a [ p ] r M e p ,
$ n y x r y a q r i u p u n v . n o aw
or'lliBoB' ce3oHl{bieu3MeHeHIiflTeMrleparypbI, noc,IIeAoBareJlblrocrl,I
c . r l o e Bo' u u t a x > x e B K J r l o q a r o3r a n r i c u , n o p o ) . r { A e H H br laeK r 4 M r rn p r r 5 o p a r , r u ,x a x 4 n Q p a K r o M e r p X - " r y u e i i ( n p e o 6 p a s o B a H t r e@ y p l e
raK U XA a H H b r Xg B . r r q e r c qc r e [ [ a , r b H o r l r e r r o r i ) . B ' p e l r e u n o f ip " a M o x e r
6urr coeor(ynHocrbro ua6.nrcgeHlrii n 4ncr<perHoM NrHoirecrBerot l e K ' p a c r o , r o x ( e H I { b r cx p a B H b r NH{ H T e p B a r ' r o M
A n npocrpaucrse. Ec_
'rr1 HMeercq n 3Trrx roqeK, oAHa rr3 KOTOpbrxecrb
t ro xoarpsfirur€HTbraA rI pA pflAa @ypre r\ror]T 6brrl sbr,rrrc,'reHHro cJrenvrcurr{M
28s
(4.e3)
-v
q r o e c r b K a K p a 3 c p e A H e en p e n a e u i l 6 r op n 4 a . l 4 H 4 e x c l t I l 3 M C H f l I O T C ' I
s e r o K o H t l e ,a s e o r l A o
o r 0 l H a t r a " r rnep e v e H H 6 r o p n r a I o n - l
n Jt.r toro, uto6r,r npaBll.nbHonepeBecrt'I Ilor'lox{eHl4en e p B o r oH a 6 , r r c . 1 e u l i tB p a A l i a H b l .
CnlreAe.rnn rioaQSnrlneHrli cxhH pr, lz-ofi rapN{oHrllill,MbI Mo}KeM
B BUAC
OII i) C]C.I IiTb A N,IN''II{TYAY BOJIHOBOii QOP IT,IST
Ar:1,7f t6.
(4.e4)
O a : o e b r i i v r o . n f t - o i i f a p N , I o H I { KpHa B e H
(4.e5)
@r : tg-I(pnlan).
3
a
AaH>>.
y
f
o
J
l
,
<
<
s
a
i
t
t
r
l
T
a
H
f
e
H
c
K
o
r
o
p
o
r
o
B l r p a r x e H r r et g - l o s H a u a e t :
E r - . 1 r rB A r r c K p e T H O M
H a 6 O p er 0 q e K C o 6 p a H b IA a H H b l eA J I ' p e f \ ' . l n p n o i i c r r H \ r c o r r A rT, ro, 4 u c f i e p c i l l s r o i i n u 6 o p x l t c B t 3 a H a c a M n " r l l l r1,1oii erofi so.rruoeofiQopvru. B npege,ne Allcnepcilfl ecrb npocro
Il O.'lO B II H a I(B a.[,p aT a a MII'll'lTyALI,
sn2: Ar,2l2:
]{,'ll{
(ar2 * Ff)12.
(4.e6)
Tali riax reopeNla @yple yrBeplKAaer, rlro BpeMeHHofipflA Mo)KHo
MHornx cuHycouAar'tlurtx tityttt<uHfiu'nu
l) a cc),rarpnBarb IiaK c-vNrNry
r z li ) r . t o H r r Kr ,o A r r c n e p c i l r rB p e M e H H 6 r op n 4 a g B J l f l e r c r f l p o c r o c y M t n r o r.it r r c n e p c r r ier r n x c a N { b l xr a p M o H u t { .M t t u o x < e u r l o s r o M y B b I p a 3 t l r b r r r c n e p c r r r cf t - o l i r a p M o r r i a x rr { a K r r p o [ o p l l u o H a J l b H y ] q
oa c r b o r
o 6 t u e i ' tA l r c f i e p c r r [ n p e v e n H 6 r o p s A a , H 3 K o r o p o r o o H a 6 u " r a n o n y 'tetta. Ec,rrr N{brBbrqnc"rrr.rM
A;IrrHHbrfi p"A fapMoHr.rK,To Ar.rcfiepcl{n
T I O C J C : I O B A T C I ' I b I I b IT
XA P M O H I I K M O X { H O
HAHCCTII HA NCPI4OAOIPAMMY,
Il.rrl, Iiari HHorAa foBopflT. lr:o6pasuru 4ucxperHuft u.rl.l .rluseiiurtfi
e H e p i e r l t q e c x n f ic n e x t o . 3 r o e c r o r i o f l D o c r v n p e A c r a B d ' I e H Isl ea B I { crrllocrn rracrorbr H.rrrr
Alrcnepcurr or qi.rc.rla"fapMoHHK k, tt tpaawI l l i o l l H on p e n c r a B n q e r c rB n r r 4 e ,y x a s a H H o MH a p n c . 4 . 5 5 . -( T e p u u IIln 3Heprrrr r'r
A r l c n e p c r J r frl B r r r o r c r r c r r H o H u M a r u rnr ;e p n u t f i H 3 I { H X
289
Mecsqnstfi croK BoAbt B
Orirn 6pr
Hox6pa
Aexa6pl
T a 6 n : n u a4 . 2 9
(eutyrxu (n corunxamfiMos)
KefinKpr.rx,
f,uBapb
@eeparb
N{apr pert
240
54
73
59
308
200
270
219
204
346
150
87
276
48
97
135
278
130
86
22
463
637
325
221
195
313
295
401
146
173
230
281
161
98
216
389
416
40
579
469
103
tt7
t12
291
532
508
518
788
449
79
466
425
73
29t
An-
Muri IlnHs l.lu.rr, iv.t
I
o
19.-r3
l 954
I'r950
lii5
CD
I 957
r958
i 959
l 9c0
Puc. 4.55. Ilepnogorpalrruar{ecsqHorororoKa Keiie-KpHr<,
I(enryxnu
Cneqaalsurre
3HaqeHHs yKa3hlBaIor, qro noroR Hneer e.nIlrcrBcHHbrrl treproAfl,lecKHil
t.oJflqlrLIIl uilKit. Stteprrtu nplIBe;let{bt a KBatrparax €,4!IHHtI u3NlepeHlIt, xoroptne paBrrbl cotLrM qactgv
rrofiua
i0
lqill
tfi62
l 963
I 9e4
19 6 5
I !r66
I 967
1ti68
1969
1970
l9
4
30
13
6
t72
t0
1 0 6 432
t7
I
36 2 6 9
79
52
i6
6
1 4 1 124
3
347
7
2
2
357
ll9
3B 27t
22
tt2
9l
5
0
2
4
7
3
6
3
t2
2
I
4
7
I
t4
7
z
147
139
59
192
392
235
102
68
476
330
52
45
146
202
50
238
237
568
354 J I
8
35
t97
28 a o
68 q A
236 l 9
24
l 9 364
414 1 5 9
79 96
25 l 4
21 l l
8
3l
332 2 5
476 33
199 9 l
74 4 0
206 38
7
l8
7614
24283
64388
6l-r2
369 170
542
133 14
48 18
3887
29 ll
8216
512
4l
t4
t4
15
29 75
27 66
14
6
CeH-
""Ono
|
t2
30
4
3
ll
7
16
17
27
c
oca,4KaMff roAa, [aqffHat
co6paHlt ts-TeqeHHe ooraroro
flprrreqaHtre.
!,aHHue
ri3'noMa nocJleu:deNarb
ceHTg6perl, ans Toro qto6u
ro,qa I ronqeq
nperLlAyilrero
.rri;r6pr
loiri,IeJIbtsoCTll B Cepe!I{He :slru
[24].
7
I
9(
n
b
n
CO
1957 1959 .|961 1963 1965 1967 1969l-o4or
1956 t958 '960
1967 1964 1966 1g5E 19',t0
P u c . 4 . 5 6 . M e c s , n r u i i noroK KefiB-KpHK,KeHryKKli3a nepHoAc oxrr6pfl 1952 r.
ao ceHrn6pq1970 r.
19 5 4
6 u r a n e g e HB 3 J r e K T p o r e x H H K er r r e n e p b u n p o K o r i c n o , ' r b 3 y e r c rB o
BCeX06,laCTgXTeXHltKIt,a:Hail:/.Se
r{3oct{tHaJIoBu pacII03HaBaHr.{u
6 p a x e H n f i . ) I 4 c x o A u u r f ic r e n e H H o r lp s A n p e A c r - a s , ' r e H
u a pHC.4.56.
BpeueHuori prA npeAcraBJrfler MecqqHbrficroK BoAbr n Kefin Kpur
s K e H r y x r u ; A a H H b r en p u B e A e H bB
r ra6Jr.4.29, nsnrofi us [24]. IIepHoAofpaMMa rroKa3brBaeT,qTo r.r3MeHeHHr
Mecflr{HbrxcToKoB r.rMeI o T f o A u q n b r i i ( 1 2 - u e c n r I H b l i i )n e p H o A , n , ' r i o c c J r y q a i i H a t r i c M r r o -
3rJiL.,aeTcfHeO6pa6OTaHHbII\tCneKTpONI Ll tlB,lfeTctl OUeHKOfI IICTHH'
H O i 0 c n e K T p a , n " l l t c n e K T p a c o B o K y n H o c T H . 3 T I { O U e H K H C B t r 3 a H b rc
KOTOpble He Mooqellb 60,'irutiil.ru craHAaprHbIMIl [ofpeuHocrtMI{,
f\-T 6l'rrb yNIeHbueHbI npI yBe.[Ht]eHrrr n no IIplrqHHaNI, Koropble 6yA-r'r oryr,qiueHbt B C,'IeA-VIO[ieMpa3Aele. HenOrOpue I'133THx 0ltr116cll(
N , l O f V TO K a 3 a T b C E. l O l K H b l N r l lB c u , q y c N r e [ I I l B a H U g r l e A o l y c T l l M o B b l C O K I i - \r t a C T O TC H u 3 K H M I t q a C T O T a M u .3 r U e H C O r u e q a C T O T b l ,A J I I ' l H b I
I J O . T HK O r o p b r x M e H b u e , q e M A B O i i H O e p a c c T o f l H l . I e M e x A y T o q K a M I {
onpo6cBaHllfl, He Nloryr 6ltrn o6HapyxeHbl. HaliBllcmax qacrora,
HafiKeHcra' ee
tioiopzlr NlolKer 6urt o6napyx{eHa, ecrb qacrora
MexAy nocJ'leAoBa'
A , 4 r r j a B o , ' r H b rp a B l l a 2 A , r l e A - p a c c r o n u t t e
re.tLlii)lliili Ha6.[IOAeHI4flNIu.flpfir{l'iHy, IIo KoTopol? AHcrlepcull qacrot' lne npeAe,'ra HaiixauCra CoBnaAaIOT c AIJcnepcusMI4 6ou'Iee HIls-
r r a c r o r , M o x { H oJ e f K o y B I I A e r bH a p r c . 4 . 5 7 .
T e i n tH e M e H e eM o x H o c r a r t t c r l l q e c K l l M l ' { M e r o A a M I In p o B e p f i T b '
c ) l u e c ' l ' B y e r. [ l l A o M i l H a H r ] t a txl o M I I o I l e H T aB n e p ] l o A o r p a M M eK. p u r e plit?, per{oMeHAoBaHHbIii
<Duuepou, ocHoBaHHa BbIqI'lcJIeHI'lH
cneKT-
HEHTA.
yxasauuuMBbrrleo6pasou,r.rHorAa
Cnexrp, BbrqucJrer{Hbrrl
Ha290
^-l.bb boooqHbrq rH'Te083n a
P nc. 4.57. BucoxoaueprerurlecKafl cHHyc o H A a " l b H a f B o , l t l a ( I I p e p b l B H c T a t lJ M l A l - t c K p e r H o MM H O Hun), tta6,rrc4eHHatB
X ( e C r B e T o q e l ( , A a e r O T t l e T ' t l I B oB U A H y I O
nonrrt' tilgxoit qacrorbl (cil,1oulIlaff ,'lu'
Hnn)
291
p a , ' I b H O r O3 H a q e H l l f l S A 2 , K O T O p O gn p e B b t g a e T 3 H a q e H U e O i i 2 e D e l t e H _
Irofo pfl,rra, cocraBJreHlrofo rr3 He3aBLrCUMr,rx
c,'ryqariHbrx roqeK. KpH_
Tepltri ocHoBaH Ha BblrltlcJeHl.nr orHolrleHu,
g:.s2-.,r/2s',
( 4 . 9 7)
r A e s 2 m a x- u a r t 6 o , r t r u l t r ?
- g,uclepctrn
n
e
p
l
l
o
A
o
t
p
a
M
M
b
I
H
s
2
.,nuN
o1l._Yeuu6roptAa. KpllrttqecKoe 3HaqeHneg Ans cneKrpa,rrb"_t^-t"t9
HoH BepoflrHocrn p p\aercs.@op;uy"rofi
lnp-1nnt
g=l--e
^-t
,
(-tr.gg)
r!,e ilt:nf2, ec;ttt npe-ueHHoir
pfl.q coAepx{ilrqer}roeqxcJrosa6.rrogeHur?,__rr
n7: (n-l)12, ecnu lt ueqeruo.Ec,rHnpoaepreMaflcrara_
crlll(a g [peRbllxaer Iipllrllr]eclio€ 3112t19sile
g, To N{o)KHonpeA[o.no)rirrrb' rrro [epuoAHqecKag r(oMroHeHTa CyurecrByer. Ec.nir IIpoBep t e M a f l c r a r l l c r l l K a H e n p e B o c x o A I I TK p l l r t i q e c K o e3 H a r { e H l . tT
eo
, Ha6,rrc,'ta-elruiicnerirpa,rluini nrrn s2-u* MolKer tso3HiJKHyrbc,ryuafi_
u u n , to 6 p a s o l r .
HenpepunHuri cnexrp
l a p u o r r r . i e c r i r f i a H a , ; l r 3I r n o c r p o e H r i en e p f i o r o r p r i M n , r bl lr. i i r r. - u r ..
Hel'iroro cIIerirpa rleleco,o6pasHurs rex c.[yqaflx, KofAa rrcc.re.!,yetrrurrinper,relruolipa4 4ericrnrireurtHo nepogHqen. B [pupo,ne Bcrpe_
qaercfl HeMHofo ecrecrBeHHblxtn,teuuti,
o6,raAatouttx rtcruHnoft
|IepllOAIIqIIOCTblO, He CTIIITafl tB.qeHtjfl,
CBfl3aIJHLIe C aCTDOHO]IIIqe_
I{l'lKJrla\'ln, TaI{llMlI, KaK MecqqHbte
npil,'t}tBbt H oT,,iltBbt
lr"'U.I
ce3OHHbre Ir:lMeIleHlrq. bo.lluuHcreo
reo.rrorliqecKllX SpeX4eUHdrX OgcltllMu
r ec, . r y u a l i l r s t e .f l o c , r e 4 0 e a r e J r b H o c rH
JOB ile nepilor'rrrrrecKia
b a3bIBaercfl c,ryqaritrofi,ec,r[r otla Mo)r{eT6lrrl oxapar{Tepil30BaHaTo.rrbtioc
nor{olublo cTaTllcrl]qecl(ll.xxapaKTepHCTIIK, B npoTaBolor'Io>KHocTb
.lerel)MHHrrponaHuor?
nocle.loBare.rrbHocrir,n xoropori cocrosHrre ivroN{er 6blrb roqHo [percr{a3aHo r]o ee r<oaip$uqueriraru.
!,ax<e B rex
c r - r y q a r x ,r ( O f A aa p e u e n u o i i p f l ! H e c o r e p x r . r r 4 e f i c r a n r e . u b H on e p r r o .x.llqecKIlxKo\4IIrJHeHT'
MeroAbI cnel(Tpar'tbHoroaHa.r]r3a rlo3BoJifllor
no"qyqilTbrleHHyronHQopuaqvro o roN{ rrpo[ecce, xoropul-r [oponr4Jl
. l J H r r y r o r o c , ' l e r o B a r e . l b H O C T bE
. oasLulructso speueHHdrx
lr":o"
M o i K H o c q l l r a r b H e n p e p b l B H b i Mn
i l o c , l e A o B a r e , ' I b H o c r g MA
Ha, x ( e H e c M o r p r H a r o , r r r o A a H H b I er r o r { H M c o 6 l r p a r c r c xB A r r c r ( p e r H o Mr v r H o ; r i e c r r r el o r r e r ( L
. . t s r a r ( r r xn o c . ' t e . l o s a r e , i b l o c r evf o
i Nso BbtrruL,rtrrb
H e r r l ) e p b r B r r rc, U
i r < r p ,r r ; r r rt p y r r x r t r r r c n e l i r p a r l H o f i [ J r o r H o c r r l ,r p r ] ne
qeM /lllcIIepcllt Bpe\tellHofopsila pa3lle.rteHa
n p o n o D u r r o t { a . t b t r oB
M H O l r i c c r r j er r a c r o r r i l , l \ n o . r o c . H e l p e p l r o i l r - , r r i c n e r < i p r r M e e r B r r A
I l e n p e p r r r B H o xf rp u n o i i , n u r p a x a l o u l e i r 3 a B r . r c l i M o c T b/ I i l c n e D c r r r o
rT
qacrorbr, rr aHa.rrorxqeH
H c r r p e p b r n H o $i ry H X r l H Hp a c I p e A e J r e r j r { B
f ep O n T t r O C r eC
u .; ' 1 l l C i l e p C U f l N ,nt lpt ,O n O p q u o r r s . r l b H b t \ 4n 1J 1
O t U a I f lU r r O A
c n e t { T p a " r r b H on rpi l r n o i t M e x < ; l yr p a t { l q H L , l M rr.rra c r o r a M r r .O 6 u t a s n " l o x { a A r , n o , l c f i e K T p o Mp a B r r a o S u r e i i A u c n e p c r r u n p e u e H H 6 r o p n l a ,
. o 6 0 p o r , , r u H e i i H U f iC n e x t D n e A . ' r f l l i o r o p o f o o r r a B b r q l r c . ' J r , T a cHs a
292
D l r o r ' l r r q e c K o f oB p e M e H H O | Op f l I a I I o K a 3 b l B a e T A l l c n e p c f i u ' I I p H c y q l l e
bl NI HHAHBxAy a,'lbHbIN'tq aCTOTa M.
oI peAeIeHH
'
Kax<;raq KoHKperHaq IIoc.te.[,oBareJ'rbHocrb ]ta6Jto.q,eHHIi, Koro'
q aK C.lV'
' O ) K e Tp a C C N I a T p H B a T b C K
D \ - l O \ I b l X O T H N Ia H a d r H 3 l t p O B a T bM
q i f r H an a u 6 o p x a . i l 3 6 o . r l b u l o r o , B o 3 M o x ( H o , 6 e c x o s e q H o r o M H o ) I { e c r B a
Tilliux Bpe\,lellHblx ptAoB, Koropble MofyT reHepIlpoBaTbcfl ri3yqae] { t ) r N r r .nrp o u e c c a M r t . l l o . n u o e N I H o x ( e c T B on p e v e u u f i x p s A o B H a 3 b l B a e r c r r a H C a M 6 " l e r ' t ,u 3 T o e c r b K a K p a 3 T a c o B o K y n H o c r b , r l 3 K o r o p o i i
IIi.rura I(OIIKperHaf nlt6opxa I',l3B.'lel{aerctl.
