C h ap ter Splines on Surfaces Marian Neamtu This chapter

Transcription

!#"$&%('*)+&,.-0/
132547698:2<;0=?>A@CBD;0E5E5BF@C6F6G@C6H>A25@I>AJK=+478LJ0MINF6F=5O74QP5@C69JKP6GR5BSMT;08C@U6GV5W;#P.;0BF@X;YJ#MZ6G=+O747P+@L>G25@CJKBS[\8CJKP^]
8C@UBGP5@UE`_4Q>A2*>A25@H8CJKP+6F>ABFR58U>G47JKPaJ0MbMcR5P58d>A4QJKP56eE+@Uf<P5@UEgJKPahi;0P54jMcJKO7E+6k4QPY>G25BG@U@d]lE+47hL@CP56F47JKP<;#OnmoR^]
8COQ47E5@C;0Pp6G=<;#8C@0qsr<JKBZ>A2+@HhLJK6F>=5;0BF>CW+>A25@9hi;#>A25@Uht;u>A478C;0Ov;06G=!@C8d>A6kJ0Mw>G25476E54Q6G8U47=5OQ47P5@x;#BG@y47Pp>A2+@C47B
47P+MT;#P58U[z;0P5E{>A25@UBG@UMcJ0BG@yh|R58:2*J0M}_2<;#>_~@y_47OQO&6G;[z25@CBF@9_4QO7O&25;0@D;#P*@?=5O7JKBG;#>AJ0BF[p8:2<;#BA;08d>A@CBUq
<LCYHzL{aDHL
132R56MT;0B4QP`>A254Q6vJ^JKp_s@L25;0@hiJ06F>AOj[a@UP58CJ0R5P>A@CBF@CE6G=5OQ47P5@D8CR5BSK@C69;0P+Eg6GR5BSMT;08C@U6y_2+JK6G@I=<;u]
BA;0hL@U>G@CBE5J0ht;04QP56;0BF@p6GR5+6G@U>G6tJ0Mk>A2+@*BF@X;0O~O747P+@pJKB|>A25@*mR58UO747E+@X;0P=5O7;0P5@0qlP=<;#BF>A4Q8CR5O7;0BCWo4QP
6G@dK@CBG;0Ob8:2<;#=+>A@UBG6yJ0M>A2+476!J?J0*_s@v@U8X;0hL@;08U8CR56S>AJKhL@CEg>GJt>A25@4QE5@X;L>A2<;#>x;z6G=5OQ47P5@|6FR5BFMT;#8C@|4Q6
>A25@KBG;0=52iJ0M;y54Q#;0BF4;#>G@ZBG@C;0Oj]$#;0O7R5@UEMcR5P58U>G47JKPLJKBUW?;#OQ>A@UBGP<;u>A4Q0@COj[KW;y=<;0BA;#hi@d>ABG4Q836GR5BSMT;08C@#W^_2+478:2
476>A2+@e47hi;0K@J0M;H=5O7;0P<;0BoE5JKhi;04QPiR5P+E5@CB~;9K@U8U>GJKBsMcR5P+8U>A4QJKPW^JKBs;H8CJ0O7O7@U8U>G47JKPIJ0M6FR58:2zMcR5P58d>A4QJKP56Cq
1325@3=<;0BG;0hL@U>ABF478ZJ0BMcBG@U@d]McJ0BGh6FR5BFMT;#8C@C6>G2<;#>o;0BF@Z>l[^=5478C;0O7Oj[D8UJKP56G4QE5@CBF@CEI47P>G25@k~ k¡9¢£OQ4Q>A@UBA;#>GR5BG@
;0BG@e8CJKhL=vJ06G4Q>G@6GR+BFMT;08U@C68CJKP+6G476S>A4QP5J0M;|8CJKOQO7@C8d>A4QJKPzJ0M}47P+E54Q^47E+R<;0O&6FR5BFMT;#8C@x=<;#>G8:25@C6kJ0Mn>A2+@McJKBGh
¤¦¥l§l¨v¥c© W5_2+@CBG@
¤¦¥nª+¨v¥&« ¬ ®C¯ °w±²0¯X³X³X³d¯:Ý¯
§µ q ²¦©
476¶;L>G25BG@U@d]l8UJKhL=vJKP+@CP>e0@C8U>GJKBeMcR5P+8U>A4QJKPY_2+JK6G@|E+JKht;#47P ¨&¥ 476¶;NF6G4Qhi=+O7@CVI=5O7;0P<;0BkBG@UK47J0PWv6FR58:2
;06Z>A2+@96S>:;0P+E<;0BGE{>ABF4;0P+KO7@J0BZ>A25@yR5P54j>6G·R<;0BF@0q
132+@oMcR+P58U>G47JKP56 ¤¥ ;0BG@R56FR<;0OQOQ[¶8:25JK6G@UPH>GJk!@o=vJ0OQ[^P5JKhL4;0OQ6vJ#M+;Zf+?@UEgNFOQJ¦_V3E+@CKBF@C@0W¸¦¹»º¼¹¾½#¿L@CÀ ÁU47@UB
>ABF4;0P50O7@C6HJKBD>G@CP56FJKB=5BGJÊ5R58d>A6J0M¶R5P54j#;0BG47;#>A@t¿~@CBFP56F>G@C47P=!JKOQ[^P5J0hi47;0O76UWJKB|BG;#>A4QJKP<;0OoMcR5P58d>A4QJKP56Cq
ÂYJKBF@CJK@UBCW>G25@t=<;u>A8:25@U6 ¤¦¥S§¨&¥Ã© NÄf5>D>GJKK@U>G25@CBFVa6FJa>A2<;u>H>G25@U[McJKBGhÅ;*KO7J0<;0O7Oj[`8UJKP>A47PR5J0R56CWbJ0B
@U0@CP6GhLJ^J0>A2W#6GR5BSMT;08C@ § 6G@U@3r4QKR5BG@ µ q ²¦© qnÆ@ZBG@dMc@CBw>G25@~BF@X;0E+@CB>GJy~2<;0=+>G@CBn^vWKMcJKB;eE5476F8CR56F6G4QJKP
JKPL8CJKP56S>ABFR58U>G47P5H6GhLJ?J0>G2LMcBF@C@]McJKBFhÇ6GR5BSMT;08C@U6s_4Q>G2i=!JKOj[?P+JKhi47;0O5;#P5EtBG;#>A4QJKP<;0O<6FR5BFMT;08U@¶=5;#>A8:25@U6Cq
132+@k=!JK=5R+O;0BF4Q>l[9J0M!=vJ0OQ[^P5JKhL4;0O^;0P+EBA;#>G47JKP<;#O?8UJKhi=!JK6F4Q>A@~6GR5BSMT;08C@U6È4QPD>A2+@k~ k¡9¢É8CJKhLh|R5P+4Q>l[
8X;0P{!@x@d?=5O7;047P5@UE{[t>A25@MT;08d>3>A2<;u>3>A25@d[z8X;#PY!@xR56G@UE*>GJIBG@C=+BG@C6F@CP>XW¼4QP{;IBFJK5R56S>3_Z;X[0Wv;|0BG@X;u>
#;0BG4Q@U>l[HJ0M!6G2<;0=!@C6o;#P5E6GR5BSMT;08C@U6oJ0Mv;0BG54j>ABG;0BF[y>AJ0=vJKOQJKK4Q8X;0OK@UP^R+6CqÊkJ¦_s@U0@CBUW?4QP6G=54j>A@ZJ0M¼>G25@3254702
Ë @d?4Q547OQ4Q>l[\;0P+E.J0>A2+@CB|;u>G>ABG;08U>G4Q0@t=5BFJK=v@UBF>G47@C6HJ0M36FR58:26GR5BSMT;08C@U6 § 6F@C@{~2<;#=+>A@UBG6H © Wo47Pht;0P[
ÌKÌ µ
ÏbÐ¶ÑeÒeÓwÔÈÕ×Ö ¹ÙØ ÒoÚÛÄÜeÔ ØÞÝ Ü Øbß Õkà?Ñ9ÏbÔ Ø
Ì0Í0Î
f3
f2
f1
r4QKSR5BF@ µ q ² qÈ~JKhiS=!JK6F4Q>A@x=5;0BA;0hL@U>GBGS4Q86GR5BSMT;08C@#q
1
2
3
6F4Q>AR5;#>A4QJKP56nJ0M5=+BA;08d>A478C;0O47P>G@CBG@U6F>w4Q>}476nE5@U6G4QBA;05OQ@>AJk@d^>A@UP5ED>A2+@Z;0!JK@È8CJKP58U@C=+>J0M<;6G=+O747P+@È6FR5BFMT;#8C@
;6F>G@C=pMT;0BS>A25@UBCqoáe;#hi@UOQ[KW^4Q>Zht;0#@C636F@CP56F@0W¼;#>3OQ@X;06S>347Pt=5BG4QP58C4Q=5O7@#W?>AJ8UJKP56F47E5@UB~>A25@xhLJKBF@K@CP+@CBA;#O
8C;06G@H47P{_25478:2*>A25@9E5JKhi;047P+6 ¨&¥ 47P §µ q ²¦© ;0BF@Lâ&ãuâ<ä7å!æjç0â!ç0è|;0P5E*25@CP58U@|;0BF@9>G25@ChL6G@UOQ0@C6e6FR5BFMT;#8C@C6Uq
lP*=<;0BS>A478UR5O;#BCW+8UJKP56F47E5@UB>G25@y=5BGJ05O7@UhéJ0Mw8CJKP56S>ABFR58U>G47P5I6G8C;0O;#B3JKB3K@C8d>AJKBÄ]#;0OQR5@CEpMcR5P58d>A4QJKP56
¤gª+ä« ¬ ê §$ëL±²K¯ Ì ¯X³X³X³ì©¯
§Tµ q Ì ©
_25J06G@*E5JKhi;047P ¨ 4Q6;gK@CP+@CBA;#O36GR5BSMT;08C@{47P ¬ ® q.1325@UBG@*;0BG@{;g25J06F>LJ0M¶6G4Q>GR<;#>G47JKP56D47P;0=5=+O747@UE
6F8C47@UP58C@U6e_25@UBG@D6FR58:2`McR5P58d>A4QJKP56¶;0BG@9O74Q0@COj[z>AJL!@DR56F@UMcR5Oqín@d>eR+6¶5BF47@ Ë [*hi@UP>G47JKPY;LMc@d_;0=5=+O74j]
8C;#>A4QJKP56Cqe1325@BG@C;0E5@CB¶_47O7OnR5P+E5JKR5+>G@CE5Oj[a!@;0+O7@H>GJz8CJ0hi@HR5=`_4Q>G2`ht;#P[YJ0>G25@CB@+;0hi=+O7@C6¶JKP
254Q6:î#2+@CBJ_Pq
ïÉMTð;#ñ 8Cç0@ æjç0¨ è|q.òor¼ó$ôdJ0æjõuB|öC@d÷p+13;0hL25@L=5O7Mc@#R5W P5¨ 8U>G478CJKJKP R+O7¤ E8Cv;0@zPÞ>GE525@U@{6G8U6GBGR547BS!MT@z;08C;{@p6GJ#8CM;0;gO;#B98CJ0f<h|@UO75EÞR56S;0>A6G476FJ0J?P8U4@C;#P5>G@CKE4QP5_@p4j=<>A2\;0BS>L>A25;0@iP56GE R5BÄ¤ ]
8UJKR5OQEgv@D>G25@D>G@ChL=v@UBA;#>GR5BG@;#6x;iMcR5P58d>A4QJKP`J0MÈO7J^8X;u>A47J0PYJKP`>G25@|6FR5BFMT;08U@0qHøBCW ¨ 8CJ0R5O7Eg!@
>G25@6GR+BFMT;08U@J0Mo>A25@|@C;0BF>G2\;0P5E ¤ JKP+@J0M>A25@|McJ0O7O7J_4QP5i·R<;#P>G4Q>G47@C6ehi@C;06GR5BF@CE;#>#;0BF47JKR+6
OQJ?8C;#>A4QJKP56sJKP ¨bª ;0Oj>A4Q>GR5E5@e;0vJ0@y>G25@x6G@C;O7@U0@COW+>A@Uhi=!@CBG;#>AR5BF@0W54QP>A@CP+6G4Q>l[tJ0M}>A25@xhi;0KP5@d>A4Q8
f5@CO7E&W3@U>A8#qÉ eP5J0>G25@CBi@d+;0hL=5O7@ ª K4jK@CPù#;0O7R5@U6tJ0M ¤ hL@X;06FR5BG@UEúJKP ¨ W36GR+8:2É;06iE+476G8UBG@d>A@
=+BG@C6F6GR5BF@C6|J0P;#PÞ;04QBG8UBA;#MÃ>x_4QP55Wn;0PJK^ûF@U8U>A4jK@Lhi4QK2>x!@I>GJYE+@U>A@UBGhL47P5@|>G25@L=5BG@U6G6GR+BG@i;#>
;#BG54j>ABA;#BF[ÒQJ?8C;#>A4QJKP56J0P>G25@L_4QP55q|üÈ@U>H;0P+J0>A25@UB9;0=5=5OQ478X;u>A47J0PWJ0M~47P>A@UBG@C6S>947P~ k¡9¢|W4Q6
_2+@CP ¤ 6F>:;#P5E56HMcJ0BH;*6G8C;0O;0Bxf<@UO7E\>A2<;u>DBF@ Ë @U8U>A6D;0P.;#6G=!@C8U>DJ0M~>G25@I?4Q6GR<;#OÈ·R<;#O74Q>l[`J0M ¨ W
6FR58:2`;#6>G25@H¡9;#R56G6F4;0P{8CR+BF#;#>AR+BG@0q
ïË ý R5ô 47ñdEzþ ãuE?èY[?òoP5;0ó$ôdhiæjõu4Q8CöC6U÷×qoÊ¶ ÿ@CBFBF@e478:>A2É2+@e6GJKJKR+^BGûF8C@U@\8U>GJ04QKMH@x@d4Q+6È;0>GhLJ|=5hLOQ@CJ?6pE5J0@UOÃMyî#BFK@C@U8U8UJK>GP5JKBp6F>GBGf<R5@C8dOQE5>~6{0@CE5O7J^@Uf<8C4jP+>l@C[IEf<@CJKOQPÉE56Z6GR5;0P+BSMTEp;08CJ0@U>A6*25@U4Q6B
Ë J¦_ ·R<;#P>G4Q>G47@C6I>A25;#>z;#BG@*KJK@CBFP5@CE£[>A2+@`áe;X^47@UBS] >AJK#@C6i@C·R<;#>G47JKP56Uq£lPú=<;0BS>A4Q8CR5O7;0BCW
4QP.hL@U>A@UJKBGJ0O7JK0[;#P5E.KOQJK<;0OÈ;#>GhiJK6F=525@UBG478ihiJÊ5@UO747P+5W}>G25@ Ë R+47E Ë J_ JKPÞ>G25@z6FR5BFMT;08U@zJ0M
>G25@L@X;0BS>A2Þ4Q6yE5@C6F8CBG4Qv@UEÞ4QP>G@CBGhL6yJ0M~>G25@L25JKBG4QÁCJKP>A;0ObK@U8U>AJ0B90@CO7J^8C4j>l[gK@U8U>AJ0B9f<@UO7E § _4j>A2
OQJKP5K4j>AR5E+47P<;0Ow;0P5E\O7;#>A4j>AR5E54QP<;0O}8CJKhL=!JKP5@CP>G6 © W>GJKK@U>G25@CB_4j>A2;#>GhiJK6F=525@UBG478D=5BG@U6G6GR+BG@ ² W
Í W µ qY eP5J#>A25@UBD@d+;0hL=5OQ@t8CJ0hi@U6HMcBGJ0hÅ>G25@t6FJ#]l8C;0O7OQ@CEhiJ^47P5YvJ0R5P5E<;0BS[=5BGJK+O7@ChL6D4QP
=5;0BF>G4;0O<E54 &@UBG@UP>G4;0O+@C·R<;#>G47JKP56UW?4QP_25478:2L>A25@k6GR5BSMT;08C@ ¨ #;0BG4Q@C6_4Q>G2L>G47hL@;0P5EtBF@C=5BF@C6F@CP>A6
Ö ¹K¹ ÛÄÜÓwÕ Ý{ß ÏkÓ}Û Ý Ü
Ì0Í ²
;hLJ?4QP5x47P>G@CBFMT;#8C@Z!@U>l_s@C@UPt6GJ0O747E|;0P5EO74Q·R547E|=+2<;06G@U6J0Mv;K4Q0@CPIhi;#>A@UBG4;#O?6FR556F>A;0P58U@0W478U@
;0P+E|_Z;#>G@CBUW6A;X[Kqb1o[^=5478C;0O7Oj[KWu>A25@~0@C8d>AJKBbf<@UO7E;#6G6GJ^8C47;#>A@UED_4Q>G2 ¨ 25;06b6G@dK@UBA;0O58UJKhL=vJKP+@CP>A6UW
McJKB}@d+;0hL=5OQ@s>A2+@~P5JKBFht;#OKK@C8d>AJKBF6b>AJk>A25@s6GR5BSMT;08C@ ¨ WK4j>A6}hi@C;0PD8UR5BF#;#>GR5BG@#W;0P5EH>A25@ÈK@COQJ?8U4Q>l[
J0M}>A2+@9hLJ^47P5I!JKR5P5E<;#BF[ q
ïÉðNFBF @Uè McU@Uç BGñ@Cô P+8C|@CViô:öd6Gó 0R5â BSMT;08C@ô ñ ¨ ãuâ+J0ö B3þ è ;0<BGñd@xþ ó$@dãuKâ!@U÷ Pa E5JK4QhiBG@C@8d>A6FOj[tR5BFE5MT;#@d8C>A@U@CBG69hL;047BFP5@@UJ0E*MÃ>A@U[zP\>G8C25O747J0636G@C6FR5Oj[`BFMTBF;#@C8CO@0;uqÈ>A@Cr<E`JKBZ>GJ*@+;{;0hi04Q=+KO7@U@0P W
;0P[t6G8X;#O;0B~f5@CO7E ¤ JKP ¨ 8X;#Ppv@e>G25JKR502>J#MnJKB~^476FR<;0O74QÁC@UEp;063;|6FR5BFMT;08U@x47Pz4j>A6ZJ_P{BG4QK2>XW
¸¹ º¼¹¾½¼>A2+@96FR5BFMT;#8C@
¨ &ª ± !#" ¤b$§ !&© %('d)¯ !+*-¨ ,¯
§µ q Í ©
_25@UBG@ %(' 4763>A25@yR5P+4Q>6GR+BFMT;08U@9P+JKBGhi;0O;#>3>G25@y=vJ047P> ! qo13254764Q6Z>A25@yBG@C;06GJ0PY_2[{6GR5BSMT;08C@U6
J0Ms>A254Q6x>l[?=!@z;#BG@L;0O76FJY6FJKhL@U>A4Qhi@U6xBG@dMc@CBGBF@CE>AJY;06`NS6GR5BSMT;08C@U6DJKP6GR5BSMT;[email protected] ²K/² qtr¼J0B9@]
;0hL=5OQ@0W ¨ 8CJKR5OQE`BG@U=5BG@U6G@UP>x>G25@H>GBGR5@H6GR5BSMT;08C@DJ0M>A25@H@X;0BS>A2W!_4Q>G2 ¨ !@C4QP5i>G25@DBF@UMc@UBG@CP+8C@
6F=525@CBF@î#@UO7OQ47=56FJK47EY;0P5E ¤ >G25@H2+@C4702>¶;0!JK@H6G@X;LO7@dK@COq3øBCW ¨ 8UJKR5OQEa!@H;#PaJ v6G@d>e6FR5BFMT;08U@
>GJ ¨ 1W 0$¹ ¸¹ ½b;a6FR5BFMT;08U@t_25JK6F@zE54Q6F>:;#P58C@t>GJ ¨ 476|;*f+?@CE.#;0O7R+@ § 4QP_254Q8:28X;06F@t>A2+@tMcR5P58]
>G47JKP ¤ 4QP §µ q Í © 4Q647E5@UP>A478C;0O7Oj[*@C·R<;0O>GJz>A254Q6#;0O7R5@ © qylP\@X;08:2J0Mo>A2+@C6G@I8C;06G@U694j>hi;X[`!@
;0E?0;#P>A;0K@UJKR563>AJLR56G@ ¨ ;06k;P<;#>GR5BA;#O=<;0BA;#hi@d>ABG4Q8E5JKhi;04QPzMcJKB ¨ q
N R5BFMT;#8C@C6J0P6GR5BSMT;08C@U6GV\8X;0P;#O76GJav@t^4Q@U_s@CEù;06|6FR5BFMT;08U@C64QP;a2547025@CBÄ]lE54Qhi@UP56G4QJKP<;0Oo6G=5;08C@#q
132547634Q63v@U8X;0R+6G@y>A25@y6G@d>
2¨ vª 3
± ?4§ !0¯¤b4§ !©G©)¯ !+*5¨ ,76É¬ 9® 8 ¬ ê0¯
§µ q ©
8X;0Pg!@|>A2+JKR5K2>yJ0Ms;06x;z>l_sJ#]lE+47hL@CP56F47JKP<;#Owhi;0P54jMcJKO7EY47h|!@CE5E+@CEg47P ¬ )ê : ® q9lP\=<;0BS>A478UR5O;#BCW&4jM ¤
476x;p6F8X;0O7;0BeMcR5P58d>A4QJKPW&>G25@CP ¨ 476y;t>l_sJ#]lE54Qhi@UP56G4QJKP<;0Ow6GR5BSMT;08C@I4QP`McJKR5BS]E547hL@CP+6G47J0P<;0O}mR58COQ47E5@C;0P
6G=<;#8C@0q
132+@Df<BG6S>x6F>G@C=g4QPahLJK6F>¶6GR5BSMT;08C@DBG@C8UJKP56S>ABGR+8U>A4QJKPWvhiJÊ5@COQ47P5+Wv;#P5E¼î#JKBkE<;#>A;u]f+>G>A4QP5t=+BGJK5OQ@ChL6CW
;047hL@CE;u>IBG@C8UJK@CBF47P5;0PR5P5P5J_PùMcR5P58U>G47JKP ¤ McBGJ0h ;g6G@d>iJ#MeE<;u>:;gJKBI;#>I6FJKOQ^47P+\;\=5;0BF>G4;0O
E5;4 v@CBF@CP>A47;0O@U·R<;#>A4QJKPW4Q6>AJpBF@C6F>GBG4Q8U>x>A2+@8CO;#6G6xJ0MÈMcR5P58d>A47J0P56>A2<;u>y;0BG@R+6G@CE&q1325@C6F@LBF@C6S>ABG4Q8U>G@CE
8CO7;06G6F@C63R56FR<;0O7Oj[L8CJKP56F476S>3J0MeNF6G4Qhi=+O7@CV9McR5P58d>A47J0P56~>A25;#>;0BF@6GR54j>:;0+O7@¶McJ0BZPR5hi@UBG4Q8X;0O!ht;#P547=5R+O;#>G47JKP
;0P5E;#>>G25@p6A;#hi@z>G47hL@t8X;#PÙ;0=+=5BGJX?47hi;#>A@L_~@UO7O3J0>G25@CB § hiJ0BG@zK@UP5@CBG;0O © McR5P58U>G47JKP+6CqÞ132R56UWs_s@
>l[^=5478C;0O7Oj[._~J0BG_4Q>A2 6G=5OQ47P5@]lOQ470@{JKBLf<P54j>A@d]@COQ@ChL@CP>I>l[?=!@aMcR5P+8U>A4QJKP56UWZ_25478:2ú25;0@NF=54Q@C8C@d_476F@
8:2<;0BG;08U>G@CBGV+<W 0$¹ ¸¹ ½>G25@U[I!@COQJKP5y>AJH;9OQ47P5@C;0B6G=<;#8C@¶_4j>A2LO7J^8X;0OQOQ[9f<P54j>A@E547hL@CP+6G47J0PqlPL>A25@k8CJKP>G@d^>
J0M3>A2+476D8:25;0=+>A@UBCW ¤ _4QO7Oov@NF8CJKhL=!JK6G@UE5V`J0MMcR5P58d>A4QJKP56 ¤¥yªÈ¨v¥¶« ¬ ê §ë± ²K¯ Ì ¯X³X³X³ © Wb_25@CBF@
>A25@ ¨v>¥ = 6k;0BG@y47Pp0@CP5@UBA;0OP5J0P?]l=5O7;0P<;0B36FR5BFMT;#8C@C6>A@U6G6F@CO7O7;#>A4QP5|>A2+@9E+JKht;#47P ¨ 0$¹ ¸¹ ½ ä@± ?¨&¥ q
Z>3>G254763=!JK4QP>CW?>G25@xBG@C;0E5@CBhi;X[t_sJKP5E5@UBCW¼;0P5E{BF47K2>AOj[t6FJ5W+_25@d>A25@UB8CJKP56F47E5@UBG4QP5IK@CP5@UBA;0O&6GR5BÄ]
MT;08C@U6 ¨v¥ WZ4QP56F>G@X;0E J0M=+O;0P<;#BLJ0P5@C6UW3476L47P5E5@U@CEÙ;K@UP^R+47P5@a;0P5E _sJKBS>A2[ùK@CP5@UBA;0OQ47ÁC;#>A4QJKPJ0M>A2+@
6G@d>G>A4QP5 §Tµ q ²¦© qb132+476È476s;DO7@UK4Q>G47hi;#>A@Z=!JK4QP>s6G4QP58C@#W?6S>ABF478U>GOQ[I6F=v@C;047P55W>A2+@eK@UP5@CBG;0Ov=+BGJK5OQ@Ch §µ q Ì ©
8X;0P{4QPzMT;08U>!@xBG@UE5R58C@UE*>GJ>A25@x6F47hL=5O7@UBZ8X;06F@xJ0Mw=5O;0P5;0BZ=<;0BG;0hL@U>ABF478¶E5JKhi;047P56Uqr<JKBZ@5;#hi=5OQ@0W54jM
¤ 4766F8X;0O7;0B §ë`±é²¦© ;0P5E\4jMÈ_s@I47P>A@UBG=5BF@U> ¤b§¨n© ;06>A25@6FR5BFMT;#8C@ ¨ 4QP §µ q Í © W>A25@UPJ0P5@8X;0P\R56F@
6F>A;0P5E<;0BFE.=<;0BG;0hL@U>ABF478I=!JKOQ[^P5JKhL4;#Ob6G=5OQ47P5@I>A@U8:25P54Q·^R+@C6D>GJ`BG@U=5BG@U6G@CP>:î#BG@U8CJKP56S>ABFR58U> ¤ q{ eOj>A@UBGP<;u]
>A4jK@COj[KW4Q>s476È=!JK6G6F475OQ@k>GJD47P>G@CBG=+BG@U> ¤ 4QPL>G25@¶McBG;0hi@d_~J0BG §µ q © W?4QPL_254Q8:2z8X;#6G@JKP+@¶8UJKR5O7Et@ChL=5O7J[
§ ¢ © =<;0BG;0hi@d>ABF478~=!JKOj[?P+JKhi47;0O6G=+O747P+@C6b>AJeBG@C8UJKP56S>ABGR+8U> ¨ ;0P5E|>A2+@CBG@U[I;0O76FJ ¤ WK!@C4QP5>A25@sMcJKR5BF>G2
8CJKhL=!JKP5@CP>oJ0M ¨ § ;06b_~;06oE5JKP5@¸¹ º¼¹¾½^47AP © qín;06S>AOj[KW47Phi;0P[6F4Q>AR5;#>A4QJKP56bJ0Mv=5BG;08U>G478X;#O+47P>G@CBG@U6F>CW
Ì0ÍKÌ
B B
C C
B B
C C
B B
C C
B B
B B
C C
C C
B B
C C
D
C C
y
f(θ)
θ
x
Cf
r4QKR5BF@ µ q Ì qÈZ;0héhL@C8:2<;0P+476Gh_4Q>A2*; Ë ;#>MT;08U@xMcJKO7OQJ¦_s@CBUq
6FR58:2`;06~47Pz>A2+@x8X;06F@9J#M;|6F=525@UBG@0W<>G25@x6GR5BSMT;08C@ ¨ 8X;0P{!@xht;0=+=v@UEpJKP>AJL;|=5O;#P<;0B~BF@CK4QJKPW^_25478:2
;0K;047Pg;#O7O7J_6R+6>AJz>A2+47P5*J0MoMcR5P58d>A47J0P56xE5@Uf5P5@CEJKP ¨ ;06¶McR5P58U>G47JKP+6_25JK6G@E+JKht;#47P`4Q6=5O;#P<;0BCq
ÊkJ¦_s@U0@CBUW}_s@I6G2<;0OQO6F@C@|>A25;#>y47P`hi;0P[`4QP56F>A;0P58U@C6x4Q>e476!@CP+@Uf<8U4;0O>GJ{;0=5=5BFJ;08:2;zK4jK@CP\BF@C8CJ0P?]