BpeueirHor? ptA Ha3brBaercs crall,I{oHapHbtM, ec,'tu efo cBoftcrBa
He rr3MeHflorcfl co BpeMeHeM. fIpocrpaHcrBeHlIbII:i pflA C-reN{II ilie
cil \rrrr)rlr xapalirepIIcTllKalVIII Ha3blBaeTctl oAHopoAHblM. trcJIlI Bper r e H t r o i i p f J . n o A p a 3 A e , l t i r b I I a . N I a . I I b l eC e r N , l e H T bI I{ c p e A H I I e n O B C e M
? r r r x ' rc e f N , l e H r a Mo ; l l ] H a K o B b I ( H c o B I I a A a l o r c o c p e A H n M B c e f o B p e rreHrrofo pfl,la), To B )TON{cJyqae foBopsr o cTaullo}IapHocTlI IIepB cpeAHer'I. Ec"'tt'i s Aolo.'IHeBofo nol)flIKa ILrl}] o cralllloHapHocrll
l O " T I b KC
O l l 3 N i e l l e l { l l e N .I - l i l i r r r e r ( 3 T O \ ' l ! ya B T O l i o B a p U a l I H f lI I 3 M e H f l e T C fT
BrlyTpH epelteHrioro pfl.4a, To
fit, a ile B 3aBuCilMOCTriOT IIO.TIO)I{eHLIfl
i o i l o l ) f l T , q T o p f l A o 6 " r a A a e r c B o i l c T B o M c T a q H o H a p i l o c T l 4B T O p o f o f l o l ) r { ; , l l i a .3 r o c e o i l c r B o H H o r J l a H a 3 b l B a l o r c . ' l a 6 o i i c r a U H o H a p H o c r b F o ,
li,-ur crauuoHapHocrblo s 6o"rlee urzpol(oM cMbtc"le. Ec;ttt ece rtotreHTLr Bbrcuefo nopfAKa 3aBHcfr ToJIbKo oT "rlara Il He 3aBllcfT oT
flo.'rolr(eHnfl, To pflA Ha3blBaercfl cl{,'lbHo crauuoHapHblM HJII4 06.1a'
: 1 i r c Tc T a u H o H a l ) i l o c T b l o B c T p o r o M c M b l c , ' l e .
E c r i r e p e l t e l l l l o r ? p r A H e r o . , j b K o c t l " r t b H oc r a t r t t o H a p e H , H o I I B c e
e f 0 c r a r r . r c T r . { K HH H B a p r r a H T H r , I o r p f A a K p f l A y B H y T p u a H c a M 6 . n q ,
l o a r r c a r , r 6 , r L l' r a 3 b I B a e r c . f l 3 p f o A n r r e c r { n M . M u o r t t e c r a r n c r v q e c l i l l e
lil)ilTepr.rr.rTeopilrr BpeMeHHbrx pgjloB o6.naAarcr cBol?crBoM 3pfoAIIqHOCTn Tat( X(e, KaK OAHOMepHbleC]'a',rilcrl.{qecKlie I(pI.rTepII[ O6"[a]arcr cnorlcreor,r oAHo3llarlHocrn Ar4ciiepcull. Ec,nu naul LIMeeM HecKoJbrio Dl)eMeHH(rx pnloe, flB"rrflIoulllxcf pea.IIH3auHflMlI oAHofo tI Tofo
;.rie c.lyuafiuofo IIpollecca, To Mr,r MoxeM npoBecTll rlpoBepKy I]x Ha
3 l ) f o j ' l r r q H o c r r . B o o 6 I l I e ) K e M F , II I M e e M T o . r I b K o0 A I I H B p e M e H H o f i n r f ,
l l B 3 T O M C , r l y t 1 2 gH H K a K a f l n p o B e p K a T a K O r o p O A a H e B O 3 U O X n a . , \ l r i
\loxe}{ npoBepr4TbcTauxoHapHocTb no cpeAHHM 3HaqeHrtM Ll llilcI i e l ) c n r r - r l , { r re A r r H c r B e H H o r o a p e u e u u 6 r o p s A a , n p n M e H f lf , p e r p e c c i t t o
l:.lll ilojlpa3Ae.rrfrI pqAbr Ha cefr,reHTbI Ir IIpoBepqtl, OAHHaKoBbl .r'lll
3r'rr crarucrruor A"rrf pa3,'rllqHblx cefMeHToB. Ec,'tu Aa, To ptA fl8,1flercl co6crBeHHo craufioHaDIrbr\,r u Mo)KHo npeAllo,'toxI{Tb, qro oH
o 6 . r a . l a e r c s o r i c r s o N , ra p r o A n u H o c r u . E c J r r p f l A H e f f B r r r e r c f f c o 6 c r i l c t l t l o c r a r l l o H a p H b n v t , T o a H c a M 6 J I b , n 3 K o r o p o r o o H l r 3 B " r e r l e H ,H e
\loxer 6r,trl eproAuqecKuM.
14lrorAa np-eueHlrori ptA N,ro>Ker 6lrrt cAe,raH crauitoHapHbtM
rrl)rrIIeHelrneu npocroii npoueAypbr ypaBHnBaHH fl , LrJrrtBbIqHTaHIleM
.rrr'eiisoro rpeHAa rr3 Ha6rroAe'r.rfi,r. e. c noMorrrbro
l,reroAaHerr\relrbu"x KBaaparoBBbrqlrcJrflercrrJtr4*ei4*agpefpeccua yi ua .
.i
lorAa ttoenii epenaenHoii
paa onpeAeJlserctr
KaK pt4 orr,roueHHft:
293
,
II
I
i
Yi,:Yi--?i,
(4.gg)
i; rJ,€ 'r ;
nPeActia:aHHbre 3HaqeHHfl, onpeAe.rrteMbre
c rloMou{blo
y p a B H e H H fpl e r p e c c H r . E c , r u r r c x o 4 r r u f i p n 1 x a p a K T e p H 3 o B a J r c ,
Ma_
ri3MeHeHHe),,r
ero cpe.qgero 3HaqeHHr, ro nonriri pl4
".rr,rNr
6yaa"
t r \ { e r b c T a r { r r o H a p H ocep e A H e e p, a B H o eH y , , r r u .
A.rrfl crauriorlapHofo c,ryuaiinoro epeueuH6ro pHAa, rBJrflroilrero_
cff HenpepbrBrrbrM
r n p e A c r a B , ' r e r r H o flou c x p e r u u l a u a 6 0 p o n p a B r r o I r e p H Op a c f l p e j l e . r r e H H bBr x n p o c r p a r r c r B e r o r r e K ,
UenpeplieuaflAHC_
IreJlcrrq (r.rrr auepreruqecxuft cnexrp) \,roxer 6r,rrl'
eriqrrcJrerraoAHir\'rrr3 ABVX Nrero.l0s.Eoiree uonrrri^u 60ree urjpoi(o
ucnoiosyenoo,r,
l r e r o f o c H o B a HH a B b r r I H c " r e H IM
r I rH O f l i xs H a q e H U I,ir u H e l i u o r oc r I e K T _
p a c n o M o t r _ l b raoJ f o p r . t r u ; r 6 u r c r p o r o r r p e o 6 p a 3 o B a H i l f l
@yple. 3aTe,1,1
3Tlt CnBt{Tp3r-rbHbre
3HaqeHrrflyCpeAHrrrOTc, BAOJTb
uaCrOr A,rrX
rro.ivlreuuff cr.raxeuuor? orleHK[ H_enpepbrBHoro
crreKTpa. Kax coe, r , J ' e ru 3 H a 3 B a r r r r r ,6 u c r p o e n p e o 6 p a s o a a H a e@ y p t e
oueno s$Qex_
rrreHurri MeroA, a rrlrerrHo,ou npnnb4'T r( )Ke,'raeMoMy
pe3yrbrary
: a n l o g 2 n a p r r Q v e r r r . r e c t * r .o\ n e p a q u f i , i i r o B p e M q
Kar{Apyfre Merolu- rpe61,ror Bbrrro,rrH
euus, n2 onep a qu fi . llpri.q., u r*l"our,ro*a_
n
ttue @1'preB BriJe
2
",,-:*
'
9l
,!'
Y,r,-i2.ik;",
(4.lir0i
'2
- lrHulrar eitrrHrJrra.
r:e i:1'-1
Bunc,lsesrie npeo6pa3oeauirii,
; l u x r y e M b r x a " l f o p r r r M o M6 u c r p o r o n p e o 6 p a s o n a u a a '@
, yple, rpe6y_
e r l l a r e N { a r l i t l e c K I I xI r B b r q l r c . i l l I T e J I b H H
L IaXB b r K o Bx, o r o p u e H a x o . r f f ' ' c r rB i r e p a M o r i ' 3 r ' r a r a e M o r oe s r o i t r ( H ' r e . f l o e r o r r y
o o o ,n a p r r BrrBaL.lI3T1rlgrt', XoTfl B HacTor{qee BpeI,{, 3TIi
MeTOAbrHarr6o,nee
rurrpoKo rrcnoxF,3yrorctrB cIIeKTpar,rbtrol4
aHa,rlu3e.Or,rrrzqHoeBtseAeH r e B T e o p u r o 6 r , r c r p o r o . n p e c 6 p a : o n a u r r nO y p u a
uraara-" a,.up"r_
o v [ 43], x oiop urir ra r{>KeA aer rrpil Mepbr rrp
jl1:^^P_.^1"ep
u x,rel):"
l e i::,
J r J ro
r b r c r p o f o r r p e o 6 p a s o n a r i n a@ a p r , en r e o r . p a s H n .
Iiepuuo oa_
H C B o I I o , l a f a l o l l { a rC T a T b f l ,n o c B r r i i e t { H a oa n . o p n i " y
6 o , a a p i r . on p e _
o6;asonau,r @yple, 6lr,ra ony6.[riiioi]aria
A r { e H T , , r b M e n o rltrr C e u A U . \ r l z u l , o H a o c H o B a H aH a M a T e N l a T f i r l e - c K ' xM e T o A a x ,
KoTopble
BnejrBrrre
6rr.rrr eseAeHuKy.'rrr Tnrcxrr
j c"ip""iJniorl pyno_r
iit
Bo.lcrra no aFra"rrH3y
npeueuurirxpflAoB (6.nroutpearl
iij, n.riau"
oror npe,1,.,rel
BecrrMaiurpoKo. HecNorr,lp'^tylor
:1..rL'.l';^o1t
Jj]l
Ko 00'1eec'apufi ivreroAnbrqucreHnqHenpepbrBlrofo
cneKTpacocroril' B saxol<Aeulunpeo6pa:oilaHirfl
(Dyple aBToKoppe,rquuorrHoii
QyHxurrrrBper.ieHi{oro
polu. prronriirl- repBoHarrar,rlHo
Eapr,rerrov [5], sror NreroA/Iaer re ]Ke pe3)rnbrarbr,qro
rr 6o",reeHoelrri
'@1,poe,
npeo6pasoeaHun-OH orr
ya]r: 6r,rcr.por.o
"rerqeA,,isrroH'MaHfls,
xorl Ir He y,ro6eu /x"rrrrBbtr{ilc,rleuHfi.
€rlle rg11p6110ilcnc.rrb3yercfl,
oco6euHo
rorra, KofAaaBToxoppe;lfluaoHHa,
6yirnur" ,un*" ,rp",1_
crats.irrrer
rjHTepecr.i KofAa apeverruofipr{A He
oqeHb4uruuurui.Eu_
ool
l i t r H c l t V o r r c [ 2 9 ] , n a l p u v e p , o 6 c y x 4 a r c r 3 r o r M e r o . [ , ,a l l e e l e '
rxAporeolr,oftlqecKl'lx3aJ,aq.
lri,r [64] npuMeHqer ero I( pe111eHrlFO
[email protected] aBrot(oppe,'IquHoHHoii tpyttt<uuu .raer
cnerrPi .q,'ltinpeveHu6ro prAa, 3a.4a.HHofo
Al1cKptlrairepr':ertruecNnii
. , H X I t s Ct t V O r r C
i r b 1 ; , tr\ i i t o l t { e c T B Ou} tr , t 6 O p O u H t ' i xX a p a K T e p I I C T I I KE
B c J e ; i y r c _ x { eB
\ ' lI ] A e :
[29] raror npeo6pasonaHlle
ol
T
t
to
l ' , g ; 2 " i 1'
(4.101)
a:-,/_-i )
2
3 ; t e c o s ; - 4ncnepcnfl u,Inr 3Hepfrrfl B r{acrorHofi no.nocec ueHTpoM
B
I] TOrliie f ; r r - a B r o K o p p e . r t r q r t a c . r l a r o l l / ; l r a x c r i u a . l l l t l t l i i l a r
1
.
:
l
L
,
i
. r L , r o K o l i l ) e r r O I - p a MeiC
l er t '
3 a i u e t r r l t , q T o 3 T o p a B e u c T B oo q e H b I I a I I O M I . 1 H a SKTO t 4 n J e K C H O e
n p e o d p a s o n a u u e@ y p r e , 3 a A a H H o ey p a B n e H I l e M ( 4 . 1 0 0 ) . - . O , 1 s a x o
p a n c H c r e o ( ' l . l 0 l ) u o x i e r 6 u l r l g u a ' l t l r e " l b H oy n p o i l I e H o . X o r q a n ror{oppe,IIru.uoHHa.s
Syuruux Mo)Ker 6ltrl sbtqltc.[eHaKaI{ A,'Ifl or'
JaIoB, oHa cll\',ll{eTpliqH-a
l,.iluaTeJlbHblx, TaK l{ ,I,ilfl IIOr-IO}KHT€,rlbHblx
I l o a r o u y B b l q H c J I e H u gu e o 6 '
orHocIireJIbHo JIara Hy"Ib; T' e' rI:r-1'
vt 3aTeM
);oJ,uMo npoAer'IaTb To!'IF,KOA,lfl3HaqeHuit I or Hy"Ifl Ao L-t
pe3yr,ibTaT yABauBaeTcR. ,[la.nee, raK KaK Harrl]i AaHHbre cocToflT II3
IiOHeqHOfO lvlHOX{eCTBaBeIqeCTBeHHbIXt{HCe"II'KOTOpble paBHOM€pHO
pacnoJro)KeHbr B tIpOCTpaHCTBe,MbI MOXeM HCrIO"Ib3OBaTbyflpoueH6o'ree
a ue..o6uryro $opvy.
Hoe [peAcraBireHlle itepe3 KocuHycbl,
npocrori BHA ypaBHeHHx (4.101), npuro4ultfi g;tn elt'Iuc,'IeHfiii, raiioB:
s t' : Ai'12 :
r; cosl"i 1')
,4,
'(
( 4 .i 0 2 )
, aK liaK
l J e o 6 x o 4 n u o p a 6 o r a r l c q a c r o r a N l i l , a H e c r a p M o H I l K a M uT
i y u t < i 1 u uu e n p e o 6 p a c n e u H @ u u e c x l i e , r a r t ta B r o K o p p e , r l q u u o H H o fQ
3vr,orcflB fipocrbre KparHble npyf Apyry B qacrorHona Cnerrpe. co'
orHomeHne MexAy ,'raroM L qacToTon AaeTcq QopMy"roll
./
I - -
Ir
( 4.i c 3)
-
2LL'
Ha6,rroAesurN{llBo
i-lc A - paccrotHue Me)KAynoc,leAoBareJIbHbIMI'I
irl)eMeHHoMprAe, H i npeg,cran.traer rar< i-ii^ d'laf, TaK H i-ro cnelirl)ar'lbHllo no,'rocy.r{acrora i-ii no"locrt ecrl f; II x3Mepflercf B I{liK'lax Ha eAilHlruy (e1uuriqu re x{e, qro Ii eAI4HItubI A, paccrolurtR
l\le)t{Ay,u,aHHbIMIr
rouraun). Ec.tlu A usltepaercn B MIIJL'lI'IMerpax'
ro f ;_saaaerctlB tlHK,'IaXHa MUJL'IHMeTp.
L l c n o , r l s y x y p a B H e n l t e ( 4 .1 0 2 ) , M b I u o " l y q a e Mr a K H a s b I B a e M b I I l
t t e o 6 p a 6 o r a n u n i i c n e r < r p .I l z - e a c r a H A a p r H o f io r u u 6 x H e x a x A o i i t t s
CIICXTpar'lbHbIX nOr'lOC efo
He,'Ib3tl
CqHTaTb
yAOBJIeTBOpIlTedIbHblM'
3ro npennrcrBr4e He,rb3q npeoAo,'ietl o6ttqsult o6pa:ou, yA.xl{Hflfl
qllcro Ha6.lIoAesuft\. lls'
npeueHHoii pa4 (yne,rrnqneas n-o6uee
BecrHo, qro rrpu yne"rnueHHun ilplr QurcuponauHoM r'lare I n Qop295
7
M I , l a x n p o r r s e e A e H u r ?{ x i - X ) ( x 1 + r _ X )
y B e J r H q r . r B a e r cK
floJrur r e c r B o u u @ o p t r a u u r ii i a B T o r i o p p e J ' r r q r { o H H a n
Q y H x u r r r 1 1 n p r . ro r o N {
6-_v-lerltN,terb_MeHbiu)'Io
craHIaprH)/ro
- n o xouru6xy.
a s t . r r r r , O4uaro aTo HeBepr11sriuQopuaq[q, coHo jl,rfl sr2. Exrrrc il Vorrc [29]
r e i r ; l i a u { a f l c f fB x t i r i f o i i o u e u r i e c r r e K T p as . i 2 ,
Iacnpocrl)aHgercg Ha
no.:l'Jcyrracror, rrurpuua xoropofi BoKpyf f panna -l-l/n. llo iuepe
Y B e , r l r q e H r r tf tl o 6 u \ a s r r H r p o p n r r u r z rc, o 4 e p ) K a u a f f c f l B A p r c n e p c r t r l
clexTpa, pacnpeAe,rrreTcfl Ha yBe,lnqflBatoUleecr rjuc,Io noJlocoK
v]reiib[rarcurerlcl runprrrilr. B pesl'"rrnrare yBeJxr{eHue /, Ae.rraer
so3r,'roTriHori
oueHr(y AHcnepcr.rr.r
e 6o"'reey3Ktix noJrocKaxqacror, AaB a f l c M e u l e H H y r oo u e H r { yr r c r r . i H H o f oc n e r ( T p a .o A n a x o o u e H K a c r a H g a p r u o i i o u r u 6 x l r s r l l x 6 o . i r e ev 3 K r { x r o . [ o c F I e v j l v q u a e r c s .
E a p r " u e r r [ 5 ] r r e p n r , r e 1 ' a i p l 6 o r a . r r t e r o f y n a e H o r l ' r e u ucrr a H l a p r r r o f i o r u i l 6 x u B c n e K T p a r - r b H bor xr l e H K a xH a o c I { o B e a . [ f o p L I T M a ,
H a 3 b r B a e M o r o , l r r 6M
o e r o A o Mc K o J r b 3 f l u l e roor \ H a , , r l r 6 od l l , r t r D a u u e i i , . r n 6 o c r , ' t a x H B a H u e u , , r n 6 on p o c r p a H C T B e H H b ryMc p e A H e H u e M .
AnroxoppenffurroHHyroQ1'uxquro Mo)KHo oirpeAeJrrirbB3BerrreHr{brM
rreror,ol{ ,raroBoro oKHa H,rH Qu,llrpa, [1 B3BerueHHataBToKopped,ror p a M M a N { o x { e r6 l t r l n p e o 6 p a 3 o B a H aB c l e K T D a ! ' I t , H v roo6 . l a c r u .
B e c a n p r r g a r c r o c o 6 o e 3 H a q e H l l e6 o . r e e N o l r o r n u r , I, t a f a M , x o r o prrte ocr{oBaHbrHa 6o,'lrllev qrJC.rre
ua6nrcAeHuft, qeu 6onee AJIHHH b r e, r r a f n .C l p y r o i i c r c p o i r b r u e o 6 p a 6 o r a s s s r f i c n e r r p r r o i l i e r 6 n r r
Bbiqllc,lleHII 3are\{ cf"rla)l(eHB3BeIIltlBaHLteM
H ycpeAHeHxeMBMecre
c nIir,'reraloitlil\,rH
c n e r { T p a " r r b i l b r M3[ H a q e H u q M 1M
1 .H o x e c r s o B e c o B
Ha3blBaercq cneKTpa"rrbHblltt
oriHoM tr;li Qlr.ltrpoM n qB,'Itercfl npeo 6 p a s o n a H r r e r ,(rD v p u e . n a f o B o r o o K H a . O 6 a I , r e r o 4 a I a r o r a K B H B a pe3\'"rrbTaTbI,
,'reHTHbre
KoTopr,tet{o}KHo xapar{Teplr3oBaTb KaK CMag L.rB
:lHrre rrr'r
rr cf Jaxiu BaHte ArrcnepcrrrlnDtiMbrKalouLlrx qacroT.
, \ { H o x i e c r e oo r { o H H . rH S r r , rr r p o n p a c i u a r p r i e a , , r o c rp, a 3 . l r r q H bMr H
a B T o p a r ' r l rc; r e M a o K o H , r r M e r o u r a rH
i a r { . [ y q u ] r r ec e o f i c r B a , n p e A c r a B ,rser co6ori HauBbrcrxee
x o c r r r ) K e H r r eB a r { a J r r . i sBep e M e H H b IpXs A o B .
O . r H o r r : u a r r 6 o . r c eu l r r p o r ( o r r c n o , r F , 3 y e l b r \o K o H- 9 T o $ r r n r , r p
T r , r o x r r - X a H n r u r a , x o r o p u r i B c n e K T p a . [ r H o i io 6 . t a c r u r r N r e e rB H I
'.t: . -
I
t
.2
":_l
'.. I
I
-. ,. 2 l _
r
o
I
I l p e o 6 p a s o B a r r r r e@ y p n e { l r i " r r r p a
Jafl ecTb
l i "' , ' - I 1 l 2 \
'. /2
tl.
Tlroxrr-Xauuuura
(4.104)
B o6ilacrrl
(4.1051
.o.-ll \
t. l
3 r a Q o 1 t r r 1 , , rot an l l e r f e J l r e rB e c a a B T o K o p p e . r t x u i r o u n or lfyi u r i u n l r , x o tX/o:1,0 npu Hy"rreBoM
. r r a r eA o
lQpar- !{.];IKo y6i'tnaer or 3Haqennn
l i T r : 0 , 0 n p r r N r a K c r r N { a . l b r { loaM
r e l . K a x i A s r i i ' x o e r p $ i i u r r e H ra B r o ,
riolti)e.rlflqnrryMrrox{aeTCffHa coorBercrByroululi eN4yBec Ao BbrnoJrH e n n f l n p e o 6 p a : o n a u r r a@ 1 ' p r , e V
. p a e H e H i r e( a . 1 0 2 ) "r r p H H H M a eB
r r.{A
/
s,'-3(l
r- I
1_l
29e
\
slil',r,cos2.ttl.
(4.1(rG)
,riaroB'
oNua, o6rtqHo .nlt6o s o6,'Iacru
I.IAPYTHe
Moxso nPeAJIoxI4Tb
qacror'
TaK K a K H X n p l l M e H e H I . r6el t e a e r J e f q e r u
,'In60B o6nacru
a
ro
4PYrorl'IIIupor<o licno.tttsyeuoe fIap3eHoBcl{oe
n oAnotiQoPve,
OKHO HMCCTBI'IA
1
V,
Jittl
'|,,
"L2
HyJIe\{,, I lq r.,
iraroB Nre)KAy
Wr:2(1-
I ,1-
I
I
UL ) '
\
)
( + 1. 0 7 1
( 4.l 08)
, r r a r o Bo r L l 2 l o L .
xapaK'
Ilpaxriluecxafl cTpaTefxs uccJreIOBaHlIfl cneKrpar'lbHblx
.l.e;,,icrrrK C,rVqaiiHL,rx epeveuHltr
pflAoB BI{.lloqaeT cJeAyloutle
uafll.
ypaBrlrrb AaIIl. Ecnn Heo6xo4lruo, u36aBilrL' or rpeHAa li'lil
p e r p e c c t i l l Y . 1u a i I I 3 a r e M u a i t r H
,'uta, *,u,,".uHe xoa$$llqrleHrbl
ocrarlill: Yi':Yi*Yi.
cra'
2. Buquc,rtlru anrot<opperflqxrc llcxoAHoro pr4a (ec'nu oH
I''
J
l
a
r
a
M
a
K
c
l
l
M
y
M
a
Y
'
e
n
,
l
o
t
l
A
o
p
s
A
a
n
.
i
u
i
n
o
"
,rrrouapeH) u.rlt
BbIpeI{oMeHAyIor
aBropbl
Hetioropue
nl3.
He
flpeBocxogut
xoropni't
lrirc,irflTb 6o,'lee y3t{ile nl)eAe'rbl A"rlfl Malicl'IN{yMa 'qara' HailpllMel;
n170.
nl\, nl6 unpr Aa>Ne
S;-'
3. Buqnc"nrrrt Heo6pa6oraHHyiO C[eXTpa!'lbHyio [,r]oTHOCTb
y
p
a
Bp
e
A
e
,
l
l
e
n
H
o
e
o
f
l
O
y
p
l
e
,
r r c n o , r r b 3 y fA
l I r c K p e T H o en p e o 6 p a e o e a a r i e
(
4
.
1
0
2
)
.
ireHHeM
4. Cr,ra,l.rrrt ueo6pa6oraHHnii cneKrp, llclloJlb3yt OKHOTbIOi(liXausrrgra (ypanueHr1e 4.104) B Kal{ecrBe cKoJIb3tlIeIo cpeAHefo
rl,irfl rro.rryqeHlltl cf,'IalKeHHOii OIIeHKII AHcrlepcua c[eKTpa'
o q e s l r A H o , B c n e K T p z t . n b H o Ma H a J i l I 3 e I I M e e T c t l M H O f o C I I O C O O O B
Ha ol(oHqaTenluuli peKOTOpoe o6_a>NeTB.rr11flHue
npuHflTr, ^peuteHrie,
oHrr
a
l l a , l s 3 H p y e n , 1 o f in o c ' [ e /
?
,
s
b
l
6
o
p
A
,
1
1
H
b
r
n
n
"
,
p
o
q
a
r
c
r
.,vnorur.
n'Ooutano"OCrtt (eC,rU 3TO HaXOAIITCtI BO B"laCTil tlCC'le4OAafe.lr) ;
NIilricrrN{ztJI)ttofOd'Iara L; U Ot<tta,IIClO.lb3yeMorO A.'Ifl Crr'laXHBaHHg.
ci:t:rr Me;^riAy 3TlrMri nepeMeHHbtNgl ri trx BJ1,19HHe KaK Ha pa3pe[ r e H i l e . T a r { r r H a 3 H a q r { N r o c T bo f J a x { e H H o f o c n e i i T p a o 6 c y ) K A e H b I I 1 O r l ') o 6 i r o B l i H I I r e E H t u t u c a u V o m c a [ 2 9 ] .
Bbtno,rnqfl aHaJIil3 Oyple, MLI IIpeodpa3oBa,lil HaIlIx AaHHble H3
olnoft o6'{acrlt s 1p1ttyro. Mlr uaqaeu c Ha6'rllof.eHtiii sa Qopuofi
r;aBncr.rMocrrl 3HaqeHltrl Yl or I{oopAIiH&T Toqel{ npocrpaHcrBa il'rltl
TOqeK O6pa3yeT ClifHar'I I'lr'IHBOJ'IIlper,ieHII ;r;. |IOC,{eAOBaTe,IIbttOCTb
KoopAllnar X s Y'
rroByro $oDlly, onpeAe.IleHrtyrc B nJocKocrll
B r i o u b r y u i e . o t o p " t , q r o A a H H b t eH a x o A s r c q B o B p e M e . H H 6uf rn u
i t i ) c l c r p a H c i B e H u o iol 6 n a " t n t t 3 a B t l c r r o r n e p e M e H n o f iX , o 6 o 3 H a .taloul'efi KoopAHHaTbrToqeK Bo BpeMeHa HJILIpaccToqHl're.OnpeAe. l l l B K o r r { I I o H e H Tqbat c r o T B c l { l H a ! ' I e , N ' l b n
l p e o 6 p a 3 o B a J I uA a H H b I eB
r l a c r o r H y r co 6 " r a c r b . @ u g l ' r q e c x a ga H a , r l oHf f l M o x { e r 6 l t t u u : o 6 p a x e co.rlHeqHblx
Ila Ha pflcyHKe, tAe [peAcraBr'leH e$Q-exr_ OTpa]KeHI'Ifl
N{o}KcBera
6e-noro
(puc.
4.58).
Cson
npr.r3M
"ryuefi or s"ep^a,noHbrx
Ho paccMarpunarl KaK KoMnJIeKcI{yrcBo,'IHoByIoQoptnty'I{3MeHflIo'
297
II
It,
I
$
I
&
t$
t
lllIiocfi Lr TerreHileMBpeMeHUlr CocTctrulvlo Il3 cBeTa pa3JIHqHbIX
n o . ; r l r ) .f l p r r : l r a . { e r i c r a y e r 5 a x q a c r o r s n l i a u a _
U L . ' ' ; o r l( i i . , i i t ; 1 . ' l u H
"Iili-li:TOl) Ii pa3Je,ritleT
O l,lJtfrTPb!
T
I
t
I
1r
B De3Vd,Ib-
l)VlO FIe.r;b,rflIIoJIyqIITb HuKaKrrM Ap)'flrM CIIOCO6Olt.
I
t
It,
I1\'(IOIi Ha efO COCTaB.rtflIOIqUe qaCtlI,
T : l r e r r e f o H a r r r c r r . r e e r r o i r y q a e r c r rp a A y r a . K a x A a q o N p a i u e H H a s
Iro.luCa or.ileirrrercHor coceAHeri nponexrl'rouuori soHoii, lllupHr-ra
xoropol:i nl)onol)rliloH2r'Ibtrzr
pa3HocTri ilx A.rtrrHBo.,tH]r,rili qacToT,
a ! n r r e H C r i u t r o c r bx a x . l ( o i i r o , t o c t r t n p o t t o l ) i l t j o H a , t b H aB r { J r a A y
AaH_
uoil x,runlr iio.,rHr,ttr o6qyrc ugregcrionocrr, I.IcxoAHoronyuxa. I4cc . l c . ' i o B a H t r cen e K T p a r r c r o r i H H K ac B ef a \ { o ) t i e r c K a 3 a r b H a M r , i H o f o e
o cTpoeHr.rillicToqHilKa cBe.t.a,efo rer\1IlepaT\,pe,
IIprrl)o.l,eBeu],ecTBa,
ci\|03b lioropoe ltpoxo.r,t{TcBer rr rari ra.[ee. Aila.lorttquo ficc"rte_{o_
B a r rI i e q a c l ' o r H o f o c n e K T pa r a u s o t i n o c , r t e r o B a r e . r t b H o cM
r HO X { e rp a c c K a ; l a r b r r a l r o e f o r r p x i l o A er . rr r c r o r t H r r r i eA, a r b r r H ( r o p l l a r l t r r or,i o r o -
@rtlurpotr
I ra 3 b t B a e r c q M a r e t r a r l r r e c r l l i . r o n e p a l o p , x o r o D b t t l z s -
MeHrersarauubril.
npeneusoilpflA s .qpy|oiiepe-veuuoir
pnA, uiraenr4uii rpe6l,er,rr,,ro-r!opuy'.
Taxrreonc'parolbrriasLrgarorcl-<QH.nlrpaIlll>, TaK Iiali fiepBoHaqa.rlbHo oHII n]leJcraB.Itflr'ILIcb 3.rreKTpoHHLIMH
]13 cerr{ cortDorr.iBr,regtrfitr
Qit"rorpvrcu:,lMtt qe.r]fl]itr, cocrofllrlutlii
evriocreii, rrc[oJlb3ye]rbr.x Ar'tfl ni,t6opouuoro
[oAaB,[eHHfl Hr'tH yc]tr e r r l r r c n e q l r r f r r u e c K u - \ .r r a c r o r B 3 , r e r i r p o H H L I . \ C r . t f H a , l a x . T e n e p l r e
x < e Q y u x u r r r r n o n p e o 6 p a 3 o B a H r r r o u r r ( r o o a u x c r i r H a . r l o BB b r l r o d , r r { r r r o r ' cfl Ha Ko:rrrrbtioTepax a,{aTeMaTl{qecKit\1[ QH,llrpaull.
ocHoelrl leo-
puri Qu.nlrpaqun6tr,ru sa,'rox{eHbr
Flop6eprou Buuepolr n pa6orax
Iro crarrrcl'r{qecxoii
TeoprrH
cBg3u,rr 3TareopuflHaxoArrrcnoerrpaxTrrrrecKoe
npHi{eHeirue
lpn o6pa6oTrie ceiiclrrrqecxrrx
cilfHaroB r{
jlaHrrbrx a3pOQOrOCbeMOK. B cn"ry erOro 6O,llnttltcrBo TepMIIHOB
Teoprlu tplrllrpaUrzl{ rpo}l3olIJ,'lo He H3 KJlacchqecKoii crarHcrllKll'
a t r a r t g > x e H e p H o i i3 " I I e K T p o H I l K uu S t t s l i x l t .
fior'tyittulHHau6onee uIIlpoKoe npuMeroAtt reopx[ Qu,rlrpaqu[
i
l
C
C
r
t
€
!
,
O
B
a
H
I
I
I
{
o
T
p
a ) K e H H b I X C e i l c N t i l q e C l i } l xJ . a H H b l x .
i
l
p
t
t
MeHeH;e
I l c c . t e A o e a H I J e C e t ? C M u q e c t i t t xc B o l i C T B O T p a i K e H r l b l x c l l f l l a " r l O B O C I I o C H r l l a . l a ( c e i t C t r . t t t u e c K r3f lH e l ) r H f f n l ) O t l a r r o r r a C o 3 4 a H f i HB x O . 1 H O t O
3aTeM
rotopufi
il3BollHrcf B3pblBoM AHHaMHTa HJIII Bu6paropov),
B pe3yJlbrare nof.noueH14q SHepfIIu cHrHa.ra no NIef'e
{rrrlrrpyercfl
qacrorbl IIof.]oefo nl,TelllecrBIifl cKB03b 3eMHyIO TO'rlilly. Bltcoxtte
q
T
O
c
e
i
i
C
x
l
l
l
.
l
e
CKIl\ Iig,le6arlllii
n
p
l
l
p
O
;
1
a
T
a
K
C
I
I
J
t
b
H
O
,
6
O
.
[
e
e
Ula1OTCfl
qro Bo"lHbI HII3tr3MeHfeTcl tro Mepe ux nepe,lBll)lieHlltl. !,o6aettv,
titrx qacroT [epeMeUarcTCff qepe3 ropHble nopOi],bI6o.,Iee 6ntcrpO,
Bcn"IIeCK CTaHOBIITCfi CMa3aHHbI}I ll
rar{ KaK Haqa,'IbHbtii OCrpuii
, l c . ' r a 6 . r e l r H b t l . {B. b t . \ o ; i H o l i c t t r u a l , x o r o p u r : t o 6 l l a p v x i } l B a e r c g H a 6 0 cttrI13 Orpa)KeH_llt?
i ) o I { r r C B e p x H o c T H b t xy i I a B . x t i B a T e . l e i l , . C o c T O l l T
ira.roe, Bo3BparuBlUuicn u: 6olee r.r,v6ot<ux rop[3oIIToB. K co;ria.teHil]o, noc,rle ilx nyreuiecTBllfl oTpa;IieHHble Bo"rIHblclL'IbHo Ae$op)rupoBaHbI tl HX TpyAHO lilrTeplpeTHpoBarb.
3 a A a q a r e o ( p r . r s H K -a y c r p a H l t r b H a c r o . : I b l t o , H a c l i o i l b l i o 3 T o B o 3 Koropblrl
],roxiHo, BpeAHbre a{r{rerrur
$H.rorpautttt,
Quslluecxoit
cer?cvuqeirHricurna"'r6u,r no4nepxes. 3ro Ae,'Iaercfl[yreM o6pauti$ponurau $ttrlrpaull, Koropble
6orxu ceiicMH.recKrrx3anucefi
qacToTut,o6ocrpanT oTpalKeH[ItlIl rovcTpaHfl}or He)Ke,rraTe,rlbHble
B
3
a
i
l
u
c
l
l
. t a B . r r f l n ru y N {
AO rex nop, IIoI{a rpe6yeurrii, uo oc.ra6.'reuHr,rii
crrrHa,rrtre 6yr1er BbIAe.rIeH.