6S>ABGR+8U>A4QJKP*=5BGJK+O7@Ch47Pp>A25@yhL47P5E^]l6G@d>J0M §µ q Ì © ;0P5E*P5J0> §Tµ q ²© qo¿~@dMcJKBG@x_s@D;0E+E5BG@U6G6>A254Q6k=!JK4QP>4QP
hLJKBG@xE+@U>:;#47O$W?4Q>3_4QO7O&!@y47P56S>ABFR58U>G4QK@x>GJLOQJ?J0t;#>k6FJKhi@x8UJKP58UBG@U>G@H@+;0hi=+O7@C6Uq
EGFIHJLK-M4N < eOQ>G25JKR502t47PL>A254Q6s8:25;0=+>A@UBs_s@x;0BF@e=5BF47hi;0BG4QOQ[H47P>A@UBG@C6S>A@UEp47Pt6F=5O74QP5@C6ÈJKPz6FR5BFMT;#8C@C6UW
>G25@ÈMcJ0O7O7J_4QP5Z@d+;0hL=5OQ@0W¦8CJKP+8C@CBFP547P+k>G25@shLJÊ5@COQ47P5ZJ#M+=5O7;0P<;0B8UR5BF0@C6UW0_47OQOK25@COQ=yhiJ0>G4Q#;#>G@b6G@dK@CBG;0O
4Qhi=!JKBF>A;0P>o=vJ047P>A6UqlPt=5;0BF>G478CR+O;0BUWv@UO7J_Ù_s@¶E+@C6G8UBG4Qv@k6GJKhL@47P>A@UBG@U6F>A4QP5yMT;08U>G6o>G2<;#>s;0BF476G@4QPL>G25@
8UJKP>A@d^>¶J0MwE5@C6F47KP54QP5I8X;0h=5BGJ0f5O7@C64QPphi@U8:2<;0P54Q8X;0O@UP5K47P+@C@CBF47P5+q
Z;0hi6;#BG@yR56G@UEa4QPpht;0P[p4QP5E563J0Mwhi@U8:2<;0P54Q8X;0OE+@U^478U@C6Cqo1325@U47B<;06F478x=5R+BG=!JK6G@y476Z>GJI8CJKPK@UBF>
BFJ0>:;0BS[IhiJ#>A47J0P47P>AJ9O74QP5@X;0BhLJ0>G47JKP>A25;#>È2<;06s;9=<;#BF>A4Q8CR5O7;0BE54Q6G=5O7;08C@Uhi@UP>s;06s;xMcR5P58U>G47JKPLJ0Mv>A47hL@0q
í@U>iR56LBG@U6F>ABF478d>iJ0R5BG6F@COQ0@C6i25@CBF@*>GJ8C;0hhi@U8:2<;0P54Q6GhL6_4Q>A2>A2+@Y6FJ#]l8C;0O7OQ@CE Ë ;#>IMT;08U@*McJKOQO7J_s@CBCq
1325@LR56FR<;0O_~;X[g>AJ{E5@C6F47KP;p8X;#h =5BFJ0f<O7@4QP`>A254Q6x8X;06F@I476>AJ{8UJKP56F>GBGR58d>y>A25@I6GJu]l8X;#O7O7@UEg6GR5=+=vJKBS>
McR5P+8U>A4QJKP ¤ W_254Q8:2ùE+@C6G8UBG4Qv@U6I>G25@pE54Q6G=5O7;08C@Uhi@UP>|J0M>A25@zMcJKOQO7J_s@CB § 0¹¾¸¦¹¾½b>G25@zK@UBF>A4Q8X;0O~E5476S>:;0P58U@
J0Me>A25@*McJKO7OQJ¦_s@CBIMcBGJ0h >A25@Y8C@CP>G@CBzJ0Me>A25@*8X;0h © ;06z;\McR5P58U>G47JKP J0M>G25@aBFJ0>:;#>G47JKP ;0P50O7A@ O?W36F@C@
r4QKR5BF@ µ q Ì q132^R+6CWn>A25@I6GR+=5=vJ0BF>yMcR5P58d>A47J0P4Q6y;p6G8X;#O;0BMcR5P+8U>A4QJKPg_25JK6F@LE+JKht;#47P ¨ 476>G25@IR5P54j>
± ?§ 8CJK6 O ¯ 6G4QRP O ©d¯ O *
8U47BG8UO7@#W=<;0BA;#hi@d>ABG4QÁC@UE[>A25@p=!JKO7;0B|;0P+KO7P@ O?W>A2<;u>476 ¤ ª~¨ « ¬ |¯i¨ª Q
Î ¯ Ì S T© , qb1325@e;06G6FJ?8U4;#>G@CEi=5BGJ0f5O7@8CR5BSK@J#M&>A2+@¶8C;0h 8X;0Piv@>A25J0R5K2>~J#Mn;06s;H=<;0BG;0hL@U>ABF47838UR5BF0@0W
0$¹ ¸¹ ½v;|K@U8U>GJKBkMcR+P58U>G47JKP V U ª+Ÿ« ¬ X W W5_2+JK6G@y47hi;0K@e4763K4jK@CP*[
V U ± ?Z§ Yw§ O ©d\¯ [&§ O ©G©¯ O * Î ¯ Ì S 4,¯
_25@UBG@y>A25@HZ;0BS>A@U6G4;#PY8UJ?JKBFE547P5;#>A@U636A;#>G476FMÃ][ ^
Yw§ O ©È± ¤b§ O © 8CJ06 § O 5© _ù`¤ c§ O © 6F47P § O ©¯ [&§ O ©± ¤b§ O © 6G4QP § O a© "Ù¤ c§ O © 8CJK6 § O ©³
1325@{JKûF@C8U>G4Q0@*J#Me8C;0hE5@U6G4QKP476D>GJJ0+>:;04QP;0=5=5BFJK=5BF4;#>G@z6GR5=+=vJKBS>McR5P58d>A47J0P56 ¤ >A2<;#>|hi@U@U>L;
=5BF@C6F8CBG4Qv@UEp6G@d>3J0MnBG@U·R547BF@ChL@CP>A6Uq1È[^=54Q8X;0OQOQ[KW ¤ h|R+6F>~>A;00@eJKPz6G=!@C8U4Qf<8k#;0O7R5@U6Z;#>~K4Q0@CPzE+476G8UBG@d>A@
Ö ¹K¹ ÛÄÜÓwÕ Ý{ß ÏkÓ}Û Ý Ü
Ì0Í0Í
r470R5BG@ µ q Í qÈøGv6G@d>¶8UR5BF0@C6k>AJL;8X;0hé=+BGJ0f<OQ@xJK+>A;047P5@UE{R56G4QP5L>GBG4QKJKP5JKhL@U>GBG4Q8e6G=+O747P+@C6Cq
0; P5KOQ@C6w;0P5E=5BF@C6F8CBG4Qv@UEE+_s@CO7OQ6 § 0¹¾¸¦¹¾½K4QP>G@CBS0;#O76w_4j>A2|8UJKP56S>:;0P>E54Q6G=5O7;08C@Uhi@UP> © W0;0P5E6F25JKR5OQE|BG@U6GR5Oj>
47PL;x8X;0h×>G2<;#>È4768UJKP56F476F>G@CP>È_4Q>A2I>A2+@kE+@C6G4QBG@UEt!@C2<;X^47JKBJ#M&K@UBF>G478X;#O5K@COQJ?8U4Q>l[0W?;#8C8C@UO7@UBA;#>G47JKPW;#P5E
>A25@y6FJ#]l8C;0O7OQ@CEHûF@CBF¼q
lP9=5BF47P58U47=5OQ@0WX>AJBF@C=5BF@C6G@UP> ¤ W_s@o8CJKR5OQEyR56G@È;3=547@U8C@d_476G@o=!JKOQ[^P5J0hi47;0OuMcR+P58U>G47JKPx>A25;#>n476=!@CBF47JÊ5478
_4Q>G2g=v@UBG47JÊ Ì S W4766FcR bL8C4Q@CP>AOj[`6GhLJ^J0>A2W;0P5Eg2<;06x@UP5JKR502 Ë @d?4754QO74j>l[ § 0¹¾¸¦¹¾½@UP5JKR502P5J#>A6 © >GJ
6A;#>G476SMÃ[>A25@e#;0BF47JKR+6shL@CP>A4QJKP5@UEt8CJ0P5E54Q>G47JKP+6CqÊkJ¦_s@U0@CBUW5>A254Q6È_sJKR5OQEzO7@C;0Ei>GJ;90@CBF[t8CJKhL=5OQ478X;u>A@CE
BG@U=5BG@U6G@CP>A;#>A4QJKPiMcJKB>G25@;08d>AR<;#O<8X;0h 6G25;0=v@#qb13254Q6s4Q6~;0=+=<;0BG@UP>sMcBFJKh×>A25@¶;0!JK@McJKBGh|R+O;McJKB U W
_25478:2476*;hi4 ^>AR5BF@gJ0M|=!JKOQ[^P5J0hi47;0Oe6F=5O74QP5@C6*;0P5EÉ>ABF47KJ0P5JKhL@U>ABF478aMcR+P58U>G47JKP56UqlP(=<;0BS>A478UR5O;#BCW
>A25@U6G@\8X;#h =5BFJ0f<O7@U6z>l[^=5478C;0O7Oj[ÙE5JP5J#>{=vJK6F6G@U6G6*=547@U8C@U_4Q6G@\BA;u>A47J0P<;0Oe=5;0BA;0hL@U>GBG4QÁX;#>G47JKP56t;06{;0BF@
@ChL=5O7J[0@CEÞ[Þ~ ¢é6S[^6F>A@Uhi6D;0P5E;#8C8C@U=+>A@UE.[Záehi4QO7OQ47P5zhi;08:254QP5@C6Uq*~JKPK@UBG6G@UOQ[0WÈ4jMZJKP+@
E5@C6F47BF@C6y; § =54Q@C8U@U_476F@ © =!JKOQ[^P5J0hi47;0OwJ0BBA;#>G47JKP5;0OBF@C=5BF@C6G@UP>:;#>G47JKP\McJKB V U W>A2+@CP\>A25@|McJKBFh J0MÈ>A2+@
E5476F=5O;#8C@ChL@CP>bMcR+P58U>G47JKP ¤ 4Q6K@CP5@UBA;0OQOQ[yMT;0BbMcBFJKh6F47hL=5O7@#W025@UP58C@kP5J0>;0=5=5BFJK=5BG47;#>A@sMcJKBbE5@U6G470Pi;#P5E
JK=+>G47hL47ÁX;u>A47J0Pt=5R5BF=vJ06G@C6Uq
132+@3hi@UP>G47JKP+@CE|6F25JKBF>G8CJKhL47P+eJ0M!=!JKOQ[^P5JKhL4;#O6G=5OQ47P5@U62<;06w>ABG4QKK@UBG@CE|;6G@X;#BG8:2McJKB6F=5O74QP5@C6}>A2<;u>
;0BG@L!@U>G>G@CBH6GR54j>A@CE>AJÈ+@C6G8UBG4Qv@LMcR5P58U>G47JKP+6HJKP>A25@i8C4QBG8COQ@0q{lP5E5@U@CEW47dP ^
4j>D2<;#6H!@C@UP6G25J_P
>A2<;u> þ èó ^ãuâ&ã etô þ èó ñ ölå!æ óÃâ&ô:ö § 0$¹ ¸¹ ½¼McR5P+8U>A4QJKP56k8CJKP+6G476S>A4QP5iJ#M=547@U8C@U6¶J0M>ABG4QKJKP5J0hi@d>ABG4Q8eMcR5P58d>A4QJKP56CW
6G@UP@ ^Kµ © ;0BF@y;0P{47E5@C;0Ov>GJ?J0OvMcJKB38C;0hE5@U6G4QKPqolPpMT;08U>CW+>A25@McJ0BGh|R5O7;HMcJKB V U ;0O7JKP+@6GR50K@C6S>A63>A2<;u>
>ABF47KJKP+JKhi@d>ABF478McR5P58U>G47JKP+6k=+O;X[p;IP<;#>GR5BA;0O&BGJKOQ@x47P{BG@U=5BG@U6G@CP>G47P5IMcR5P58d>A47J0P56JKPp>A25@y8C4QBG8UO7@0q
lPú>G25@g8CJ0P>G@d^>{J0My8C;0h E+@C6G4QKPW>ABF47KJKP+JKhi@d>ABF478{6G=5OQ47P5@U6p;0BF@g;0PÉ;#>F>ABA;#8U>A4jK@a;0OQ>G@CBGP5;#>A4jK@Y>GJ
=vJ0OQ[^P5JKhL4;0O6F=5O74QP5@C6Uqbáe;#hi@UOQ[KW0BG@C=+BG@C6F@CP>A4QP5y>A25@36FR5=5=!JKBF>McR5P+8U>A4QJKP ¤ ;06o;>ABF47KJ0P5JKhL@U>ABF478È6G=5OQ47P5@
O7@C;0E56>AJY;p=547@U8C@d_476G@LBA;u>A47J0P<;0O=+BGJ0f<OQ@8CR5BSK@ V U qiÂYJ0BG@CJ0@CBCWw4Q>>GR5BGP+6HJKR?>x>A2<;#>y>G25@C6F@i8UR5BF0@C6
2<;XK@È>A25@ÈBG@Uht;0BFu;05O7@=+BGJK=!@CBS>l[9>G2<;#>n>A2+@C47BnJ v6G@d>A6;0BG@È;0OQ6GJk=547@U8C@U_4Q6G@sBA;#>G47JKP<;#O q}13254Q6whL@X;0P+6
>A2<;u>s>G25@¶8UJKBGBF@C6F=vJKP+E547P5D8X;0hÇ=5BFJ0f<OQ@C6CW?;06È_~@UO7Ov;06È>G25@e8UR+>G>G@CBs=<;#>A2+6sMcJKB~ZáÙhi;08:254QP547P5+WvJ0>G2
=vJ06G6G@U6G6¶;6F>:;#P5E<;0BFEagá fGhk¿ BF@C=5BF@C6F@CP>:;#>G47JKP&q
bÏ Ð¶ÑeÒeÓwÔÈÕ×Ö ¹ÙØ ÒoÚÛÄÜeÔ ØÞÝ Ü Øbß Õkà?Ñ9ÏbÔ Ø
1325@oO7@C6F6GJKPx>GJk!@O7@C;0BGP+@CExMcBGJKh>A254Q6@d+;0hL=5O7@476>A25;#>@U0@CP9>A25JKR+K2y=vJKOj[^P5JKhL4;0Ou6G=5OQ47P5@U68X;#PH!@
R56F@CEI>AJyBG@U=5BG@U6G@UP>oMcR5P+8U>A4QJKP56JKP|>G25@38C4QBG8UO7@0W4j>b4Q6bhiJ0BG@INFP5;#>AR5BG;0O7V;0P5EL;0E+#;0P>:;#K@CJKR+6b>AJy@ChL=5O7J[
;YMcR+P58U>G47JKP.6F=<;08U@t>A2<;u>\NFhi;#>A8:2+@C6GV`>G25@t8U47BF8CO7@#iW 0¹¾¸¦¹¾½wJKP5@t>G2<;#>D476DE+@CBG4j[email protected]ÿ>ABF47KJ0P5JKhL@U>ABF478
=!JKOQ[^P5J0hi47;0O76Uq
1325@P5@d^>y@5;#hi=5OQ@D6F25J_6y>G2<;#>>G25@D>l[^=!@J0MÈ6G=<;08U@|_~@R+6G@hi;[YP5J0>v@kûFR+6F>y;z·R5@U6F>A4QJKPgJ0M
8UJKPK@CP+47@CP+8C@0qslPY6FJKhL@98C;06G@U6¶4j>3hi;[z;0O76FJIv@9;ht;u>G>A@UB3J0MwP5@C8U@C6G6F4Q>l[0q
EGFIHJLK-M4Nkj ín@d>R56P5J_8CJKP+6G47E+@CB|>A2+@phiJKBF@zE54 bi8UR5OQ>D=5BGJ05O7@Uh J0Mk8UJKP56F>GBGR58d>A4QP5\6GhLJ?J0>G2
McR5P+8U>A4QJKP56¶JKPY>G25@D6F=525@CBF@ ¨ 47P ¬ ® q1325@|hLJK6F>¶JK^47JKR+6e;0=+=5BGJ;#8:2`476>AJiht;0=*>A25@H6G=52+@CBG@DJKP>AJ
>G25@|=5O7;0P5@0W!R56F47P5z6F=525@UBG478C;0O}8CJ^JKBGE54QP<;#>G@C6CW!>A25@UP`@ChL=5OQJ¦[^4QP5t8UO;06F6G478C;0On54Q#;0BF4;#>G@9>G@CP56FJKBS]=5BGJÊ5R58d>
6F=5O74QP5@C6Uq1}J¶6S>:;#>G@È>G25@o=5BGJK+O7@Ch hiJKBF@o=5BG@U8C476F@COj[KWu6GR5=5=!JK6F@È>G2<;#> ¨ 476hi;0=5=!@CE9JKP>AJ>A25@ÈO7JKP+K4Q>GR5E5@d]
O7;#>A4j>AR5E5@xBF@C8d>:;0P50O7@
l ª ± ?§ O T¯ mv7© n pÎ o O oÌ S q¯ _ SsrKÌ o m otSsrKÌ ,
;0P+Et>A2<;u> ¤guª l£«¬ 4Q6~;9K4Q0@CPtMcR+P58U>G47JKPqwÆÞ@k8X;0Pi?4Q@U_ ¤ ;06Z;yMcR5P58U>G47JKPiJKP ¨ W^=5BGJ^47E5@UEt>A25;#>
4j>4763=!@CBG4QJ?E+4780W^>A2<;u>¶4Q6
¤b§ Î T¯ mv©± ¤b§ Ì S T¯ m&©¯ _ S(rKvÌ o m okSsrKÌ ¯
§Tµ q K©
;0P+EY8UJKP56F>A;0P>;u>3>A25@y=!JKO7@U6 0¹¾¸¦¹¾½
¤b§ O q¯ _ S(rKÌ ©È±(¤ w<¯ ¤b§ O ¯ S(rKÌ ©± ¤ xk¯ yÎ o O o(Ì S ¯
§Tµ q ^©
_25@UBG@ ¤ w ;#P5E ¤ x ;0BF@y>G25@x#;0O7R5@U63J0M ¤ ;#>3>G25@y6GJKR?>A2Y;0P5E*P5JKBF>G2{=vJKOQ@C6UW5BG@U6G=!@C8U>G4Q0@COQ[0q
1wJ.BF@C=5BF@C6F@CP>î0;#=5=5BGJX?47hi;#>G@`6G=52+@CBG4Q8X;0OMcR5P58d>A4QJKP56CW4j>t4Q6iP<;u>AR5BG;0Ok>GJ.8CJ0P56G4QE5@CBL>A25@Y6G=<;08U@`J0M
>G@CP56FJKBS]=5BGJÊ5R58d>¶=!JKOj[?P+JKhi47;0O!6G=5OQ47P5@U6CW 0¹¾¸¦¹¾½<>G25@y6G=<;08U@HJ#MwMcR5P+8U>A4QJKP56J0M}>A25@xMcJKBFh
x /

¤b§ O T¯ mv©± { ¥}z|~ { |~I ¥ ¥l§ O © $§ m&©d¯
§Tµ q ©

_25@UBG@ ¥ ;0P+E ;0BF@|R5P54j#;0BG47;#>A@H¿È]l6F=5O74QP5@C6e;06G6FJ?8U4;#>G@CEa_4j>A2\;tP5J#>x=<;0BS>A4Q>G47JKP*J0Mo>A2+v@ O¦]3;0P5E
m ]Ä;u?@C6UW5BG@U6G=!@C8d>A4Q0@COj[KqÆÉ2547OQ@¶McR5P+8U>A4QJKP56ZJ#M}>G25476sMcJKBGh 8X;0Pp!@hi;0E5@x;#BG54j>ABA;#BG47Oj[6GhLJ^J0>A2 § JKP l©
[|8:2+J?JK6F47P5¶>A25@ZE+@CKBF@C@3J0M<>G25@Z6G=+O747P+@~6G<R bi8U47@UP>GOQ[H254702W#>G25476_4QO7OP5J0>b;0R+>GJKht;u>A478C;0O7Oj[KR5;0BA;0P>G@C@
>G2<;#> ¤ 4766FhiJ^J0>G2\;069;tMcR5P58U>G47JKP\JKP ¨ W@U0@CPÞ4jMÈ4Q>x6G;#>A4Q6Ff<@U6xvJ0>G2 §µ ~ q K© ;0P+E §Tµ q ^© q|lPgMT;08d>XW4j>
_~;06e6F25J_P`47P ² ?W Í s§ 6G@C@H;0OQ6GJ Ã© >A25;#>>AJLJK+>:;#47P*;L6FhiJ^J0>G2 4§ JKBk2547K2+@CB © McR+P58U>G47JKPW<>G25@
McJKOQO7J_47P+|6G@d>eJ0Mw@C·R<;u>A47J0P56h|R56F>2+JKO7EpMcJKBZ>G25@y=<;0BF>G4;0OvE5@CBF4Q#;#>G4QK@U6 ¤ ;0P5E ¤ ª
¤ u§ Î T¯ mv©b± ¤ ¦§ Ì S T¯ m&©¯ _ S(r0yÌ o m odS(rKÌ ¯
;0P+E
¤ 5§ O q¯ _ S(rKÌ ©
± Xw 8CJK6 O "Gw 6F47RP O ¯ ¤ ?§ O ¯ S(r0Ì ©± Xx 8CJK`6 O "Xx 6G4QRP O ¯ vÎ o O oÌ S ¯
_25~ @UBG@ Xw5)¯ Xw<\¯ Gx W^;0P+E Xx ;#BG@8CJKP+6F>:;#P>G6Cq1325@U6G@¶@C·R<;#>G47JKP56o@+=+BG@C6F6s>G25@8CJKP5E+4Q>A4QJKP|>A25;#> ¤ 4Q6
]l8UJKP>A47PR5J0R56e;#O7JKP5>G25@H=+BG47hL@xhL@CBG4QE54;#P O ± Î ;0P5E`;#O76GJi;#>>A2+@H=!JKO7@U6CW5_254Q8:2a4Q6k@U·R54Q#;0OQ@CP>
>GJi8UJKP>A47PR54j>l[zJ0M}>A2+@y>A;0P5K@UP>¶=+O;0P5@yJ0M ¤ JKP ¨ q
Ì0Í
Ö ¹+¹ÙØ ÏÑÚÑÕ Ø ÒoÚÛÄÜeÔ ØÝ Ü Ø ÞÝ9Ý ÓwÐ Øbß Õ¶à^Ñ9ÏbÔ Ø
Ì0Í >y8C;0P\v@I6F@C@CP\>A25;#>XWR5P+O7@C6F6x>A25@|McR5P+8U>A4QJKP ¤ 476 Ë ;u>9;#>>A2+@L=!JKOQ@C6CW20¹¾¸¦¹¾½nR5P5OQ@C6G6 GwY±Xw*±
Xx
± Xx± Î WwP5J*>A@UP56GJKBÄ]l=5BFJ?E+R58U>D6G=5OQ47P5@IJ0Ms>A25@LMcJKBGh §Tµ q © 8C;0PÞ!@L6GhLJ?J0>G2Þ;u>H>G25@i=!JKOQ@C6Cq
1325476oMcJKOQO7J_6McBGJKhÇ>A2+@kMT;08d>~>G2<;#>È>A25@¶BG4702>S]l2<;#P5Ei6F47E5@U6~J0M&>A25@¶O;06S>s>l_sJ|J0M>G25@;#vJK@¶@C·R<;0OQ4Q>G47@C6
47PKJ0OQK@¶>ABG4QKJKP5J0hi@d>ABG4Q8=vJKOj[^P5JKhL4;0OQ6Cq}132^R+6CW<P5J|hi;#>F>A@CB~25J_(2+47K2t>G25@E5@UKBG@U@xJKB~f<P+@e>A25@xP5J#>
=<;0BS>A4Q>G47JKPxJ#M5>A25@ÈO7J0P5K4Q>GR5E5@]lO;u>A4Q>GR5E5@;¦+@U6CWK=+47@C8U@U_4Q6G@~=!JKOj[?P+JKhi47;0O76;0BG@È47P52+@CBG@UP>AOQ[y4QP58CJ0hi=<;u>A47+O7@
_4Q>G2{>G25@y6G=52+@CBG@#W!;#>O7@C;06F>4QP{>G25@9;0!J¦0@d]E5@C6F8CBG4Qv@UEa6F@U>G>G47P5+q
~J0P56G@U·^R+@CP>AOj[KW>AJJK?>:;04QP£KO7JK5;0O7Oj[ 6FhiJ^J0>G2£6G=525@UBG4Q8X;0OMcR5P+8U>A4QJKP56UW¶_s@hDR56F>*;05;0P5E5JKPÉ>A2+@
47E5@C;pJ0MZR56F47P5{>A2+@i8UO;06F6G478C;0O¿È]6G=5OQ47P5@U6Cqií470@L47P\JKR+B9=+BG@U^4QJKR569@d+;0hL=5O7@#W}4j>94769;*0J?JÊ\47E5@C;p>GJ
R+>A4QO74QÁC@~>G BG470JKP5JKhL@U>GBG478~6G=5OQ47P5@U6CqoÂYJ0BG@=5BG@U8C4Q6G@COj[KW^4Q>_~;06È6G25J_Pz4QP ² >G2<;#>È[LBG@C=+O;08U47P5x>A2+@¶¿o]
6G=5OQ47P5@U6 ¥ 4QP §µ q © _4Q>G2>A25@U47Bb>ABF47KJ0P5JKhL@U>ABF478s8CJKR5P>G@CBG=5;0BF>G6CW+4j>4764QP5E5@U@CEL=vJK6F6G4Q5O7@3>AJy8UJKP56F>GBGR58d>
6GhLJ?J#>A2p6G=+25@CBF478X;#OMcR5P58U>G47JKP+6kJ#Mw>G25@xMcJKBGh §µ q © q
132+@H;#vJK@>l_sJI@d+;0hL=5O7@U632<;XK@yE5@UhiJKP+6F>ABG;#>A@UEp>A2<;#>~>A25@y6F>GBA;04QK2>GMcJKBS_Z;#BGE{;0=5=+BGJ;08:2p>GJBG@C=^]
BG@U6G@CP>G47P59McR5P58U>G47JKP+6ÈJ0P ¨ 476oP5J#>~P5@U8C@U6G6A;#BG47Oj[IJK=+>G47hi;0O$q}mbK@UPz4QM ¨ 476o6G4Qhi=5OQ@3@CP5J0R5K2i>G2<;#>È4Q>È8C;0P
v@yhi;0=5=!@CE*JKP>AJt;0PY4QP>A@CBS#;0OJKBk;L=+O;0P<;#BkBF@CK4QJKPW<4j>ht;X[p6S>A47OQOv@yR56F@UMcR5On>AJÞNF8UR56F>GJKhI]E5@C6F47KP+V
;|6G=5OQ47P5@¶6G=<;#8C@x>A2<;u>3476Z8UJKhL=<;#>A4Q5O7@_4Q>G2z>A25@x04QK@UP{6GR5BSMT;08C@#qÈ ¶6Z_~@x25;0@y6G@C@UPW<47Pp0@CP5@UBA;0O!>A254Q6
_47OQO&O7@C;0Ep>AJMcR5P58d>A4QJKP{6G=<;08U@C6>A2<;u>e;#BG@â&ãuâ<ä7å<ãuæ uâ&ã eóTç0æ}4QP{P<;#>AR+BG@0q
6F8C@C=?>A478C;0O3BG@C;0E5@UBihL47K2>6S>A4QO7O3;0BFKR5@p>A25;#>>A25@UBG@*476I;0Oj_Z;X[^6I>A25@{=!JK6G6F4754QO74Q>l[>AJ\R56F@Y6S>:;0P^]
E<;0BFEg=<;0BA;#hi@d>ABG4Q8|6GR+BFMT;08U@=<;#>A8:2+@C6CWn_254Q8:2;#BG@=54Q@C8C@d_476F@=vJKOj[^P5JKhL4;0OW!>GJpBG@C8UJKP56S>ABGR+8U> ¤ q|r<JKB
47P56S>:;0P+8C@0Wv47Pamb+;0hL=5OQ@ Ì _s@|8CJ0R5O7E`R+6G@|=<;#BA;0hL@U>GBG47896GR+BFMT;08U@|=<;#>G8:25@C6e>GJzhLJ?E5@UO}>G25@D6FR5BFMT;#8C@ ¨ 47P §µ q Í © ;#P5EL>G25@CPiJK+>A;047P>A2+@k8UJKBGBF@C6F=vJKP+E547P596G8C;0O;#BoMcR+P58U>G47JKPL;06 ¤b4§ !©o±§l¨ 4§ !© _!© %s')¯ !*¨ q
ÆÉ2547OQ@k>G25476È476È>ABFR5@e4QPz=5BG4QP58C4Q=5O7@#W>A25@UBG@x;0BF@e6F@UK@UBA;0O&E5;4 bL8CR+OQ>A4Q@C6s;06G6FJ?8U4;#>G@CEt_4j>A2t>G25476s;0=5=+BGJ;08:2&q
r47BF6F>CW3R56G4QP5=<;0BG;0hi@d>ABF478*6GR5BSMT;08C@U6pBG@C·R54QBG@U6z_~JKBF47P5._4j>A2úK@U8U>GJKBS]$0;#O7R5@UEúMcR5P58U>G47JKP+6CWk;06pJK=?]