B cH.ny roro qro MHorHe ts03MylleHIIf ceiic\,{rlrlecxllxcurHaJoB
L l a c r o r H oc o f . q a c o B a u l t ,r e o o u s u x o e o c o 6 e l l H o l l l l r e p e c y l o r S u " l s r creulleHepllpy]or IIJiI YCTpaHtlloT
p b r , r i o r o p b r e n p e J . I ] o q T l l r e . l b HrO
r p r r . r e c x r rqea c r o r b r . C e f i c u l t q e c x a a Q H n l r p a u t t x q a c r o [ p o B o A I I T c f l
e a r o i i o 6 " n a c r l 4q a c r o r c r l o M o x l b l on p e o 6 p a s o n a u t i n@ y p l e c e i l c \ I l l qACTCfi CNCKTPA H
IICCIi}I,\ CHfIIAJIOB Ii
YCTPAIIEH}Ifl HEX{€r'ISTC,TIbIIbIX
roc"ireitYroulefo
n p e o 6 l ) a 3 o B a H I { f lo r Q t t l i ' r p o n a H H o f o c n e x r p a o 6 i ) a r H o u ! . e i i c r s r r r e J b H y l oo 6 " l a c r r . O A I r a x o B T o t l H o c r l lT o r x e n p o I l e c c ) i o T i i e r 6 r ' t r r p e a . l t t 3 o B a Hn p e o 5 p a s o n a H u e M$ l i , r l r p a o 6 . ' I a c r n
Oypue B pea.rbHbleAaltubte u iloc"reA,vloiueiicBeprKofi ero npeo6pa'
: l ( ) B a l r r r cf f c e i i c r r r r q e c x l l M l3r a t l t t c r M I tc H f H S , r ' t oT
Ba. t i x a x a r l t Q H . l r r qacToT H IIOonpeAed'IeHHbix
npetrHa3rraqeHbr
ilpo)ioxiAeHtlfl
I.ltl
1)l,r
ti
1l
ti
ll
li
i
Puc 1.58. flpu::'la crlxHr r{acrcrubr\{iiHarH3aroposr,npeo6pa:_vroulrru
6e,ruir
Hi,i r na p e v e H r r 6or i6 . r a c r r r )B e r u c o c r r B r i r r ev r : r u D a g caei (u npocrpancrBerruo
HIJx qBeroB (o6racrr uacro,r)
298
jla B"rleHtrrrApyf Hx qacToT, TO OHII H 33 biBaIOTCtl BIjCOKOqaCTOTH
blMi{,
]I II3KOqACTOTHbIMIIII.T]
HbIMII QH.] bTPA MU,
H IIO.r'IOC
T e o p e r r r u e c l i l r M o I K I { o n o c r p o l l r b c o B e p I I J e H H b i eQ t t . l l r p u l , I i o r o p r r e 6 y , r . y r r r p O n 1 r g 1 1 2 1C
6 I i f H a r ' t b tC n e U l t Q l t U e C K ] l xr l a c T O T I I I l e n p O '
Ilvcriarb .npyrrre qacrorbt, Ho ratitle Qultrpu
o6blqHo rpy-lllo pea'
.lrt3oBarb. Kar npanur'ro, 3Tu reopertrqecKl,t coBeprueHHble QlJ,'Ibrpbl
rlle6vror 6ecxoHe.rHoro qttc,'ta rI"teHoB. Ec,rrt oHlr yceKalorcfl Ao llpllel,treMbtx pa3\repoB, ro $u,rsrpu caMH HarlllHaloT oKa3blBarb BJrr7fl'
ltlte Ha er,rxoAHoiicIIrHaJ. fIo4o6pars Qu"'rnrpst raKrlM o6pason uo-
299
xreT TO,,r
b^o Bbrcor{oriBaJ,[*HU r,poBa HHbrir
p a 6oTH' K, Tari r(aK
Qu,,]bTp
Ao''ririerr6r,ri'n ;foctaroqHo nopbrLurt It
3r(oHo\lrrqecKlrBbIfoAHriM
*n,
I'r
r(o"ii{ieH AaBa'b xopouyrc arrllloKcr
\Iaqrrrc rpe6yenoro
c l l f H a ' [ a c t u H r r N l u r ' T b H b t rq' I, C r ' r o M
Her{ie.TaTer'lbHr,tx
"or"oAa
eerron. flo.lpo6soe.Ir3,rio)ke'He reoprirr (przrbrpoB r o 6 o .
.".*";T,""tJ.;,_?;
rlacror coneprirrct
Bo \,rHoriIX
rHMcfl r( r{onrlerrryr.l^uj:- 6o.nee" n u r ( i , o . r o n u r .xrH H r a x . , & l r , tx e o 6 p a _
npo.ro,* rarraM
H r( Bo_
npocaN{ rrrr.rpoKororlicflo.rrbsoBa
r ! r r u , r r D r u buni
d u r .aauc
l lHt a . . I I I 3 an p e nSu,rrrrpon
r e H H d t px r i r o B B o
M H o t H xo 6 n a c r g x .
xorop
rrr1Ao"I]rieH
rHyr
,r,,,,1
a?,t#:[i".T.t;"#'
9::1 l"qrep
u"i i'p Qanrrp
onp'r,r,
oaarurrrr 6
:.:: "II " ^ "''en'n
ii?:'X #fi i6"1
11.x
", ""i?f
pau,au
.oopou"J,e,
pxorsuruii
psAc ;l,"ffijiil 3xHll**l.m.
J y q a e r c f l e H x o A q u l u r ip s A :
Ec,r
u-ua BbrxoAe
r,.,:
1:rr,i:'r;!i[tip
eAerreH
Hy
ro
:::l
auopaHraKrrM *",.l:
Nro]Ker
6rrir
i?^[?_f:_ro 0rr,161p
o6pasou,vro
AercrBr{re/'roHsrfi
sbrxol:Ti1 p".l
ICj 6u"r Hacro.,rrxo,
6l,rsox r
rpe6yeuonrv
Bbrxorflrrde),),
po,qy,
-a.qbx.{e'rbr
3ToBo3Mox{no.
r{ro6or
3TO c-qe,'rarb,Bbiqrrcr'rriNr
"rino'r"no
4rinrrpa,_ xoropr'i
Mr{HrrMH3rrpyercyMrryriBaAparo.B
pa:uocrefr
ni,xay'Jc1; fri.'e#ii"".ruy-ureroA
roulurl rrareMarfi qecxrrri
oqerrb
ninoru"u"T a.{fopHTM BbrqrrcJ ' r e H f i fxi o : & o r r u r r e H r o e n u H e f i H O t
perpeccr'r. po6rHCOr u
Tpefire.lu
[44] ta*' oqeHb noapoouo"";';,.:;5;;rre.,rbHo
rcHoe urr.o*"n,.,.
3 T o r o N l e r o q a , H a 3 br ul B
q La* reulrl ouf o u
c"x\ cerM
\ t uol li r H
Haal l N { e H b I r I e r o I { B a A p a T I I t l H o f o
plLIIbTpa.
Paccvorpiiu no1c19ri nprrN{e1l.
llpgAno.lox<Hnr,qro exoAqrurrft
B e K r o pB u i r e e r : ' s u ^ r n e r e H T o j r r . ' ? r l i .
, o r g a e H , r s r l )r a r ( x i e c o _
, r r e p x r rnr B f ls , r e l r e H r a
lfo,i,J. Tri rax'
cr cBeprr(oii
nroxa
u rp,,.oripa,
;;';;":i'J,:i,iT ,$:ll"lf3r,:1ff::
IC]:[B]X[I],
I iolrl
-f1'.lf f o b ol r b o l ,
tcl-lo,
(a.tfiS
Iottt frbr l
I C ] : lfobo fobt * f t b o f t b r l .
Ec"rut ltt t xorlrM,
u: Qrrntrpa paBus,rcflHer(oropoMy
s a 4 a u H o u y[ D ] , ;1o.9:..1!t"o,r(
To Mo}KHoHanr{caTbcJrer,Iynuylo
CricTeilry
coBMecrnErxypaeueuufi
ll
foboag:do,
fobr*fft,,:1,,
o+ftb,:6,
rr'TrrB nrarpauuor?
Qopnae
300
(4.111)
ibn 0
lr, ho
obt
tli:lt;il
(4.n2\
E1'r,e-lt
o6osHaqarlMarpluy 3 ,'reeoir
qacrr.r.repes
Ipl.
,Marprr.rnoe
vpaBHer{rre
nepeolrl)eAe.rleHo,
r. e. lt}teercqrpri ypaB_
Herirfl c '4Byxlg Helt3BecrHLllrut.
OAHatto ec,rll o6e ,tacrlt yDaeueHltg
\'.\iHol{r.rrr,Hj oluy ll ry x(e Be.{riqilHy,ro ypaBHeHaeociaercs He-
,ily."Tljlil:.Tar, y,vuoxnn o6e qacrri ua rpaHcroHupoBaHuyro
K
l p J M a r p r r u i ' ,i l o , ' r y q r J M
[B]',[B]
ffl : Ipl'[D]
II.I Ii
'u','u,flilrl
lo
nt:i?i:i,il::]
lbo
q T o M O I K H O3 a n l c a T b B
BrrAe
bt'
fbn'+
boh,
b'b'
:li:i:Ii',!,1(4,,8)
'lIi:]
bo,* b,
L
feoSusnxu Ha3brBatorNrarpirqye,reeorl qacrr.raBToKopper,rqrllroHuori lrarpxqeft BxoAa. flpaeaa qacrb rorAa ecrb KpoccKoppeJlsIII{II Mex(A!'BxoAoMLl BbtxoAoM.,!,elicrnHre,nrgo, s,,IeMeurbl grl{x
Marpal{ He ffe,'rrroTcrxoaQQuu[eHToM Kopperqq]r[,
a flBJrsrorcfl
Heuc[paBJieHHbrMr.i
cyMMaMHKBaAparoBr.rKpocclpoasnegeHrafi
. 04_
HaKo 3HaMeHarer'ra
.lrn6oro Koppe.rrflr{r{onoro
q.ryeHa
oAr.rHaKoBbr
ll
noroMy orcyrcrBylor; peueHrlesroro ypaBuenrrs 6yaer
oAHltMlt
reM )Ke He3aBrrcr.Mo
or rofo, Hcnonrsyrcica.rinro:QqiaqaeHrarxopxrru KBaAparbrH Kpocc.rpor.r3BeAeHrzs.
peuieHueHaxoAnrcs
l]:i111l
oopailIeHr{eM
Marpnrlbl,ctosulerl e reeofi ltacru, no"r"Aytouf"*
yMHolI(eHr{eM
Ha Ber{ropnpanori qacrn. Ec,ru uarpHuy
"
n .,reiofi
ctrr o6oguaqrrbrrepe3-.[Rj,a Beriropnpanofi or"i"-i.p.;*[Xi,; ua_
r
ro"ryrrrrM
[i]: [RJ-,[X].
uAHo r'r3o6uux npu'laeHeHuri
Teop,,uQu.nlrpaqaucocror.rrB HcBcrper{aeMocrncrreur.rantnoii-no.rrnbaofi
Soprrln riJrr.ree
:1.:lo^":^11r
quqlpoBoronpeAcraBJiegntr
B HeKoropoMnpelreug6u ps.qe.Aua.nll_
;1:#"#";Jr:'#;"1r#rffi
";l:#'"??#""^?"?t;l,r*lHerr
I lycrb BxoAtlrlatj,oJrH-q ecrt
l2ll
_8.
u rpe6yeuuft
nsrxo4Hofi
IDJ: t3091. Orrr-upeAcraBrreHbr
ua
pnc.4.59.
fl,:i:j^:.I._.1_:.rA
r r o A c r a B . ' r f l fsl r u 3 H a q e u u na ( 4 . 1
l3), no"rryuaeu
ti?lnt
fsl
301
;t
f"
-l
"l
?-
'f
-tt,;7lll
.,
;l,al80 :
r.r Ii '| +eI z,s;z: - oI,l4j-l
I
,;7ll
I 1,4:s';
1f
rL
JF
B i , r x o 4 Q r r . , r r r p ay x a 3 a r r H a p f i c . - 1 . 5 9 ;o q e e n A u o , M b I H e n p e y c n e . q l l
n c o 3 A a H r r rqr r r c r o r o o c r p u f l [ 3 0 0 ] , H o B b r x o A f l B J r f f e r c f l o q e H b
xopoutefi anfipoKcu\{aq[eii. AeiicrBHTeJbHo, aro ecrb Hafi,'ryquraff
Bo3lIo)KHac rnnpoKcr{1"{aufiflL,'Ifl 3Tofo qacrHoro BroAa n Su,rr,rpa,
^
2i
|
of
/\
/ \
i
---->--J
\\
;L
COCTO'IuIEfO TOJbKO Ii3 ABYX IIJ'IEIIOB. TCNCPI
\-/*
'ljr;,'t3,i'
Ei?fii;$jr
o,r,i
ji;
i"1,,
rffe?r;f
{s':
#i +il"Jiit il{,1?T.
V M u o N a r r c " , i e s ao 6 e q a c r r
Ha
fr , urf, ,,-l
IpJ', no,ryvaelr
:ij,l:f;j:l[;J:
1,,, ,11,1
;J
;ltfl-tsl
fs
L2
flo4crauoaxaN.rarprrrrbr,resolr
rracTrr
naer
f5 21-'
lz sJ
| 0,338I _ 0.0953
I
0,2381
L_-0,0952
J
14cxomue
r<oe@@aqrzeHru
Qn,rttpa ecrl
f i , l _ -f
0,2381
_ 0 , e 8 5 2f-rlj t
r
1,4286
l
L/,J L_o,oes2
o,238rJLoJ:
L_0 , 5 7 1 2
raHo
Haprrc.
iltiaJ;;ff"'"Tl'A'J1"^*?':'^j1r:lq,
4.be.
Mrrrro.;.i::,:g_"13;:
Ha prlc. 4.b9. Mr,r rroxeM orpeAe,rari u.o np.oOpl,[;;;;[:ri""'
sosaHl'Iqn.puonuorrbHoro R,..'..,n.^.^
^,,-:::j"tyj ero r/'Iq npeo6pa-
:ffi5J;"#.fff#il,x1"x1l"1;*1?ii:riJ:#:*,ff
tr'1'rr' rro Jerlaelcfl
no'lxoa$Qrrur'reHroB
B onpene,'flK
:3:ai iA
9 :aa-H
* "H
f iooee
)
I[ee ypaBHeHIIe
H
H
uB
un
" "ri.*r e (M4 . 1 00g9)): :
ypa
Hae'H
Qrr.rLrpa,
[C] : [2 I] * [1,4286_0,52 t2].
Cneprra aMeerBlrA
302
I
: [ 2 , 8 o 7 2{ 1 , - 1 i 8 61- , 1 4 2 4-i0 , 5 7 1 2 J
j
-- 0,5712J
: l2,il.l7
0,28tj:
N,IbI }1OX{CM I13MCPHTb,
\opou Qlr,r;rp, cpaBHlrBero Bbrxor c reM BbrxoAoM,KoHarcrioJrbKo
roplrfi Mbr xorer'rlr noJlyqrrrb. 3ro 4e,raercfl Bblt{uc,rreHttel,t
outu6KH,
o r r j l e A e . r r e H H or ai rx c y M M a r ( B a A p a r o Bp a s H o c r e l ' rM e x ( A y C w D :
:0,1428.
e : (3-2,8572)2
+ (0-0,2862)2+ (0+ A,5712)2
Ec,ru saArrb Ha BbrxoAe Apyfue cuflra.rbr, He flBr'rtlouluect nHI(OM, TO B HeKOTOpr,rX
C,'i)'qar-x OHH .{a,XyT 6O,lee aQrlertusHuft
$H"rrrp. O6utrre runu Qrr.rrrpoB HocflT Ira3BaHr.{rnulnx (xeaAparr r a R n o , u H a ) ,S r r " r s r p f a y c c a , n u , r a .
CrraxnnanHe H BpeMeHnoiirpen4-aHaJIr{3
re,
Bosuoxuo, rrau6oree rr3BecrHbre reo,rrofaM $rulrpsr-3To
iroTopbre npeAHa3rraqeHbiAJrf yMeHbueHlifl AHcnepci.rlrBpeMeHHoto
psAa. 3ro - fipor]3BodrluuteQn.nl'rpu, o6ulee Ira3HaqeHLIe Koropbr-x-crJraAHTb AaHHyro noc.reAoBareflbHocrb; BbIxoA us Qtt.nrtp a - 3 T o a l f l p o K c r { M a q H f lT
, e c H o c B f l 3 a H H a fcl B x o A o r " I o. 6 o c H o s a rnre geo6xoAr.rMocTH
TaKoro ripouecca @N,rlrpaqnu cocrollr B ToM,
- <<AJ'IHHHo4eftcrr{To BpeMeHuolipxA cocrour r{3 AByx KoMnoHeHT
t s y r o u l e r o >c n r H a J r aH r r r rH e c y u , e r ol t u Q o p u a r l n r c t r H a r ' i o ] K € H H o rHo&
r{ero c,ryqaiisoro [IyMa. B cirry ero npripo!,n raroii tuyM AoJr)KeH
cufHa.[
6nrr <<xopornoAerlcrsyrcqei;i>>
xolrnoseuroii.
flocxo,rrxy
rIa,:lo u3MeHfercg oT Tor{Klt t( ToqKe, a [IyM HMeer ripoTliBonoJlo;{iHyro TeHAeH(rto, To cpeAHeeIIo Hecr(o.rrbKHM
[puMbrKa]oulHMToqKaM
6 y a e r c r p e M f i T b c qK 3 H a q e H I r I coa N { o r oc u r H a / ' r a .
OAHu lrs MeroAoB crJraNi[BaHHs cocrolr B artnpoKcur,IalrnlrKoporKrix cefMeHToBHcxoAuofi nocJleAoBarer'rbnocrr.I
f,'raAKIiMIlJII{HHg\rH r.{JrrrKpr.rBbrMr{.
Srtr xpunrte r,rofyr 6urr no4orHanbl I!{eroAoM
riarrrlcr{brilux KBaApaToBc lroMoxlblo r.r3JTo)KeI{Hoii
pauee TexHr{K}r
[oAXoAfluIHMll
aHa,'rrrca.finn atofi qe.ilr Han60.neef)ef1,rggg11orrHofo
oxa3brBarorcr oproroHaJlbHbreMHoroq,rreHbr,TaK KaK oun rpe6yrcr
To.rbxo nepeilrHox(eHr{fl
psAa qJreHoBu ua6,'trcAeuufie annpoKcllMlll , y e u o M c e f M e H T e ,3 a T e M c y M M I { p o B a H H f lH A e r ' l e H l r gu, r o 6 u n o n y qilrb rreKoropufi xoaQ$uqHeHr aflnpoKcnMllpyronrefi rpunotl. Ec"rytt
i'crrp$uuneHrbr Bblqficr'reHbl,
MO)KHO[OCTpOHTbypaBHeHI{eH IICXOAli!3
-
Hbre Ha6JroAeHHbre
3Iraqe]JirflAO,'IX{HbI
6nrr caN,retteHbr
Ha npeAcKasarrHbre3HarreHrfl ?,. Ao rex rrop, noKa iropsAori alnporic,Nrr,pyroueri r<punori lreurure lrric,ra roqer{ e cer^aeHre,r,lpltaia 6yger ann p o K c ' M a u u e f i , n o A ' e p x e H u o r ? M e H b [ r l i M r . i 3 M e H e H r r r Nq re,M
ricxoAu r,re^H_a
6,1ioAeHLIfl u, cJIeAoBare,,tb Ho, Oo.,,Ieern a.q,rofi.
O 6 u q H o n o c , r r e A o B a r e , l b H o c rHLe, c f J r a x i l B a e r c g p f l A o M
HenepeKpbIBaIoilrIIXCtlcerMeHToB,Tai{ IiaK oiirr rr}relor pe3r{rre il3.,io}Jbr
B
cBorrx 3BeHbgx.Buecro 3Tofo onepat(tirl cfJS]r{trBaHrj.rl
cocrorlT B IIo_
crpoeHrlll annpoKcrlM2llllu^ K Ma'xo'Iy cerr'IeHTy I't onpe/f,eneHIrfi
n p e A C r i a 3 a H r r b r3xr r a q e Fnli \ ) , i , c o o r B C r c r B ) . r o [ I H xc p e , I l ] e N t y
ua6;iro_
AeHHTOB CefMeHTe.c,re,1yr,ou1ilr?
cer^neur err6rrlraercr ron. uro o"
r l e p e K i l b r B a eB
r c e , K p o M e o A H O r 0 ,u a 6 , ' i i o l e u i l r e r r e p e o u c e f r r e H T e ,
H 3 a r e M r l p o q e c c I r o g r o p f l e r c t . I l a r i o u e u , r r c x o fi r o e M H o ) K e c r B o
-tali_
HbIX 3ar.{eHflercf Ha crJ'ra)KeirHbrr.'r
pn;1, no,'ryveulrurl r.r3I{prBbrx, IIoA O | H a H H b i xr ( 3 T i l M n e p e K p r r t B a r o r q r r t r c e
f lt r { e H T a M n .