=vJ06G@CEI>AJy>A2+@¶6F47hL=5O7@UB6G8X;#O;0BbMcR5P+8U>A4QJKP56Uq @C8UJKP5EW^8CJ0P56F>GBGR58d>A47P+D6GhLJ^J0>A2I8CJ0hi=!JK6G4j>A@3=<;#BA;0hL@U>GBG478
6GR5BSMT;08C@U6|476D;a254QK25OQ[P5J0P?]>GBG4Q^47;0Ob>:;06F6F47P58U@t>A2+@z6GhLJ?J#>A25P5@U6G6|8UJKP5E54j>A4QJKP56D!@U>l_s@C@UPù;0EuûFJK4QP547P5
6GR5BSMT;08C@y=<;u>A8:25@U6¶;#BG@yhiJ0BG@E54 bL8CR5Oj>3>AJI47hL=vJ06G@e>G2<;0P{47Pp>A2+@x6G8X;#O;0B38C;06G@#qÈ132+47BGE&W5>A25@x8UJKP56F>GBGR58]
>A4QJKPÞJ0M>G25@z=<;0BG;0hL@U>ABF478i6GR5BSMT;08C@ph|R+6F>KR5;0BA;0P>G@C@t>G2<;#> ¨ 476H6F>:;#BS]lOQ47#@0iW 0$¹ ¸¹ ½b6GR58:2>A25;#>@U0@CBS[
2<;0OjM]lO74QP5@e@Uht;#P<;#>A4QP5|McBGJ0h>A25@yJKBF47K4QPp47P>A@UBG6F@C8U>G6 ¨ JKP5Oj[pJKP58U@0W<McJKB3J0>G25@CBS_476G@ ¤ _~J0R5O7E*P5J0>k!@
_~@UO7OsE5@Uf<P+@CEqín;06F>GOQ[KWJKP58C@ ¨ 2<;#6|v@U@CP8CJ0P56F>GBGR58d>A@CE&WÈ>GJ`BG@U8CJK@UB ¤$§ !© McJ0B|;`K4jK@CP=!JK4QP> !
JKPY>G25@96G=525@UBG@#W4Q>k476kP5@U8C@C6F6A;0BS[a>GJi8UJKhi=+R+>A@9>A25@90;#O7R5@ ¨ $§ !© q1325476k476¶;iE54 bL8CR5Oj>k>A;06G{6F47P58U@D4Q>
BG@U·^R+47BG@U66GJKOj?4QP5I;I6G@U>kJ0M;0OQK@C5BG;0478e@C·R<;#>G47JKP56Uq
132+@H<;#6G478y·R5@U6F>A4QJKP{>A2<;#>¶;0BF476F@C647Pp>A2+@98UJKP>A@?>eJ0M §µ q Ì © 47625J_(>AJL8CJKP56S>ABFR58U>¶6G=5OQ47P5@x6F=<;08U@C6
J0MMcR5P58d>A4QJKP56~J0P ¨ >A25;#>ZBF@C6G@Uh|5OQ@e>A25@eR56GR<;#O6G=<;#8C@C63J#Mn=547@U8C@U_4Q6G@=!JKOj[?P+JKhi47;0O76o4QPt>A25@e=5O;0P+@ § 4jM
>A254Q6~4Q6~47P+E5@C@UEp=vJK6F6G4Q5O7@ © q eP+J0>A25@UBZ47hL=!JKBF>A;0P>~·R5@U6F>A4QJKPp476È_25@U>G25@CBZ>G25@_s@CO7O ]l@U6F>:;#5O74Q6G25@UEtE<;#>A;
f5>G>G47P5D;0P5EphLJ?E+@CO74QP5y>A@C8:2+P547·R5@U6ZMcJKBsMcR5P+8U>A4QJKP56Z4QPi>G25@=5O7;0P5@e8C;0Pp!@@d^>A@UP5E5@UE{>GJ|>A25@eK@CP5@UBA;0O
6G@d>G>A4QP5{J0M3;#BG54j>ABA;#BF[`6FR5BFMT;#8C@C6Uqi132+@i25J0=v@I476x>G2<;#>9ht;#P[aJ0M~>G25@IR56GR5;0Oohi@d>A25JÊ56x_~J0R5O7E8X;0BFBF[
JK@CB3>GJI>G25476K@UP5@CBG;0O6G4j>AR<;u>A47J0Pz_4Q>A2+JKR+>3>AJ^Jh|R58:2Y@d^>ABG;L@ &J0BF>Xq
1}JY;0E5E5BF@C6G69>A25@U6G@i·^R+@C6F>G47JKP+6CWw_s@I_47O7O=5BG4Qht;0BF47Oj[YMcJ^8CR56yJKR+BH;u>G>A@UP>A47J0P4QP @U8U>G47JKP Ì J0P>A2+@
476F6GR5@|J#Mo8CJKP56S>ABFR58U>G47P5z6F=5O74QP5@D6F=<;08U@C6xJKP ¨ q eOj>A@UBGP<;#>G4Q0@|;0=5=+BGJ;08:2+@C6>AJi>A254Q6e=5BFJK5O7@Uh _4QO7On!@
O74Q6F>A@UEp47P @U8U>A4QJKP Í q
j ¨ V#z I¨ ÈU E ¨ L I¨ ¡ tLV¢ ¨ p£2z E ¨
Êe;X^47P5iO7J^JK0@UEg;#>e@d+;0hL=5O7@U6J0M6F=5O74QP5@C6¶JKPg6G=!@C8U4Qf<8|hi;0P54jMcJKO7E+6CW<O7@d>R56eP5J_8UJKP56F47E5@UB¶>A2+@|8X;06F@
J0MK@UP5@CBG;0OZ6GR+BFMT;08U@C6Cq\Æ@t_47OQOÈf<BF6F>IE5@df<P5@z>G25@p8CJKP>G@d^>IJ0MkJKR5BH6G@U>F>A4QP55q\lP>A254Q6D6G@U8U>G47JKP>A2+@
Ì0Í ^
S
T
T
f
IR k
r4QKR5BF@ µ q q1wBF4;0P50R5O;#>G47JKPtJ0Mb;6FR5BFMT;08U@ ¨ q
6FR5BFMT;08U@ ¨ _47OQOv@ ¥¤ ]l6FhiJ^J0>A2*47P{>A2+@HR56FR<;0On6G@UP56G@DJ0MbE54&@UBG@UP>G4;0O0@CJKhL@U>GBF[Kq~1325476k476kv@U8X;0R+6G@
JKR+BÈhi;04QP|47P>A@UBG@U6F>o_47OQO+!@347Pzöetãã þZ¦ 6G=5OQ47P5@U6JKP ¨ W_254Q8:2L_sJKR5OQEL!@k;0PL;X__~;0BFEtBG@U·R547BF@ChL@CP>
4jM ¨ 4Q>A6F@COjMÈ_s@CBF@IP5J0>y6GR<bi8U47@UP>GOQ[a6GhLJ?J0>G2qøeMÈ8CJ0R5BG6F@0WMcJKBx;0OQO=5BG;08U>G478C;0Ob=5R5BF=vJ06G@C6x>G25@47P+f5P54Q>G@
E54 &@UBG@UP>G4;0+47O74j>l[|8UJKP5E54j>A47J0PL8C;0Pt!@eBF@CO7;u?@CEi>GJHhi;#>G8:2i>A2+@¶JKBFE5@CBÈJ0M6FhiJ^J0>G25P5@C6F6sJ#M ¤ qb ¶O76GJ+W_s@
_4QO7OBF@C6F>GBG4Q8U>JKR5BF6G@UOQK@U6¶2+@CBG@y>AJ>G25@y8X;06F@9J#M6F8X;0O7;0BS]$0;#O7R5@UE{McR+P58U>G47JKP56 ¤§ 0¹¾¸¦¹¾½ ëL±² 4QP §µ q Ì ©G© q
=5O74QP5@C6|;0BG@pR56FR<;0OQOQ[JK+>:;#47P5@UE[.E54Q^47E+47P5`R+=>G25@pE5JKhi;04QP.J0Mk>A25@U47B|E5@df<P54j>A47J0PW ¨ 47PJ0R5B
8C;06G@#Ws4QP>GJÈ54Q6cûFJK4QP>D6GR5+6G@U>G6Cq1325@phiJ06F>|MT;0hL47OQ4;0BxhL@X;#P56|J0Mk=<;0BS>A4j>A47J0P547P5Y;`K4jK@CPE+JKht;#47PÞ4Q6
>GJ`>ABG47;0P5KR+O;#>G@i4j>XqgM>A25@pE+JKht;#47PÞ4Q6|=5O7;0P<;0BUW>A25@tBG@C6FR5OQ>G47P5a6G=5OQ47P5@z6F=<;08U@p476H>G25@z_s@CO7O ]lP5J_P
6F=<;08C@YJ0M¶=547@U8C@U_4Q6G@*=vJ0OQ[^P5JKhL4;0OQ6DJKPù>ABF4;0P50R5O;#>G47JKP+6CqÞÆÉ254QO7@z>G25@CBF@Y@+4Q6F>t;gKBG@C;#>I0;#BG47@d>l[J0M
54j#;0BG47;#>A@o6G=+O747P+@C6CW08CJKBFBG@C6F=vJ0P5E547P+¶>AJeht;0P[x>l[^=!@C6J0M<0BG47E+6;0P+E|=vJ0OQ[^KJKP<;#O=<;0BF>G4Q>G47JKP56UW#=+47@C8U@U_4Q6G@
=!JKOQ[^P5J0hi47;0O763JKPY=5O;#P<;0B>ABG47;0P5KR+O;#>G47JKP56;#BG@y>A25@HhiJK6S>eR+P54Q0@CBG6G;0O6F47P58U@|;0OQOJ0>A2+@CB¶>l[^=!@C68C;0P`!@
^47@d_~@UE.;0P+EBF@C=5BF@C6G@UP>A@CE;#696F=5O74QP5@C6xJ0P>GBG4;#P5KR5O7;#>A4QJKP56CqH1325@CBF@UMcJKBF@0Wn>AJY;0E5E5BF@C6F69>G25@I=5BGJK+O7@Ch
JKPLK@UP5@CBG;0O<6GR5BSMT;08C@U6 ¨ W_~@_47OQO5;0OQ6GJ9;06F6GR5hL@3>A2<;#>o>G25@6GJKR502>S]McJKB6F=5O74QP5@36G=5;08C@_47OQO+8CJ0BGBG@U6G=!JKP5E
>GJt;|>ABF4;0P+KR5O;u>A47J0PtJ0M ¨ q
e6R+6GR<;0OWK;>ABG47;0P5KR+O;#>G47JKPxJ0M ¨ 4Q6;k8CJKOQO7@U8U>A4QJK¥P § J0M<K@UJ?E5@U6G4Q8È>GBG4;#P5KO7@U6nJKP ¨ W#_25J06G@Z4QP>G@CBF47JKBF6
;0BF@IE5476ÃûFJK47P>9;0P5E6GR+8:2>A25;#>y>A25@IR5P54QJKPJ0MZ;#O7O>GBG4;#P5KO7@U647P §4Q6 ¨ sW 0¹¾¸¦¹¾½ ¨ ¨± ?v©ªq«7¬ qLÊk@CBG@#W
;zK@UJ?E+@C6G4Q8|>ABF4;0P50O7@ ¬ 4Q6;z8COQJK6G@UE\6GR556F@U>yJ0M ¨ W25JKhL@CJ0hiJKBF=5254Q8H>AJ{;i=5O;0P5;0B¶>GBG4;#P5KO7@#Wv_25J06G@
!JKR5P5E5;0BF[8UJKP56G4Q6F>G6iJ0Mk>A2+BG@C@*K@UJ?E5@U6G4Q8*6F@CKhL@CP>G6tJKP ¨ 8CJKP+P5@C8d>A47P+Þ;g>ABF47=5OQ@pJ0Me=!JK4QP>G6I47P ¬ W
8C;0O7OQ@CE{>A25@xK@UBF>G478C@U6eJ0M ¬ qs1325@U6G@9>A25BF@C@9K@CJÊ5@C6F478U6e;0BF@x>A25@y@CE+K@C6¶J0M ¬ qÈ1325@90@CBS>A478U@C6¶J0M ¬ _47O7O
!@tE5@UP5J0>G@CE.L[ § ¬© ;0P5E>A25@i@CE50@C6D[ ® § ¬e© qz1325@i@CE50@C6H_4QO7O!@i4QP5E5@+@UE.L[ Z§ ¬e© 6GR58:2
>G2<;#g> ¯° * ® § ¬© _4QO7OvE5@CP5J#>A@y>A25@y@CE+K@yJ0M ¬ JK=5=!JK6G4j>A@>GpJ ± * Z§ ¬e© q
²w@CBF2<;0=56>A2+@9hLJK6S>3=vJ0=5R5O;#B~_Z;X[{J0MwBG@U=5BG@U6G@UP>G47P5L6G=+O747P+@C63JKP{>ABF4;0P50R5O;#>G47JKP+6s4Q63[zhi@C;0P563J0M
>G25@p¿~@UBGP56S>A@C4QP?]Ä¿L@CÀ ÁC4Q@CBDMcJ0BGhi;0O74Q6Gh*q{¿~@CBFP56F>G@C47P^]Ä¿L@UÀ ÁC47@UBD>A@U8:25P54Q·^R+@C6I;0BF@t@d^>GBG@ChL@COj[ÞR+6G@UMcR+Os>AJ^JKOQ6
McJKB98CJ0P56F>GBGR58d>A47P+`=547@U8C@d_476G@L=!JKOQ[^P5JKhL4;#Ob6GR5BSMT;08C@U6|JK@UBH>ABF4;0P+KR5O;u>A@CE\=5O7;0P<;0ByE5J0ht;04QP56Cqp ¶6H4Q6
E5@UhiJ0P56F>GBA;#>G@CE`4QPYhi;0P[{8:2<;0=+>G@CBF6J0M>G25@D!J^JK § 6F@C@|~2<;0=+>G@CBG6^ © Wv>A2+@U[*=5O;X[*;0PY47hL=vJ0BF>:;#P>
BFJKO7@È47PD~ k¡9¢|W¦E<;u>:;3f5>G>G47P55Wu8CJ0hi=5R?>A@CBn^476F47JKPW#;0P5EH@COQ6G@U_2+@CBG@ § 6G@U+@ ÌKÌ W Í µ © q}1wJ¶E5@Uf5P5@Z;0P5;0O7JK06
J0M<¿~@CBFP56F>G@C47P^]Ä¿L@UÀ ÁC47@UBw>G@C8:25P54Q·R5@C6;#6G6GJ^8C47;#>A@UEH_4j>A2 ¨ W0_s@~P+@C@CEH>AJ¶f5P5EHf<P+4Q>A@]lE54Qhi@UP56G4QJKP<;0O06G=<;08U@C6
J0M&McR5P58U>G47JKP+6s>A25;#>~=+O;X[>A25@¶BGJKOQ@J0MJKBFE547P<;#BF[I=!JKOQ[^P5JKhL4;#O76b4QPi>A2+@¶=5O7;0P5@#qb1325476s47PL>AR5BFPtO7@C;0E56ÈR56
>GJk>G25@·R5@C6S>A47J0PHJ0M?E5@df<P547P+¶;#PD;0=+=5BGJK=+BG4;u>A@b8UJKR5P>A@UBG=<;0BS>}J0M?>G25@o6G=<;#8C@oJ0M?O747P+@X;0B&McR+P58U>G47JKP56UW#6F47P58U@
>G25@CP`2+47K25@UBS]E5@CKBF@C@YNF=!JKOQ[^P5J0hi47;0O76FVD_47OQOv@9JK+>A;047P+@CEY;06¶=+BGJÊ5R58U>G6¶J#M>A2+@`NFOQ47P5@C;0BGVMcR5P+8U>A4QJKP56Uq
1}J¶!@o;05OQ@b>AJ3@+=+BG@C6F66FR58:2H0@CP5@UBA;0OQ47ÁC@UEy=vJKOj[^P5JKhL4;0OQ6v4QPy;k¿s@CBGP+6F>A@U47P?]l¿L@CÀ ÁU47@UBS]lOQ47#@bMcJKBGh*W47Px@dK@CBS[
>GBG4;#P5KO7@ ¬¨* §pWn_s@L;0O76FJpP5@C@UE>GJ{f5P5EÞ;#P<;0O7J0K6J0MÈ>A25@|_s@COQOj]^P+J¦_´P ³:ç0Tè ñ ôdâ þ èó ñzñ ããuèFõ0óÃâ!ç þ ô:ödq
Ö ¹+¹ÙØ ÏÑÚÑÕ Ø ÒoÚÛÄÜeÔ ØÝ Ü Ø ÞÝ9Ý ÓwÐ Øbß Õ¶à^Ñ9ÏbÔ Ø
Ì0Í R58:2*K@CP+@CBA;#O747ÁU@CE{8CJ^JKBFE547P<;u>A@C6Z_4QO7O!@xE5@UP5J0>A@UE`;06
µ ©° ª ¬«¬ |¯ ± * Z§ ¬e©¶¯ ¬·* § ³
1325476yBF@CE5R58U@C6y>A25@L=5BFJK5O7@UhJ0M~;0P;0=5=5BFJK=5BG47;#>A@E+@Uf<P54j>A4QJKP\J0MINF=+47@C8U@U_4Q6G@I=vJ0OQ[^P5JKhL4;0OQ6GVzJ0PL§
>AJzf<P+E547P5*;zBF@X;06FJKP<;05OQ@|_Z;X[`>GJ{E5@Uf<P+@I>G25@|McR5P58d>A4QJKP56 µ ©° q|1}JY;#P56F_s@CBx>A2+476·R5@UBF[KW}O7@d>xR56xOQ476F>
6GJKhL@xJ0M}>A25@yhi;047Pp=+BGJK=!@CBS>A47@U6;06G6FJ?8U4;#>G@CE{_4Q>G2{>G25@y8CO7;06G6F478X;#O¿~@CBFP56F>G@C4QP?]Ä¿L@UÀ ÁC4Q@CB3McJKBGhi;0OQ476Gh ª
§S²¦© ákJKP?]lP+@C;#>G4Q^4Q>l[i;0P+Ez=<;0BS>A4Q>G47JKPLJ0MnR5P+4Q>l[LJ0M}¿~@UBGP56S>A@C4QPp=vJ0OQ[^P5JKhL4;0OQ6o;06G6FJ?8U4;#>G@CEt_4j>A2p;#P[
K4jK@UP*>GBG4;#P5KO7@ ¸
§ Ì © 1325@98CJ0P0@dY2R5O7O&=5BGJK=!@CBS>l`[ ¸
§ Í © h@C=5BFJ?E+R58U>G47JKP{J0Mb;0O7K@U5BA;#478e=!JKOj[?P+JKhi47;0O7/6 ¸
§ © 9 biP+@H4QP#;0BF4;0P+8C@ 0¹¾¸¦¹¾½v¿L@CÀ ÁU47@UBk8UJ?@ bL8C47@UP>A6_47O7O&P5J0>k8:2<;0P50@D;#MÃ>G@CB3>ABG;0P56SMcJKBGhL47P5|>G25@HmoR^]
8UO747E+@X;0P{=5O7;0P5@x[*;0P*; bLP5@x>ABG;0P56FMcJ0BGhi;#>A4QJKIP ¸
¹§ K© 1325@y=!JK6G6F4754QO74j>l[IJ0M}JK+>:;#47P54QP5|;0BF54Q>GBA;0BF47Oj[I6GhLJ?J0>G2p=547@U8C@d_476G@x=!JKOj[?P+JKhi47;0O76oJKP{;#P[t>ABG47;0P?]
KR+O;#>G47JKIP ¸
$§ ^© hLJ^J0>A25P+@C6G6!@U>l_s@C@UPú;0E¦ûG;08C@UP>L¿L@CÀ ÁC4Q@CBD>GBG47;0P5KOQ@C6D8C;0Pv@p@?=5BG@U6G6G@UEÙ4QP.>A@CBFhi6DJ0MkO7J^8X;0O
¿L@UÀ ÁC4Q@CB8CJ^/@ bL8C4Q@CP>A6UW¼8CJKBFBG@C6F=vJ0P5E547P+I>GJL>G25@C6F@x>ABG47;0P5KOQ@C6Uq
ÆÉ2+47O7@>A2+476Èht;X[I6G@U@Ch 6GJKhL@U_25;#>Z6FR5BG=5BF476F47P55W^47PL>A25@¶8CJKP>G@d^>ZJ0Mn6F=5O74QP5@C6ÈJKPz0@CP5@UBA;0O!6GR5BSMT;08C@U6
>A25@yhLJK6F>McR5P+E<;0hL@CP>:;0OJ#M>A2+@D;0!JK@94Q>G@ChL6>GR5BGP*JKR+>>GJi!@H=+BGJK=!@CBS>A47@U6 ¹§ K© ;0P5E $§ ^K© q~1325;#>k476CW
6G=5OQ47P5@¶6G=<;#8C@C6JKPp0@CP5@UBA;0O6FR5BFMT;#8C@C66F25JKR5OQEpv@6FR58:2{>A2<;#>~>A25@d[z8X;#P*!@xR56F@CEp>AJ5R+47O7EiMcR5P58U>G47JKP+6
>A2<;u>{;0BG@`;0BG54j>ABG;0BG4QOQ[ 0æ7ã ³:ç0æÃæ ù6GhLJ?J0>G2 § =5BFJ?4QE5@CE£>G25@gE5@C0BG@C@g4Q6z6G<R bi8U47@UP>GOQ[£2+47K2 © ;0P5E£[K@d>
>A25@U6G@i6G=<;08U@C6H6G25JKR+O7EÞ!@ Ë @d?47+O7@L@CP5JKR+K2Þ6FJY>A25;#>D4j>94769=vJK6F6G4Q5O7@>AJY8CJKP+6F>ABFR58U>tæ7ã ñ ç0æ~hL@U>G25J?E+6
J0MxBF@C8CJ0P56F>GBGR58d>A47J0Pq ¶P5J0>A2+@CBt4Qhi=!JKBS>:;0P>L=5BGJ0=v@UBF>l[ J0M>A2+@a8CO7;06G6F478C;0O=547@U8C@U_4Q6G@`=!JKOj[?P+JKhi47;0O76UW
>A2<;u>i6F25JKR5OQE !@*ht;04QP>:;04QP5@CE4QPù>G25@Y0@CP5@UBA;0O8X;#6G@0W~476>A2<;u>L>G25@U[ù;#BG@*K@CP5@UBA;#>G@CE 47Pù;6F47hL=5O7@
_Z;X[.McBFJKh OQ47P5@C;0BHMcR5P+8U>A4QJKP56IJKP@X;#8:2 >ABF4;0P+KO7@#qÞlPùJKR5B6G@d© >G>G47P55Wo>A2+@Y;#P<;0O7J0gJ0M¶>G25@{6G=<;#8C@{J0M
O74QP5@X;0B¶McR5P58U>G47JKP+6y_4QO7Ob!@I>A25@I>A25BF© @C@]lE54Qhi@UP56G4QJK© P<;0Ob6F=<;08U»@ º Wn_254Q8:2Þ476>G25@LO747P+@X;0Bx6F=<;0PÞJ#M~>A2+@
<;0BS[?8U@CP>ABF478y8CJ^JKBFE547P<;u>A@C6UW 0¹¾¸¦¹¾½ º ª¾± 6G=<;#P µ ° © ¯ ± * § ¬eT© , q
>~476ÈP5J0>~E5;4 bL8CR+OQ>È>AJD6F@C@e>G2<;#>s>A25@¶6G=<;08U@C¼6 º 8X;0P5P+J0>Z!@e·R54j>A@¶;0BG54j>ABG;0BF[0qblPz=<;0BS>A4Q8CR5O7;0BCW>A2+@
<;0BS[?8U@CP>ABF478y8CJ^JKBFE547P<;u>A@C636F25JKR5OQE{47P>A@UBG=!JKO;#>G@y;#>3>A2+@y0@CBS>A478U@C6UWv;#P5E{47PpMT;08U>
§µ q ½ ©
µ ©° § ± ©±² ;0P5E µ ©° § ¯° ©± Î ¯ ± * § ¬©³
13254764Qhi=5OQ47@U6~>A2<;ug> º © BG@U6F>GBG478d>A@UE*>GJt;0P[{J0Mw>A25@x>G25BG@U@H@UE5K@C6¶J0M ¬ 4763>l_sJtE54Qhi@UP56G4QJKP<;0OW+BA;u>A25@UB
>A2<;#P*>G25BG@U@HE54Qhi@UP56G4QJKP<;0OqlP`;0E+E54Q>G47JKPW5;LBF@C·R547BF@ChL@CP>kMcJKBKO7JK5;0O8CJ0P>G47PR54j>l[ $§ ¾© J0M;I6G=5OQ47P5@
McR5P58d>A47J0P*4QPz>A25@YNFOQ47P5@C;0BGV6F=5O74QP5@x6G=5;08C@
¿Á~ À ~ § § ©~ª 3
± #¤`ª+ä« ¬ |¯#¤ n © * º © ¯ ¬·* § ,¯
476>G2<;#>9>A25@I6G=5;08C@UV6 º © n Â ;0P5E º ©ÄÃ n Â W}8CJ0BGBG@U6G=!JKP5E54QP5{>AJY;0P[\=<;047ByJ0MsP5@U47K2!JKBG4QP5p>ABG47;0P5KOQ@C6 ¬
;0P5E ¬ W<6F2<;0BG4QP5L;8CJKhLhiJ0Pp@CE5K¥@ ¯ ± ¬ÆÅ¬ W<6G25J0R5O7E{!@94QE5@CP>G478X;#O$cW 0$¹ ¸¹ ½
§µ q µ©
º © n Âo± º © Ã n Âd³
Ì0Í ½
øe>A2+@CBF_4Q6G@L4Q>x_sJKR5OQE!@I47hL=vJ06G6G4Q5O7@H>AJDûFJK47Pg>l_sJYP+@C4702^!JKBF47P5z>GBG4;#P5KR5O7;0B=<;#>G8:25@C6947Pg>G25476 § JKB
;0P[{4QP5E5R58U@CE*2547K2+@CBS]E5@C0BG@C@ © 6G=5© OQ47P5@x6F=<;08U@H8UJKP>A47PR5J0R56GOj[KW<O7@d>k;0O7J0P5@6GhLJ^J0>A25Oj[Kq
e6G6FR5hL47P5|>G2<;#>k;0OQOv6F=<;08C@Ug6 º ¶¯ ¬Ç* §pW56G;#>A4Q6FMÃ[ §µ q ½ © ;0P+E §µ q µ© W?_~@y8X;#P*E+@Uf<P5@x>G25@x6G=<;#8C@xJ0M
8UJKP>A47PR5J0R56¶6F=5O74QP5@C63J#ME5@UKBG@U7@ È\© JKP ¨ ;06
¿ É ¾ § § ©Zª¾± #]
¤ *Ê ¾ §¨n©¯#¤ n © *Ë É ¶¯ ¬·* § ,¯
_25@UBG@ Ë É © 476Z>G25@y6G=<;08U@HJ#MxNF=!JKOj[?P+JKhi47;0O76FVDJ0MwE5@UKBG@U7@ È\JKP ¬·* §pW5E+@Uf<P5@UE`;06
Ë É © ª ± #¤*± { ©¥ ¥ÉÍ © ¯ ©¥ *`¬ V ,¯

Ì¥ Ì| É
;0P+E*_25@UBG@ ¥ÉÍ © ;0BF@y>G25@YNG¿~@UBGP56S>A@C4QPY=!JKOj[?P+JKhi47;0O76FVDJKGB Î3ä7å<ãuæ #â&ã eóTç0æ ö
¥ÉÍ © $§ !©Zª ± Ð ° ªqÑ2È5Ò©cÏ Ó §T° °Ï © Ô § µ ©° $§ !©F© ¥ Ö ¯ !*¬¯
° ªÕÑIÒ©Ó
McJKB{@dK@CBS[h|R5OQ>G4j]47P5E5@ °`± §T° ° © ° ªqÑIÒ©cÓ _4Q>G2 n /° nHª¾± × ° ªqÑ2Ò©cÓ0° ° © ± Èwqéá¶J#>A@\>A2<;#>{>G25@¿È]
=!JKOQ[^P5J0hi47;0O76wBG@CE+R58C@3>AJx>G25@JKBGE54QP<;0BS[ § ;#O7K@U5BA;04Q8 © =vJKOj[^P5JKhL4;0OQ6w4jM µ ° ;0BG@Z>G25@R56GR<;#O<<;0BF[^8U@CP>ABF478
8UJ?JKBFE547P5;#>A@U6¶;#6G6GJ^8C47;#>A@UEp_4Q>A2*;I=5O;#P<;0B~>GBG4;#P5KO7@ ¬ q ¶O76FJLP+J0>A@x>A25;#>
É
{ ¥ÉÍ © ± ØÙ { µ ©°`ÚÛ ¯
° ªÕÑIÒ©Ó
Ì¥ Ì| É
;0P+EÞ>A2<;u>H>G25@t¿o]l=!JKOQ[^P5JKhL4;#O76x;0BF@iOQ47P5@C;0BGOj[`4QP5E5@C=!@CP+E5@CP> § 25@CP58U@iMcJKBFhÅ;Y<;#6G476yMcJKB Ë É © © Wb;06H;
8UJKP56G@U·R5@CP58U@|J0M §µ q ½ © q
¢J¶8UJKP5E54j>A47J0P56 §µ q ½ © ;0P5E §µ q µ© KR<;0BG;0P>A@C~ @o>A25;#>w>G25@È6G=<;08U@C6 ¿1É ¾ § § ©¯ ÈÝÜ ² Wu_47OQO;0R+>GJKht;u>A478C;0O7Oj[
8UJKP>:;04QPP+JKP>ABG4j^4;0Ow6GhLJ?J0>G2`McR5P58d>A47J0P56CW 6G;X[ Þ>H6F25JKR5OQE\P5J0>y8CJ0hi@I;06y;p6FR5BG=5BF476F@I>G2<;#>x>G25@
;0P+6F_s@CB{476zP+@C;#>G4Q0@0q1325476p8C;0PÉv@`6F@C@UP(4QPú>A25@`=+O;0P<;#Bz8X;06F@ ¨±¬ W 4QMx_s@\8:25J^JK6G@\;.6F@U>
J0MHP5JKP^]l6F>A;0P5E<;#BGE£McR5P58d>A47J0P56 µ ©° qlP>AR54j>A4jK@COj[KW>A25@\BF@X;06FJKP£McJKBt>A2+476p476i>A2<;#>{8UJKP5E54j>A4QJKP56 §Tµ q ½ ©
;0P+E §Tµ q µ© E5J{P5J0>x@UP+McJKBF8C@I8CJKhL=<;#>G4754QO74j>l[pJ0MsE5@CBF4Q#;#>A4jK@U6xJ0Mo>A25@U6G@McR5P58d>A47J0P56y;08CBFJK6G6x>G25@@CE50@C6
J0Mw>A25@x>GBG4;#P5KR5O7;#>A4QJKPq
EGFIHJLK-M4N´ß lPm+;0hL=5O7@ Ì W>A2+@t6G=+25@CBF@ ¨ _~;06|=<;#BA;0hL@U>GBG47ÁU@CER56G4QP5a>A2+@t6G=+25@CBF478X;#O~8CJ^JKBÄ]
E54QP<;#>G@C6Cq eP ;0OQ>G@CBFP<;#>A4jK@{476>GJ=5;0BA;0hL@U>GBG4QÁC@ ¨ [>A25@*6F>A;0P5E<;0BFEÙJ^8U>A;025@CE+BGJKP_4Q>G2ù0@CBF>G478U@C6
± ~e± § Î ¯ Î ¯X²¦©¯ ± W ± §Ä²K¯ Î ¯ Î ©d¯ ± ® ± § Î ¯X²0¯ Î ©d¯ ±Ià ± &§ _9²K¯ Î ¯ Î ©d¯ ±aá ± § Î ¯ _H²K¯ Î ©d¯ ±Iâ ± § Î ¯ Î q¯ _H²©
§ JKBt[ ;0P[Ù=!JKOj[?2+@CE5BFJKPÙ4QP56G8UBG47!@CEÙ47P ¨© q1325@*K@CBS>A4Q8C@C6tJ0Mx>A25@YJ?8d>:;02+@CE5BFJKPúK4jK@*BG476F@Y>GJ.;
>GBG4;#P5KR5O7;#>A4QJKP §éJ0Mb>G25@H6F=525@UBG@0Wv8CJKP+6G476S>A4QP5tJ0M@C4QK2>e6F=525@CBF478C;0O>ABG47;0P5KOQ@C6Uq~JKP56F47E5@UBk>l_sJp;0EuûG;¦]
8U@CP>x>ABF4;0P50O7@C6k47P §pW&6A;X[ ¬ ;#P5E ¬ WvE5@U>G@CBGhL47P+@CE`[*>A25@U47B¶0@CBS>A478U@C6 Z§ ¬e©3ã± © ± ©Ä~:Ã ¯ ± ® ¯ ± W , ;0P5E
± ± ~d¯ ± ® ¯ ±Ià , WÈBG@C6F=v@U8U>G4QK@UOQ[0qín@d>LR56IP5J_éE5@df<P5@p>A25@pMcR5P+8U>A4QJKP56 µ ° ¯ µ ° McJKB|>A2+@z>l_~J
§ ¬ ©Lä
>GBG4;#P5KO7@U6y;06x>A25@IR56FR<;0Oo<;0BS[^8C@CP>GBG478L8CJ^JKBFE547P<;u>A@C6y;#6G6GJ^8C47;#>A@UE_4j>A2\>A25@|å!æjç0â!ç0èt>GBG47;0P5KOQ@C6e_4j>A2
0@CBF>G478U@CG6 Z§ ¬e© ;0P5E § ¬ © qsøP5@x8C;0PY8:2+@C8:p>A2<;u>k>G254763OQ@X;0E+6Z>AJ
µ ©°å 4§ !©± Y"æ[" ¯ µ ©°ç $§ !X©È± Yy"Æ[[+" ¯ µ ©°Õè $§ !©o± Yv"Y [X" ¯
æ
æ
_25@UBG@ !e±Z§ Yn\¯ [!¯ æ æ é© *¬ ;0P5E
µ ©°åÃ 4§ !©± _RYy"Ææ [+" ¯ µ ©°qç Ã $§ !©o± _RYy"Æ[ [+" ¯ µ ©°qê Ã $§ !©o± _RYy"Æ_RY [" ¯
æ
æ
æ
Ö ¹+¹ÙØ ÏÑÚÑÕ Ø ÒoÚÛÄÜeÔ ØÝ Ü ØÞÝ9Ý ÓwÐ Øbß Õ¶à^Ñ9ÏbÔ Ø
Ì0Í µ
_25@CBF@ !e±§ZYn¯\[!¯ æ ©é*¬ q1325@BG@C;0E5@UB476b4QP^4j©>A@CE|>GJK@UBG4QMÃ[H>A2<;u> §µ q½ © ;#P5E §µ q µ© ;#BG@36A;u>A476S© f<Ã @CEI4QP
>A254Q6w8C;06G@#qÊ¶J_s@U0@CBCW04QK@UP;kMcR+P58U>G47JKP ¤Ý*Ë ~ W W04j>hi;X[yv@s47hL=vJ06G6G4Q5O7@b>GJef<P5E|;0P ¤ *Ë W 6FR58:2
>A2<;u>H>G25@i>l_s© J`McR5P58d>A47J0P563ûFJ047PÞ6FhiJ^J0>G25OQ[ §4 © ;08UBGJK6F6D>A25@i8CJKhLhLJKP@UE5K@p± ~ ± ® § McJKBH@+;0hi=+O7@0W
>:;0#@ ¤*±§ µ °å © W © q
132+@eMcJKO7OQJ_47P59=5BGJ0=vJK6F4Q>G47JKPLK4Q0@C63;HP5@C8U@C6G6G;0BF[z8CJKP5E+4Q>A4QJKPIMcJKBZ;D6FhiJ^J0>G2yûFJK4QPzv@d>l_~@U@CP{P5@U47K2?]