T a r x a N M H o x e c r e o x o : e Q u q u e H r o B A o , r ) K H o6 u r t o r p e r e . r e r i o
I i B b l r r i r c , r e HAoj I f l I { a } K A o f of i e p e K p b r B a i o i u e r o ccf le r ] r e H T al,r r r n e c r ct lloqrrl TaK t'l{e MHoro cerMeHToBllo BpeMeHHo\IptrAe, Kar( r\{eercfl xcx0;LlrbrxHa6,rrc4euuit,ro ero satg;{irroir npouecc
rla}r(e IIpil ircti:l_t-::o_uunrr oprofoHa,rrbHbrx)iHofoq.rrerroB. o,lHaro cauu iio:QQliuueHTlr He f BJIfllorcs geo6xoAIrMbI:t{u,Bce, rrro rrar{ IraAo,_ 3ro
o u e H K r . fr; B { e H T p a , t b H b r xr o q K a x c e f M e H T O BC. e r a r a o f D a H r r q e H H _
e M M o ; K H on e p e n H c a r by p a B H e H r I 'oI p r o f o H a . r b Hr , l N] , r H oof L l . r e r r orea x ,
I I T O O b IN O J Y I { H T bA J b T C P H A T U B H O C
I d I { O X C C T B OO P T C f O H A . I I b H b IqXJ C HOB, KOTOpbre I]pfltlio o6ecneqar troJ]'qeHue olleHol( B ueilTpaJbHr,ix
ToqKax. Aera"'ru 3Tofo Mero,la nplrao,larcn
caeuqr<uu u' lo.reelr
[48J.
flocro,rrny..Mbr uHTepecyeMcfl To,sbKooqeirrioir n qeurparluoit
TOTIKei<oportiol'r
n no,r)KHo 6nrl ecer.;.iar
Heq e r H b r Mq f i c , r o M .3_noc,leAoBare,rrbHocrr.r,
H a u i i t , K a K K B a A p a r H q H a gT, a K I r X y 6 a u n a n x p n nue 6yayr uMelb oAHo H To >xe 3t{aqeHre B r{eHTpaJirrltou.rr,r.{xe.
f l p r r 3 T o M g r t o 6 0 N 1H 3 s T H XC . ' r y q a e B
6 y a e r r r c r o . l b 3 o B a H o0 A H Or r r o
)Ke MHO)r{eCTBO
BeCOB.3rO eepHo H f.lrr KpriBbrxqerBeprofo tr rfiroro noprAKa. KoHevHo, ec,rruK AaHHbrMnoAorsart .eaHeiinyrocbvHr<I{uIo, To sHaqeHIteB I{eHTpa"rbHor?
ro.{Ke 6y;1er npocro cpeaurril roqEK B CCIMCUTC. 3TO
TaN rar MHox(ecrBo qr'teHoB cttMr,ierpuqHo orHocuTeJlbHo ueHTpaJIbHOrO I{,'IeHa' pe3yr'lbTaT OAI4HaI{OB'eCJII Ml,l [pI'lMeHiIM MeIOA CI{OiIb3rru{efo cpe.f,llefo, I(oropoe ecTb IIpocTo cKo"lb3flIqee KpoccflpcusBerl.leHoB II Bpe],leHHblM pflAoM, Ae,IISHHblNi
Leriile MeI'KJV \iHo)KecTBONI
B
o
3
M
o l K t t o , 6 o . l l t r r g 3 H a l i o M r e o . r o r a N r rt I o A H a n
p
o
u
,
e
c
c
,
3
r
o
r
)
o
.
Ha
3 B a H i l e M o p e r , t e u H 6 i - r r p e l t J . - r t t a . r t t 3 t l. C p e . l l r . v p a n u e u l r i t , I I c t l c J I b 3 y IIIeunapetrrrrx A"rrfl )rria3ar{FIbrxBblue IleJeti, nlttt.t,leHulrii
su,rlrp
KaI( cIioJb3fluree cpelHee Ir
o6ttuuo gantlcusaelttiit
aa-To.q4u,
BHAC
?,:+ir7yt+l!1)',,
,JO
cpelrrerO LUettE C , ' t uc l t a n u I I T b B e C a y p a B H e H L I f l c K o J I b 3 f f r q e f O
qJIeHaMIl,[pIIBeAeHilapAa c oitrofoHa.rlbl'lbIMllno,rl.{HoMIla,'IbHbiMIl
i r b r M l rB r a 6 r . 4 . 3 0 , T o M b I y B I I J . H M , q r o 3 T o I l p o c r o l < B a A p a r n o e
vpaBr{eHlre,HaTflHyTOeMeTOAOM HaI'lMeHbuI4xKBaApaToBHa flflTb
e o BpeT o q e K . , [ , p y r n e c r , r t a x { t t B a l o u t t ey p a B H e H H t , I l c f l o " { b 3 y e M b l B
uess6r.r ipeu4-aua,rrr3e, TaK)Kelu6o LiAesrI{qHbI,.nu6o oqeHa Hano3ru cr"l axuB alourueQyHf gl'1.lr
Mi{Ha lor op rof oHa,IIbHbIeMHofoq,rIeHbI.
orrricaubr B K,xaccr{qecxofipa6ore Vlirrexepolt It Po6uscoHou [60] '
O
cfJraltiriBaglrs BpeMer{HOf
FIa pnc. 4.60 npe.lcraB,'reHbrpe3yJrbTaTbr
pflAa KaporalKa cKBaxilH c rloMolrlblo pa3rHqHbIX ypaBHeHnii. CottTO3TIi $yHXUttU CKO,'Ib3fIIerOCpeAHerOqBJ'iflBCeM,He OqeBI,1AHO,
rcrcn SrtnurpaMII, Li"rtIrltro rlpoqecc cKo,'lb3tlurefo cpeAHero MareTa6nntra 4.30
B e c o B b l eQ y u x q t t t t A J I f l a n n p o x c u M a q u l l
Op'rorona,ruuue noflttnoMHaJtbHble
(crraxrxeauun). OyHxqrl npcMo Aaer olIeHKy cpeAHero 3HaqeHl{fl
rlHcJto or 5 1o 17 [481
n-HeqerHoe
B noc,ler.oBareJlbHocrn Il3 t roqex, r\e
l{BaAparncHbIe
5
TIOP'AKOB
KPIIBbIX
2 U 3,
a raKx(e AJrfl[oprAKos 4 N 5.
,[,"na euuonHeHl4flcf,rra]KuBaHr.rfl
c Ircro,tb3oBaHreMoprofoHa,,IbHbrx MHoroqJ{eHoB
Mbr [pocro cBepHeMAaHHy]O[OC,']e!,OBare.rbr{ccrb
qJIeHoBIl 3areM pa3AeJ'IrrM
c MHoxecrBoM noJIuHoMI.Ia,'IbHbIX
pe3y.rjbT a T H a c y M M y q J r e H o BT, . e .
c : Bra [r'i]
H fiy6HqHble
11
I
13
Llreribt
qneHLI
15
17
n
qcrBaproro
7
9
Ii ngroro
ll
13
Ii0pt.,1r(oF
15
17
-36 -u
-78 -21
-13 -6
90
449
427
69 16 87 18
loo
oa
84 21
89 24 t47 34
84 25 162 39
1 4 69 24 1 6 7 4 2
ol
4 4 2 1 162 43
t47 42
916
-36
I 122 39
0 87 34
-l I
42 27
-13
t8
-78
7
-6
-21
3 K B I , I B A , I I C H T H O B L , I C K A 3 b I B A H T I I O ,T I T O B C C q J C H b I
TNfl
7
-3 -2 -21
t2314
t7639
12754
-3659
354
.nltrrcfiuorooproroua,IIbHoro MHofort,rtellapanuu l.
T a 6 . i r u q a4 . 3 0 o r p a x t e r ' 3 ; t o l K e H H o € B b r n e ; o n a A a e r o p r o r o _
HaJrbHbre
no,'tr]HoMnar'tbHble
BecoBbteQynxquu (D A,rrflHeqerHofo {juc_
JIA TOqCK B IOCJIEAOBATCJIbHOCT]i
r;-,)J.
i,,yi r)-3irii,:
Xio
5 15 18 110 2t4!t 195
-30 -55 -45 - 198-2850 - 195
75 30-10 -160 -2937 -260
1 3 1 1 3 5 6 0 11 0 t c s l t 7
75 175 120 390 3755 135
-30 135 143 600 7500 415
oao
5 30 120 677 10125 660
-55 60 600 I 1053 825
l5 -10 390 10125 883
-45 I r0 7500 825
1 8- 1 6 0 3 7 5 5 6 6 0
-198 -165 415
r10 -2537 135
-2850 - I 17
2t45 -260
_ 195
195
35 2t 231 429 143 1105 323 )ro 231 429 429 2131 46189 4i99
X rtl
304
20-201
305
N I A T I , I I I C C K I .3{ K I ] H B A J C H T E H C B C P T K C A I ] Y X B E I { T O P O B , O , q H A K O O H I . I T I O J I .
3iiBllBa.IIeHTHbI, t{To
"rlefKo AoKa3aTb, LICIo"tb3vfl rIIIC"rleHHbtIi
flpu h{cl), pacc\{oTpeHHr,riiBbrrle. Heo6xoJIl.ro npeA,ocTepeqbqr{TaTeJlfr'. AJrv.TOfO r{TO6brricrroJrb30Barb t!lr.rrr.p, Har?4euulrri NicroAo}r
H a t i M e t l b r u r r xx B a A p a T o B , I ( a K B 3 B e n e H H O e C K 0 , r t b 3 f l U I ec ep e A H e e ,
a i l c l i a i i u e r i o r o p u i i B e K T O pB c B e p ' f r i e ,u e o 6 x o A r r l r oo 6 p a r l r r l n o Ilrr'Iori 3.ii3Nrer{ToB$rr.rrlrpa. 3ro suaqr.rr, qro nepauil 3.rreMeHT
Qttnupa craHoBHTctrIIoc.xe;iHrilr q.telo\.1 ctio.rtb3flirler.o
cilcAHero,
q,rreFroi{u 1'ar.rAo rex nol), rroKa [ocJIeAeropofi- fipe.qflocJ]e.r,Hri\{
uriii a"rrerveurHe craHer UeilBbtN{rr,TeHotlB rJbipaiKeIIIilictio.xb3riiliero cpeAHero.
T a r x a x Q u , r l r p r , i c r i ] i , \ t e r p H q r r r rri,,o c o B e p u e H H oH e o q e ' H A H o ,
qro nopflAori g,rreMeHTon
e 60JluuHcrBe cKo"rrF,srurl4x
cpe4uux 6u.n
u 3 1 l e H e HH a n p _ o r l r B o n o r o x u u f i , r . e . f ; 1 r . : f r _ j . B r e o Q n e H u e c r r r x
i l D I { M C H C HL If i X 6 O , T I U I { H C T U O
QIINITP OB'
B J T fIl O T C '
ol
ll
nl
-jl
ctl
NI
...0 0 0 2 1 0 0...,
4,,
€-
--
-"1
<1.
=->"
/
-)
{
\
,'t'
'.--..,>-
1
a'
2
{.
)
r-=--z
)
-)
(
<l
t
-;:=*
Psc.4.60. Pe:-y,rsrartt crraxti.rBalrits roc,teiloBare'lbHocrlI 3llaqeHlrii xapora;ttuoil
r u a r p a M r . r b r B c r i B a l K H H ec n o M o u l b n p a 3 J r r L r H b l x1 ' p a e u e t l u i r [ 2 6 , p u c . 4 . 2 ] :
d -- ricxoxlllir
A C H M M E T P I I T I H b I MI , I
a o6pauieurre co6creel{Hofo nopflAKa 3,1er{eHToB A,rrflIicno,,rb3oBaHItfl B CKO/'Ib3fiqeMCpeAHeMOKa3bIBaeTCf,
KpI.tTItqecKI.IM.
Mlr
ceiiqac rrpH.MeiluN{AByx3.rreMerrruufi acHMMerpHrtecxnrt
.
rf u rr p, BbirrirLr,rreHH
r,rft nepnoHauaJrbHol.rrr BpeMeHu6ro p r4a
"r
_->
>
I{ocTbIo
.{aHHrrie:6-d
-
quc,ro qreuoe:
i
(tr); 9
(a), Ii
\-],. l7
te,
eroii Qyunurn IIa 3To\,rIIHTepna.re6yAer 6"rusxa I{ Hy"llo. 6o'[ulrran
IIO"lOx{UTe"rlbH2f II.r'ltl OIpHIIaTe"rIbHafl IlpOll3BOAHafl
yKa3blBaeT
Hit
c x a r r o r (r r 3 N { e H e H rHr fal K , r r o H aB,o 3 l r o } K H oo, 6 g : a u g u t t t c K a q K y c p e A H e io
3HaLleHIrfl IiJil
H a , T I U r l l i r cO C T p O f O n t { r i a .
O p r o r o u a , r o H b r eM H o l c q , r e i r b r , t . a r i xri e
\ { o r V T6 i , i r o n o e o 6 D a 3 o B abHI
T a K , q T o 6 i , rA a r b A p l r f o r i n o . l e : u l r r j T i l n B b r x o A a$ u , t a r p a . X o p o u r o
ti3BecreH cnocoS BbtqucJleHrsinepuorl npoLi3BoAHoi.r
no,rllrror.lnalru o i i K p H B o t i .f l e p n a n n p o r 4 - ? B o A H a fMl o x i e r p a c c M a r p x B a r b c q K a K
Mepa u3tyleHelillgIIaKJoHaro.lt-ittjteltoii ntigtll Hd'tr.r
cKopocTb fi3MeIreHufl 3HaqeHufi I/. Ec,rra I yne,urruneaercr H,'rHyMeHbruaercr{BHyrpli HHTepBaJra
c npuMepHo frocTofllruoftcxopocTbro,To npou3BoArlat
E c " r n r o l r o u f l e M a r K p l r B a r o n p e A e " r e H ao p r o r o H a J l b H b l Mt t l t o r o r r J e l r o N ,Tr o
, n p o f i 3 B o ; l H a qM o x { e r 6 b l r b B b l p a x e H a l l e p e 3 O p r o f o H a , ' l b Hbreq,teHbr.Tar xax Hac [HTepecyeTTo,'IbI{oBblqlicr'leHnenpoll3BoATo iIoJIllToqKe ItHTepBa"IIa,
lroli nollfoHseuoii "rrilililHB I{€HTpar'IbHoii
H O M r r a , ' r b H yopea B H e H E eM o x e r 6 u r n n e p e n H c a H o r a K , r l r o 6 b l n p f l M oA a r b 3 H a r r e u r r e
n p o r . r 3 B o , r , H o3rrio. r n p o q e c c o n r l c a H C a s u u K I r [ l u
forreert [48J, xoropble Aalor raK]tie ra6,rrliubrA.irr Haxox{.l,eHrtflnepoDToroHa"rIbHbrx\4uororlreHoe. Ta6,1.
Borl rr Bbrcruux IIDoH3tso.IlHbrx
-1.31 co4epx<lr q,'ieHbrA"rs HaxbxAeHnfl repBoft [polr3BoAHoii, nstrbre il3 pa6oror[481.
Oneparop nporr3BoAHofiucno"rns,vercflB TorlHocrt{ KaK cr.rrax(t'tn a r c u u f i Q u n l r p B A B y x c d ' I y q a r x : r t t 6 o r p l t c B e p r b t B a H I r ut r p o t ' t 3 BoAHbrxq,reHoB c ucxoAgori noc.rreJoBareirbHocrblo AaHHHx, .[u6o
r u a r H a 6 o p B e c o BB c K o r ' r b 3 f l l r . ecMp e A I I e M ., r l r o 6 o i i u 3 s T r l x n p o q e c c o B A a e r o T K , r r u KK, o r o p b r [ 3 K B u B a r e H T e H
noAfoHKenoJI]lHoMI{a.iIbIIpOllLlX KpuBblX K nOC"rreAOBaT€;'IbHblM
CeIMeHTaNIlI BblqHCr'leHIIiO
rr3BOAHbtx
rrolfoHfl eMbIXKpHBblx.
sleparopa npoll3M u u o x e l r y B u A e r b p e 3 y , ' r b r a rn p r r M e H e H r r o
ro4Hori K npou3BolrbHor?
cryneuqarofi QyHxquu, npercraBr'IesHoiiua
p u c . 4 . 6 1 . K p y r o f i y r o " r r M e x { A yr B y M f l c e r M e H r a v l l B p e } r e i l H o r op f l . ] a B b r p a l h a e T c rKr a K I I H K B n p o n 3 B o A H o f in, t o B p e M f l K a K o c T a T o K
I l p e M e l l H o r op f l A a H M e e TJ o K s r - l b H b ln€p O X 3 B O A H b ipea, B H b i eH - V . [ r c .
flo"rlrrour.raJbHbrecr,-ralKuBarorrr4eQu,rlrprr Moryr 6blrb HCn o , r r b 3 o B a HB
b r c o r { e r a H u uc Q r r , r r r p a u H 4 u Q Q e p e H r { r 4 p o B a H, uef c , ' l l i
rcxoAHbrii BpeMeHHorlpflA coAep)Kr.rrraK MHgro ou[6oK, rlro npou 3 n o A H b r ec r a H o B t r c f l H e H H r e p n p e r n p y e M b r M H
B. ra6t. 4.32 u na
p l c . 4 . 6 2 [ p r . r B e A e H b3rH a q e H f i r n o p ] r c r o c r u , H 3 M e p e H H o IBi H e Q r r -
306
20*
rJ
_KCTopoM
qltrareJrb !'refKo Mo)Ker y3r{arb BoJ'rHoByIo
Qoprrry
pt,tc.
4.59, nnoxeHHVroB rroc.ireroBare,rbirocrb
HyJreft.ecna iroilaior{ Koe$$uqrreuronQn.rrrpa o6parurr rr r.{cfio,'rb3oBarb
B KaqecrBetsecoB
B cKo.ub3flille]!
cpeAHeM,
ro pe3yJrbrar6yAer raxofi:
n
n
1,+286
0 ...
3lo n ror{Hoclir ror x(e i)e3j'..iLTar,
H e H i . t e \ ,or n e p a u H l t c B e p T r i t r .
ybt
I l o , r t v r tr t . l H I I p i l M e -
ilpaa:no4uue
307
Ta6na(a 4.Bl
_ Opronona,rarbrenoJrnHoMnaJlbHbte
Syurqun Aas nepnofi npofiseo;ruofi.
oynxqun npflM-oAaer oueHKynep"ofi-nporiroanon J
d";;;;;;?;il.
noJlHHoMr'raJrbHoft
xpunofi, no.qnonneruofi
n tt roqxax MeroAoMHaIlMeHbIrrHX
KBaAparoB,rLe n - HeqeTHOe
qr{cJrooT b nO l?
rlpoH3BOAHat
KDaapaTHcHoro
t1
I
;i
1l---
MnoroqreHa
ll
{' n
Pr
0,8l0,6l0,4l.
0,2r
u- --
ID
17
lo
6L
-2
-3
-4
-5
-l
-2
-3
_+
0-l-2_3_4_5
l0-l-2_3_+
2t0_t_2_3
2t0_l_2
3210_t
3210
4321
432
543
_6
_5
_7
_6
-4
-3
o
Ilpoueao4Hal
60
ry6u.{Horo
I
-8
0
X
-l
I lopuaJ'lH3yro-
uluii u,'reH
t2
182
ll0
I
22
86
-67
-t42
-58
-193
0 -126
580
67
125
-22
193
r42
-86
252
I l8B
tI
t3
300
-294
-532
-503
-296
0
296
503
lt32
294
-300
I 133
-660
-1578
-t796
-1489
-832
0
832
1489
1796
t578
660
--l 133
5118
o
o
J
}rnoroqJreHa q MHofoqresa qe.TBeprofi crercHs
7
S
0
I
2
6
7
l0
iilrHrrq
P u c . 4 . 6 1 . C r y n e r r , r a r a ac l r y n r u u r ,c o c r o r u r a f l I r 3 n o c , t e . f o B a r e n r u o c r e A
cryneuuaroiiQyur<ri rpoeK (a). fpailuuecroe lr-;o6paxeHne
nepeoirnporr3BoitHoir
na ocrtl'B! r,rrrrrr.lerrrroii
xnalpariruHoii no,IirHoyr{a"rrbHorl
an{urr, Bb)glrcal0Hsol'r
npoxculraqnu(6)
a
-t
54
65
i(D.
-8
-7
-6
l5
o
*
5
6
7
8
408
c
[,ig]
t7
12922
748
_4121
-98
_ 1 4 1 5 0 -613
_ 1 8 3 3 2 -930
_t7842 - 1 0 0 2
_ 1 3 8 4 3 -902
_7506
-673
-358
0
750G
0
13843
358
17842
673
18332
902
14150 1002
4t2l
930
_12922
643
98
-748
2 4 0 2 + 3 3 4 1 5 2 23256
6
G
s
E,
tlllllll
oa
r5101520
HoMep
ln
??
cKBahtrtHbl
PIrc.4.62. I4:r'repeuuanopltcrocrr,r.
10 $yroe (3 u) n
cle.laHrrbrec nHrepBa,'IoM
cKBariurre,upo6ypeHHoft
cnno:s uc{rrruori pe:epayap Ha apKri{qecxouno6epexte
AJrrcxn:
a -
n e o 6 p a 6 o r a H H b r e, r a H r r b l e t 6 -
n e p a a x n p o u 3 B o r r , u a rH e o 6 p a 6 o r a H u r t x A a H ( H X
Hoir cKBalKHHe.Ha pnc. 4.62 Tax)t{e [peAcraB,reHbl HX rlepBble npoLI3BOAHbTe
lrr'rl.l,CKOpee,nepBble npoH3BoAHbleKBaApaTHqHbIX
QyHKqHft, noAorHaHHbIxK noc,'teAoBareJlbHblM
MHolKecrBaMil3 nffTIr roqeK. I43MepeHuflnopgcrocrtr o6JIaAaIor 6onntnofi I'I3MeHr{LBocrbIo,
q a c T H g H o l I 3 - 3 a H 3 M e H q I . { B O C T I I3 K c n e p l J M e H T a J I b H b I X A a H H b I X ' I { O T a K '
MAJ'ICHbKI'IX O6bCMOB
XC B CHJIY TOTO' IITO I{CNOJIb3OBAHI,{C OqCHb
' on p o 6 n p u n o A u r K H e n p e A c r a B u r e , r b u oB
i l b I 6 o p K eI ' I 3p e 3 e p B y a p a X
309
r_
I
' Il
Ta6anua 4.32
3laqeulr-c nopncrocru (" o/o),
3 l r e p e n H b l eB n p o A y K r a B H o M cloe aeQrnnoii
c K B a x r , r H b r ,n p t 6 y p e H u o f_i xH
a a p K T l . t q e c K o nnl o 6 " p e * o " A,nscxl,r.
Ilpo6u errru c uHrepna.torn n J u
(Bepx)
1 13,2
2 t2,6
3 14,3
4 16,2
5 t5,2
6 14,1
7 n,2
8 15,3
I 6,7
IO I 2 , 8
n 14,2
l2 16,3
r3 r5,4
l4 14,0
l5 15,0
t6 23,2
l7 18,9
1 82 2 , 5
l 9 2 r, 6
20 23,2
2122,8
2 2 2 1, 7
23 20,0
2423,4
lt
2 - ,2t l . 2
2 62 t, 7
27 23,0
2822,1
29 22,4
302l,8
3l 19,8
32 24.7
rpu.rilrpaqurr c Arcltepcrreli noc"rye $u,rlrpaulru.
Heo6xoAlMbte
\lrrr i{BaApaToB Anfi BL,rqrrc.Ter{I,Ifl
AlictlepcI'lH TalioBbt:
;{.Tfl l.{cxo,1;{oro Bl)e\reHHofo pffAa
cvN{-
Sio =-:l''-;(It'',
S S n o ' -X Y ' - - 1 - 1 \ ) ' ' ' ,
"
AJrtIpflAa, Ilpouelluefu
OCTATKTI.
H a p r r c ' ' 1 6 3 [ p e ; I C T a B ' x e H rl r 3
r Mepe'rfl noprrcrocrr roc.1e
.
cf,!:i"i
ilvrBa
Hlr.Bnnrnq"regHbr\{ KBarp aruqHir Hr
xo.o
orr"or"
Su.rlipou,
B n o p u c r o c r r r M e l K . t ) -a e p x u e f i l r s r x i H e f i q a c i . q l ' r
p e r e p n . _ r p ac o xpaHflroTcfl,60'rlurrre
or rorrKrr K Toqrie norauarorcff.
$;rfKTla[r[r
E c n r t u e o 6 p a 6 o r a s s u r eA a H l r b r e
4elicrcure.lrro cocraB,reHbl KaK
cMecb <<rcrrrHHbrx>>
''oplrcrocreri co c.ryuar?aurlrn oau6i*orn,
To
f ' T a A K a f l a n n p o K c r ' r M a r l HN
f roxer '1aeart 60.lee
o"rusxl,Lo-i 4eficrB U T e d I b H O CrTi af lp T r r r { yu 3 M e H e H t r gn o p u c T o c T r r q
, eM HCXOAHbTe
AaHnDlcf l e p n a r n p - o r r 3 B o A H acf fl , r a x e ' H b r x
A a H H b r \ T aK ) r i e l r p e l r r a B . r r e Ha Ha puc. 4.63. feHoe H3MeHeHiie-_[opucrocrrr
r { e x A y n p o 6 a n r u rc
H o M e p a M r rI r r l 6 f f c H o r r o r { a 3 a s o .
K a x ' u c . r r e , l o B a , r oo x r . r A a r b ,B C e
npoH3BoxHbreocrarrio_Bcr"raNeuHor?xprreot?
6.rusxrr * ny,fr
leoSu:uxu ycralraBJuBaror xa.reciBo
eir,rbrpa, rrcc.rervHr{ac_
rorsnir cneKrp ,ro H rroc.ne
Srrrr_rpauur,. ur'*.ii.rir;; ;;;;_;e
yria3 b r B a l o rH a r o , x a x
Q i l " l t r p g e r i c r n l , e r , f i H a r o , H a c K o " l b r i oB b r c o _
rail eQ$exr oH ,1aer. i\{r,r'r,rox;ern
u ,o - o n n , , r l n p o c r o r l a r r a n r r s ' a
I i a q e c T B ot p r r , r n r p a ,c p a B H r r B a r r
A r r c n e p u . l r c B p e N r e r i H o r ol l f l . l l ] A o
rr*
tlePe3
$rt.tr'lp
ssr: :i'- -lrrfl',
n
(Ocuonauae)
rn rpaQrrn repnofi rrpousBoAlroii rc'o
r r o ^ a 3 r , l B a e rM a . c r i r l a , / r b H o e
r'r3ivielreHu
, .eo p r r c r o c r r rn o 6 p a : { e c H o } l e p o r f r o , o r u n o x u . ' B
rrcx0.L_
HbIX
A A H H b I X T A K J . I ( EO X A 3 b I I ] A } O T B . I ] i I g H I I E H A
l
l;rt ort<;tctiruufi
s s' n, :* - - ] _ ; q y - i ; ' .
I l l ) i i 6 , ' I t l x i e l l i i o e I I p O U e i { T I { O e O T I I O l u e H t l c ' C V N T MI i u a ] { p a T O B I l N l e e T
s u r ( S S r / S S i - { ' ) 1 0 0 % . B e r n x p a B e H C r B a . \B c e c y M M H p o B a H u qn p o H"[l{
BCjlflTCfl IrO 12 nallHbINI TOqlia\I llcxo.l.Hou IIOCJIeAORaTe'lbHOcTI{
B qactuocra, orNlerro roql{aM cr",rar*ieHHorl noc.reAoBare.rbllocrtt.
TTIN{,IITO BI,IqIICJ'IOTCfl IBA 3HAqEHiJ' I,'Ifl CYMMbI KBAAPATOB TIEP.
BoHarla,irbHbrx AaHHblx. lleDsas lr3 IIHx vr{ttrblBaer Bce roqKll AaHuofi ncc,reAoBare,'rbHocru or l:1
Ao n, BTopafl BK,'lrcqaer ro.lbl(o re
Ha6.rrrcAeHrfl,, Ailn Koropblx Bblqltcilfllorcr oIt,eHKI.II;. Taxulr o6pa3oM, u3-3a IIoTeDIJ .r,aHHblx I{a KoHIlax cr.latxeguoii nocJe.loRare.rtr'. Xorn B sToM cJlyqae, KaK lI B perHocrli rJbI H\ieeM n*-n-(tn-l)
peccucHHoM aHaJIu3e, MoiKHo 6u;lo 6u oxitt,q,arb Bbtno.rlHeHIIn pa'
T E M H C \ I E I I C C C I O H E T B M E T O A CC K O J I b B C H C T B AS S o * : 5 5 ' A S S . 1 ,
3qulero cpeAnero. 3ro nlloucxoAlIT Ilo roti nptlunt{e, qro BbIIlfic.[eHne oueHoK Yi s6nwsv, KoHtloB nocJleAoBare.nbHocrt{ AaHHbIX orqacT I , I o c H o B a H o I { a H c [ o " ' r b 3 o B a H H I Ig H a . I e H l t f i , r r e B f o . r f l l r l t t Y B B b l r t H c cyMM
olHouleltt{fi
Jleuue SSo*. I-IoaroM.v 3HaqeHl4e fiportetlrHofo
KBarl,paToB fBJ'IfeTcfl rrpil(l,uurt<euHLI\{, li{) efo l\4ox(Ho t{cIIO.lt3OBa'fb
Kar( [r,l{a3arc"rl eQQerirltBllocrtt rtpoltecca @u.llritaqrrti.
A HAJI H3 B3AI,IMO3AM E H g EMOCTII
,5
10
1
P,oc'4'63' Cr'taxeHulre SHaqeHrrf
toprcroc*
a-AaHHbte,
310
crJIaxeHHble
s
10 rs
zo zS--lo-ls
rr3 ap^ruqecKoircu.eaxirrru:
c noMorqbto nsrrqJeHHoto
KBa,ap,aTfiqHoro MHoroqneHa;6_rrepeaa
nPoH3BOAHar cfraxeHHbtx
!agBbtx
H a p a c . 4 . 6 4 n p e 4 c l a B , I I e Hr l t r l o r e r r . { q e c x t t fct r p a r u r p a @ n u e c x r r i ' r
p 33pe:i c 3 a lioJ,ilpoBaliHcil noc"leJoBareJ'lbHocrblop a3JIuqHbIxJIHTOIOpOA. EC,rU BbI IICC,TeAVeTe3aKOAH.rrofl]riecKrrlrpa3HoBI4AHOCTeft
poBaHHyro IIoc,'teAoBare.rbHocrb,To 3aMerHTe, .qro B Heft- qacro
3ro uau A-D*C.
r r* B - C
B c T p e q a r o r c r n o c J l e r , o B a r e , l b H o c rA
Bo-rlr Ha Nibrc,'ibo roN,r.qro cocrottHttfl B n D KaK-To cBfi3aHblIi
oJIHo Moxer 6lrll 3aMeI{eHo,cpyful"'tn npeg,,laraeuofi noc,'IeAoBare.lbnocrrr. 3ro ceoricrBo AByx u,rlr 6o,ree cocrogHttft Bcrpel{arbct B
O,lHONl II TONI Xie OKl)\')lieHnli
Ha3blBaeTCtl
83aHMO3aMeHtleMOCTbIO'
Jl
I
r1 ricc.rreAoBaHrreSTO|OrB,IIeHHg6nA3Ko
r ( B b t r r B J r e H r irtpoy n I I c o c T o r H u r i ,3' a p a H e e
Ire oqeBlltrHbrx. Taxue LIcCJleloBaHtrt
npIIMeliflJIlCb B pa3JrrqHLIX 06.[aCTgx,
r i a l i , I r a I j ) r r M e p ,n l ) r r a H a , r l r . r 3qea c T e i i p e _
q i l i l a B T o M a T r . r 3 a u iIllH
pouecca doronDa_
4 ) u p o B a r r r r f[l4 6 ] . 3 r r r v e r o g u n f e a c r i a . t t f f I o T c fnl e p c l e K T I t B H b r M I ti l ! r f l r r c c J e _
A O B a H r r f le o r . t o t l q e c i { r i xA a H H b t x .
A n a . l ^ u s M a r p t r u b r n e p e x o i l H b r xB e p o -
B
t
I
I
lD
I
It .
r
C
D
r
I
lI c
flTHOCTCIIIIO:TBOJIflET
YCTAHOBI-JTb
ABC BCr]IIrirrHbI:83ailN{O3aIlerrfleMocTb IiepBoro
nopfl;lr{a cJreBa rr 83arrMo3aMeHrreMocTb
I
nepBofo nopflIria cIIpaBa. Srrl repr,rrrur,l
t^
l6
I l o 3 H u K , . I i rn p t J r r c c . l e A o B a H H i l H ' l f t I { c a H _
I
Hbrx TeKCTOB, B riOTOpbtx cocToqliltrl
le
L
nperlcTaB"leHbl C;lOB8Mti,a qTeHIIe OCyrrlecTB,r'rfleTcfl c,'IeBa HanpaBo. Ec.rttt sa
C
Karilriurr-.iril60 AByl{fl OTAe!'IbHOB3fiTbt}IlI
c"roBaNril nocrofHHo c.nellyeT OAHO fl TO
rie c.rloBo! To OHII MOfyT 6sItn gaueHe_
Hbr Apyf .a,pyfoM. 3ro qe,'reHne Ha3brBa€TCfl JI€BOii 83AI.IMO3AMCHqCMOCTbIO,
TAK
Kati c"rroBo, KoTopOe frIOX{eT 6ttro saN.{elI "
HCHO APYIHM
B NOCJIEAOBATEJ'IbHOCT}I.
pac[o,rafaeTcfl cJeBa. fIOCXO,rlxv crnaTHfpa0ilqecKae I]ocJleLoBaTe,lbHOCTkrqnI
I
TaroTcfl
cHu3y BBepr,
TO 6o,,ree yAo6_
ln
HLINI B STOM C,ryqae flBr'ifleTcfl TepMrrH
< < B 3 ayr or 3 a l t e H q e M o c T bc H H 3 y > . , \ i a f p r r u a
']CBOI? 83AI{MOsAMEHflEMOCTH
NOJIVqACTCfl
t^
il3 Marprrr{br nepexofHbrx BepoflrHocreri
l6
I
B pe3v.[bTaTe Bbrq]ic.leHrrfl oTHO[reHHft
rrporrsBe.letrrrI'r cTpori M aTpHrlbr.
flpe,qno.rroxuna, qro Mbr i.rMeex{ MaTPuc. 4.64. gacra qerr,rnpy- prJUy [epexoAHLIX BeporrrHocreir nopngqneHHori ..prt".pr6"uei,.,i
Ka mXnL, rle P;; - BepoflTHocTb noJryqeHI'ltl cOCTOtHHs ,4; nOC,{e
nocJIeAOBaTelbHOCTlI
BHIa
cOcTOsHrig
t^
l,
I
l'
!,.ril HaxoxAeIrIJs 3gaMeHarer'rflBo3BoAr{MB KBaApar Ka)KAbIftareN r e H rc r p o l { r I l s , c y M M I l p y e Mr i B a A p a r b rn o c r p o K a M , I I e p e M H o > K a etl c,vMNlbrr{ HaxoAL{M KBaAparHbrfixopeHr H3 sToro npoLI3BeAeHtiff. A.rIfl HaxoxjleHl,rfl r{uc,,'ILITed'IflHyx{Ho yMHo)xIlrb Ka)KAbIti
s-ft cTpoKu II
3.leNieHTr-ri crpoi{ti Ha cooTBeTcrnynuluft 3.rreMeHT
H a i i r r r c y N , r N r3yT I I X r r p o r t s B e A e H I r f i .O r u o r u e g H e A B y x n o , ' r y r i e H H b t x
l p o u 3 B e A e u u fui n u M e p a J r e B o f B
t 3a[MOB e J U q i l HH e c T b o T H O U e H T I e
3 a M e t r f l e r t o c T rl r . * . 3 a l t e t u u , r l T o e c . [ l I c T p o t { i l c H o M e p a M Hr r r s
l l A e l r T i l r t H b(tr : s ) , T o t I H c J l r r r e . rllIb 3 H a M e H a T e J Icbo B l a A a n T , H o T p a B H o 1 , 0 . l l o s r o u y M e p a B 3 a x M o 3 a M e H f l e M o c r tl{r 3 M e H f f Hourerrrre
l. TaN xar< 3HaqeHrfl
e r c s B r r p e A e J r a xo r 0 A o 1 , 0 , r . e . 0 ( 1 , " g ,
I(a)l(AOfO3,'IeMeHPij Haxo!,tlTct c noMOxIblOAe.IIeHII.g
BepOffTHOCTefi,
TO TOT
Ta CTpOI{IIMaTpIIUbI[epexoAHtlx qacroT Ha CyMMy CTpOKI'I'
oTHo[IeHI]fl
>Ke pe3y,'IbTaTMOIKHOno.rryqllTbnpgMblN{BbIqItcd'leHI{eM
n p o r r 3 B e A e H r rci rl p o x M a r p t r l l b tn e p e x o A H b l xq a c r o r .
Koueqnuii pe3yJ'rbrar Bblqltc,'reHllti, npoBoAHMbIXco crpoKaMII
MATprllrbI lepexo.q.HbixBepoflTHocreft
, - [o,'Iy'IeHIIe cHurr,terpiauHoti
M a r p l l u b l o r H o u e H l l f i [ p o l l 3 B e - q e H u f 'i [. , l t a r o u a , r I b I I L I3e. r l e M e H T bKI 'o HeqHo,6yAyr paBHbI 1,0. flpyrrre 3,'IeMeHrbIxapa.KrepH3yforcrefleHb
c x o A C T B aM e ) K A yn a p a M u p a 3 , I x t l H b l xc o c r o t H l l H , o c H o B a H H y I o H a
npoueHrHorr oTHoiueHu[ qHce"r],xapaKTepH3y]oulix [opflAoK cJIeAoB a H U f l r e K o r o p o r or p e r b e f o c o c r o f l H l t f 3 a A a H H o l in a p o i i c o c r o f H l 4 f t .