vJ0BG47P+|>ABG47;0P5KOQ@C6 q
7ëì K ì`!qíîí4ì`% < ín@d> ¬¶¯ ¬ * § !@`© >l_~J ;0EuûG;08U@CP>{>ABF4;0P50O7@C6tJKP © ¨Ã 6GR58:2>A2<;u> ¬ ïÆ¬ 4Q6
25JKhL@CJKhLJKBF=525478o>AJy;¶E5476FD47P ¬ X W qín@d> µ ° *] ¤ © Z§ ¬e©d¯ ± * Z§ ¬e© W;#P5E µ ° *Ê© Ã ¤ § ¬ ©d¯ ± * § ¬ © q
R5=5=!JK6F@t>A2<;u>DMcJKBH~ @UK@UBFL
[ È£;0P5E.@dK@UBF[ ¤ *Ë É >G25@CBF@z@d?476S>A6;#P ¤ *Ë É 6GR58:© 2>A25;#> ¤ ;#P5E
¤ ûFJK4QP`_4Q>G2 É À 8UJKP>A4QP^R+4Q>l[g;#O7JKP5i>A25@8UJKhihLJKP`@UE5K@ ¬´Å¬ qD1325@UP@C;08:2 µ ° ¯ ± *Æ¬ W8C©;0PÃ
v@L@d^>G@CP5E5@UE;06H; ¥¤ McR5P58d>A47J0PÞJKP ¬dï]¬ _254Q8:2W[email protected]@U6F>ABF478d>A@CE>AJ ¬ W!@COQJKP5K6y>AðJ º q
m·^R+4Q#;0O7© @UP>AOQ[0Ww© >G25@CBF@t@d?© 4Q6FÃ >A6|;Y©>A25Ã BF@C@]lE54Qhi@UP56G4QJKP<;0Oo6G=5;08Cñ@ ºJ0M ¤ McR5P58d>A47J0P56DJKP ¬tï¬ 6FR58:2
>A2<;uR> º n ± º ;0P5E º n ± º q
8UJKP56G@U·R5@CP58U@yJ0M>A254Q6~BF@C6GR+OQ>34Q6s>A25;#>~>G25@8:25JK4Q8C@J#M>A25@kMcR5P58U>G47JKP+6 µ ©° © 4Q6~KBF@X;#>GOQ[IBF@C6F>GBG4Q8U>A@UEqolP
=<;0BS>A478UR5O;#BCW+>G25@H=+BGJK=!JK6G4j>A4QJKP{6A;X[^6¶>A25;#>;#O7O<;0BS[^8C@CP>GBG47898CJ^JKBFE547P<;u>A@C6 µ ° 8CJ0BGBG@U6G=!JKP5E54QP5i>GJt;#P[
K4Q0@CP.>GBG4;#P5KO7@ ¬ Wb8X;#P© v@z6FhiJ^J0>G25OQ[@d^>G@CP5E5@UEÙ;#8CBGJ06G6@CE+K@C6J0M ¬ >GJgP5@C4QK2vJKBF47P5*>ABF4;0P50O7@C6
;0P5EL25@CP+8C@x;0OQO56G=5;08C@U¼6 º hDR56F>¶æ7ã ç0æÃæ |!@CO7J0P59>GJD;ödóÃÄâ 0æ7ô>A25BF@C@]lE54Qhi@UP56G4QJKP<;0O<6F=<;08C@¶J0MNSO747P+@X;0B
McR5P58d>A47J0P56GXV ºeq1325@ZMcJKOQO7J_47P+e@d+;0hLñ =5OQ@~6G2+J¦_6>G2<;#>6FR58:2t;¶6G=<;08UR@ º.hi4QK2>bP5J#>8CJKP>A;047pP 0æ7ã ³:ç0æÃæ
8CJKP>G47PR5JKR563McR5P+8U>A4QJKP56UW 0¹¾¸¦¹¾½¼McJKB36GJ0hi@x6FR5BFMT;08U@C6kJKP5@yhi;[tv@9;0+O7@>AJIE5@df<P5¥@ ºÉJKP5OQ[tO7J^8X;0OQOQ[0q
EGFaHJK5MZNðò í@U> ¨ !@y>G25@y8C4QBG8CR+O;0BZ8d[^O747P+E5@CB=<;0BG;0hL@U>ABF47ÁU@CEp[
§ 6F47P m}¯ 8CJK6 mn¯ æ ¼© *`¬ ® ¯ m*a¬ |¯ æ *`¬ |¯
;0P5E{O7@d>
º ª¾± 6F=<;0P ²0T¯ m}¯ æ ,³
Ê¶@UP58C@#W^>G25@=vJK4QP>oJKP ¨ _2+JK6G@¶=<;0BA;#hi@d>A@CBF6È;0BG@ $§ m}¯ æ © 4Q6s;#6G6G4QKP5@UEL>G25@k#;0OQR5R@ ó " µ mR" æ W_25@CBF@
ó ¯ µ ¯ ;0BF@|BG@C;0Ob8UJ?@ bi8U47@UP>G6CqDá¶J0>G@D>A2<;u+> º 476P+J0>xE5@df<P5@CEKOQJK<;0OQOQ[{6G4QP58C@|>G25@CBF@476¶P5J{KO7JK5;0O7Oj[
8CJKP>G47PR5JKR563McR5P+8U>A4QJKP{47P{4Q>CqÊ¶J_s@U0@CBCW!JKP*@U0@CBF[ NS6F>ABF47=5V
?¹§ mn¯ æ ©d)¯ mð*ù$§ ôÈ\¯ õw©d¯ æ *`¬ V ,¯
_25@CBF@ õ_Æô oÌ S W?>A25@y6G=5;08C¥@ ºÉ476Z_s@CO7OE+@Uf<P5@UE`;0P+EYK@UP5@CBG;#>A@UEY[ ¤ McR+P58U>G47JKP56Uq
¼M § 476y;pK@UJ?E+@C6G4Q8>ABG47;0P5KR+O;#>G47JKPYJ0M ¨ 8UJKP56F476F>G47P5*J0M|NF6Ghi;0OQO7Vt>GBG4;#P5KO7@U6 § 0$¹ ¸¹ ½>ABG47;0P5KOQ@C6McJKB
_25478:2z>G25@#;0O7R+@C63J0M m ;0BF@47P{;#Pp47P>A@UBF#;0O&J#MwOQ@CP5#>A© 2pP5J0>Z@d?8C@U@CE54QP5 S © W?>G25@CP{4j>3476ZP+©J0>3E54 bi8UR5© OQ>
>AJ6G@U@>G2<;#>{McJKBp@dK@CBS[6GR58:2>ABG47;0P5KOQ@ ¬ WE54Qh ö÷º n Â&øÉ± Ì ¯ ¯ * ® Z§ ¬e© W¶_25@UBG@ º ª ± º n q
1325476McJKOQO7J_63McBGJKh >A2+@DJK56F@CBS0;u>A47J0PY>A25;#>e@dK@UBF[ L¤ * º0;#P5476F25@C6e;0O7JKP+iK@UJ?E+@C6G4Q8C6Uqeá¶;0hi@UOQ[0W!4jM
¤b¹§ mn¯ æ ©± ó " µ mv" æ W<_25@UBG@ µv± ù Î W?>A25@UP ¤b$§ m}¯ æ ©± Î ;#O7JKP5|>G25@y8CR5BSK@
?§ 6F47P §F§ ó " æ © r µ ©¯ 8CJK6 §G§ ó " æ © r µ ©¯ æ ©d¯ æ *`¬ V ,¯

_25478:2É4Q6p;.25@COQ4jvWk25@CP58U@;.K@CJÊ5@C6F478#qÇøe>A25@UBF_4Q6G@0W¶4QM µ ± Î W æ 4Q6p;8CJKP+6F>:;#P>CW¶_254Q8:2;0O76FJ
8CJKBFBG@U6G=!JKP5E563>AJi;K@CJÊ5@U6G478yJKP ¨ q
ÌKÎ
r4QKR5BF@ µ q q1wBF4;0P50R5O;#>G47JKPtJ0Mb;8d[?OQ47P5E+@CBCq
31 25@L;0vJ0@LE+476G8UR56G6F47JKP\6F25J_69>G2<;#>xMcJKBx@dK@CBS[\6GRcbL8U47@CP>GOQ[`6Fht;#O7O0@CJÊ5@C6F478|>ABF4;0P+KO7@ ¬ú* §pW
JKP+@i8C;0PE+@Uf<P5@ ñ #æ óÃâ!õ0èó ñ ç0æû³:ç0èT ñ ôdâ þ èó ñzñ ããuèFõ0óÃâ!ç þ ô:ödqI>H>GR5BGP56yJKR?>9>G2<;#>9hi;0P[g=5BGJ0=v@UBF>A4Q@C6yJ0M
>G25@C6F@8CJ^JKBGE+47P<;#>G@C6s;0BG@¶6G4Qhi4QO;0B>GJH>G25@e=5BFJK=!@CBF>G47@U6sJ0M&>A25@U47BÈ=5O;0P5;0Bo8CJKR5P>G@CBG=5;0BF>G6CqolPz=<;0BS>A4Q8CR5O7;0BCW
>G25@38U[Ô74QP5E5BF478X;#O?<;#BF[^8C@UP>GBG4Q838CJ^JKBGE54QP<;#>G@C6bhi;00@~4Q>b=!JK6F6G47+O7@~>GJE5@Uf5P5@k;6G=5OQ47P5@s6G=<;08U@0W_254Q8:2L8C;0P
!@ZR56F@CE|>AJ¶8CJKP+6F>ABFR58U>b6GhLJ?J0>G2|6G=+O747P+@C6}JKP ¨ ~ qbr4QKR5BG@ µ q 6G2+J¦_6b;0P|@d+;0hL=5OQ@~J0M¼;¶8U[Ô74QP5E5BG4Q8X;0O>GBG4j]
;0P+KR5O;u>A47J0yP §Ç;0P5Eir47KR+BG@ µ q ^ 6F25J_6~; 6GhLJ^J0>A2I6G=+O747P+@347PI>A25@6G=5;08C@ ¿1W¾ § § © W8CJ0BGBG@U6G=!JKP5E54QP5
>GJL>G25476Z>GBG4;#P5KR5O7;#>A4QJKPq
mb+;0hL=5OQ@ BG;0476F@C6>A2+@k·R5@U6F>G47JKPI_25@U>G25@CBs;x6G=<;#8C9@ ºWJKBÈ;x8CJKOQO7@C8d>A4QJKP|J0Mv6G=<;#8C@CÁ6 º © 6A;#>G476FMÃ[^4QP5
>G25@\8CJKP5E+4Q>A4QJKP56z4Qhi=+O747@UEút[ ²BGJK=!JK6F4Q>A4QJKP ² W¶;0OQ_~;X[^6*@?476F>G6{JKP;0P[ ¨ ;0P5E&W4QM96GJ+We25J_8C;0P
JKP+@Lf<P+EÞ6GR+8:2.6G=<;#8C@C6Uqz 6G47hL=5OQ@;0=5=5BFJ;08:2>AJ*8CJKP56S>ABFR58U>G47P5ð º4Q6y>GJ*>A;00@i;0E+#;0P>A;0K@IJ0MZJ0R5B
P5J_O7@UE5K@¶J0M ¨ <W 0$¹ ¸¹ ½^>G25@¶4Qhi=+O7478U4Q>b;06G6FR5hi=?>A47J0Pi25@UBG@>A2<;u>s_s@¶8C;0Pt@d#;0O7R<;u>A@ ¨ ;#>Z;#P[I=!JK4QP>CqblP
=<;#BF>A4Q8CR5O7;0BCW¦_s@Z8X;0PDE5@Uf<P+¼@ º.;06}>A25@s6G=<;#PJ0M5>A2+@s>A2+BG@C@sMcR5P58U>G47JKP+6 Yw4§ !©d\¯ [&$§ !X©d¯ æ 4§ !© W#>A25@ZZ;0BF>G@C6G47;0P
8UJ?JKBFE547P5;#>A@U6sJ0M ! 0¹¾¸¦¹¾½ !e±Z§ Yw$§ !X©d\¯ [&$§ !©¯ æ 4§ !©G©)¯ !¥*¨ qb132+476s_sJKBF^6s_~@UO7O¼47PL>A25@¶47hL=vJKBS>:;0P>o6F=v@U8C4;#O
8C;06G@9J0M;I6F=525@UBG@947P ¬ ® q
EGFIHJLK-M4N.ü 1325@I=5BGJK+O7@Ch J0Ms8CJKP+6F>ABFR58U>G47P5{6F=525@CBF478C;0O;0P<;#O7JKK6¶J0M~¿i@CÀ ÁU47@CB>GBG47;0P5KOQ@C6e25;06y;0P
4QP>G@CBF@C6F>G47P5H25476S>AJKBS[Kqb>s2<;06sBG@U8C@C4jK@UEp;0hL=5O7@k;#>F>A@CP>G47JKPL47PI>A25@¶6G=5OQ47P5@OQ4Q>A@UBA;#>GR5BG@3McJKB>G25@eJK^47J0R56
BF@X;06FJKPi>G2<;#>È6G=5OQ47P5@U6oJKPt;y6G=+25@CBF@¶2<;X0@ehi;0P[=vJ#>A@CP>G4;0O<;#=5=5O74Q8X;#>G47JKP+6b47PIK@UJK6G8U47@CP+8C@C6UW+4QP58COQR5E547P+
hL@U>G@CJKBFJKO7JK#[KWK@UJK=52[^6G478U6CWs;0P5EK@UJ?E5@U6F[0ýq hk@U6G@C;0BG8:25@UBG6L2<;0E!@C@UP 6F@X;0BF8:2547P5gMcJKBDht;0P[[K@X;#BG6
McJKB;#=5=5BGJ0=5BG47;#>A@¶6G=525@UBG4Q8X;0O;#P<;0O7J0K6ZJ0Mw¿L@UÀ ÁC47@UBZhL@U>A2+J?E56UW55R+>3_s@CBF@y2<;0hL=v@UBG@CE{[t>G25@xE54 bi8UR5OQ>l[
J0MeE5@Uf5P547P5ölå ¦ ôdèó ñ ç0Ræ ³:ç0Tè ñ ôdâ þ èó ñ`ñ ããuèFõ0óÃâ!ç þ ô:ödq r<JKB@d+;0hL=5OQ@0WÈ6G@U0@CBG;0O¶8C;0P5E54QE<;#>G@C6IMcJKBI6GR58:2
8UJ?JKBFE547P5;#>A@U6Y2<;X0@Þ!@C@CP 47P>ABFJ?E5R+8C@CE(47þP ² Í W ² W ² W¶5R+>Y>A25@d[ÉO;08:#@CE hi;0P[É0@d[(=+BGJK=!@CBS>A47@U6
J0M>G25@p=5O;#P<;0BD8UJ?J0BGE54QP<;#>A@U6Cq\ e64j>D>GR5BGP5@UEJKR+>XW>G25@phi@UP>A47J0P5@CE;#>F>A@Uhi=+>G6D_s@CBG@pE+@C6F>G47P5@UE>AJ
!@\R5P56GR+8C8C@U6G6SMcR5OHMcJKBi>A25@\6G4Qhi=+O7@`BF@X;06FJKP>G2<;#>p>G25@U[É;#O7Oe4QP56G4Q6F>G@CEJKP£>A25@\=<;0BS>A4j>A47J0PúJ0MHR5P54Q>l[
=5BFJK=!@CBF>l[0W_254Q8:2Þ476y_s@CO7OoP5J_PÞMcJKBx>G25@t8UO;06F6G478C;0O<;0BS[^8C@CP>GBG478i8CJ^JKBGE+47P<;#>G@C6Uqpáe;0hL@COj[KWn4Q>y_~;06
6F25J_P`47P ² >A25;#>k6G=525@UBG4Q8X;0O<;#BF[^8C@UP>GBG4Q8H8UJ?JKBFE547P5;#>A@U6Z>A2<;#>k6FR5hé>AJLJKP5@9;0P5E*6A;u>A476SMÃ[{;IO7476S>3J0M
J0>G25@CB~BG@X;#6GJKP<;#5O7@e;06G6FR5hi=?>A47J0P56CW?E5J|P5J0>~@d?476S>Xq13254Q6ZP5@U;#>A4jK@¶BG@C6FR5OQ>~=5BGJ^47E+@CE{;0Pz@?=5O;0P5;#>A4QJKP
_2[Þ>G25@i#;0BF47JKR+6H@C;0BGOQ47@CByK@UP5@CBG;0O74QÁX;#>G47JKP+6y_s@CBF@zR5P56FR58C8U@C6F6FMcR5O34QPÞ5R54QO7E54QP5*6GhLJ?J0>G26F=5O74QP5@C6HJKP
6F=525@CBF478C;0O>ABF4;0P50R5O;#>G47JKP+6Cq
×5BG@C;0>A25BFJKR5K2g4QPa>A2+476eE+@UK@UO7JK=+hi@UP>y8C;0hL@H_25@UP\>G25@;0R?>A25JKBF6J0gM ² BF@X;0OQ47ÁU@CEWv[Y6F>GR5E+[]
4QP5\47E5@UP>G4Q>G47@C6DJ0Me6F=525@UBG478C;0OZ>ABF47KJ0P5JKhL@U>ABS[KWb>G2<;#>>A2+@CBG@{4Q647P.MT;08d>L;\P5;#>AR5BG;0OZ_~;[.J0MeE+@Uf<P54QP5
r470R5BG@ µ q ^ q ~
Ì ²
6FhiJ^J0>G2p·^R+47P>A4Q896F=5O74QP5@JKP{>A2+@98d[Ô747P+E5@CBUq
<;0BS[?8U@CP>ABF478p8UJ?JKBFE547P5;#>A@U6HMcJKB|6F=525@UBG478C;0Os>GBG47;0P5KOQ@C6Cq\í@d> ¬ !@p;`6G=+25@CBF478X;#Os>ABF4;0P+KO7@L_4Q>A2K@CBÄ]
>A4Q8C@C6R± ~d¯ ± W ¯ ± ® *¨ q132R56e>G25@D@UE5K@C6eJ0M ¬ ;0BF@9>G25@H>G25BG@U@D6G2+JKBF>G@C6F>K@CJÊ5@C6F478U6e8CJ0P5P5@C8d>A4QP5t>A2+@
K@UBF>A4Q8C@U6CqsøP5@y8X;0P*E5@Uf5P5@9>G25@y6G=52+@CBG4Q8X;0O5;0BF[^8C@UP>ABG4Q8y8CJ^JKBGE54QP<;#>G@C63J0M;L=!JK4QP> !¥*¬ ;06
µ ©°qÿ $§ !X©3ª ± 6F47P §6F47P<¥ "¥ ¥Ã© ¯ °w±²K¯ Ì ¯ Í ¯
_25@CBF@ ¥ 4Q6>G25@9K@CJÊ5@C6F4789E5476S>:;0P+8C@ § hL@X;06FR5BG@UE`;0OQJKP5>A25@9KBF@X;#>¶8C4QBG8COQ@y=<;06G6F47P5I>A2+BGJKR502 ! ;#P5E
± ¥c© J#M ¥ ;0P5E ! W¼;0P5E ¥ 476Z>A2+@90@CJÊ5@C6F478yE5476S>:;0P+8C@xJ0M ! ;#P5AE ± ¥Z§ 6G@U@Hrw47KR5BF@ µ q © q
¢@U6G=54j>A@z>G25@{47P5@d?4j>:;0+O7@iMT;#8U>>A25;#>>A25@*;0!JK@{8CJ^JKBFE547P<;u>A@C6DE5J\P5J0>L;0E5ER5=>AJ\JKP+@0Wo4Q>I2<;#6
v@U@CP6G25J_P.4QkP ² >A25;#>H>G25@U[\BF@C6F@Ch|5OQ@L>G25@L6F>:;#P5E<;0BFEÞ<;0BS[^8C@CP>GBG478i8CJ^JKBGE+47P<;#>G@C6y47Phi;0P[gBG@]
6G=!@C8d>A6Cqr47BF6F>XW!>A25@H<;0BS[?8U@CP>ABF©478|8UJ?J0BGE54QP<;#>A@U6;0BF@D4QP+f<P54j>A@COj[{6GhLJ?J#>A2YMcR+P58U>G47JKP56eJKP ¬ ;0P5Ea>G25@U[
6A;#>G476SMÃ[ §Tµ q ½ © q1325@`6F=<;08C@ º W3>A25@Y6G=<;0P£J#M>A25@Y>A25BF@C@`8UJ?JKBFE547P5;#>A@U6CW3BG@UE5R58U@C6z>AJE547hL@CP+6G47J0P
>l_~JY;0OQJKP5z>A2+@L@UE5K@U6HJ0M ¬ ©;#P5E4QP`MT;08U>H;0OQJKP5p@dK@CBS[\KBG@C;#>98C4QBG8COQ@|47P>G@CBG6F@C8d>A47P+ ¬ qLÂYJKBF@I=5BG@]
8C4Q6G@COj[KW&>G25@BG@U6F>GBG478d>A4QJKPgJ0ÁM º >AJ*;0P[`6FR58:2ÞKBF@X;#>8C47BF8COQ@|8X;0P\!@6G25J_P\>AJ{!@|>A25@OQ47P5@C;0Be6F=<;0P
J0M 6G47P ôÈ¯ 8CJ06 ô#, W_25@CBF@ ô 4Q6y>G25@L;0BG8UO7@UP50>A2E54Q6F>:;#P58C@IhL@X;06FR5BG@UE.;0OQJKP5p© >A254Q6x8C4QBG©Ä8CÃ OQ@0qL eP5J#>A25@UB
47hL=vJ0BF>:;#P>8UJKP56F@C·R5@CP+8C@J0Mw>A25@D;0vJ0@HE5@df<P54j>A47J0PY4Q6k>G2<;#>k>A25@96G=<;#8C@CG6 º ;0P+ÊE º Wv;#6G6GJ^8C47;#>A@UE
_4Q>G2ùP+@C4702^!JKBF47P5g>ABF4;0P+KO7@U6 ¬ ;0P5E ¬ W~6G;#>A4Q6FMÃ[ §Tµ q µ© q r<R5BF>G25@CBFhiJKBF@0WÈ>A25@{=5BFJK=v@UBF>G47@C6LJ0gM º ©
;0BG@H8CJKP+6G476S>A@UP>e_4Q>A2Y>A25JK6F@|6G=!@C8U4Qf<@UE\47ÊP ²BFJK=vJ06G4Q>G47JKP ² qlP`=5;0BF>G478CR+O;0BUW!>G25476¶6G=<;08U@|8X;#Pgv@|@]
>A@UP5E5@CE`>GJ{;i>A2+BG@C@]lE54Qhi@UP56G4QJKP<;0O}6G=5;08C@ º J#Mo47© P+f<P+4Q>A@UOQ[{E54 &@UBG@UP>G4;0+O7@yMcR5P58U>G47JKP+6JK@CBy;#O7OnJ0M ¨ q
~JKPK@UBG6G@UOQ[0W¼McJ0B;0P[z>ABF4;0P50O7@ ¬ >A25@y6G=5;08C¥@ º 476wûFR56S>k>G25@yBG@U6F>ABF478d>A47J0P*J#5M º£>AJ ¬ q
132+@t6G=5;08Cp@ º2<;#6Hhi;0P[g47P>G@CBG@U6F>G47P5*=5BGJ0=v@UBF>A4Q@C6y>A2<;u>H4QP5E54Q8X;#>G@I>G2<;#>96G=+25@CBF478X;#OÈ5;0BF[^8C@UP>ABG4Q8
8CJ^JKBGE+47P<;#>G@C6UW¼;06¶E+@Uf<P5@UE`25@UBG@0Wv;0BF@HR5P+47·R5@0qkÂ*JKBG@9=5BG@U8C4Q6G@COj[KW º476>A25@9JKP5Oj[z>A25BF@C@]lE54Qhi@UP56G4QJKP<;0O
6G=<;#8C@oJ0M+McR+P58U>G47JKP56J0P9>G25@o6G=525@UBG@ ¨ >A2<;u>w4Q6BGJ0>A;#>A4QJKP<;0OQOQ[4QP#;0BF4;0P>};0P+EH6FR58:2H>G2<;#>n4Q>G6E547hL@CP+6G47J0P
476BF@CE5R58U@CED;0O7JKP+k0BG@X;u>n8C47BF8COQ@C6CqÂYJKBF@CJK@UBCW º\8C;0PH!@È@X;06F47OQ[eE5@C6F8CBF47!@CE9R56G4QP5k>G25@o47E5@C;36GR5K0@C6F>G@CE
@X;0BFO74Q@CBCqná¶;0hL@COQ[0ÕW º\476=5BF@C8C4Q6G@UOQ[e>G25@6G=5;0PHJ#M?>G25@ÈZ;0BF>G@C6F4;0Py8CJ^JKBFE547P<;u>A@C6 Yw4§ !©d¶¯ [4§ !©d¯ æ $§ !© W¦^4Q@U_s@CE
;06~McR5P+8U>A4QJKP56sJKP ¨ q132+476Z4Q6Z@C·R54j0;#O7@CP>Z>GJ|6A;X[^47P+|>A2<;#¼> ºú476~>G25@6F=<;08C@xJ#Mbölå ¦ ôdèdó ñ ç0æ ¦ ç0Tè etãuâ<ó ñ ö
J0MwE5@CKBF@C@yJKP5@» µ
q
132+@¶4QP>G47hi;#>A@s8CJKP+P5@C8d>A47J0Pi!@U>l_s@C@UPt6G=+25@CBF478X;#O<2<;0BGhLJKP54Q8C6o;0P+EL6F=525@UBG478C;0O<<;0BS[^8C@CP>GBG478k8CJ^JKBFE54j]
P<;#>G@C6È476ÈP5J0>sR5P5@d?=!@C8d>A@CE&qslPiBG@U>GBGJK6F=v@U8U>CW+4Q>s6G@U@ChL6~·R54j>A@kJK?4QJKR56o>A2<;u>s>G25@C6F@eMcR5P58d>A47J0P56s6F25JKR5OQE
2<;XK@Lv@[email protected]@UBG@CE@X;0BFOQ[gJ0P.;06y>A25@LhLJK6F>9P<;#>GR5BA;#O8X;0P5E+47E<;#>G@C6yMcJKBYNFO74QP5@X;#BMcR5P58U>G47JKP+6GV*JKP
ÌÌ
γ1
3
δ3
δ1
2
δ2
γ2
2
1
γ3
3
r4QKR5BF@ µ q^qo¢@Uf<P54j>A4QJKPpJ0Mw6G=525@UBG4Q8X;0O<;#BF[^8C@UP>GBG4Q8H8UJ?JKBFE547P5;#>A@U6Cq
1
>G25@i6F=525@UBG@0qi e6H;pht;#>F>A@UBxJ0M~MT;08d>XWn6GR+8:2McR5P58d>A4QJKP56CWw;0OQJKP5z_4Q>G2>G25@I8CJKBFBG@U6G=!JKP5E54QP5Y5;0BF[^8C@UP?]
>GBG478H8CJ^JKBGE+47P<;#>G@C6¶E5@Uf<P+@CE\;0!JK@0W&2<;0Eg!@C@CPg8UJKP56F47E5@UBG@CEg6FJKhL@ ² Î [K@C;0BG6x!@UMcJKBF@H>G25@|=<;0=!@CB /² ;0=+=v@C;0BG@UEqÉ1325@`;0R?>A25JKBF6tJ0Me>A2<;#>i=<;0=!@CBIMcJKR5P+EÙJKR+>iJKP5Oj[O;#>G@CB>A25;#>i>G25@C4QBi4QE5@X;\J0MxE+@Uf<P54QP5
<;#BF[^8C@UP>GBG4Q8x8CJ^JKBGE54QP<;#>G@C6~_~;063P5J0>ZP5@U_ ;#MÃ>A@UB3;0OQO$W6G4QP58C@>G25@6A;#hi@E+@Uf<P54j>A4QJKPz2<;0E*;0OQBG@C;0E+[Lv@U@CP
K4jK@UPY[YÂ JK
+47R5¥6 q
=525@UBG478C;0O<;#BF[^8C@UP>GBG4Q898UJ?J0BGE54QP<;#>A@U6ZK4jK@xBG4Q6G@>GJi¿s@CBGP+6F>A@U47P?]l¿L@CÀ ÁU47@UBS]>l[^=!@xhi@d>A25JÊ56UW5_4Q>A2p4QhI]
hL@CE547;#>A@;0=5=5OQ478X;u>A47J0P56È>GJL;D0;#BG47@d>l[tJ#Mw=+BGJK5OQ@ChL6ZJKPz>G25@x6G=52+@CBG@#qslP+E5@C@UEW<v@U8X;0R+6G@yJ0Mn>A25@x8UO7JK6F@
;0P5;0O7JK#[t_4Q>G2Y6S>:;0P+E<;0BGEY¿~@UBGP56S>A@C4QP?]Ä¿L@CÀ ÁC4Q@CB>A@U8:25P547·R5@U6CW¼^47BF>GR<;0OQOQ[t;0O7OJ#Mw>G25@H8UO;06F6G4Q8X;0OhL@U>G25JÊ56
McJKBH=547@U8C@d_476G@p=!JKOj[?P+JKhi47;0O76xJ0P.=5O;#P<;0BH>GBG47;0P5KR5O7;#>A4QJKP56x8C;0Pv@t8X;[email protected]K@UBD>AJ`>G25@z6G=+25@CBF478X;#O
6F@U>G>G47P5+W+;0P+Et47P+E5@C@UEi>AJH;0P[L6G@d>G>A4QP5y_25@CBF@e<;0BS[^8C@CP>GBG478¶8CJ^JKBGE+47P<;#>G@C6È;0BF@e;X#;047O7;05OQ@0qn (E+@U>:;#47O7@UE
>GBG@X;u>AhL@CP>LJ0Me6FJKhL@pJ0M¶>G25@C6F@YhL@U>G25JÊ56I2<;06Iv@U@CPùK4Q0@CPù47P Ì W Í q132+@Y6F=525@CBF478C;0O¿~@CBFP56F>G@C4QP?]
¿L@UÀ ÁC4Q@CBkhi@d>A25JÊ56k;0BG@9;0OQ6GJLJ0Mw47P>A@UBG@C6S>e4QP*>G25@yE5@C6F47KPYJ0Mw6GR5BSMT;08C@U6CW!@C6G=!@C8U4;0OQOQ[t6F>:;#BS]lOQ47#@96FR5BFMT;#8C@C6UW
@dK@CP.>G25JKR502Þ6GJ0hi@LJ0M~>G25@LK@CJKhL@U>GBG4Q8L=+BGJK=!@CBS>A47@U6HJ#MZ=5O7;0P<;0B9¿L@UÀ ÁC47@UBHhL@U>G25JÊ56D;#BG@Lhi4Q6G6G4QP5{JKP
>G25@y6G=525@UBG@#Wv6FR58:2`;06Z>G25@y8CJKP0@dY2R5O7O=5BFJK=!@CBF>l[0q
1È[^=54Q8X;0O}6G8C;#>G>G@CBG@UEgE<;#>A;t47P>A@UBG=!JKO;u>A47J0P¼î0;0=5=+BGJX?47hi;#>A4QJKPthL@U>G25J?E+6eJKP*>A25@|6F=525@UBG@|6S>:;0BS>¶_4j>A2
;|>ABF4;0P+KR5O;u>A47J0PtJ0Mn>A2+@x6G=525@UBG@#W¼McJ0BZ@d+;0hL=5O7@¶>A25@y6GJu]l8X;#O7O7@UEp¢@CO7;0R5P<;X[L>ABF4;0P50R5O;#>G47JKP&q}Æ@yBG@UMc@UB
>G25@BG@C;0E5@CB¶>AÝJ ^Kµ W&McJKBe;t6GR5BSK@d[gJKP`>ABF4;0P+KR5O;u>A47J0P56CW!;0P5E\;#O76GJL>AJ ²K² W Í µ WvMcJKBe;tE54Q6G8CR+6G6G4QJKPgJ0M
>GBG4;#P5KR5O7;#>A4QJKPghi@d>A25JÊ56yJKPK@CP+@CBA;#OÈ6FR5BFMT;#8C@C6Uq{ÂY@d>A25JÊ56HMcJ0By>GBG47;0P5KR5O7;#>A4QJKP`J0M~6G8C;#>G>G@CBG@UEÞE<;u>:;
=!JK47P>G6e6G=!@C8U4Qf<8C;0O7Oj[{JK@CBk>A25@D6G=525@UBG@;#BG@9E5476F8CR56F6G@CE\4QýP ² W ½+W ^ ^
q¶rw47KR5BF@C6 µ q µ ;0P5E µ q ² Î 6G2+J¦_
_4QBG@=5O7J#>A6J0M&6GhLJ?J0>G2 ~ ·R<;0E5BG;#>A4Q8;0P5EL8CR554Q86G=525@UBG4Q8X;0O¼6G=+O747P+@C6CWBF@C6F=v@U8U>A4jK@UOQ[KW^8CJ0BGBG@U6G=!JKP5E54QP5
>GJ § ;|=<;0BS>3J0M © >A25@¶>ABG47;0P5KR+O;#>G47JKPi47Ppr4QKR5BF@ µ q ½+q¢@U>A;047OQ6Z;0!JKR+>~0;#BG47J0R56~E<;u>:;u]$f5>G>G47P5|hL@U>G25JÊ56
>G2<;#>kO7@C;0Ep>AJI6GR58:2Y6G=52+@CBG4Q8X;0O6F=5O74QP5@C6;#BG@yE5476F8CR56F6G@UEa47P Í q
¿~@C6F47E5@U6y>G25@|6F=525@CBF@0W>A2+@6GR5K0@C6F>G47JKPg>GJpR56G@LZ;0BS>A@U6G4;#P8UJ?J0BGE54QP<;#>A@U6e>AJpE+@Uf<P5@>G25@6G=<;#8C@vº
hi;00@U66G@CP+6G@0W!;06OQJKP5I;06Z>G25@x>ABG47;0P5KR+O;#>G47JK»P §J0M ¨ 8CJ0P56G4Q6F>A6J0Mn>GBG4;#P5KO7@U6~_25JK6F@y@CE5K@U6¶BF@CE5R+8C@
>G25@iE+47hL@CP56F47JKP\J0éM ºqi132+476y476y@C·R54j#;0O7@UP>y>GJ*>G25@i8UJKP5E54j>A4QJKPg>A2<;#>y>G25@I@CE5K@U6DJ0éM §ÿ;0BF@L=+O;0P<;#B
;0P+Ep47Pi>G25@e6G;0hL@e=5O7;0P5@¶_4j>A2L>A25@J0BG47047P § Î ¯ Î ¯ Î © qw1325476s476~;08C8U@C=+>A;05O7@kMcJKB~8U@CBS>:;04QPt6GR+BFMT;08U@C6 § McJ0B
@5;#hi=5OQ@0W0McJ0Bw6S>:;0BÄ]lO74Q0@s6GR5BSMT;08C@UR6 Í Ã© WK5R+>476hLJKBF@sBF@C6F>GBG4Q8U>A4jK@Z4QPD8C;06G@U647PH_2+478:2|>A2+@3;06G6FR5hL=+>A4QJKP
J0M8CJK=+O;0P<;#BG4Q>l[L_sJKR5O7E*BG@U6GR5Oj>47P{6G@dK@UBG@COj[{E5476S>AJKBS>A@UE*>GBG4;#P5KO7@U6 § BF@CO7;#>A4jK@>AJ>G25@yK@CJÊ5@C6F478xJKP+@C6 © q
1wJ8CJK=!@*_4j>A2>A254Q6IE5;4 bL8CR+OQ>l[KW~;=!JK6F6G47+47O74j>l[.4Q6I>GJhi;0#@a;\8CJ^JKBGE+47P<;#>G@p>ABA;#P56FMcJKBFht;u>A47J0P.>AJ
ÌKÍ
r470R5BG@ µ q½+q >GBG4;#P5KR5O7;#>A4QJKPtJ0M}>A2+@96F=525@UBG@0q
hi4QP547hL47ÁU@>A25@E+476F>GJKBF>G47JKPaJ0M>A25@|>GBG47;0P5KOQ@C6CWn¸¦¹»º¼¹¾½JKP5@8UJKR5OQE`6G254jMÃ>>A2+@JKBG4QK47PYJ0M>A25@LZ;#BF>A@U6G47;0P
6F[^6F>G@Ch*q9ÂYJKBF@|K@CP+@CBA;#O7OQ[0WvJ0P5@|8CJ0R5O7E`4QP`=5BF47P58U47=5OQ@9>A;00@\NF;0P[?Vz>G25BG@U@d]E547hL@CP56F47JKP5;0On6G=<;08U@ ÅJ0M
6GhLJ?J#>A2{McR5P58U>G47JKP+6¶4QP ¬ ® ;0P5EYE5@Uf<P+V@ º ;#6k>G25@DBF@C6F>GBG4Q8U>A4QJKP*J0M >GJ ¨ q3lPa>A25@96G=+25@CBF478X;#Ow8C;06G@#W
>A254Q6_~J0R5O7EO7@C;0Eg>AJ º ± n W_25@CBF@ ª ± 6F=<;0P ÕYn\¯ [!¯ æ , qlP\>A25@L=5O7;0P<;0B8C;06G@ ¨ù± ¬ W W_s@
8X;0PY>A254QP5{J0ûM º ;06 n W!_25@CBF@ ª ± 6F=<;0P ²K¯ Yn\¯ [`, qklPa>G25476k_Z;X[YJKP5@|8C;0Pg;0OQ6GJt4QP>A@CBF=5BG@d>>A2+@
8CJKP+6F>ABFR58U>G47JKP{J0-M ºÉMcJKBZ>A25@y8d[?OQ47P5E+@CBCqlP*=<;0BS>A4Q8CR5O7;0BCW^_~@y8X;#P*>A;00@xMcJKB;0P[pf+?@UE ôý*`¬ W
ôÊ_.[ 6F47P ô ¯ ¯X²{¯
ª ± 6F=<;0Po;0BG8d>:;0P YY 8U6G4QJKP 6 ô
"[ 8CJK6 ô æ
47Pz_254Q8:2Y8C;06G¥@ ºÉ476Z>G25@yBG@C6S>ABF478U>G47JKP{J0M >GJ>A25@y6F>GBG4Q=
?¹§ mn¯ æ ©d\¯ ô_ S(rKÌ m ô" S(rKÌ ¯ æ *a¬ V ,³
øPt>A25@¶J0>A2+@CBZ2<;#P5EW+4j>~4Q6sP+J0>Z8UO7@X;#B~25J_É>AJ|8:2+J?JK6F@ McJKB~;DK@CP+@CBA;#Ov6FR5BFMT;08U@ ¨ 6FJ;06È>AJ|JK?>:;04QP
NFO7@C;06F>ZE5476S>AJKBS>A@CE+VL>GBG4;#P5KR5O7;#>A4QJKP56Cq
¶vJ0@0W_~@{2<;X0@p6G@C@UP>l_~J\@d+;0hL=5OQ@C6|J0MP+JKP?]l=+O;0P<;#BD6GR+BFMT;08U@C6|McJKBD_2+478:24Q>D476|=!JK6F6G47+O7@i>GJ
8CJKP+6F>ABFR58U>{hL@X;#P547P5#McR5Oe;#P<;0O7J0K6tJ0M96F=5O74QP5@`6G=5;08C@U6Cq×1325@g8:25;0BA;08d>A@UBG476S>A4Q8g=5BGJK=!@CBS>l[ú6F2<;0BG@UEÉ[
vJ#>A2I>l[?=!@C6sJ0M6F=5O74QP5@C6UW^;06È_s@COQO!;06s[>G25@¶8UO;06F6G4Q8X;0O<54j#;0BG47;#>A@36F=5O74QP5@C6ÈJKPL=5O;0P5;0B>ABG47;0P5KR+O;#>G47JKP56UW
476Z>G2<;#>>A25@d[p8X;#PY!@H0@CP5@UBA;#>G@CE*[*;>A2+BG@C@]lE54Qhi@UP56G4QJKP<;0Ov6G=<;#8C¥@ º(J0MNFOQ47P5@C;0B~McR5P58d>A4QJKP56GVLJKP ¨ q
132547636F=<;08U@H4Q636GR58:2*>A2<;#>
ï r< R5P5ª¾± 8d>A4QJK!P56k*47¨bP ¯º¤$§ #!;0©ZP5± 476F2`Î , ;0OQ47JK6¶P5;tLKK@C@CJ^JÊ5E5@U@U6G6G47478#8Uq¶6¶~J0JKP P¨K@C0BF¹¾6G¸¦@U¹¾OQ½v[KMcWvJ0McB¶JK@dB¶K@d@CKBS@U[aBF[YP+JKKP@C>AJ^BGE54j^@C46F;0478O ¤ * JKP ºW¼¨ >AW!25>G@925@C6G@dBF@>
@+4Q6F>G6e;P5JKP+ÁC@CBFJLMcR+P58U>G47JKP ]¤ * º£0;#P5476F2547P5J0P q
ï º4Q6GJK4QhL6t@U47>GPBF#[ ;0BF§ 4¸¦;0¹»º¼P¹¾>i½v;IR5P5BFE5J0@U>:;uBp>A4747J06GJ0PhiW+4j@dM >ABG¨ 4Q8*4Q6Z>GBA>A;025P+@y6F6GMc=+JKBF25ht@CBF;#@ >G© 47W<JK>GP+256i@CPJ0M ¤ ¨ q »¬ 13* 2ºR56CMcW¶J04QBM ;0¬O7O Ý¤ªx¨ * ºe« q ¨ 476t;0P
Ì
r4QKR5BF@ µ q µ q ~
6GhLJ?J0>G2p·R<;0E5BG;#>A4Q896F=525@UBG478C;0O6G=+O747P+@0q
>476k8COQ@X;0Bk>A2<;u>¶>G25@C6F@|>l_~Jz=+BGJK=!@CBS>A47@U6e4Qhi=5Oj[z>A25;#>Xº(476k·^R+4Q>A@H6G=!@C8U4;0Ow;0P5Ea>G2<;#>¶McJKBe;iK4Q0@CP
6FR5BFMT;08U@ ¨ JKP+@Y8C;0P5P5J0>L@+=!@C8d>t>GJ2<;X0@YhLJKBG@p>G2<;0PùJKP5@*6GR58:2ú6F=<;08U@0qÙlPùMT;08U>CW~4QPù>G25@p>A25BF@C@
hL@CP>A4QJKP5@UE8X;06F@C6CW º4Q6R5P54Q·R5@COj[DE5@d>A@UBGhL47P5@UE[H>A25@;#vJK@Z>l_sJx=5BFJK=v@UBF>G47@C6Uqb>4Q6b;0P4QP>GBG4QKR547P+
JK=!@CP·R5@C6S>A47J0P_25@d>A25@UB9>G25@CBF@t;0Oj_Z;X[^69@d?476S>A6H;*6F=<;08C@L6A;u>A476SMÃ[^47P5*;#>9O7@C;06F>y>G25@Lf5BG6F>9=5BFJK=!@CBF>l[0q
13254Q6¶4QP*>GR5BGP*4768UO7JK6F@COQ[zBG@CO7;#>A@UE*>GJL>G25@98C@CP>GBA;0O}476F6GR5@9J0M>G254766F@C8U>G47JKP*J0Mw_25@U>G25@CB¶JKP5@98X;0P{f<P5E
;0P5;0O7JK06xJ0MZ6F=5O74QP5@6G=<;#8C@C6HJKP\K@CP+@CBA;#OÈ6FR5BFMT;#8C@C6Uñq fk6G47P+{>G25@I_~@UO7Oj]P5J_PÞ¿~@UOQ>GBA;0hL4 = 61325@UJKBG@Uh
;0!JKR+>~>A25@@?476F>G@CP58U@xJ0M}O7J^8X;0O¼K@UJ?E+@C6G4Q8hi;0=5=54QP5K+6 ² ½ W+4j>Z8C;0Ppv@e6G25J_Pp>A2<;u¼> º£8X;#Ppv@eMcJ0R5P5E
McJKBs6GR5BSMT;08C@U6ZJ0Mn8UJKP56F>A;0P> § ¡y;0R56F6G47;0P © 8CR5BS0;u>AR5BFv@ qoÊ¶J_~@dK@UBCW<4Q>s476ÈP5J0>~P5J_Pp4QMJKP+@e8X;#PzKJ
!@U[0JKP5Ea6FR58:2a6FR5BFMT;#8C@C6Uq
>D6F25JKR5OQE!@I6A;04QE>G2<;#>XWnMcJKB9;0OQOb=5BA;#8U>A4Q8X;0O=+R5BG=!JK6G@U6CW}_~@iP5@C@UEÞP5J0>HBG@U·R547BF@I>G2<;#7> º6S>ABF478U>GOQ[
6G;#>A4Q6FMÃ[>A25@zhL@CP>G47JKP5@UEÞ8UJKP5E54j>A47J0P56CqY1325@zO;#8:J0Mk;*>A25@UJKBG@d>A478C;0OÈ=5BGJ^J0M3J0M3>G25@z@+4Q6F>G@CP58U@zJ0RM º
6F25JKR5OQEiP5J#>o=5BG@dK@CP>sR56McBGJKhv@U47P5y;0+O7@Z>AJy@U6F>:;#5O74Q6G2IR56G@dMcR5O¼6G=5OQ47P5@~6G=<;08U@C6ÈJKP ¨ qr<JKB@d+;0hL=5O7@#W
McJKBe;iK4jK@UPaf+?@CEgK@UJ?E+@C6G4Q89>GBG47;0P5KR5O7;#>A4QJKAP §pWvJKP+@D8CJ0R5O7E`R+6G@|;i6G=<;08UV@ º _2+478:2`2<;#6;iBF@CE5R+8C@CE
E54Qhi@UP56G4QJKP;0O7J0P5*;0O7ObJ#MZ4Q>G6y@CE5K@U6CW}5R+>9_25478:2E5J^@C6yP5J0>9P5@U8C@C6F6A;0BF47Oj[\2<;XK@i>G25@I=5BGJ0=v@UBF>l[g>A25;#>
ç0æÃæoMcR5P58d>A47J0P5647P º 0;#P5476F2\;0O7JKP+zK@CJÊ5@U6G478U6Cq R58:26G=5;08Cv@ º _4QO7O}6F>A4QO7Ow;0O7OQJ_ >A25@8UJKP56S>ABGR+8U>A4QJKP
J0M~<;0BS[?8U@CP>ABF478L8CJ^JKBGE+47P<;#>G@C6xMcJKBy;0OQO>ABF4;0P+KO7@U6xJ0¼M §pW}25@CP+8C@i;0O76FJ*>G25@I8CJKP56S>ABFR58U>G47JKPJ0M3;{6G=+O747P+@
6F=<;08C@98CJ0BGBG@U6G=!JKP5E54QP5I>ApJ §pq
eP5J0>G25@CBY=vJ06G6G4Q547OQ4Q>l[£4Q6Y>GJÙBG@UO;u>G25@.;06F6GR5hL=+>G47JKP >G2<;#>*>A25@>ABG47;0P5KOQ@C6{47·P § ;#BG@Þ6S>ABF478U>GOQ[
K@UJ?E+@C6G4Q80q.lPMT;08d>XWo=<;0BG;0hL@U>ABF478i6GR5BSMT;08C@U6 ¨ 8CJKhL=vJ06G@CEJ0M>GBG4;#P5KR5O7;0B|¿L@UÀ ÁC4Q@CB=<;#>G8:25@C6L;0BF@{;0Oj]
BF@X;0E+[a@C·R54Q=5=v@UE`_4Q>G2g;zP<;#>GR5BA;0On>ABF4;0P+KR5O;u>A47J0ðP § 47PY_25478:2g@dK@CBS[a>GBG4;#P5KO7@98CJ0BGBG@U6G=!JKP5E56>GJp;
¿L@UÀ ÁC4Q@CBy=<;#>G8:2q R58:2.;z>ABF4;0P+KR5O;u>A47J0P`476x4QP0@CP5@UBA;0O3â&ã þ 0@CJÊ5@C6F4780qI© lP\>A254Q6y6G4Q>GR<;#>G47JKP`>G25@CBF@L4Q6
;L=<;0BF>G478UR5O;0BFOQ[i6G4Qhi=5OQ@_Z;X[{>AJL8:25J^JK6G@9>A25@9<;0BS[^8C@CP>GBG478yMcR5P58d>A4QJKP56 µ ° ¼q hk@U8X;0OQO>A2<;#>¶m+;0hL=5O7@ Í
Ì r 470R5BG@ µ q ² Î q ~ 6GhLJ?J#>A2{8CR5+478y6G=52+@CBG4Q8X;0O6F=5O74QP5@0q
K4Q0@C6BF@X;06FJKP56x_2[`4j>x4764QP`K@UP5@CBG;0ObP5J0>x;{0J?JÊ`47E+@X;t>AJpR+6G@|>A2+@6F>:;#P5E<;0BFE5;0BF[^8C@UP>ABG4Q88CJ^JKBS]
E547P5;#>A@U698UJKBGBF@C6F=vJKP+E547P5{>AJ{>A2+@L>GBG4;#P5KR5O7;0BeMT;08U@U>A69J0Ms>A25@L=547@U8C@d_476G@LO74QP5@X;#Bx47P>A@UBG=!JKO;0P>x>GJY>A2+@
K@UBF>A4Q8C@U6kJ#iM §pqo132547634Q63v@U8X;0R+6G@y>A254Q6Z_47O7Ov47PpK@UP5@CBG;0OP5J0>=!@CBFhi4j>3R563>AJIE5@U6G4QKPY6FhiJ^J0>G2p6G=5OQ47P5@U6
JK@CB ¨ q*ÊkJ¦_s@U0@CBUW4Q>y>AR5BFP56DJ0R+>H>G2<;#>9>A254Q6D;#=5=5BGJK;08:2 óÃæÃæ~_sJKBG\4jM ¨ 476H;Y8UJKhi=!JK6F4Q>A@I6FR5BFMT;08U@
8CJKP+6G476S>A4QP5HJ#M>ABF4;0P50R5O;0B=vJKOj[^P5JKhL4;0O5=5;#>A8:25@U6CqÈáe;#hi@UOQ[KWK>G25@¶MT;#8U>È>A2<;#>sP5@U47K2!JKBG4QP5x>ABG47;0P5KR+O;0B
=<;#>G8:25@C6;0BF@sûFJK47P+@CEz6FhiJ^J0>A2+OQ[LKR<;0BG;0P>A@U@C63>A2<;u>Z>A25@eJKBGE54QP<;0BS[Lå!æjç0â!ç0è9<;0BS[?8U@CP>ABF478x8UJ?JKBFE547P5;#>A@U6
8CJKBFBG@U6G=!JKP5E54QP5¶>GJe>A25@U6G@~>GBG47;0P5KOQ@C6w;0BG@s8CJKhL=<;#>G475OQ@0W¦47P9>A25@Z6F@CP56F@ZJ0`M ²BGJ0=vJK6F4Q>G47JKP ² q132R5647P|;#P[
K4Q0@CP*>ABG47;0P5KOQ@x>A25@U6G@|8UJ?JKBFE547P5;#>A@U6e8X;#P`v@H@d^>A@UP5E5@UE\>GJi>G25@DP5@U47K2!JKBG4QP5i>GBG47;0P5KOQ@C6k;06e6FhiJ^J0>G2
McR5P58d>A47J0P56 § _25@UBG@y>A25@yE5@UKBG@U@yJ0M6FhiJ^J0>G25P5@C6F6k_4QO7OvE5@C=!@CP5EYJKPp>A25@y6FhiJ^J0>A2+P5@C6F6kJ#M ¨© q
Æ@~25;0@36G@U@CP|>A25;#>>G25@~6FR58C8U@C6G6oJKB}MT;047OQR5BG@oJ0M58CJKP56S>ABFR58U>G47P56F=5O74QP5@~6F=<;08U@C6bJKPDK@CP5@UBA;0O?6GR5BSMT;08C@U6
2547P+K@C6kR5=!JKPY>G25@H@?476F>G@CP58U@|J0M5;0BF[^8C@UP>ABG4Q8D8UJ?JKBFE547P5;#>A@U6CqZ>e476k;0O76FJi8UO7@C;0BkMcBFJKh JKR5Bk@d+;0hL=5OQ@C6CW
>A2<;u>H@d[email protected]=5OQ@L6FR5BFMT;#8C@C6H6GR58:2Þ8CJKP56S>ABFR58U>G47JKP56Hht;X[\!@LMT;#ByMcBFJKh>ABF4Q^4;#O$q >A4QO7O$W>G25@tE+476S]
8CR56F6G@UEaMcBA;0hL@U_sJKBFzJ0Mb6F=5O74QP5@C6JKP*6GR+BFMT;08U@C6eJ &@UBG6ht;#P[zv@UP5@Uf5>G6CW!8CJKhL=<;0BF@CE{>AJLJ0>A2+@CBk@d?476S>A47P+
BG@U8CJKP56S>ABFR58U>G47JKPzhL@U>G25JÊ56Cqb132+@ht;#47Pi;0BGKR+hi@UP>s6GR+=5=vJ0BF>A4QP5H>G25476s8CO7;047h×4Q6È>G2<;#>s>A25@e¿~@CBFP56F>G@C47P^]
¿L@CÀ ÁU47@UBnMcJ0BGhi;0O74Q6GhÉMcJKBn6G=5OQ47P5@U6wJKP96GR+BFMT;08U@C64Q6>A25@È6A;0hL@oMcJKB};0O7OK6FR5BFMT;#8C@C6Uqb132<;#>w476UW#4j>n476n@C6F6G@UP>G4;0OQOQ[
47BFBG@COQ@U#;0P>y_25@U>G25@CBH_~@t_sJKBFJKP>A25@i6G=525@UBG@#W47P>G25@t=+O;0P5@#WJKBHJKP;0P[J0>G25@CBH6GR5BSMT;08C@#qa e6D;
8CJKP+6G@C·R5@UP58C@#WÈ_s@p8X;#PR56G@t>G25@z6G;0hi@z;0O7KJ0BG4Q>G25hL6yMcJ0BD6G=+O747P+@C6DJ0P;0O7Oo6GR+BFMT;08U@C6CWÈ;06DO7JKP5a;06D_s@
R56G@;|8CJKBFBG@C8d>=5BGJ^8C@UE5R5BF@>AJ|8UJKhi=+R+>A@e>G25@x<;0BS[^8C@CP>GBG478x8UJ?J0BGE54QP<;#>A@U6 § _25478:2{E5JE5@U=v@UP5E{JKPz>A2+@
>l[^=v@yJ0M}>A25@y6FR5BFMT;08U@ © q