Marpuqu ilepexoAHbrxqacror u BepoffTgocrefi AJIfl no.rlgofi noc . t e A o B a r e J r b H o c r trr,,r 3x o r o p o i i n s l T t r s o 6 p a ) K e H H b I i tH a p T c . 4 . 6 4
,\'rracToK, r{Melor cJreAyrculHfiBLIA
Cvurra no
cTpoxa \r
ABCD
L
k
I
,4 l- 0 ll 210-l
3l
Bl1013
6 0 9l
clt4
Dl_ 4 315 0_l
t
A-->B+C n A+D+C
Ar. OruoueHr.rerporriBeAeHlrft,ofipeAe-
lTeByto
,r'lfltoulee
AByX COCT0SHHft,
cKa)r(eMA r V I A s p a B H O
83atIM03aMeHfeMocTb
ltla rpu4a treDexoAHbtx BepoflTHocreil
(Anr trepexoAoB cilrr3-v BBepx)
A4r'rDHqa nerrexoAHbtx !rr ('Tor
CyMMa no
crp oKl 1I
ABCD
23
20
29
22
l - 0 , 0 0 0 , 4 80 , 0 90 , 4 3 - l
| 0 , 2 00 , 0 00 , 6 50 , 1 5 |
| 0 , 4 80 , 2 10 , 0 00 , 3 1 I
l - o , t s o , 1 40 , 6 80 , 0 0- l
n
B
c
D
,00
,00
,00
,00
u H B
A { e p a , r e e o i l e s a u [ 4 o s a M e H t t e M o c r rM
t exiAy cocroflFIHflMA
B bII{H C,I'IETC f
KAK OTHOIICHI,IC IIPO IT3BCACHI,Ift CJICAYIOU].UX CTPOK:
I
I
B
[0,00
[0,20
0,48
0, 0 0
0,09
0,6s
0,431
0,lsl
B r , r q r r c , r s 3q r o 3 H a q e H I Jneo Q o p M y r e ( 4 . 1 1 4 ) , n o " l y u a e ML A B :
:0,27, qro Aaer Ha\{ 3.rreMeFlTbt
Lp Lr L21 MaTprlllblMep ,'IeBofiB3aH\ , l O 3 A N T E H f i E M O C T I , IA. H A . T I O f I I q H b I I \ { O 6 P A S O U H A X O A S T C f l C C O C T A , ' I b H I T I E
3.re i\,rei rr r,r. lI o.ns a s Mar p Hu a rrMeer c JreAy Iouln ii BHA:
t_
(4.114)
i,'?,i'3,
i=l
312
i=l
l- 1,00
| 0,27
I
l-
o,oo
0.25
0,27
I ,00
0,34
0 ,lt6
0,60
0,34
r,00
0.27
0,25 -l
0,96 |
0,27 |
I ,00 -l
313
B l t c o x a q B 3 a H N , r oM
3a
e H fel N { o c r bc B e p x y n o x a 3 b l B a e r ,r t r o c y u l , e c r B y er cH"IlbllagreHileHu,HqI{ noflBileHlrtooAHofo H Toro )xe cocrofHrifi
BCJIEA 3A NBY'\4'
.N.pyfliMI-I coCToflHIJflMH,
T. e. oHII
IIoflB,I'{I0TCfl
\ I 0 3 A N , I C I I ' J C M O C T XH M C C T I } U N .
B
;.it
i.:il
*:?
ftif;
o J r r r a K o B o r uo K p y x { e H r ' r r H
r . u g x a s 8 3 a H M O 3 a \ 4 e H f e M o c cr bH l i s y , H a o 6 o p o r , [ o r ( a 3 i - ] B a e r ,r I T OB c d t e A3 a A B y M f l c o c r o r r H l r f l M H
flogBd,rsrorc a p a 3 n H q H L , rceo c T o f l H H g .
M a r p r r q a v e p n p a e o l i B 3 a u r , i 0 3 a M e H s e M o c(rl iri. r r rs : a u u o 3 i ) r r e Hfl CI,IOCTH CAEPXY)
}IAXO!IiTCfl
C TIOMOUIbIO BbIII]4CJCHII'I OTHOIIJE}I]If
n D o n 3 B e r ' l . e H UCi rr o " l 6 q o B M a r p u r r b r n e p e x o A H b r x B e p o f lT H o c r e l i ( c a e p -ry nHus), Koropbre B cBolo oqepe:Ib HaxoAflTCfl c rroillorrlblo
.4eJ,reilrrfi
liax<Aofo 3.'le\lellTa MaTpiltlbr nepexo,lHblx rIacToT Ha cvMMV
S J I Cile H _
T O B C O O T B e r c T B y r o u eof c r o . ; r 6 I { a . 3 T a r , r a T p r r u ae e p o n r H o c r " e i l
coaep; l { } l r o r H o c i l T e J l b H b r er r A c r o r b r , c K o r o p b l M l t a n 6 P a H H o e c o c r o r H i r e
ffB"'lflercfl ltl)eAlllecrBylourrM H,rrrl noc.relyroultiu
Co_
n.ts r]pyfofo
croflHlr,q. Marplrqa B Toru{ocru raiiaq irie, KaK rvu ltorru- 6n
no,rvrilrrb' ecJlri 6u nprrra"lir rioHeq
Aairuofi loc,lreAoBare.lbHocrH 3a Haq a ' 1 o ' B b l r l H c " r I I { J IB
He p o f i T H o c r l r n e p e x o A o B c B e p x y B H H 3 H s a r e N I
ruarplruy repexoAHbr
x Bepoff
rHocreii.Marplrua neperolu brx BeporrrHocreiicBepxyBHr3yria3aHaHu)Ke.
{
,1
dl
t
M,-r rLrrrur
AlBl
cl
Dt_
Cyuurr no
crol6uau
trepexortHbt-\
AB
0 ll
40
l,+ 6
Aa
,Uarpuua nepexoAgbrx neponrnocrefi
{lJr nepexoroB cBepxy BHH3)
":'";
ABCD
2 l0-l
13 3 |
0 el
rs o_l
22 20 30 22
A
lB
I
c
|
D
l_
C y n r r ul o
cro"r6uau
0,00
0.18
0,64
0,18
1,00
0,55
0,00
0,30
0.15
I,00
0,07
(r,43
0,00
0.50
1,00
( ) . 4 5_ r
0 .t 4 |
o . qI I
o,oo_l
1,00
B n r o 6 o l t c r ' r y q a e ,r r M e e MJ ' I r r\ , r b rA e J o c o c r p o K a M l r u n r t
cro,n6uaMII, BCe a.rreMeHTbr
crl)oKlr l.r,qlrcro,ri6ua J.e,1flTcflHa cyMMy 9..rle_
MeHToBeroii crpoxu r.ul cro,ti6qa, npr{qeM sTH cyMML,r
coKpau{aIorcfl rrpi{.Bbtqric.leHtrriorHorrleHrrflnpou3BeAeirnftlrex<r1y
crpoxa Mr
il.'ru cron6uarnIlr.llosroMy ror xe pesyrmar noJryqaercr,
ecJrHnpol r 3 B e c r ns r r i o f l e p a r l r H n p r M o c u a r p n u e f r n e p e x o 4 u u r xq a c r o o .
Ir[ep a n p a n o f i 8 3 a r r M o 3 a M e H r e M o c r l rc o c r o n H r i i i A
u B uo,u"ar""r.o
i(ari ornoueHtie irpoi.r3BeAeHtri
Anyx cro"r6uoe:
AB
Is:?3I-:f:;;]
| 0,64l**
| o,so
I o,18l--._lo,rs
Mepa npaaofi esaul4osaMeHreN{ocru
paBHaRa.e:0,4g. flpyrrre
3JreMeHrbr
Haxo,{rrcfl aHa!'rofrrr{Ho.
lIo.THaqMarpr{qanpanoii uiair314
I
I 4 u r e p n p e r a q r r aa r o r i M a r p l r u b rr a K a f l x { e , K a K I I L i H r e p n p e r a l l l { x
oTr'rutqilecocToHTJII{lUb
xrarpirubl uep rrenoii B3alrNt03alvreHrreI,rocTt'l;
{ a o c t t o B a H l i HT e H A e H n T o \ { , ( i r o c x o A c r B o n H e f ry c r a H a B x t t B a e r c t H
LIr'II{lloullrr oj(HIIX Ir rex iKe coclosHufi 6utru npe.l.ruecrByloul.HMH
c.'reAyIoxIHMH.
H a x o u e u , M r , r l { o r i e r , r o f l p e A e " r t H T bM a r p l t q y M e p 8 3 a H M H o i ig a \ . r e H f l e M o c r rKl a K M a r p r l u y n p o u s e e . l . e u t r t tB c e x n a p s u a q e u u l ?u e p
l t n p a a o f i 8 3 a H N { o 3 a N I e H t t e M o cTr.IeI ,.
"resoii
Cii:
Li1Ri1
(4.1l5l
3 r a n , t e p ax a p a x r e p r r 3 y e r 6 " r t t s o c r bo A I I o f o c o c r o r H l l f l c A p y f l r N {
OTHOCHTeJIbHLIe qaCTOTbl' C l(OTOpbIlIlI sTIl COCTOflHI'1flIIoflB.IlfflOTCff B nocr'lelotsaTe,'lL'HOCTII, T. e. BXOAflT N{eX{Ay CXOAHbIMII COgneN{eHToB AByx I\IarxrHo}KecrBeHHLIx
crofllruiRN{rr. flporrsaerleHlre
I
,
I
N
I
C
C
T
B
I
{
N
,
B
3
A
I
,
t
M
0
3
A
M
C
H
f
E
M
O
C
T
I
t
NIIII
qepes
l-t ,oo o,l3
I o,l 3 l ,Oc
| 0,22 o,og
l_0,16 0,90
0,22 o,I 6-l
0,09 0,90|
l,o0 0,06|
(1,06 1,00_l
> p a p x r l q e c K o r op a 3 l l e u i e H l r f l .
Mlr lroxte,v nocrpourb <(AepeBo>
ue
i J i { o r c l ) o N ,}Ir r { a 3 a H bcr B f l 3 r i o A r r o f o c o c T o f l H u t c A p y f H M I { a o c H o B e
I r - \ 8 3 a u M H o i ie a r 4 e H s e N , t o c r u
r B r i o r o p o N { } t 3 y q a e N { b tceo c r o q H i l f
l)aciloJox(eHbr B rroDfl.l,Kerrx ualt6o,rrtulefi egattlto3aNleHtteN{ocrtl.
&lero;r.r.rnocrpoeHufl raKHX <<AepeBbeB>>
c rroMourbro3BM 6yayr
p a c c l { o l p e H r ) rB f . r r . 6 . T e n e p r i K e \ r b r o f p a H u q f r M c f lr 3 y r { e H u e Mp e 3 y " 1 b ' r ' , , l T fopBy n l i l p o B a l l r r r < < I e p e B a >N>r a T p [ u 8 3 a l , r M o 3 a M e H t e N , r o c T l , l ,
I l o c T l r o e H l r o f oA r ' t f l c r I a r u r p a ( r r r r r e c K o f o p a 3 p e 3 a , I I p e A C T a B " r e r ] H o f o
H a p r i c . ' 1 . 6 , 1T. a x u e r p r r < < A e p e B ar>r s>o 6 p a x < e H rl ,rra p H c . 4 . 6 5 . f l c n o ,
q r o B r r D r e u r o c B f l 3 a H bK
f l6 u r e r o l p e A u e c r B y r a r {c r o q K U 3 p e H r . r o
I0lqef(1,Tari r{ c TortKrt3peIIufl rrocJleAyloqeto cocToflHufl.
f l c R e r . r a u t r e c t {H e J a B H o n y 6 , n n x a q l n r , n o c B f u { e H H b r e a H a J I I I 3 y
B 3 a t l . \ l O 3 i l , \ , { e H f l e X { O C T I IB f e O , r I O f l t t t e C I ( i l X 3 a A a q a X , H e M O f y T C , ' l y > K H T b
eule'l)riHN{
;r(oKa33Te,,tbcTBOMnO.te3HOCTX, IIpilMeHeHilfl 3T14X MeTO-
A o B I J r e t ) . r r o r r r r3r x. c n e p r r M e H T b ri l,c r r o J l b 3 y l o u r r e
A a H H b r en o c r p a r l t r p a Q r r u e c r o M yp a 3 p e 3 ) ' B K a r . r 3 a c eo, r ( a 3 a r ' u r c rbr o . r r e 3 H b r M
Br r. r{ t r r e p I I p e r a u r t L It l r { K . [ o r e M .B c e o r l o x e u H s , B o t r r e A t r t l rB
e gror 6olnurot?
p a 3 p e 3 , 6 t l n r r p a c x , r a c c r r $ n q l p o a a H o r H a l 8 / ' r H T o . r r o r n q e c K l {cxo 315
pe3y"IlbraroMHatrIHXucc!'IeAoBaulifiAo.ltNtto 6urt
roAl,l. KogeqHbINI
c
n
e
u
v
Q t t u e c K l l x3 a A a q , a p a c u l l p e H r l e H a r l l l x g u a u n f t o
p
"
t
a
u
n
a
nu
lpolicxoAfr BHyTp]l 3eu.nu.
npoU"aau", KOTOpble
,t
L n eB
C
B aa
Cnpaaa
B3aruso
P u c . 4 . 6 5 .lpynnri crparurparpu,tecKt_\
cocrornuli, nocrpoeuHbre
no rperr r'na\4
CNLiCOKTII,ITEPATYPbI
IIep 83atr.It03aMeHfi
eMOCTIt.
C o c r o r n t g B U D agaAOrllqsbl
IrO tx
nolo)KeHHr\1
n crparrrpa$avccKoii
Iofje:lcBAreILll.)aIfi
arch Soc. Jottr.,
2. Anderson R. Y. and,Koopnnns L. H. Harntot.ticanalysis of varve time ser i e s .J o u r . G e o p h y s i c aRl e s e a r c h1, 9 6 3 ,6 B ,p . 8 7 7 - 8 9 3 .
3. Annstrbng,ll. and R. !abin (. Vario-grantmodels nrust be-positivedeiinite.
Gle o l o g y ,1 9 8 1 ,1 r , N 5 , p . 4 5 5 - 4 5 9 .
J o u r .I n t ' l A s s o c . - r \ \ a t h e n r t i c a
l . B a r d a e l l C . E . S o m e s t a t i s l i c a lf c r i L t r e so f t h e r e l a i i o n s h i pb e t u ' e e nR o c l i y
r \ l o u n t a i nS a r s e n a l' w a s t ec l i s p o s aal n d i r c q u c n c yo f e a r t h q u a l i e sG. e o l .S o c .A m e r i c l , E n g i n e e r i n gG e o l o g yC a s eH i s t o r i e s '1 9 7 0 ' - N8 , p . 3 3 - 3 7 .
S illarttett,l4. S. Smbothing periodogramsirom tinre seriesrvith spectracont i n r r o L r sN.a t u r e , 1 9 4 8 ,l 6 l , p . 6 8 6 - 6 8 7 .
6 . B t ' n d a t / . S . a n d P i e r s o LA . G . R a t t d o t nd a t a : A n a l l ' s i s a n d m e a s t t r e m e t t l
p
' r o c e d r r r c sW: i l e i ' I r t t e r s c i e r i cIen c . , N c r v Y o r l i , l 9 7 l , 4 0 7 p
r. iley In7 . B ! o r t n ti ft l c i .I ) . F o r r r i e ra n a i l ' s i so i t i n r e s e r i e s ,A l I n t r o C t r c t i o t W
i e r s c i c n c cI n c . , N e l ' \ ' o r l < .1 9 7 6 ,2 5 8 p .
8 B r a d l e g / . V . D i s t r i b u t i o n - f r e es t a t i s t i c a lt e s l s . P r e n t i c e - H a l lI t t c . , E n g l e r v o o dC l i ff s . N . J . , 1 9 6 8 ,3 B Bp .
9 . C l a r h , / . P r a c t i c a lg e o s t a t i s t i c sA. p p l i e t l S c i e n c eP u b l i s h e r sL, o n d o n , 1 9 7 9 ,
1 2 9u
1 0 . C o r t o i ' e ri V . " / . P r a c t i c a i n o n p a r a m e t r i cs t a t i s t i c s .J o h n W i l e y a n d S o n s ,
, 93 p.
I n c . , N e r vY o r k 1 9 8 0 4
l l . C o c t l e lJl . l V . a n d T u t e y J . W . A n a l g o r i t h m f o r m a c h i n ec o m p u t a t i o no i
c i r r r l - ) i eFx o u r i e rs e r i e s . , \ l a t h t n r a t i c aCl o r n p r r i i r r g1,9 6 5 ,p . 2 5 7 - 3 0 1 ,
1 2 . C o x D . R . a n d l e a i s P . A . \ V . T h e s t a t i s t i c a la n a l y s i so f s e r i e so f c v e n t s .
, \ ' ! r . i h r r cann d C o . , L t d . , L o r d o n , 1 9 6 6 ,2 8 5 p .
13. Cox D. R. and MiLler H. D. The theory ol stochasticprocesses.John Wil e v r n d S o n s ,I n c . , N e t Y o r l t , 1 9 6 5 ,3 9 8 p .
1 4 . D a u i s / . C . a n d C o c h eJ . . l l . I n t e r p r e t a t i o no l c o m p l e xl i i h o l o g i c s u c c e s s i o r t sb y s u b s t i l u a b i l i i ya n a 1 1 ' s i si n, t \ t e r r i a n tD . F . , e d . , M a t h e m a t i c a lm r . , d e l os f
seditrrcrLaryprocesses.Plenunr Press,Nerv Yorli, 1982,p. 27-52.
1 5 . D o t , e t o nI . H . A n a p p l i c a i i o no f l l a r k o v c h a i n a n a l y s i st o 1 h e A y r s h r r e
C , r : r l, \ l e r s r r i - essu c c e s s i o rSr .c o l t i s hJ o u r . G e o l o g y ,1 9 7 1 , 7 ,p . 1 l - 2 7 .
16. Dortetonl. H. and Skipper (..Nlalkov chain and substituabiliiy analysis
o i t u r b i d i t es u c c e s i o nC. l o r i d o r m eF o r m a t i o n ( I l i d d l e O l d o v i c i a n ) .C a s p ? ,Q u e b e c .
C a t : i t d i a nJ o u r , E a l t h . S c i c n c e s1, 9 7 4 ,1 i , ,p . 4 7 2 - 4 8 8 .
1'l. Draper N. R. and Sntith H. Applied regressiorl anall'sis 2nd ed. John
\ \ ' j l e v a n d S o n s ,I n c . , N e r v Y o r l < ,l 9 8 l , 7 0 9 p .
l B . F i s h e r R . A . S t a t i s t i c a lm e t h o d s f o r r e s e a r c hw o r l i e l s . i l t h e d . H a l n e r
Publ. Co., Nerv York, 1970,362 p.
1 9 . F i s h e r R . , 4 . a n d Y a t e s F . S t a t i s t i c a lt a b l e s i o r b i o l o g i c a l ,a g r i c u l t u r a l
r r t c li n e d i c a lr c s e a r c h , 6 t he d . ,O l i v e r a n d B o - v d L
, o n d o n . 1 9 6 3 ,1 2 6p .
20. Gentleman IV.,\1. ancl Sande G. Fast Fourier Transforms-for fun ancl
p r o f i t . B e l l T e l e p h o n eL a b o r a i o r i e sM
, u r r a y H i l l , N . J . , 1 9 6 6 , 6 5p .
21. Gill D. Ao
- aoni iaclaytsi o
i sn.o f s t a t i s t i c a l o n a t i o u m e t h o d t o r e i e n o i r e r a l u a t i o n
and_digitized-Jog
B u l l . A m e r i c a nA s s o c .P e t r o l e u mG e o l o g i s t s 1, 9 7 0 ,5 4 ,
no.5, p. Ztg-729.