EGFaHJK5MZN 1wJ`4QO7OQR56F>GBA;#>G@I>G25@p;0!JK@z=!JK4QP>CW6FR5=5=!JK6G@z>G2<;#> ¬¯ ¬ * §Å;0BF@i>l_sJ\;0EuûG;08U@CP>
>ABF4;0P50O7@C63J0P ¨ W<_4Q>A2{K@UBF>G478C@U+6 § ¬e©Èþ± ± ~:¯ ± ® ¯ ± W , ;0P5ÊE § ¬ ©s± ± ~d¯ ± ® ¯ ±2à , q3í@U> ¤ ;0P5E ¤ v@>l_sJNS=vJKOj[^P5©JKhL4;0OQ6GVDJ#ME5@UKBG@U@ È© J#ÃMw>G25@xMcJKBGh
¤{± { ¥ | ©¥ ¥ÉÍ ¯ ¤ 5± { ¥ | ©¥ Ã ¥ÉÍ ¯
ÌÌ É
ÌÌ É
Ì ^
_25@UBG@ ©¥ ¯ ©Ä¥ Ã *ú¬ ;0BG@LK4Q0@CPÞ¿i@CÀ ÁU47@CB98CJ^@/bL8U47@CP>G6Cqp1325@UP ¤ ;#P5E ¤ ûFJK4QP8UJKP>A4QP^R+JKR56GOj[;0O7J0P5
>G25@y@CE5K@± ~ ± ® 4jM
©¥ å Ã ¥ ç ± ©¥ å ¥ ç ¯ ° ~s"° ± È ¯
®
Í Í¾ Í Í¾
~
;0P+E*>G25@U[DûFJK4QPz_4Q>G2 8CJKP>A4QPR54Q>l[p4jMw;0P5E*JKP5OQ[t4QM
©Ä¥ å Ã ¥ ç ~ ± ©¥ å ~ ¥ ç µ ©°å § ±2à a© " ©¥ å ¥ ç ~ µ ©°ç § ±Ià a© " ©¥ å ¥ ç ~ µ ©°qè § ±Ià ©¯ °&~a"ù° ± È _£²K¯
®
Í Í : Í Í¾
Í : Í¾
Í Í
_25@UBG@t_s@tR+6G@CE>A25@i;055BF@U^4;u>A© 47J0P56 ° ª ±° °"! $¯ #g± ²K¯ Ì ¯ Í qpÂYJKBF@CJK@UBCW>G25@i#;0OQR5@C6 µ ©°"! § ±Ià © ;0BF@
JK?>:;04QP5@CE*[pf<BG6S>¶@^>A@CP+E547P5 µ °"! ;066FhiJ^J0>A2pMcR5P+8U>A4QJKP563>AJ ¬Æï¬ W¼;0P5E{>A25@UPY@d#;0O7R<;u>A47P+|>A25@Uh
;#é> ±Ià¦q13254763@^>A@CP+6G47J0P*4Q6Z=!JK6G6F475OQ@;063OQJKP5;06s>A25@x<;#BF[^8C@UP>GBG4Q8x8CJ^JKBGE54QP<;#>G@C63;0BF@8CJ0hi=<;u>A47+O7@e4QP
>G25@y6G@CP+6G@DJ#iM ²BGJ0=vJK6F4Q>G47JKP ² q
1325@k;0vJ0@¶8UJKP5E54j>A47J0P56McJKBo;y6GhLJ?J#>A2¶ûFJK4QPL!@U>l_s@C@UPi>l_sJH0@CP5@UBA;0OQ47ÁC@UEL¿i@CÀ ÁU47@CB>GBG4;#P5KO7@U6b8X;#Pi!@
4QhihL@CE547;#>A@UOQ[{6F@C@CPg>GJpv@DMcJ0BGhi;0O7Oj[\óTõ^ôdâ þ ó ñ ç0æb>GJz>A25@8UJKBGBF@C6G=!JKP5E+47P5p8UJKP5E54j>A47J0P56e4QPa>A25@=+O;0P<;#B
6F@U>G>G47P5+qb1325476@?=5O;04QP56_2[_s@k25;0@P5J0>È;0E5E+BG@C6F6G@UEi4QPI>G254766G@C8d>A4QJKP>A25@k;08d>AR<;0O?BG@U8CJKP56S>ABFR58U>G47JKP
=5BFJK5OQ@Ch § ¸¹ º¼¹¾½w47P>A@UBG=!JKO;u>A47J0PJ0BD;0=+=5BGJX?47hi;#>A4QJKP © R56F47P5Y6G=5OQ47P5@U6HJ0PÞ6GR+BFMT;08U@C6Cq*1325@zBF@X;06FJKPÞ4Q6
>G2<;#>>G25@|6A;#hi@Hhi@d>A25JÊ56eP5J_P\47PY>A25@|=+O;0P5@H8X;0Pg!@H>GBA;0P+6FMcJKBFhi@UEg;0O7hLJK6S>;0R?>AJKhi;#>A4Q8X;0OQOQ[i>AJ
;0P[t6GR5BSMT;08C@#&q %È;#BG47J0R56Z@d^>G@CP56F47JKP56J0Mn6FR58:2*=5O;0P5;0B~hL@U>G25J?E+6Z>AJ|>A2+@6G=52+@CBG@9;0BF@E54Q6G8CR+6G6G@UEY4QP Í ;0P+Ea4Q>k4Q6k4QP5E5@U@CEa8UO7@C;0B3McBGJKh>G2<;#>¶=<;0=!@CB3>A25;#>XW¼@d?8U@C=+>¶McJKBk;LMc@U_ E5@U>A;047OQ6CW5>A2+@H=5O7;0P<;0B3hL@U>G25JÊ56
8C;0BGBS[pJK@CB>AJ>G25@y6G=525@UBG4Q8X;0O6F@U>G>G47P5+W¼;0P5E{47P5E+@C@CE{>AJI>A2+@96F@U>F>A47P+LJ#Mb;0P[p6FhiJ^J0>G2*6FR5BFMT;#8C@ ¨ q
ß ñ & E pð 99( ' E ¡ E V ¢gL ¨ £3ä
£3{g|9¦I ¨ L ¨ p £2z E ¨
lP>A254Q68:2<;0=+>G@CBIJKR5B|McJ^8CR+6I_~;06Ihi;047P5Oj[JKPE5476F8CR56F6G47P+6F=5O74QP5@C6J0P 6FR5BFMT;08U@C6UéW 0¹¾¸¦¹¾½o;#P<;0O7J0K6|J0M
=54Q@C8U@U_476F@=vJKOj[^P5JKhL4;0OQ6wJKPL=5O7;0P<;0B>GBG47;0P5KR5O7;#>A4QJKP56UqwÊkJ_~@dK@CBUW^>G254766F25JKR5OQEIP5J0>oO7@C;XK@3>A25@3BF@X;0E+@CB
_4j>A2>G25@L47hL=5BG@U6G6G4QJKP\>A2<;#>9>A2+@CBG@i;0BF@iP5J#>DJ0>G25@CB9hL@U>A2+J?E56y>A25;#>D25;0@t!@[email protected]@UE.6GR+8C8C@U6G6SMcR5O7Oj[
4QPÙE<;#>A;u]f+>G>A4QP5;0P5EúBF@C8UJKP56F>GBGR58d>A4QJKPÙ=5BFJK5OQ@ChL6iJKP 6GR5BSMT;08C@U6CqÉ1325@UBG@UMcJ0BG@0W34QP >G25476L6G@U8U>A4QJKP _s@
_4QO7OK4jK@y;I5BG4Q@UMwE5@C6F8CBF47=+>G47JKP{J0MwJ0>A2+@CBk;X0;#47O;#5O7@¶hi@d>A25JÊ56;0P5E*=5BFJ¦^4QE5@yBG@UMc@UBG@UP58C@U6¶McJKBZMcR5BS>A25@UB
6S>AR5E+[0q1325476476¶;0OQ6GJL;iKJ^JÊ*=+O;08U@9>GJihL@CP>A4QJKP*J0>A25@UB¶6FR5BF0@U[^6e>G2<;#>¶2<;XK@D!@C@UPY_BF4Q>G>G@CPYJKPY>G25@
>GJK=5478xJ#M6F=5O74QP5@C6JKP{6GR+BFMT;08U@C6CW¼6FR58:2`;06¶~2<;#=+>A@UB µ q |47P Í µ ;0P+LE ½ q
ß <t í4!*) ë N î N ! ë,+ H ) N !
Ê¶;^4QP5È54Q6G8CR+6G6G@UE>A25@z4QE5@X;#O747ÁU@CE=5BGJK+O7@ChÅ4QP_254Q8:2 ¨ _~;06;a6FhiJ^J0>A26GR5BSMT;08C@#W4Q>D6G25JKR+O7E.!@
hL@CP>A4QJKP5@UE`>A2<;#>e47P`6FJKhL@|;0=5=+O7478C;#>A4QJKP56k6GR5BSMT;08C@U6x8CJKhL@|;#6E5476F8CBF@U>A@D8CJKOQO7@C8d>A4QJKP56kJ0MÈ=vJK4QP>A6Cqr¼J0B
@5;#hi=5OQ@0W ¨ ;0P5E ¤ 8CJKR5OQEv@{6A;#hi=5OQ@CE;#>i;g6G@d>LJ0MeE+476G8UBG@d>A@{=vJ047P>A6 !UV¥ *¬ ® Wo_25@CBF@*>G25@ !U¥
8UJKR5O7EaBG@C=+BG@C6F@CP>>G25@D>ABF47=5OQ@ § O;u>A4Q>GR5E5@#W!OQJKP5K4j>AR5E+@0W¼;0Oj>A4Q>GR5E5@ © W¼E5@U>G@CBFhi4QP547P5i;t=52[^6G4Q8X;0O}O7J^8X;u>A47J0P
JKPY>A25@H6GR5BSMT;08C@HJ0Mb>A2+@D@X;#BF>A2`;0P5E ¤¥ 8UJKR5O7EYv@9>A25@D;047B=5BF@C6F6GR5BF@;#> !U¥ qk¿~@UMcJ0BG@H_s@D8C;0Paf<P+Eg;0P
;0=+=5BGJX?47hi;#>A4QJKP\>AJ ¤ R56G4QP5a>G25@t6F@U>G>G47P5YE5@C6F8CBF47[email protected]>A2+@t=5BF@U^47JKR+6D6G@U8U>G47JKPWw_~@tf5BG6F>DP5@C@UE;
=5BF@C=5BFJ?8U@C6F6G47P+6F>G@C=DMcJKB}BG@U8CJKP+6F>ABFR58U>G47P5k>A25@È6GR+BFMT;08U@ ¨ qwÆ@sBF@UMc@CB}>A25@ÈBG@C;0E5@UBw>AJe~2<;0=?>A@CBF6}|4QP
>G25476o!J?JKD;0P5Ei;0O76FJ>APJ ^W ²K² W Í µ W ^ W W0McJ0Bo;0PiJ0@CBF^4Q@U_£J0M&;0P5ELBG@dMc@CBF@CP58U@C6ÈJKPi6F@U0@CBA;#O!hL@U>G25JÊ56
McJKB6FR5BFMT;08U@yBG@C8UJKP56S>ABGR+8U>A4QJKP{McBGJKh6G8X;u>G>A@UBG@UEaE<;#>A;=vJK4QP>A647P ¬ ® q
ß j i H.- í HM0/-H !í$!1+ %2)îÕí4ì`%(!
¶PL4QP58CBF@X;06F47P50OQ[y=!JK=5R5O7;0B8UO;06F6bJ0M¼hL@U>A2+J?E56wMcJKB4QP>G@CBF=vJKO7;#>A4QJKP|;#P5EI;0=5=5BFJX+4Qht;u>A47J0PHJ0M!6F8X;#>F>A@CBF@CE
E<;u>:;y;0BG@Z>G25JK6F@k5;06G@UEiJKP{èFçõ0óTç0æ ³:çuödó7sö â ñdþ ó$ãuâ+ö § h¶¿Zr © W 0$¹ ¸¹ ½McR+P58U>G47JKP56b>G2<;#>È;0BF@3BA;0E+4;0OQOQ[y6F[^h]
hL@U>GBG478#q1325@3BF@X;06FJKP|_2[|6FR58:2ihL@U>G25JÊ56;0BF@ZJ0MÃ>A@UP=5BG@dMc@CBFBG@CE>GJJ0>A2+@CBb>A@U8:25P54Q·^R+@C6476w>A2<;#>>A25@U6G@
Ö ¹43^¹ ÑeÚnÓwÔoÕkÜ¶ÑeÓ}Û65bÔ ÔÓwÐ Ý yØ à Ý Õ à ß ÜDÏkÓ}Û Ý Ü ØÞÝ Ü Øbß Õ¶à^Ñ9ÏbÔ Ø
Ì hi@d>A25JÊ563;#BG@vetô:ö ¦ æ7ô:ö:ödq132+4763hL@X;0P56Z>G2<;#>Z>GJ47P>A@UBG=!JKO;u>A@;6F@U>J0MnMcR5P58d>A4QJKP<;0OvE<;#>:;;#6G6GJ^8C47;#>A@UE
_4Q>G2.6G8C;#>G>G@CBG@UE=vJK4QP>A6|JKP;`6FR5BFMT;#8C@p4Q>D476HP5J0>P5@U8C@U6G6A;#BF[>AJa8CBG@C;#>A@{;a>GBG47;0P5KR5O7;#>A4QJKPW}JKB|;#P[
J0>A2+@CB>l[?=!@DJ#MbhL@C6G2Y>A2<;#>k8UJKP5P5@U8U>A6¶>A25@HK4Q0@CPaE5;#>:;I6G4j>A@C6UWv=+BG47J0B>GJi>G25@D;#8U>AR5;0OwBF@C8UJKP56F>GBGR58d>A4QJKP
=52<;06F@0q
²}@CBF2<;0=56I>A25@zf5BG6F>I>l[^=!@C6IJ0M¶BA;0E547;0O~5;06G4Q6|McR5P58U>G47JKP+6R56G@UEÙ47P.>G25@{8CJKP>G@d^>LJ0Me4QP>A@CBF=vJ0O;#>G47JKP
J0M}McR5P58U>G47JKP+6kJ0P*6FR5BFMT;#8C@C6k_~@UBG@y>A25@ 7xç0èFõ Pe æ þ 9ó 8 çõ0èó ñ ödW547P>ABFJ?E+R58C@UE*McJKB;#=5=5O74Q8X;#>G47JKPp4QP{K@CJ#]
=52[^6G478U6D4QkP Í ^,: Í ½ ¶§ 6F@C@z;#O76GLJ ½+W Ì ² W Ì ^ W ^ Ì Ã© qz1325@t;0E+#;0P>:;00@iJ0MZR56G4QP5YBG;0E547;0O<;06F476yMcR5P58U>G47JKP+6
JK@CB¶J0>A2+@CBkhi@d>A25JÊ56k47PY>G25@96G@U>F>A4QP5tJ0MMcR5P58U>G47JKP+6¶JKPY6GR5BSMT;08C@U6e4Q6k>G2<;#>e;iK4jK@CP*McR5P58d>A47J0Pa476¶;0=?]
=5BGJX?47hi;#>G@CE.;#P5E¼î#JKB947P>G@CBG=!JKO7;#>A@UEÞ[.;YO747P+@X;0By8CJ0h|547P5;#>A4QJKPJ#M3>ABA;#P56GO7;#>A@U6DJ0M;\ödóÃÄâ 0æ7ñô hk¿Zr~W
_25478:2*K4jK@C6k;|K@UBF[{6F47hL=5O7@BF@C=5BF@C6F@CP>:;#>G47JKP*J0M}>A25@yBF@C6GR+OQ>A4QP5IBG@U8CJKP56S>ABFR58U>G47JKPq
ÂY;0P[z=<;0=!@CBF6Z2<;XK@x!@C@UPz_BG4j>G>A@UPpJKPt>G25@R56F@xJ0(M h¶¿~r6~4QPt>A25@e6G=525@UBG4Q8X;0Ov6G@U>F>A4QP55W+6F@Cp@ Ì0Í W Ì W
^ Ì W Ì W;0P+E\;0O76FJt>A25@D6GR5BSK@U
[ Ì q h@C8C@UP>AOQ[0sW h¶¿~r6JKP`>G25@|6G=+25@CBF@L25;0@v@U@CP\@ChL=5OQJ¦[0@CEgP5J#>
JKP5Oj[p47P*>A25@H8CJKP>A@^>xJ0M4QP>G@CBF=vJKO7;#>A4QJKP{5R+>e;0O76FJi>G25@D8UJKP>A@d^>xJ#M6GJKOj^47P5LE5;4 v@CBF@CP>A47;0On@C·R<;#>G47JKP+6
JKPp>A25@96G=+25@CBFñ@ ½ qo1325@CBF@D;0BF@9;0O76FJL6F@U0@CBA;#O}=5;0=v@UBG6kJKPYí};#KBA;0P+K@y;0P5EYÊ¶@UBGhL4Q>A@x4QP>A@CBF=vJ0O;#>G47JKP
JKP|K@UP5@CBG;0O h47@Uht;#P5P54;#PDhi;0P54QMcJ0O7E5Á6 ²µ W Ì0Î W Î W#_254Q8:2i;#BG@~J#Mv4QP>A@CBF@C6S>bMcJKBwMcR+P58U>G47JKP56JKP6GR5BSMT;08C@U6
J0M;0BG54j>ABG;0BF[L>AJK=!JKOQJK0[Kq
Â*@U>A2+J?E56e<;06G@UE`JK]P hk¿Zr6kK@UP5@CBG;0O7Oj[{6GcR v@CBkMcBGJKh =!J?JKB8UJKP5E54j>A47J0P547P5IJ0M>G25@DOQ47P5@C;0B6F[^6F>G@ChL6
>A2<;u>3;0BF476G@e47Pp47P>G@CBG=!JKO7;#>A4QP5HO7;0BG0@e6G@d>A6J0MnE<;u>:;+qoÊkJ¦_s@U0@CBUW!O7;#>A@UOQ[I>A2+@CBG@x25;06Z!@C@CP{8UJKP56G4QE5@CBG;05OQ@
=5BGJ0KBG@U6G6ÈJKPi8UJKhL=<;08U>GOQ[6FR5=5=!JKBF>G@CPE h¶¿Zrw6 § 6G@Uv@ Ì © W_25478:2L2<;XK@k>A25@k=!J0>A@UP>G4;0O5>GJHBF@CE5R+8C@>A254Q6
6G25J0BF>A8UJKhL47P5J05M hk¿Zr6Cq
ß ß ' H ëí H îíZì`% HM#JLN î,;sì - !
_~@UO7Oj]@C6S>:;05OQ476F25@CE ;0=5=5BFJ;08:2ù>AJ8CJKP56S>ABFR58U>G47P554Q#;0BF4;#>G@zMcR5P58U>G47JKP+6i4QP>G@CBF=vJKO7;#>A4QP5g6G8C;#>G>G@CBF@CE
E<;#>A;y4QPL>G25@k=5O;0P+@k4Q6>AJyR56G@k>A25@k6GJu]l8X;#O7O7@UE|#;0BG47;#>A4QJKP<;0O?hi@d>A25JÊ56CW_254Q8:2z;0BF@¶5;06G@UEtJKPLhi4QP547hL47Á]
47P5*;0P NF@UP5@CBF0[\McR5P58U>G47JKP5;0O7Vp6FR5^ûF@C8d>|>AJ*K4jK@CP47P>G@CBG=!JKO7;#>A4QJKPg8CJKP+E54Q>G47JKP56Uq >ABG4Q8U>GOQ[g6F=v@C;047P55W
#;0BG47;#>A4QJKP<;0O}hi@d>A25JÊ56x!@COQJKP5p>AJp>A2+@L=+BG@U^4QJKR56y6GR5+6G@C8d>A4QJKP6F47P58U@>A25@I0@UBGP5@UO76H;06G6FJ?8U4;#>G@CEg_4Q>G2
6GR58:2g@^>ABG@Uht;#O=5BFJK5O7@Uhi6¶;0BF@|;0OQ6GJzBG;0E54;#O7OQ[t6F[^hLhi@d>ABG4Q80q¶1325@|hL@U>A2+J?E56¶2<;XK@!@C@UP`McBG@C·R5@UP>AOQ[
R56G@UEa4QP*0@CJK6F8C47@UP58C@U6CW!6G@Uñ@ Ì ,µ : Í ² W Í0Í W ^,: ½ qb ¶P5J0>A2+@CB=vJ0=5R5O;#B3hi@d>A25JÊW<J0MÃ>G@CPY;0=5=5OQ47@CE{4QP*hL@d]
>A@UJKBGJKOQJK0[0W<4763>A25@H8CO7;06G6F478X;#Oölå<ô ñdþ èFç0sæ etô Zþ ¦ ãCõ0q~1325476¶hi@d>A25JÊYR+6G@C6e6G=525@UBG4Q8X;0On2<;0BFhiJ0P5478U6kJ#M254702
E5@C0BG@C@U63>AJi;0=5=5BFJ?4Qht;#>G@eMcR5P58d>A4QJKP56E5@Uf5P5@CEYJKPp>A25@y6G=+25@CBFñ@ q
ß ò t í4!/î H %) N=<?>VN í9@A;îí4%B@ JLN î,;sì - !
13254768UO;06F6IJ0MehL@U>G25JÊ56CWÈ6GJKhL@U>G47hL@C6I;0OQ6GJ\8X;#O7O7@UE 25@U=52<;0BFE?]>l[^=!@YhL@U>G25J?E+6CW~R+6G@C6i;`_~@U47K2>G@CE
8CJKhD547P<;u>A47J0PHJ0M+McR5P58U>G47JKPH0;#O7R5@U6w>A25;#>;0BF@~!@C4QP547P>G@CBG=!JKO7;#>A@UEDJKPD>G25@Z6FR5BFMT;08U@ ¨ W0>AJBF@C8UJKP56F>GBGR58d>
;0PR5P5P5J_PÞMcR5P58d>A4QJKPMcBFJKhE54Q6G8UBG@U>G@iE5;#>:;+qi1325@I_~@U47K2>A6D;0BG@I8:25J06G@CPÞ6GJ`;#6y>GJYE+@C8CBF@X;06F@t>A2+@
47P Ë R5@CP58U@|J0Ms;t=<;#BF>A4Q8CR5O7;0BeE5;#>:;t=!JK4QP>eJKP`>A2+@|6GR5BSMT;08C@I;#6e_~@hLJK@I;X_~;[YMcBGJKh >G25476=!JK4QP>CqxlP
>A254Q6s_~;X[t=!JK47P>G6~>A2<;u>3;0BF@¶MT;0BÈMcBGJKh ;|K4jK@CPtBG@C047JKPzJ0Pt>A25@e6GR5BSMT;08C@_4QO7O¼2<;XK@xOQ4Q>G>GO7@JKBsP5J|/@ v@C8d>
JKPÞ>G25@pBG@U8CJKP56S>ABFR58U>G@CEMcR5P58U>G47JKPÞ47PÞ>G2<;#>BF@CK4QJKPq\r<JKBDE+@U>:;#47O76HJKP25J_ >AJ`8:25J^JK6F@z>A25@z_s@C4QK2>
McR5P58d>A47J0P56CW+_s@9BG@UMc@UB3>A25@yBG@C;0E5@UB>GðJ ²K² W ² Ì ;0P5Ea~2<;0=+>G@CB µ q |J0M Í µ q
ß ü t ë H %-!DC5%(íZî NJLN î,;sì - !
Âa;0P[D>G@C8:25P+47·R5@C6McJKBwE5@Uf5P547P5McR+P58U>G47JKP56JKP|>ABF4;0P50R5O;#>G@CE § JKBbJ#>A25@UBF_476F@Z=<;0BS>A4j>A47J0P5@CE © 6GR5BSMT;08C@U6
;0BG@y<;#6G@CEYJKP{>A25@947E5@C;J0M>GBA;0P56Sf<P54j>A@y47P>A@UBG=!JKO;u>A47J0Pq1325476hL@U>G25J?E*6F>A;0BF>G6k_4j>A2{>A25@y8UJKP56F>GBGR58]
>A4QJKPtJ0M};HP5@U>l_sJKBGiJ0Mn6GhLJ^J0>A2tMcR+P58U>G47JKP56~E5@Uf<P+@CEpJKPz>G25@@CE+K@C6ZJ#M>A25@=5;0BF>G4Q>A4QJKPz;#P5Et>A2+@CP{R56G@U6
>ABG;0P56Ff5P54Q>G@e>ABF4;0P50R5O;0Bo4QP>G@CBF=vJKO7;0P>A6È>AJ47P>G@CBG=!JKO7;#>A@k>A25@P+@U>l_sJKBGzJ#Mn8CR5BSK@C6[p;|6FhiJ^J0>G2tMcR5P58]
Ì ½
>G47JKP`J0Pa>A25@DE5JKhi;047PY6GR5BSMT;08C@ ¨ qx1325@|=5;0=v@UBG6y ²K² W ² Î W Î W ² W ½+W ^ ^ W ^ E+@C6G8UBG4Qv@I;t8UJKP56S>ABGR+8U>A4QJKP
J0MÈ6FR58:2g>ABA;#P56Ff<P+4Q>A@|>GBG47;0P5KR5O7;0B47P>A@UBG=!JKO;#P>G6¶McJKB¶>A25@|6F=525@UBG@0W_25@UBG@C;06p ^?²
8C;0Pgv@|;0=5=5OQ47@CEY>AJ
;0BF54Q>GBA;0BS[z6FR5BFMT;08U@C6>A2<;u>k;0BG@9;#>OQ@X;06S> ¥W E54;v@CBF@CP>A47;05OQ@0q
ß i JLK-M íE)uíî JLN î,;sì - !
lPL *: Wóeeå!æ ó ñ ó þ ¿~@UBGP56S>A@C4QP?]Ä¿L@CÀ ÁC4Q@CB3=<;u>A8:25@U6 § ;0O76FJL8C;0O7OQ@CEp ]l=<;#>G8:25@C6 © ;#BG@xR56F@CEY>GJI6G47hDR5OQ>A;0P5@d]
JKR+6GOQ[YBG@U8CJKP+6F>ABFR58U>y>G25@|6GR+BFMT;08U@ ¨§ 04QK@UP\;06y;t6F@U>yJ0MoR5P+JKBG;#P547ÁU@CEg=!JK47P>A6 © ;0P5E`>G25@|R5P+^P+J¦_P
McR5P+8U>A4QJKP ¤ W!_25J06G@H#;0OQR5@C6¶;#>k>A25@U6G@|=!JK4QP>G6e;#BG@9K4Q0@CPq eP`;0E+#;0P>:;00@HJ0M>A254Q6¶hL@U>G25J?E*476>A25;#>
4j>sE+J?@U6sP5J#>sBF@C·R54QBG@¶;0P[L;06G6FR5hi=?>A47J0PLJ0Pi>A2+@k8UJKPK@+4j>l[z;#P5E¼î#JKBoE54 &@UBG@UP>G4;0+47O74j>l[9J0M ¨ ;0P5EI>A25;#>
4j>D8C;0P.2<;0P+E5O7@iJKBG4Q@CP>[email protected];#P54QMcJKOQE56xJ0M3R+P5BG@U6F>ABF478d>A@CE.>GJK=!JKO7JK0478X;#O>l[^=v@U6Cq\øP>G25@zJ0>G25@CBH2<;0P5E&W
>G25@IE5BA;X_<;08:gJ#M~R56F47P5{4Qhi=5OQ478U4Q>k6GR5BSMT;08C@I=<;u>A8:25@U6H4Q6>A2<;#>x>G25@U[`BG@C·R54QBG@@U6G6G@UP>A4;#O7OQ[Y>ABF4Q#;0BG47;#>A@
¿~@UBGP56S>A@U47P?]l¿i@CÀ ÁU47@CB3>G@C8:25P54Q·R5@C6UW!_254Q8:2a;#BG@y2<;0BFE5@CBZ>GJiE5@C;0O_4Q>G2p>A2<;0P{54j#;0BG47;#>A@J0P5@C6Uq
ß G Fv{ î,; N ëpîIH K1N !pìJ+g! K5M í4% N !
¿~@U6G4QE5@C6z6F=5O74QP5@C6IJKPù>ABF4;0P50R5O;#>G47JKP+6J0Mx;6GR5BSMT;08C@ ¨ W~#;0BF47JKR+6LJ#>A25@UBi>l[^=v@U6tJ0M6G=5OQ47P5@U6L8C;0Pú!@
8UJKP56F>GBGR58d>A@UEqr<JKBi@d+;0hL=5O7@#WZ>A25@a=<;0=!@CBG6 Ì W ^ Î K4jK@g;8CJKP56S>ABFR58U>G47JKP£J0M|ölå ¦ ôdèó ñ ç0æZödó eeå!æ7Lô K
ölå!æ óÃâ&ô:ödqi BF@C8C@UP>|47P>GBGJÊ5R58U>G47JKPJKP6G4Qhi=5OQ@d\6F=5O74QP5@C6y4Qñ6 Í qt1325@i=<;0=!@CPB Ì R56G@U6|6G=+25@CBF478X;#O
6F=5O74QP5@C6¶JKPa>ABF4;0P+KR5O;u>A47J0P56Z>AJzE+@Uf<P5@D2[^5BF47E`8UR554Q8|¿L@UÀ ÁC47@UBe=<;u>A8:25@U6CW&_254Q8:2\;0BG@H;0P<;#O7JKK6kJ0M>G25@
8UO;06F6G478C;0OoBA;#>G47JKP5;0Oo¿L@CÀ ÁU47@UBH=<;u>A8:25@U6Cq{1325@p;0R?>A25JKBy4Q6HP5J#>|;X_~;0BG@iJ0MZ6F47hL47O;#Bhi@d>A25JÊ56yMcJKB9J0>A25@UB
>l[^=!@C6kJ0Mb6FR5BFMT;08U@C6 § @?8C@C=?>=5O7;0P<;0B © q
ß N M ¡ (M îí4ë N !ì M9 îíZì`% JLN î,;(ì - !
13254Q6JK@CBS^47@U__~J0R5O7E!@p47P58UJKhL=5O7@d>A@t4jM3_~@{E54QE.P5J0>IhL@CP>G47JKPÞ>G25@p=!JK6G6F4754QO74Q>l[\J#M¶R+6G47P+Þö ³Cä
õ0Gó Oó7ödó$ãuâ`J0PB ÈQç O0ôdæ7ô þ ]>l[^=v@LhL@U>A2+J?E56H47P8CJKP5P+@C8U>G47JKP_4Q>A2>A25@iBG@C8UJKP56S>ABGR+8U>A4QJKPJ0MZMcR+P58U>G47JKP56HJKP
6FR5BFMT;08U@C6Uq R5!E54Q^4Q6G47J0Pghi@d>A25JÊ56x;0BF@I;z=vJ_s@CBSMcR5Ohi@C;0P56J#Ms8UJKP56S>ABGR+8U>A4QP5{6GR5BSMT;08C@U69;0P5E\25@CP+8C@
JKP+@s_sJKR5O7EH@d?=!@C8U>>A2<;#>}>A2+@U[Hhi4QK2>;#O76GJkO7@UP5EH>G25@ChL6G@UOQ0@C6>GJe=5BFJK5O7@Uhi6n4QPH>A2+@Z;0BF@X;¶J#MÈNF6GR+BFMT;08U@C6
JKP{6FR5BFMT;08U@C6FV5qo1325@CBF@x476ZP5J·R5@U6F>G47JKPp>A25;#>Z_~;0@COQ@U>k;0P5E{6FR5vE+4Q^476F47JKPt>G@C8:25P+47·R5@C6k;0BF@!@C8CJ0hi4QP5
4QP58CBF@X;06F47P5KOj[=!JK=5R5O7;0B47PLht;#P[;0=5=5OQ478X;u>A47J0PI;0BG@C;06CW^BA;0P+K47P5xMcBFJKh×6G4QKP<;0O¼;#P5Et4Qht;00@3=5BGJ^8C@U6G6G4QP5
>GJI~ k¡9¢ ;#P5Ep8CJKhL=5R+>G@CB~;0P547hi;#>G47JKPqn132<;u>36A;04QEW>A25@UBG@E5JDP5J0>Z6F@C@Uh>AJH@d?476S>3hi;0P[ihL@U>G25JÊ56
<;#[email protected]!E54j?4Q6G4QJKP.;0P+E¼î#JKB9_Z;XK@UO7@d>A6|E5@U6G4QKP5@CE6F=v@U8C4jf<8X;0OQOQ[g>GJaE5@C;0Os_4j>A2>G25@z=5BFJK5OQ@ChÿJ0M
McR5P+8U>A4QJKP56nJKPy6GR+BFMT;08U@C6Cqá¶J0>A;05OQ@b@d?8C@U=+>A4QJKP56};0BF@o>G25@b#;0BG4QJKR56@?476F>G47P58UJKP56F>GBGR58d>A4QJKP56nJ0M_Z;X0@CO7@d>A6
JKPi>A25@¶6G=525@UBG@ § 6G@Uy@ q² ^ W ÍKÌ W Í0Í W KÍ W ^² W ^ ½ Ã© ;#P5Et>A2+@e=<;0=!@CXB Í W_25@UBG@¶_~;XK@UO7@U>G6;0BG@k8CJ0P56F>GBGR58d>A@CE
JKP*K@UP5@CBG;0O6GR5BSMT;08C@U6Cq
ß 7 ' í$! sHM í9R H îí4ì`%ÆìJ+g! ë,+ H ) N !pì%d! ë,+ H ) N !
¶OQ>A2+JKR5K2\^476GR5;0O74QÁX;#>G47JKPg4Q6xP5J0>D;0E5E5BF@[email protected]>A254Q698:25;0=+>A@UBCWw4Q>y476y4Qhi=!JKBF>A;0P>>AJ*6F>GBG@U6G6H>G2<;#>H;
KJ^JÊi^476FR<;0O74QÁX;#>G47JKPIJ0M>G25@eBF@C8UJKP56F>GBGR58d>A@UE¼î#hLJ?E5@UO7@UEp6GR5BSMT;08C@U63;0P5EtMcR+P58U>G47JKP56s476È@C6F6G@CP>G4;0Ov47Pt>G25@
8UJKP>A@d^>xJ#MMcR5P58U>G47JKP+6¶JKPa6GR5BSMT;08C@U66G4QP58C@#W;06_~@D2<;XK@|=!JK47P>G@CEaJ0R+>@C;0BGOQ47@CBUW<>A25@U6G@|6FR5BFMT;08U@C68C;0P
!@L^4Q@U_s@CE.;#69!@C4QP5*47h|!@CE5E+@CE47P;*2+47K25@UBS]E547hL@CP56F47JKP5;0O6F=<;08C@#qt1325@UBG@dMcJKBG@#Wb;0P;0=5=5BFJK=5BF4;#>G@
>G@C8:25P54Q·R5@¶>GJHE54Q6G=5O7;X[|>A25@BF@C6GR+OQ>A6ÈJ0Mv>A25@kBG@U8CJKP56S>ABFR58U>G47JKPL8X;0Pi6G4QKP54Qf58X;0P>AOj[|@UP52<;0P58U@eJKR+BÈR+P5E5@CBÄ]
6S>:;0P5E+47P5IJ0Mn>A2+@xv@U2<;X?4QJKB3J0Mn>A2+@xBG@C8UJKP56S>ABGR+8U>A@UEYMcR5P+8U>A4QJKP56;0P+E*6FR5BFMT;#8C@C6UqÆÉ2547OQ@e^476GR5;0O74QÁC47P+|;
6FR5BFMT;08U@D4QPY>A2+@9McJKR+BS]lE+47hL@CP56F47JKP<;#O6G=<;#8C@D4Q63K@CBS[aE+;4 bL8CR5Oj>XW<>A2+@CBG@H;0BF@9_~;X[?6¶>AJtE+476G=+O;X[z>A2+@Ch [
;ûFR5E5478U47JKR+63R56G@HJ0Mb4QP>G@CBG;08U>G4QK@y8UJKO7JKB38UJKhL=5R+>A@UB¶0BA;0=52+478C6Uq~1325@y>AJ0=5478yJ0Mw?4Q6GR<;#O747ÁC;#>A4QJKPpJ0M6GR58:2
6FR5BFMT;08U@C6k4763E54Q6G8UR56G6F@CEg;#>OQ@CP5#>A2{47P{hi;0P[z=5R5+O7478C;#>A4QJKP56UW+47P+8CO7R+E547P5A W µ W Ì ½+W ?W 0µ W ^ Í :<û
q
Ì µ
E £ E E \ E ¨
² q ²wqK ¶OQMc@UO7EWKÂqá¶@C;0hD>AR&W;0P5EIíq íq 8:2^R+ht;0#@CBUq?¿s@CBGP+6F>A@U47P?]l¿L@CÀ ÁU47@UB=vJKOj[^P5JKhL4;0OQ6}J0PL6F=525@UBG@C6UW
;0P5E{6G=+25@CBF@d]lOQ47#@96FR5BFMT;#8C@C6UqTSsãeeå ôdèUeóTõ^ôGõV¶ô:ãetô èó |ô:ödó0â<W ² Í ª ÍKÍKÍ ] Í µ W ²µKµ^ q
qÌ ²wq ¶OQMc@COQEW}Âq}á¶@C;0hD>GRW};0P5Eíoqìí?q þ 8:2R5hi;00@UBCqw¢47hLþ @CP5ñ 6F47JKP\;0P+EOQJ?8C;0Ob<;06F@C69J0Ms25JKhLJKK@d]
P5@CJ0R566G=5OQ47P5@x6F=<;08C@U6Cq Xð W UY[Z5÷ Ygç þ ¦ \÷ Ueâ!ç0æj÷7W Ì ªj² ½ Ì :!² Î ² W ²µKµ ^ q
Í q ²wqÈ eOjMc@CO7E&W3Âqsá¶@C;0hD>AR&W;0P5E£íqìíoq 8:2R5hi;0#@CBCqZr4Q>F>A47P+6F8X;#>F>A@UBG@CE£E5;#>:;JKPú6G=+25@CBF@d]lOQ47#@
6GR5BSMT;08C@U6¶R+6G47P+L6F=525@UBG478C;0O6G=+O747P+@C6C]q Z5^÷ Ssã eeå&_÷ UZåå!æj÷ Ygç Zþ ¦ ÷7`W Í ª *: Í W ²µKµ ^ q
q eq¿Z;¦ûG;¦ûo;0P5Ez¡IQq èRq?ÂYJÊ5@COQ47P5y;0P+Ei^476FR<;0O74QÁX;#>G47JKPDJ0M6F8X;#>F>A@CBF@CELMcR5P58U>G47JKPLE<;#>A;xJKPi8UR5BF0@CE
6GR5BSMT;08C@U6CqulP a+q#~25@UPWKá9q¦132<;0O7hi;0P5P&QW bq1w;0P5+W0;0P+E|¢|q132<;0OQht;#P5PW¦@CE54j>AJKBF6CWò â!õç etôdâ þ ç0æ ö
ã Ssã eeå ^þ ôdè VZèFçdå ¦ ó ñ ödW5=<;00@C6 ²,µ : Ì µ q+ÆJKBGOQE 8C4Q@CP>A4jf<¥8 ²oR+5O74Q6G254QP5L~J5qjW ²µKµ q
q eq5¿Z;ûG;¦ûUW5r~q?¿~@UBGP<;0BFE547P+4$W?;0P5E{¡qcèRq+ ¶R+>AJ0ht;#>G478kBG@U8CJKP56S>ABFR58U>G47JKPpJ0Mn6FR5BFMT;#8C@C6;#P5Ep6G8C;0O;0B
f<@COQE56eMcBFJKh Í ¢×6G8C;0P56Cq Ssã eeå ^þ ôddè VZèFçdå ¦ ó ñ ödW& ¶P5PR<;0Oo~JKP?Mc@CBG@UP58C@ @UBG4Q@C6CW e~èAã ñ ô:ôGõ0óÃÄâ uöIã XW VfVÁÛeT7hgji0W ² Î µ ] ²K² ½?W+ k3Â S¡H¡hk G²oÊHW ²µ0uµ q
ð
^ q eq¿Z;ûG;¦ûUWr~qv¿~@CBFP<;0BFE547P54W;0P+E¡IJq `Rq& eE<;0=?>A4Q0@|BG@U8CJKP+6F>ABFR58U>G47JKPgJ#Mo6GR5BSMT;08C@U6H;#P5Eg6G8C;0O;0B
f<@COQE56McBGJKh E5@UP56G@D6G8X;u>G>A@UBG@UEa>ABF4Q#;0BG47;#>A@xE5;#>:;+qv~JKhL=5R+>G@CB 8C4Q@CP58U@D1}@C8:25P+478X;#5O h@C=!JKBF>CWvR1 h
uµ ] ÎÌ ½+cW ²oR+BGE5R57@ f¶P+4QK@UBG6F4Q>l[KW ²XµKuµ q
?q eq¿Z;¦ûG;¦ûUWer~q3¿~@UBGP<;#BGE54QP54$Wk;0P5E ¡kq `R¼q hk@U8CJKP56S>ABFR58U>G47JKPJ0MH6GR5BSMT;08C@U6Y;#P5E(6FR5BFMT;#8C@C6Ä]lJKP^]
6GR5BSMT;08C@U6kMcBFJKhR+P5JKBGK;0P547ÁU@CEp_s@C4702>G@CEY=vJK4QP>A6C.q Ueæ ^ãuèdó þ ¦ eó ñ ç0W ²µ?ª Ì KÍ ] Ì ^?² W ²XµKµ ?q
½+q h9qìm3q¦¿Z;0BFP52547OQOK;0P+EH1xq Dqur<JKO7@d[Kq¦Â*@U>A2+J?E56nMcJKB8UJKP56F>GBGR58d>A4QP5¶6FR5BFMT;#8C@C6}JKP96GR5BSMT;08C@U6Cq¦lP|Ê9q¦Êe;u]
K@CP ;0P5EÙ¢|ûq hkJ0O7O7@UBCWo@CE+4Q>AJ0BG6CW V¶ô:ã etô þ èó ñ YãCõ^ôdæ óÃÄâ mlnYô þ ¦ ãCõuöaç0â!oõ U~åå!æ ó ñ ç þ ó$ãuâ+ödWÈ=<;0K@U6
(² :!² q =5BF47P50@CBCW¼¿s@CBGOQ47PW ²µKµ+² q
µ q h9qìm3q¿Z;0BFP5254QO7O$W¡Iq 1xqÈÂa;0u;#>GR5BA;+WÈ;0P+E q m3q >G@X;0Eq P+@U_éOQJ?J0Þ;#>I2+47K25@UB|E54Qhi@UP56G4QJKP<;0O
6GR5BSMT;08C@U6k>G25BGJ0R5K2*8CJKhL=5R+>G@CBKBA;#=525478U6Cq<lP`¡Iqìm3q¼r!;#BG47P&W5@CE54j>AJKBUpW V¶ô:ã etô þ èdó ñ YãCõ^ôdæ óÃÄâ jqrUeæ ä
^ãuèó eDöHç0â!õ1sHô(ut+è:ôdâ!õuödW?=<;0K@U6 ² Ì0Í :!² Í0Î q l ÂW²2547O7;0E5@UO7=52547;+W ²µ ½u
² Î ðq h9qìm3qZþ ¦ ¿Z;0BFP5254QO7O$wW vqoø=54Q>GÁ0WÈ;0P5EÊ91q ²wJ0>F>Ahi;0P5Pqbr!;u>6GR5BSMT;08C@U6 ª ;`>ABF4Q#;0BF4;#>G@t;0=+=5BGJ;#8:2>GJ
>ABF4;0P50O7@d]<;06F@CE`4QP>G@CBF=vJKO7;#>A4QJKPaJ0Pg6GR5BSMT;08C@U6CqSsãeeå ^þ ôdènUeóTõ^ôGõxV¶ô:ãetô þ èó ñ |ô:ödó0â<W µ+ª Í û*:
Í ½+W ²µKµ Ì q
²K² ðq h9qìm3q5¿Z;#BGP5254QO7O!;0P5EzÊHq q<øRq R5BFMT;#8C@C63E+@Uf<P5@UE{JKPz6GR+BFMT;08U@C6Cq Ssã eeå ?þ ôdè UeóTõ^ôGyõ V¶ô:ã etô þ èó ñ
|ô:ödó0â<W ª ÍÌ#Í : ÍKÍ ^ W ²µKµ Î q
² Ì ðq h9qìm3q}¿Z;0BGP+2547OQO$Wn¿eq h9(q ²47=!@CBUW;#P5E vqìío(q h@C6F8CJKBFO;+qnlP>A@UBG=!JKO;#>G47JKPg>GJ`;0BF54Q>GBA;0BS[gE<;#>A;*JKPÞ;
6GR5BSMT;08C@#q~lP¡q m3q~r!;#BG47P&WZ@CE54j>AJKBUW V¶ô:ã etô þ èó ñ YãCõ^ôdæ óÃÄâ jqzUeæ ^ãuèó þZ¦ eDö`ç0â!zõ sH(ô {t5èAôdâ!õuödW
=<;0K@U6 Ì ½ (² : Ì µ Î q l xÂW ²254QO;0E5@UO7=52+4;+W ²µ ½u^q
² Í q a+q hyq<¿Z;#R5hiK;0BGE5P+@CB3;0P+ðE ²}q<r<BG@UE5@CBF478:6GJKP&q<l8CJK6G;025@CE+BA;0OE+476G8UBG@d>A47ÁC;#>A4QJKPpJ0Mn>A2+@>l_~J#]6G=52+@CBG@#q
UY|Z+÷ s etôdèU\÷ Ueâ!ç0æj÷7W Ì0Ì ªQ²0² Î :!²0²K² W ²µ ½ q
² q a+Xð qW íq+¿~BGJ_P* ;0P5Ep H4q a+q+ÆJKBF6G@U[0q ²BGJK+O7@ChL6~_4j>A2pE5@df<P547P+<;0BF[^8U@CP>ABF478x8CJ^JKBFE547P<;u>A@C6sMcJKB~>A2+@
6G=52+@CBG@#}q Y\ç þ ¦ ô eLç þ ó ñ ç0Aæ YãCõ^ôdæÃæ óÃÄâ zç0â!õ s etôdèdó ñ ç0.æ Ueâ!ç0æ ¦ödó7ödW Ì ^+ª Í : µ W ²µKµ Ì q
² qa¡Iqìíq¿~BFJ¦_P+47P55^W a+4q a+qoÊ¶;08:¼WZ;0P+´
E ²}q á9q _Z;0BFÁU>GBA;0R5!@CBUqo 8UJKhL=<;0BG4Q6GJKPJ#Me>A2+BG@C@{PR5hL@CBÄ]
478C;0O3hi@d>A25JÊ56McJKBL6GJKOj^47P5\E54 &@UBG@CP>G4;0O3@U·^R5;#>A4QJKP56LJKP >G25@Y6F=525@UBG@0rq Yãuâ!÷ ~`ôGç þ ¦ ôdñè k(ô Ou÷7W
²K² ªj² Î ½ :!² Î W ²Xµ ½ µ q
Õ² ^ q q¢x;02+O70@#W&Æqn¢x;025hL@CP&W:q&Æ@C47P+BG@C4Q8:2Wn;0P5Em3q 8:2+hi4j>G>XqÂYR5Oj>A47BF@C6FJKO7R+>G47JKP`;0P<;0Oj[?6F476x;#P5E
_Z;X0@CO7@d>A6kJKP ¿1W ;0P+E ¿ ® _q s etôdèU÷}ò â ñdþ }÷ Ueâ!ç0æjk÷ wå þ ó eó ÷7W Õ² ^?ªQ²6µ : ² W ²µKuµ q
² ?qð²wq¢4Q@CBF8:vq ¶O7KJKBF4Q>G25hi6nMcJKB6FhiJ^J0>A2+47P5E5;#>:;xJKP>A2+@36G=525@UBG@3_4Q>G2>A@CP+6GJKBo=5BFJ?E5R+8U>o6G=+O747P+@C6Cq
Ssã eeå ?þ óÃÄâ 0W ÍÌ ª Í ²X,µ : Í Ì W ²µ ½ q
² ½+qaÂq ²wqnE5JgZ;#BGhLJ55q yó ôdèAôdâ þ óTç0æ V¶ô:ã etô þ Tè ã S Iè O0ô:öpç0â!õ ð è Uç ñ ô:ödsq ²BG@CP>G478C@]ÄÊ¶;0O7OWwák@U_
ÌÎ
² µ ^ q
²µ q`áHqZ¢e[?P&Wr~qa+q3áe;#BG8CJ_4Q8:2Wx;0P5Ea+qì¢|q~ÆÞ;0BGEq~ McBA;0hL@U_sJKBGùMcJKBp47P>G@CBG=!JKO7;#>A4QJKPú;0P+E ;0=^]
=5BFJ?4Qht;#>G47JKPpJ0Ph47@Uht;0P+P54;0Pphi;0P54jMcJKO7E+6Cq+lPoUZåå!èAãDKKóeLç þ ó$ãuât ¦ ô:ãuèTzç0â!õowå þ óeóç þ ó$ãuâ<W
§ Z;#h|5BG4QE5K@#W ²µKµ ^K© W+=5;0K@C6 ² Í0Í :!² q<Z;0h|+BG47E+K@ f¶P54j!q ²oBF@C6F6CWvZ;0h|5BF47E50@0W ²µ0µ ?q
Ì0Î q`áHq~¢e[^PWkr~4q a+qsáe;#BG8CJ_4Q8:2We;#P5E a+q ¢|qÈÆ.;#BGE&q %È;0BG47;#>A4QJKP<;0O3=+BG47P+8C47=+O7@C6t;0P5E J0vJKOQ@U]>l[^=!@
@C6S>A4Qht;#>G@C6kMcJKB¶0@CP5@UBA;0OQ47ÁC@UE`47P>G@CBG=!JKO7;#>A4QJKPYJ0Pgñ; h47@Chi;0P5P+4;0P*ht;#P54QMcJKOQEpq Ssãuâ+ö þ èU2÷ U~åå!èADã K÷7W
² ?ªj² *: Ì0Î ½+W ²µKµ0µ q
Ì ² qgÂqsm8:!q3oÂ ¶]l8CR+BFK@U6{;0BG@a8CR5BSK@C6p4QPÙ>A@UP56G4QJKPqÈlP Y\ç þ ¦ ô eLç þ ó ñ ç0ræ Yô þ ¦ ãCõuöaóÃâ Ssã eeå ^þ ôdè
UeóTõ^ôGõ V¶ô:ã etô þ èó ñ |ô:ödó 0â<WoG § ¿~4QBG4$W ²µ0µ+²¦© Wo=<;#K@C6 Ì ² : ÌKÌ ½+Wo e8C;0E5@Uhi4Q
8 ²oBF@C6F6CW¿~JK6S>AJKP&W
ÂY HW ²µKµ Ì q
qÌKÌ g¡qr¼;0BG4QP0q S Iè O0ô:öiç0â!õ ð è Uç ñ ô:¼ö Xãuyè Ssã eeå ^þ ôdnè UeóTõ^ôGzõ V¶ô:ã etô þ èó ñ |ô:ödó 0â<W >G2\mE54Q>G47JKPq
e8C;0E5@Uhi4Q8 ²oBF@C6F6CW!¿~JK6S>AJKPW ²XµKµ ^ q
Ì0Í qg¡q m3q3r¼;06F6G2<;0R+@CBCq ¶E<;0=+>G4QK@\OQ@X;06S>{6G·R<;0BF@C6{f5>G>G47P5_4Q>G2ÉBA;0E547;0Oe5;06G4Q6{McR+P58U>G47JKP56pJ0P>G25@
6G=+25@CBF@0q5lP{Âq5f¢ Z25OQ@CPW?1xq+í[^8:25@0W¼íqìíq 8:2R5hi;0#@CBCW<@UE54Q>GJKBG6UJW Ygç þ ¦ ô eLç þ ó ñ ç0Jæ Yô þ ¦ ãCõu5ö Xãuè
S è(O0ô:ö9ç0â!õ èUç ô:ödW5=<;#K@C6 ² ²I:!² Î qc%È;0P5E5@UBG54QOQ>RfkP54Q0@CBF6G4Q>l[²oBF@C6F6CWváe;06F2^4QO7O7@#W ²µ0µu q
qÌ g¡q m3q}r¼;06G6F2<;0R5ð @U BCqwÊ¶ñ @CBFhi4j>A@L47P>A@UBG=!JKO;u>A47J0P`_4Q>A2BA;0E+4;0Oo<;06F476yMcR5P58d>A47J0P56HJ0P.6G=52+@CBG@U6Cq U¶Qõ Ou÷
Ssãeeå ^þ ÷BYgç þ¦ ÷7W ² Î ª ½ (² :?µ ^ W ²µKµ0µ q
Ì qg¡q m3q^r¼;06G6F2<;0R5@UBZ;0P5Etíq íq 8:2R5ht;#0@CBUq 8C;#>G>G@CBF@CEzE<;u>:;9f+>G>A4QP59JKPt>A2+@¶6F=525@CBF@0q?lP{Âq?f¢ s]
25OQ@CPW?1xq<í[?8:2+@0W!íq íq 8:2^R+ht;0#@CBUW!@UE54Q>GJKBG6UAW Ygç Zþ ¦ ô eLç þ ó ñ ç0]æ Yô Zþ ¦ ãCõu5ö Xãuè S Iè O0ô:öHç0â!õ ð èä
Uç ñ ô:ö WLW W5=<;#K@C6 ²K² :!²Õ^ ^ qc%È;0P5E5@UBG54QOQ>RfkP54Q!q²BF@C6G6UW&á¶;06G2^47OQO7@#W ²µKµ ½+q
Ì ^ qa1xq DqÈr<JKO7@d[KqblP>A@UBG=!JKO;u>A47J0P>GJ\6G8X;u>G>A@UBG@UEúE<;#>A;JKP ;\6G=525@UBG4Q8X;0O3E5J0ht;04QPqblP a+q¾eqÈÂa;#6GJKP
;0P5EÂq¾¡qn~JXvW}@UE54Q>GJKBG6UBW Ueæ ^ãuèó þZ¦ eDéö Xãunè U~åå!è:Dã KKó eLç þ ó$ãuâ WLW Wv=<;0K@U6 ÍKÎKÍ : Í ² Î q&~2<;0=5hi;0P
Ê¶;0O7OW5íJKP5E+JKPW ²µKµ Î q
Ì ^qa1xq Dqsr¼J0O7@U[0W3¢|q Dqsí};#P5@0Wk¡q¾Âq~ák47@COQ6GJKP&W h9qsr<BA;0P+0@0W;#P5E£ÊHqsÊe;#K@CPqÈlP>A@UBG=!JKO;#>G47JKPùJ0M
6G8C;#>G>G@CBF@CE E5;#>:;JKPÉ8COQJK6G@UE 6GR+BFMT;08U@C6Cq Ssã eeå ^þ ôdè UeóTõ^ôGõ V¶ô:ã etô þ èó ñ Dô:ödó 0â<+W ª ÍKÎKÍ : Í ² Ì W
²µ ½ µ q
Ì ½?qa1xq Dqvr¼J0O7@U[0W!¢|qì Hqvín;0P+@0W&¡Iq Âq!á¶4Q@CO76FJKPW!;0P5ÊE h9`q hk;0ht;#BA;¦ûUq %e476GR5;0O74QÁC47P+|McR5P58U>G47JKP+6eJK@UB;
6G=+25@CBF@0q
Ssã eeå&0÷ VZèFçdå ó ö U~åå!æj÷7W ² Î ª ÍÌ : Î W ²µKµ Î q
µÌ qYÆqr<BG@U@CW"E5&@UP&q? øxPL6G=+25@CBF478X;#O<6G¦ =5OQñ 47P5@34QP>G@CBF=vJKO7;#>A4QJKPI;0P5Ei;0=5=+BGJX?47hi;#>A4QJKPqjY\ç þ ¦ ÷]Yô þ ¦ ÷JUZåå!æj÷
óT÷7W Í ª ?I² :c W ²µ ½ ² q

ð
ñ
ÍKÎ qYÆqr<BG@U@CE5@UPq =525@UBG4Q8X;0Ob6F=5O74QP5@47P>G@CBG=!JKO7;#>A4QJKP?]l5;06G4Q89>G25@CJKBS[\;0P5E8CJ0hi=5R?>:;#>G47JKP<;#Ob;06F=v@U8U>A6Uq
Z+^÷ Ssã eeå&_÷ U~åå!æj÷ Y\ç þ ¦ ÷7W ²K²Kª Í ^ : Í W ²µ ½ q