. 2 2 . G o o d n a n L . A . T h e a n a l y s i so f c r o s s - c l a s s i f i edda t a . I n d e p e n d e n c eq,u a s i - i n d e p e n d e n caen d i n i e r a c t i o n si n c o n t i n g e n c yt a b l e s w i t h a n d r i ' ; i i h o u n
t rissing
e n t r i e s .A m e r i c a nS t a t i s t i c a A
l s s o c . J, o u r . ,1 g 6 8 ,6 J , p . l 0 9 l - 1 1 3 1 .
crofl rrr{r1.Aua,rns B3aHMO3a
Mer{ffeMocrrr 6r,r,r uclo,,rl3cBaH c qe"irbro
llaxox{AeHIIfl trtHHIIM&rbrlororII.rc,'rad-'ir.{ToJorHqecKIIX
pa3HoBr4AHocTeir, Heo6xoAurvrbrx
r"r1fl onpeAe,rrerlrflnoc.rJefoBare",rbHocrrr.
6.ryaro_
NAPfl 3TOMY YAA,'IOCb rI36C}IiATb I{JIACCII(bI4KAIIHH II3BECTHflKOB
IIO TIX
p s c n o J o x i e H r r l oB p a 3 p _ e 3 e
r r_o 6 b e r ( T r l B H OC O 3 r a T b o n p e r e . D e H H v r O
r{uK"rrrrecKyroMoJ,eJb
.
Ir4] Beporr'o, sTOT MeroA rvroxH. y"n"tutio
I I C n o J b 3 o B a T [bp ] r p e u e H r i ] r . C p y f u x c r p a r r r r p a c p f i r r e c r ( ] r x
3a!,a.t,
a TaK;'r{enpH ncc,rreAoBaHrjflx
MfiHeparbHbrxIIapafeHe3lrcoB.
gro)'r
Ha
Mbr 3alia.rrrtlBaelrpaccN{orpeHrieMeroAoBrlccJeAoBarrrfl
roc"rleAoBare,'IbHOCTeii
AaHHbtx.Ha ult o[ircaHbl Hali60,rieeqacro IIcnoJbS]'eMIrleB Hacrofltqee BpeN'rfl' teo,'roflrt npor{eAypbr
r MeroJL,r,
]ioTopbre rro3Bo,'rlJrrrnoaryt11j16
rrHTepecHbre
pe3yilbraibr Ir B ApyfHX
o 6 . l a c r s x . o ^ r r a r < oH a ' ' r e r . { 3 r ' ] o x i e H rHeH K a K r i u, i o p r r o * t
naian .ur,T a T b r c q e p n b r B a r o u l i r MI,i ^ M O ) K e 'cr , l y q l l T b c r , q T o
B KOHerrHoM
r.rofe
rroJre3HbrMrr
n,'rfi riayri o 3eM,1eoKa)Ky.r'cfl coBceM Apyfxe }rero_ibr.
oruaxo paccMorpeHHbre
B o n p o c b ro x ; a r b r B a r o r 3 H a q l i r e J b H b r rK' rr ) y r
3atraq I{ cocTaB"rrfroTocl{oBy A"rrflrloc,,relyrorllero
rr3yqeHlt'I tr til)oA O , r l K e H r rr9r c c , ' l e n o B a H H I i .
o r v e r l l i u t , q r o r e o " l o f u t e H 3 y q a . r l rn p o 6 r e v y a H a J r 3 a
rocJ.reAoBare,'rbtocrer?!aHHbrx B Tofi xg Mepe, r{arx3ar,aqt
tccr,IeroBaHrfi
p a c n p e A e J l e r { r r bA
r xa H H b r xB n p o c r p a H c r B e .
B u o , r u e B e p o f l T H O',r O
aHa"rr,3r{apr [or'ryqrrr ctsoe pa3tsurrre 6narogapn roMy, qro
oH rrHr r o x o H C I I O , ' I r b 3 0 B a ,r' ,r{cga n p e r c r { a 3 a H I r t { r u H a u c o n u x ' : a r p a r n p r r
PA3BCAKE }IECTO-POX(ACHIIii
IiAr HCOTflHE,IX,IAK H TBCPAbIX NOJIC3HbIX
I r c i { o f l a e \ , t r r l x .F I e c o r r a H e H H oM
, eroAbr aHarl3a
AByMepHbtx .qaHHbrx
o q e H b B a x ( r { b r 'r . {M r ' r p a c c M o T p r r MH X B r d r . 5 . o a H a x o
npeAcKa3aHrre
Quuaucoer'r-x npn6u,refi
He Mo;^r{er cJry)Krrrb AoKa3are,rbcr.BoNr
B
n o.r'rb3yrrp rnvreHeHaq p acc M^oTpeHH
brx MeTOAOBAJrg usyrreHHfl rrocJle-
A o B a r e . r b r - r o c r eAf ia H H b r x .C x o p e e c , r e A y e T o 6 p a r u r l ' u n i i * u n , r .
uu
noreHl{ua r'rr,Hbre
BO3MO)KHOCTn
MeroAa a nro Maru,IecKofi Kopper,Irqrr
Lr
x a l ) o r a x r b r x A r r a f p a M M C K B a I K u HH J t r rH a M e r o A
r r 3 y q e H l r fnl p o A o . r i il{llTeJIbHOCTrr
BpeMenlr Mex{Ay Byr,rKaHHqecxu,r.ta
rrsnepx(eHuflMrrHJrH
selt"r]eTpflCeHHffMLL
SfH saAaqrr erue He peueHrJr,II Hlt ojlHH tls rr3_
r'lo)I{eHrIbIX
3Aecb MeroAoB He Mo)KeT-npereHAoBarbHa
ro, qro oH
peueHre.oaHaxorro Meperoro riaKxrbr
1.1:1"y1^"j.erBopr.rre"rbHoe
y3HaBarb
o feoJrofrJqecKr.rxnocJieAoBare,rrbHocrflx,
:L{:_y
*u-Tor.
oyAyr no-aBrtrbcfl
Bce 60"qeeMou{Hbrelr ycoBeprueHcrBoBaHHbre
Me-
olu
i
oll
23. Gordon A. D. and R-egmentR. ,4. Slotting
of borehole sequences.Jour.
Int'l Assoc.r\,Iailr.Geology, 197'9,11, no. g, pl^S;0g_SZZ.
metirods
ii''rtioiorogv.IorvaStateuniv. press.,
Arr":nr^:131,r.tr[
ntt'littical
25 Harbauph
1. rv/.and G. Bonham-carrer.
c_omputer
sirruratiorl
in gcolo*,' jlh'L)l-i1:1
arrdSorrs,
Inc .\errlioirr,rSzri.
;zSp.
insr*rigrr
,,',.',1,,il{ii:lf#,r'r,
[,' ?li j;;l:'i;.?.[.'.Vfl1:\.Jr6,utjiX,',,'.
27. Haaktns
D M.'and hrerrianto.'r. oprn-'r:i
digitizedsequenr i a l d a t a .J o u r .I n t ' l A s s o c . . , \ l a t h e m u t i c u l ' C - e ';;^;;1tr;:t
ol gi o1 gB.S
,y,, n o . 4 , p . 3 g 9 _ 3 9 5
28. Haithins D. ,1I.ancr
b. r."Zoi;tion oi ,riii,*iJie"r"qu.,,.es
o f d i g i l i z e dg e o l o g i cr r a t a .J_ilIerriartt
our.i"i'r-arr"i"rtlrli..rti.ri"i;;i;;r.,
tgz4,6.
rro.3, p. 263-269.
anarlsis
andtheappricario.s
n"'{r1,{?l'31'oii|.i.'i,1,Ytlf lrrc. Spectral
30' KenLenu
- I . G . a n d S n e r ' J . - -i .' F i n i t e ^ t a r k o v c h a i n s .
V a n N o s t r a n dc o . ,
I r r c . . ^ P r i r r c e t o n , N1 9 6 02. 1 0p
{.
S l K e r t r t a c k, ( . A . a n d H i r d a n e B . s . o r g a n i c
c oUr'rret r d
a irirounrat n
r rdu ia' l r o m a t r r . .
s u r r r wL
B i o m e t r i k a1, 9 5 0 , 3 7p, . 3 0 - 4 I
32. Krumbein lyl.-C..-FORTR4NIV computer progranr
for r\Iarl<or.chain er-
iil'fl:?';
in geology.KansasceologtcJ5rr,.i. iorpri.i Co"ii.:lrrion,
1.t,
3 3 K r u s k a l w . o n t h e u n i r l u e n e sos f t h e I i ' e
o f o r g a n i cc o r r e l a t i o nB
. iomet r i c s , 1 9 5 3 ,9 , p . 4 7 - 8 8 .
34. Kuno"H. catalogue oi the active'orcanoes_of
the.*,orld including sol-
iiiii:i]',J3;,%1iJt'
'i"r.,*r"gi,r
Jal,an,
rai*'an
unJ.uuiiln,',
I'i.i
Assoc
,
35. Li l. C. R. Statislic.alInf_erence,
r.. 'I 'and 2. EdrvardBros.,Inc., Ann.
Arbor,\lic-h,1964,658p (v ll, SZSp. i,:lZl.
i6 Miller R' L' aricrKani t. s.'stiiisri'caranarl,sis
in l'c georogicar
sciences
.lohn^Wile1.
and Sons,I'rc..NervVort,'ifieZ,iij:],.
37' illorrison D. E.. Ap^pliedlineai .t'"iiriilir rnethods.prertice-Ha',
I'c.,
E n g l c w o oC
d l i i f s ,N . J . , l 9 S 3 S
; O ip . - - - - '
38. Olea R. ,4. .Mteasuring
sp'i_tiat
clepedence_tith
I(ansas
ceologicalSu^'ev Serieson fprtirl a"rli.!L."is'tz,,;". semivariograms.
& L;";;;F;,.iiins., zs p
39. OstleB.-and Mensing Striirii*1"'"research,
3rd edition,Iowa State
L - r r i rP
. r e s sA. m e s . l o .1 9 7 56, i Z-R.
';o f
D . B . H a n c l b o o k s t a t i s t i c atl a b l e s p
. e r g a r n o np r e s s ,L o n d o n ,
l9621gS0O;r,
5 0 . S i e p a l S . N o n p a l a m e i r i cs i a t i s i . i c sf o r b e h a v i o r a ls c i e n c e si .\ ' l c G r a r v - H r l l .
l"; i c . . - N e rYv " o r kl'9 J 0 ' J l 2 i '
l a - r o n o t n J1l.r e p r r n c i p , c s
5 1 . S t t c a t hP . H . . A . r r l r l S o i ' ' : ' R . R . N u n r t r i c ; r T
. . H . f r e e r n e t ta u d C r - r .S, r n l : - r a t t c i s . : , t ,
, , , c 1p i a c t i c eo f n u n t e r i c : rci l i t s s i i i c a l i o t rW
'1 . , -; i,ZJ . 5 7p3.
f i t R . S t a t i s i i , : l l m e l l i o d si n E a r t h s c i c i t c e sJ. o h n \ t r I i l e ,1, ; t c lS l t t : , I i : , - ' . .
ll.e.,vYor'li,197'1'154 P'
l L l t - r ' cli' : . 5 3 . l i p p e r J . C . S r L l f a c em o t J e l l i r l gi e c h n i q u c sl.i a l i s a s C e o i o g i c r l S
. ,9 7 9 ,1 0 8 p .
, , . ' ,-,c, 4S.' ini tur itit, r lA n a l y s i s .n o . 4 , L a r ri c n c c ' 1 1 : r n s 1
O . T r a n s i i i o t t a n a l i . ' - s its- : f s l r u c t u r a l s e q u c l t c e sD. r : c u s s i c n G c , r i .
S , r c .A m e r i c aB u l l e i i n , 1 9 7 9 ,P a r t 1 ' 9 0 ' p . 9 8 9 - 9 9 2
5 5 . V i s t e L i u sz r l .B . S e d i m e n l a t i o nt i m e t r e i t d i u n c t i o n s a n d t h e i r a p p l i c a t i , . r r
I , r i c o l r c l a l j o r to f s e d i t n e n t a r id' e p o s i t s J. o u r . G e o ) o g 1 '1, 9 6 1 ,6 9 , p . 7 r ) 3 - 7 3 8 .
? l. l i o n l a i i c s o i l - b o t t n d a r y] o c l r , i o nl r o t n t r a n s e c i d a i . a .J o u r .
i 6 . l [ r 1 . , . s 1 e , ' IA
Gl e o l o g . u1" 9
, 7 3 , 5 ,n o . l , p . l 7 - 3 7 .
i n l l A s s r : c..\ l i L i l t c t i l i i i i c a
5 7 . l Y ' e b s l e rR . , D I \ ; I D E : A F O i i T R A N l V ' p r o g f a r n f o r s e g t t t c ;irn g r n u i l i r r i r i a t co n e - t l i m e t t t i o n as lp a t i a ls c r i e s .C o n l p u t c r sa t l d ( i e o s c i e t t c e s1 ,9 1 j 06, , t r o . 1 ,
n 6l-68.
R. C.. Baiieg R. r(. arrd Ilenderson E. P. Saliniiy of :he rvalir li
58. lV'e11.s
1, p. I05-1J2.
y . U . S . C e c i o g i c a l5 u r v e y , P r o f . P a p e r , 1 9 2 8 , 1 ' 5
C 1 ; t - s s ; r l r e aBJai e
5 9 . l Y l e s / l a l lJ . I l . A h a r c i l , o o l oi i n t t m e r i c a lm r l r i x i n v e r . . . r ; nr i n d s o l u t i o n
t , i i r r r e a le ( l u : r t i o l r -Jso. h u W i l e v a n d S o r t s ,i n c . , N e r v Y o r l i , 1 9 6 t 3 i,7 l p .
l t ) . V l t i t t a k t ' r E . T . a : r r dR o b i r t s o nG . T h e c a l c u l u so i o b s e r v a t i o n s , 4 t i ei d . ,
, 9 4 4 , 3 9 5p .
I l l r c l < i ea r r d S o t t ,I - t d . ,G l a s g o r v 1
. rkrl firr -\lincralo6 1. \ V ' i c h r r r cln. E . R e p o s e . p e r i opda t i e r n s o i v o l c a n o e sA
g i o c h G c o l o g i ,B d . 4 , 1 9 6 6 ,p . 2 9 1 - 3 6 6 .
62. lf'r//rr'.s.\1. V. A short introduciion to nunrerical arreiysis. Cambridge
U : r i r ' .P r e s s ,C a n r b l i d g e 1
, 9 6 6 , 7 6p .
6 3 . ) u l e G . U . a n d K e n d a l l . i l . G . A n i n t r o d u c t i o ni o i h e i h e o r . ;o f s t a t i s t i c s .
1 . 1t l r e d . ,H l I r r e r P u b l .C o . ,N e u , \ ' o r k ,I 9 6 9 , 7 0 1n .
6 4 . Y e tj'e i : i t l t V . S t a c l u ; s 1 i pc r o i e s s e si n h 5d r o l o g y . W a t e r R e s o r i r c e P
s ubli.
c i rt i o u s .F o r t C c l l i n s ,C o l o . ,1 9 7 2 ,2 7 6 p .
4 1 . P a n n f s h rHt . A . a n r l
B r i e r G . . WS
, .o r r r ea p p l i c a t i o nosf s i a t i s l i c sl o n r e i e o rologv
Pennsrlr:rrrrS
i i rl a i e t ' r r i r : . _
1 , v .o;,1,1)l:i:''"r,slft.^ll,li-,::,Unii-rriiu
p r ; ' k : "p",'isdslbi,i"i
p ' r . 1 9 6 5 . 2 c an
U n i i e r r i i , Firrl
42.
Qur'nbui!e,41 ff. Associa
iatedrneasdrernents,
Butter;"rthr', London,1952,
2 7 9p .
43. Rar.,rr,r
J A r . A n i n t r o d u c t i o nt o s p e i - i r a la n a l l . s i s .p i o n
l _ t d . .I _ o n d o n .
1 9 7 1 , 1 7p4.
l :i : 1'''
nl
T,Xl,:t,S";Geo
phr.sicat signal anarysis. prentice.Hatr,
!,?0":::3r.f;,3^i"r;
9
,'. .o?:n;:),-r.,'I';
"
oi );o^*{i'#.i.1: t
aticaI etem
enrs rorcom
putergra.
":?gg,,rdq
g 7 6**m
.2 - i ' 9 ' ;
n n ' .1t^rfdf;{:,?i,
;^,t;9:l:
In
"Tc . , , N c uY u r t i .*"f
rb
^ H i t t .. , a n d H t g n g . i
i .' '' nAq;_" _ 6i 8p'p' t i c a l i o no f c l r r s t e d
,1t ee_\,xl4tia6' nr .dd. Rp oi cst uerne f e rA
ld
r e t e c t i o nt o
p r oocceessssi ni ng g
. . , T e . cr fyi .. -
rriclrrre
Tec-h R
Roenp . 6 g - 6 l i l ^ ^ _ ^ , , , o r e ^ i ^ _ ^ ^ - ^ _ r ^ _ t r . - . ,
o i , \ l a r v l a n d . . . C o l l e g- upea r i < 'I.l d . , j g O g fO + p . " " c o m p r r e r S c i t , n c ec e n t e r , U n i *
4'/."s aski n M. i . ^;a'' th; ; I;i;,,;"
tuur u
b:'
, l;- ..'.r{ir
l \ u l1ooanssssoc
o ci,
i ass
ssion,a neti, geological too l . J o u r . I n t ' l A s s o c .M a t h e n t aitci r l G e o l o g y , 1 9 6 9 ,
/ , n o . rl ,, n
p.. 7
/ _-l _
b .1 6 .
fv-- s(!"<t(s
f t ' a ' . , u o t a , a J . q_lil?ilQ';i.,
tsr Smoothing and d
.
Iiii if feer ernet n
ant i oor
diiferentiation
i att i o
f d
data
ata b
by
y
srnrprrrred
,i$,.:",,:,jifr.;X:io"S:!iy'"1^
least
r639.
squares
procedures.
Analytical
a'ir."rirtii;,'ibb?,',1il,
,i.]'e, rozz_
andquantirati'e
srrarigraphy.
ur..X,e..i',l;i''3ti"u{^,Y,oni'ff#:l!"iolon.'.
318
r
ft-
J
4 '.')-
l
t
,t
r
t
t'.,.
HOE (NPAKTHI{ECKOE) H3AAH14E
N POI,T3
BO.U,CTBEH
Aesnc AxoH C.
CTATIICTHgECKI,IH AHAJII,I3 trAHHbIX B TEOJIOTHI,I
3anegynquir pegaxqlrefiB. A. Kpuutanolctittfi
Pe-{ariropA. M. Auroxor'tbctafl
flepen",rerxyAoxHnKaA. H. Kgpoepoeoil
XyAoxecreeuunlipe,laxropf . H. IOpaeacrcan
peAar{ropC. f . Becerrruua
TexHu'recritrrl
Kopper<ropH. A. f ponoaa
aE Nb8701
CAarros ua6op 06.04.90.flo.qnucaHoB rerrarb 06.08.90.Oopnar 60X90'/ro.6yruara rnn. Ne l. f apurrl'pa ,rlureparypnaa. flc,{ars BbICoKaq.Vc,l. neq. ,'t.
2b,0.Vq.-Hsa.,j*?tft;
4060exs.3axas20112262-2
20,0.Vcn.r{p.-orr.
]ff?l*
Opg,eua<.3sar floqera) u3Aare,rbcrBo<He.{pa>. 125047,Xtocxea, n,'I. Ee,'lopyccl(o'
ro goxga,'ra,3
.Itocxoecxaaranorpa$ur Ne 1l focy,rapcrBenHoroKolILlrera CCCP no fleqaTt'l'
1 1 3 1 0 5M
, o c x e a ,H a r a r u H c K a tyrf l . , A . 1