Í ² qYÆq¦r<BG@U@CE5@UPW#1xqu¡x@CBSK@UP56CW0;0P5EDÂq 8:25BF@C47P+@CBCAq Ssãuâ+ö þ è ¼ñdþ Gó O0wô UZåå!èADã KKó eLç þ ó$ãuâtãuâ Zþ ¦ ô ð å ¦ ôdèAô
~pó Zþ ¦ U~åå!æ ó ñ ç þ ó$ãuâ+ö þ ãV¶ô:ãeLç þ ¦ ôeLç þ ó ñ ödq<øe^McJKBFEAf¶P54jK@CBF6G4j>l[A²oBF@C6F6CWvø¶?McJ0BGEW ²µ0µ ½+q
ÍÌ qYÆqr<BG@U@CE5@UP;0P5EÂq 8:2+BG@C4QP5@CBUq}øBF>A2+JKKJKP<;#Ob;0P5E\P5J0P5JKBF>G25JKKJ0P<;0OhDR5OQ>G47BG@U6GJKOQR+>A4QJKP`;#P<;0Oj]
[^6G4Q6CW¼6G8C;0O7@yE54Q6G8CBF@U>G@D;0P+EY@5;#8U>kMcR5O7Oj[zE54Q6G8CBF@U>G@9_~;XK@COQ@U>¶>ABA;#P56FMcJKBFhéJKP{>A25@96G=+25@CBF@0Tq Ssãuâ+ö þ èU÷
U~åå!è:Dã K÷7W ² ª µ Í :c^² W ²XµKµ ½+q
ÍKÍ qYÆq¦r<BG@U@CE5@UPWÂq 8:2+BG@C4QP5@CBUWK;0P+VE hyq¦r<BA;0P5#@0q¦ 6GR5BSK@d[HJ0PH6F=525@CBF478C;0O6G=5OQ47P5@o;0=+=5BGJX?47hi;#>A4QJKPq
(è O0ô f
ö Ygç ÷ â!õ ö ÷7W ª Ì ,µ : ½ W ²µ0µ ?q
Í q`r~ð q `|qb¡y4QBA;0OQE5ZþJ5¦ q}ínW ;0KBA ;#P5þ K@d]Ä¡9;#O7@CBF47Phi@d>A25JÊ56JKP6F=525@CBF478C;0O~K@UJ?E+@C6G4Q8pKBG4QE56 ª >A2+@p6G2<;0OQO7J_
_~;#>A@UBk@U·R<;#>A4QJKP56U}q Z5^÷ Ssã eeå B÷ e ¦öC÷7W Õ² ^ Î ª Í0Í ^,: Í ^ ½+W Ì#ÎKÎKÎ q
Í Êq hyq Ê94q a+qw¡xhi@UO747pÂY@U[Ô74QP5Y;0P5^.E þ ²}(q ¦ ² Ë R5K@CBUq}¿È]l6F=5O74QP5@L;0=5=5BFJ?4Qht;#>G47JKPgJ#M3;{8CO7J06G@CE6GR5BSMT;08C@#q
W YUuZ5÷ s etôdèC\÷ Ueâ!ç0æj÷7W ª Í :?µ ^ W ²µ ½u^q
Í ^ Êq hyq íqbÊ¶;0BGE?[KqoÂYR+OQ>A4Q·R<;0E5BF478t@U·R<;#>A4QJKP56|J#Mk>GJK=!JKKBA;#=52[.;0P+EùJ#>A25@UB|47BFBG@C0R5O;0B96GR+BFMT;08U@C6C^q Z+÷
V¶ô:ã:å ¦ ödó ñ ç0æ ô:öC÷7W ^+ªj²µ Î *:!²µ+² W ²µ ² q
a0@CBF6G@d[KW
Ì ^²
Í ?ðq h9qìíqKÊ¶;0BGE+[|;0P5E|Æq Âq¡JK
=+Mc@UBF>Xq0í@X;06S>o6G·R<;0BF@C6o=5BG@UE5478d>A4QJKP|J0M!KBG;^4j>l[;0P5J0ht;0OQ47@U6CWuK@CJK4QE<;0O
R5P5E5R+O;#>G47JKP56UWe;#P5EÉE5@ Ë @U8U>G47JKPJ0M9>A25@`0@CBF>G478C;0O_4Q>G2hDR5OQ>G47·R<;0E5BF478Y2<;0BGhLJKP54Q8aMcR5P58d>A4QJKP56Cq
V¶ô:ã:å ¦ Ka÷ kô:öC÷ nô þTþ ôdèAödW Ì ª Ì0Í : Ì ^ W ²µ ½ ² q
Í ½+ðq h9qìíq+Ê¶;0BGE?[z;0P+E qì Hq5ák@CO76FJKPq^ h|R5Oj>A4Q·^R5;0E5BG4Q8d]5472<;#BGhLJKP5478~BG@C=+BG@C6F@CP>:;u>A47J0P{;0P5E{;0=5=+BGJX]
47hi;#>A4QJKPtJ#MbE54Q6F>AR+BG54QP5=vJ#>A@CP>G4;0Oq V¶ô:ã:å öC(÷ kô:öC\÷ }ô ôdè:ödW ² Í ªQ² ½ : Ì ² W ²µ ½ ^ q
Í µ qa+q3Ê¶J06G8:25@UÉ;0P5E¢|q3ín;06G6F@CBUqeò â!õçetôd¦ â þ ç0æ ö\ã SsãeeþTþ å ?þ ôdèUeóTõ^ôGõ.|ô:ödó0â<W v ²}@U>G@CBG6UW
¿~JK6S>AJKPW ²XµKµ Í q
Î qaeq íquín;X_6GJKPq R55BFJKR+>G47P5@U6}McJKB ~ 6GR+BFMT;08U@~47P>G@CBG=!JKO7;#>A4QJKPx>AJeE5;#>:;kE5@Uf<P+@CE|JK@UB>A2+@s6FR5BFMT;08U@
J0M;I6F=525@UBG@0Iq oå þ ~ _÷ J.XJW a ²oíoW!Z;#O$q51}@C8:2W ²µ ½ Ì q
² qaeq íq#ín;_6FJKPq 6GR5BSMT;08C@Z4QP>A@CBF=vJ0O;#>G47JKPxMcJKB}6G8C;#>G>G@CBG@UE|E<;#>A;eJKPD;¶6G=+25@CBF@0Äq ã "ñ Yã â þ ç0óÃâ
Z+÷Y\ç þ ¦ ÷7W ² ªj² : Ì0ÎÌ W ²µ ½ q
Ì yq `|q!í47R*;0P5Eaíq íq 8:2R5hi;00@UBCqvÊk[^5BG4QEa8UR55478H¿L@UÀ ÁC47@UB¶=5;#>A8:25@U6eJKP*6G=+25@CBF@C6x;0P+Ea6G=+25@CBF@d]lOQ47#@
6GR5BSMT;08C@U6C\q Z+^÷ Ssã eeå ?þ }÷ U~åå!æj÷ Y\ç þ¦ ÷7`W Í ªj² :!² Ì W ²µKµ ^ q
Í q*1xqZí[^8:25@\;0P5Eúíoqìíq 8:2R5hi;0#@CBCq~ h|R5Oj>A47BF@C6FJKO7R+>G47JKP>G@CP56FJKBz6G=+O747P+@ahL@U>A2+J?EÙMcJ0Bif5>F>A47P+
McR5P58d>A47J0P563JKP{>A25@y6G=+25@CBF@0q UY|Z+÷ óTk÷ Ssã eeå&÷7W ÌKÌ ª Ì : ?W Ì0ÎKÎKÎ q
q Y¿eqvÂa;08:25@UP52<;0R+@CBCq&1325@|6G=!Xð@C8dW >ABG;0OwhL@U>Gð25ñ JÊq¼lPzs etôdèó ñ ç0æ}Yô þ ¦ ãCõuööôGõpóÃâU þ etãölå ¦ ôdèó ñ
YãCõ^ôdæ ödWKJ0O$qGJ0Mn¡yG
hg²Æ²R5q @CBUq5ákJ5q ² ?q aø9eWÆJKBGOQEpÂY@d>A@CJ0BGJKOQJKK478C;0O!øBG;#P547ÁC;#>A4QJKPW
¡y@UP5@U#;+W _4Q>AÁU@CBFO;0P5E&W ² Ì ² ] Ì W ²µ µ q
ðq fHqÂY;[0@CBUq £P^R+hi@UBG478C;0O56F8:25@ChL@3McJKBbhLJ¦^4QP5xvJ0R5P5E<;0BS[=5BFJK5O7@Uhi6w>A2<;#>;0BG@3KBG;0E54Q@CP> Ë J_6
McJKBZ>A2+@H;#BG@X;|McR5P+8U>A4QJKP<;0Oq Á è:ã:å<ôGç0oâ Z+\÷ U~åå!æjB÷ Ygç Zþ ¦ ÷7W ²K²0ª ^+I² : ½ Î W Ì0ÎKÎKÎ q
^ qðh9qÈÂ*@CP58UOe;0P+EúÊHqsÂR5
OQO7@UBCqlP>G@CBG=!JKO7;#>A4QJKPù;0P5Eú;#=5=5BGJX?47hi;#>G47JKPJ0Me6GR5BSMT;08C@U6iMcBFJKh >A25BF@C@]
E547hL@CP+6G47J0P<;0Oe6F8X;#>F>A@UBG@CE(E<;#>A;=!JK4QP>G6CqZlP ðñ ó$ôdâ þ ó ñý ó7ö ç0æ ó ç þ ó$ãuâ<W¢x;006F>AR+25O =ìµ ?WkÄmomÈm
²R55O74Q6G25@UBG6UW Ì0ÎKÎKÎ q
Â J0
547R56U1q f¶@Uv@UB@C4QP5@pP5@CR+@Y¿s@C2<;0P+E5O7R5P+K6F_s@C4Q6G@*E5@CBI;0P5;0OQ[>A4Q6G8:25@UP =5B2 ;0
BF47¼qblP U+³Cä
?q* Dqìr~qo
â ³dôdñó Î¹ô 0\è â!õ Äâ õ^ôdè ãu â<ó 0æj÷ ð ç )ñ ¦ öC÷ V¶ô:öôdæÃæ ö )ñ ¦ ç þ õ^ôdè ~pó7ö:öôdâ+ö )ñ ¦ ç þ ôdâ<W
¦ ç0â!õ+æ Äâ ^ôdú
aK;05OQJKP5J_6G4<¡x@C6F@COQO76G8:25;#MÃ>XW0ín@U47=5ÁU475W 6: ½ ^ W ² ½ ^ ¸uh@X;#=5=v@C;0BG@UE47P ª Hq r~q0ÂJK
+47R56UW\V¶ô:öCçeä
etôdæ þ ô ~`ôdè ôdW¼r~.q vxOQ@C47P&W+@CE+4Q>AJ0BCW %oJKOq Ì W<í@U47=5ÁU475W ² ½ ½ ^ W (² :c q
½+q*1xq5Â*JKBF>GJKP{;0P5E{Âq+ák@X;0hD>GRq5mBFBGJKBsvJKR+P5E56~McJKBÈ6GJ0OQ^47P5H=56G@UR5E5JÊ5;4 v@CBF@CP>A47;0O&@U·R<;#>A4QJKP56sJKP
6G=52+@CBG@U6¶[{8UJKO7OQJ?8C;#>A4QJKPi_4j>A2{ÁCJKP5;0O0@UBGP5@UO76C\q Z+\÷ U~åå!è:Dã K÷ t ¦ ô:ãuè uW R5+hi4j>G>A@UEq
Â R5
OQO7@CBUq ð å ¦ ôdèdó ñ ç0pæ 7xç0è etãuâ<ó ñ ödWoí@U8U>AR+BG@*á¶J0>G@C64QPùÂa;#>A2+@Chi;#>A4Q8C6CWb0JKO$q ² ?W =5BF47P50@CBS]
µ qaeqo
%o@CBFO;05W+¿~@CBFO74QP?]ÄÊk@C47E+@CO7!@CBF5W ²µ ^ ^ q
Î qYr~q a+q5áe;#BG8CJ_4Q8:2q!¡y@UP5@CBG;0O74QÁC@UE{Ê¶@CBFhi4j>A@4QP>A@CBF=vJ0O;#>G47JKPt;0P5E{=vJ06G4Q>G4Q0@E5@Uf5P54Q>G@x0@CBFP5@COQ6JKP{;
hk4Q@Chi;0P5P547;0Pzhi;0P54jMcJKO7EJq Z+÷ Y\ç þ¦ \÷ Ueâ!ç0æj}÷ U~åå!æj÷7W ²µ Î ªjÕ² û*:!²µ Í W ²µKµ q
?² qYr~q a+qKáe;#BG8CJ_4Q8:2t;0P+PE a+qì¢|q#ÆÞ;0BFEqá¶J0P56F>A;#>A4QJKP<;0BS[H_~;XK@COQ@U>G6sJKP|>G25r@ t]l6F=525@UBG@McJKBb6G8C;#>G>G@CBF@CE
E<;#>A;+Jq U~åå!æj^÷ Ssã eeå ?þ B÷ 7xç0è etãuâ!\÷ Ueâ!ç0æj÷7W Í ª ÍKÌ : ÍKÍ ^ W ²XµKµ ^ q
Ì qaÂq5ák@X;0hH>ARq+Ê¶JKhLJKK@UP5@CJKR+6~6G4Qhi=+O7@di6F=5O74QP5@C6Uq]Z+÷0Ssãeeå&÷AUZåå!æj÷}Y\ç þ ¦ ÷7W Í ªQ² Í :!² ½ µ W ²XµKµ ^ q
Í qaÂqá¶@C;0hD>GRqKÆÉ2<;#>È476>G25@¶P5;#>AR5BG;0O5K@UP5@CBG;0O74QÁX;#>G47JKPJ#MR5P54j#;0BG47;#>A@Z6F=5O74QP5@C6>GJH254QK25@UBE547hL@CP?]
6G4QJKP5)6 ÞKqvlPg1xqí[?8:2+@I;0P5E\íq íq 8:2R5ht;#0@CBUWn@CE54j>AJKBF6CW Ygç þ¦ ô eLç þ ó ñ ç0Bæ Yô þ¦ ãCõu¼ö XãuPè S Iè O0ô:ö
ç0â!õ è Uç ô:¡ö qosödæ7yã ¢£j£j£u}q %È;#P5E5@CBF547Oj¥> f¶P54jK@UBG6G4j>l[ ²oBF@C6F6CWbá¶;06G2^47OQO7@#W}1á9Ww=+=q Í 6: Í µ Ì W
Ì0ÎKÎ ² ðq ñ
qaÂq¼á¶@C;0hD>GRq<¿Z;0BS[^8C@CP>GBG47898CJ^JKBFE547P<;u>A@C63E+@Uf<P5@UEaJKP{6FR5BFMT;08U@C6Uq!lP*=5BF@C=<;0BG;#>A4QJKPq
qaÂquá¶@C;0hD>AR&WKÊHq ²wJ#>G>Ahi;0P5P&W0;0P+Eíq íq 8:2R5hi;00@UBCqK¢R5;0OKMcJ?8C;0O6G=5OQ47P5@U6;#P5EDBG;#>A4QJKP<;0O8UR5BF0@C6
_4Q>G2*BG;#>A4QJKP<;0OvJ v6G@U>G6C}q Ygç Zþ ¦ ÷ Äâ ÷ W â!õ÷7W ªj² Í ,µ :!Õ² W ²XµKµ ½+q
^ qaÂq#á¶@X;#hD>ARWKÊHq ²wJ0>F>Ahi;0P5PW0;0P5Eíqìíoq 8:2R5hi;00@UBCq¢@U6G4QKP547P+egá fGhk¿ 8X;#h=+BGJ0f<OQ@C6wR56G4QP5
>ABF47KJKP+JKhi@d>ABF478e6F=5O74QP5@C6U_q Z+÷ Yô )ñ ¦ (÷ Dô:öC÷7W ² Ì0Î ªQ² 6:!² ½ Î W ²µKµ ½+q
ÌÌ
^qg¡q¾Âq}ák47@COQ6GJKP&qÂ*J?E5@UO74QP5`;0P+E^476FR<;0O74QÁC4QP5*0JKO7R+hi@d>ABG4Q8L;0P5E.6FR5BFMT;08U@d]JKP?]l6FR5BFMT;#8C@tE5;#>:;+q}lP
ÊHqsÊe;#K@CPWkÊ9qZÂYR+@CO7OQ@CBUW;0P5EÉ¡q~ák47@UO76GJ0PWZ@CE+4Q>AJ0BG6CWeò}ã ñ öãuâ ðñ ó$ôdâ þ ó ñÙý ó7ö ç0æ ó ç þ ó$ãuâ<W
=5BF47P50@CBS¤] %o@CBFO;05W?¿~@UBGO74QPW Ì ²X,µ : Ì W ²µKµ Ì q
½?qg¡q¾Âqá¶47@UO76FJKP\;0P5
E hyaq h¶;#ht;0BG;¦ûUq&lP>G@CBG=!JKO7;#>A4QJKP`JK@UBH;p6F=525@CBF@I<;06G@UER+=vJKP;zhL47P54Qh|R5h
P5JKBFhP5@d>l_~J0BG¼kq Ssã eeå ^þ ôd¥è UeóTõ^ôGõ V¶ô:ã etô þ èó ñ |ô:ödó 0â<W ª (² :c ½?W ²µ ½u^q
0µ qovq5ø=54j>AÁe;0P5EpÊ9q²wJ#>G>Ahi;0P5P&q5~JKhL=5R+>G47P5H6G25J0BF>A@U6F>3=5;#>A256~JKPz=!JKOQ[^25@UE5BA; ª ;0=5=5OQ478X;u>A47J0P56s4QP
K@UJKhi@d>ABF478khiJÊ5@COQ47P5H;0P5Ep6F8C4Q@CP>A4jf<8e^476FR<;0O74QÁX;#>G47JKP&q W â þ B÷ Z+0÷ Ssã eeå&&÷ V¶ô:ã eL]÷ U~åå!æ ó ñ ÷7W ªQÕ² ^ 6:
² ½?W ²µKµ q
^ÎÊ
q hyq á9q ²bMc@C4 Ë @x;0P5E{Ê9q ÷] ²wq @C4QE5@COq =+25@CBF478X;#Ov>ABF4;0P+KR5O;#B~¿È]6G=5OQ47P5@U6s_4j>A2p;0=+=5O74Q8X;#>G47JKPL>AJ|E<;u>:;
f5>F>A47P+5Aq esèAã ñ ÷ Á èA¶ã 0èFçdå ¦ ó ñ ödW ½ ,µ :^µ ^ W ²XµKuµ q
^+² q`ÊHq5²wJ0>F>Ahi;0P5PqwlP>A@CBF=vJ0O;#>G47JKP.J0P6GR5BSMT;08C@U6R56G4QP5ghi4QP547hDR5hÿP5JKBFh P5@d>l_~J0BG6CqnSsãeeå ^þ ôdè
UeóTõ^ôG
õ V¶ô:ã etô þ èó ñ |ô:ödó 0â<W µ+ª ?(² :Ä^ ?W ²XµKµ Ì q
^ Ì q`ÊHIq ²wJ0>F>Ahi;0P5P\;0P5EÂqmo8:¼qwÂYJÊ54Qf5@CEgh|R5Oj>A4Q·^R5;0E5BG4Q8DhL@U>G25J?E+6McJKB6G8C;#>G>G@CBF@CEE<;#>:;p4QP>G@CBÄ]
=!JKO;#>G47JKPtJ¦0@CBk;I6G=525@UBG@#0q Ssã eeå ^þ ôd¥è UeóTõ^ôGoõ V¶ô:ã etô þ èó ñ |ô:ödó 0â<W ª Í ² Í : ÍÌ ² W ²µ0µ Î q
^ Í q`ÊH<q ²wJ#>G>Ahi;0P5P&W+Ê9q+Ê¶;0K@CP&W5;0P5Et Dq?¢4Q^4Q^47@UBC=q %e476GR5;0O74QÁC47P+yMcR+P58U>G47JKP56sJKPp;96GR5BSMT;08C@#]q Z<ã èâ!ç0æ
ã ý ó7ö ç0æ ó ç þ ó$ãuâç0â!õ Ssã eeå ^þ ôdè Ueâ<ó eLç þ ó$ãuâ<W Ì ª Ì :< ½+W ²µ0µ+² q
^ q`ÊH-q ²wJ#>G>Ahi;0P5P;#P5
E vqø=54j>AÁ0q~R5BS0;u>AR5BF@p;0P<;0Oj[^6G476D;0P5E.^476FR<;0OQ47ÁX;u>A47J0P\McJ0BHMcR5P58d>A4QJKP56|E5@]
f<P5@UEDJKPHmR58COQ47E5@C;0P96G=<;08U@C6}JKBn6GR5BSMT;08C@U6C]q Ssã eeå ?þ ôdwè UeóTõ^ôGõ V¶ô:ã etô þ èó ñ |ô:ödó 0â<W ²K²Kª û 6:Ä^ W
²µKµ q
û Ê
q hyiq hk;0ht;#BA;¦ûUqnlP>A@UBG=!JKO;#>G47JKP.;0P5EE54Q6G=5O7;[J0M6F8X;#>F>A@CBF@CEùE<;#>A;aJK@CBI;`6F=525@UBG@0qÈÂ >A25@U6G476UW
eBF47ÁUJKP<; >A;#>A¥@ f¶P+4QK@UBG6F4Q>l[KW ²Xµ ½ ^ q
^^Ê
q hy4q a+Áq hk@UP5u;+qÈlP>G@CBF=vJKO7;#>A4QJKPÙJ#MyE<;#>:;JKPÙ>G25@`6GR+BFMT;08U@`J0M9;6F=525@UBG@0rq US2Y t5èFç0â+öC¥÷ Ygç Zþ ¦ ÷
ð ã þ Èç0è:ôdW ² Î ª ² : KÍ ^ W ²µ ½ q
^ ^qÊhyq4a+q-hk@UP5u;+q} eO70JKBG4j>A25h ^ Ì0Í ª lP>A@UBG=!JKO;u>A47J0PJKP>A25@i6GR5BSMT;08C@zJ#M;Y6F=525@CBF@0q&US2Y t5èFç0â+öC÷
Ygç Zþ ¦ ÷ ð ã þ Èç0èAôdW ² Î ª Í : Í µ W ²µ ½ q
^ ½?Ê
q ²wq 8:25*B JK
E5@CB;0P5E`Æq _~@UO7E5@UP56Cq =525@CBF478C;0O}_~;XK@UO7@U>G6 ª im bL8C4Q@CP>AOj[*BG@C=+BG@C6F@CP>A4QP5pMcR5P58d>A47J0P56
JKPp>A2+@96F=525@UBG@0}q esèAã ñ ô:ôGõ0óÃÄâ uö|ã ð ó Õ0èFçdå ¦ W ²µ0uµ q
^Kµ q`íq íq 8:2R5ht;#0@CBUq ð å!æ óÃâ&ô\ò â ñdþ ó$ãuâ+¡ö q@Î¶çuödó ñ t ¦ ô:ãuTè #q¶lP>A@CBF6G8U47@CP+8C@0WIák@U_ÅüÈJKBG¼W ²µ ½ ² q
h@C=5BF47P>A@UEY[yvxBG4Q@CK@UBCW¼ÂY;0O;05;0BCW<rwO7JKBF47E<;+W ²µKµ Í q
Î q`íq íq 8:2R5hi;00@UBCqs1wBF4;0P50R5O;#>G47JKPhL@U>G25JÊ56i4QP£~ k¡y¢|q W"&& Ssã eeå ^þ ôd¦
è VZèFçdå ¦ ó ñ öaç0â!õ
U~åå!æ ó ñ ç þ ó$ãuâ+ödW ² Í ª :c Ì W ²µKµ Í q
² q`íq íq 8:2R5hi;00@UBy;0P5E\eq h9q!1}BA;K;06Uqr4j>G>G47P5L6G8C;#>G>G@CBG@UEgE<;#>A;tJKP`6F=525@CBF@COQ470@D6GR5BSMT;08C@U6R56G4QP5
>A@UP56GJ0BZ=5BGJÊ5R58d>A6ZJ#M>ABG4QKJKP5J0hi@d>ABG4Q8;0P5Ep=!JKOQ[^P5J0hi47;0O56G=+O747P+@C6CJq s etôdèU\÷ Ygç Zþ ¦ ÷7W ^ Î ªj² ÍKÍ :¼² W
²µKµ?² q
Ì q qìíq K@UP56G6FJKPqvr47P54j>A@¶@CO7@Uhi@UP>A6JKP{>A25@y6G=+25@CBF@0\q Z+\÷ UZåå!èADã K¥÷ t ¦ ô:ãuTè uW Î ª Ì ^,: Ì ^ Î W ²µ ½ q
Í qYÆq _~@UO7E5@UP56Cq01325@ZO74jMÃ>A4QP56G8:25@Uhi@ ª ;e8CJ0P56F>GBGR58d>A47J0P|J0M¼6G@U8CJKP+EK@CP5@UBA;#>G47JKPH_Z;XK@UO7@d>A6Cq ðXW UY
Z+÷ Y\ç þ ¦ \÷ Ueâ!ç0æj÷7W Ì µ?ª ?²0(² :c ^ W ²µ0µ ½+q
qgeq h9q1}BA;K;#6Cq hLJ?J#>A2;0=5=5BFJX+4Qht;u>A47J0P`J0MZE5;#>:;pJKP\>A25@I6F=525@CBF@L_4j>A26G=5OQ47P5@U6Cq Ssã eeå ^þ óÃÄâ 0W
Í ½ ªj² :!² ½ W ²µ ½ ?q
Ê
q hyq %o@COQ>Gu;0hi=&pq Sbæ7ãöôGõ{ã ³E§Xô ñdþ ³dã â!õç0èó$ô:1ö èAã eö ñ ç þTþ ôdèAôGõHå<ãuóÃâ þ ödW¼í@U8U>AR+BG@Há¶J0>G@C6k47PY~JKh]
=5R+>G@CB 8U47@CP+8C@0W ½½ W =+BG47P+K@CBÄ¨] %o@CBFO;0+W5¿~@UBGO74QPW ²XµKµ q
^ qg¡q¼ÆÞ;02<;+q =5OQ47P5@947P>A@UBG=!JKO;u>A47J0PY;#P5E`6GhLJ^J0>A254QP5LJKPa>A2+@D6G=+25@CBF@0q Xð W UY©Z+÷ ðñ óT÷ ð¼þ ç þ ó7ö þ ÷
Ssã eeå ^þ ÷7W Ì ª 6:!q² ^ W ²µ ½ ² qbmBGBG;#>:; ª ¡qwÆÞ;02<;+W =5OQ47P5@i47P>A@UBG=!JKO;u>A47J0PÞ;0P+Eù6FhiJ^J0>G2547P5YJKP
>A2+@96F=525@UBG@0q Xð W UY[Z+÷ ðñ óT÷ ð¼þ ç þ ó7ö þ ÷^Ssãeeå ?þ ÷7W Í ª Í ½ 6: Í ½ ^ W ²µ ½ Ì q
^qg¡qCÆ.;#2^5;+6q %o@C8U>GJKBn6G=5OQ47P5@U6nJKPH>G25@o6G=525@UBG@#W0_4Q>G2D;0=+=5O74Q8X;#>G47JKPe>GJk>G25@È@C6F>G47hi;#>A4QJKPxJ0M^KJKBS>A4Q8C4Q>l[
Ö ¹43^¹ eÑ ÚnÓwÔoÕkÜ¶ÑeÓ}Û65bÔ ÔÓwÐ Ý yØ à Ý Õ à ß ÜDÏkÓ}Û Ý Ü ØÞÝ Ü Øbß Õ¶à^Ñ9ÏbÔ Ø
ÌÍ
;0P5E£E54jK@UBGK@UP58C@gMcBGJ0h E54Q6G8UBG@U>G@0WkP5JK4Q6F[ E<;#>:;?q~lP£Æq 8:2+@ChL=5= ;#P5Eªvqrb&@COQO7@UBCW3@CE+4Q>AJ0BG6CW
Y æ þ Gó Ouç0èdóTç þ ô U~åå!è:Dã KKóeLç þ ó$ãuâ«t ¦ ô:ãuèT W?W W+¿~47BF2B;0
R56F@CB § ¿Z;#6G@CO © W Î : Ì µ W ²µ ½ Ì q
½+qa¡IqKÆÞ;02<;+q R5BSMT;08C@kf5>G>G47P5y_4Q>G2t6F8X;#>F>A@CBF@CEzP+JK476S[IE<;#>:;9JKPzmR58UO74QE5@X;0PP¬0]l6G=5;08C@¶;0P5EiJKPt>A2+@
6G=52+@CBG@#Iq kã "ñ 1Yã â þ ç0óÃoâ Z+÷ Y\ç þ ¦ W ² ª Ì ½ (² : Ì µKµ W ²µ ½ q
µ qY¢|q íqÆÉ47OQO747;0hi6FJKPI;0P5Ep¡Iqìíq?¿sBGJ_P547P+5q5~J0hi=<;#BG476FJKPtJ#MKBG4QE56s;0P5EzE54 &@UBG@UP58C@x;#=5=5BGJX?47hi;u]
>A4QJKP56eMcJKBxPR5hL@CBF478C;0O_s@X;#>G25@CBy=5BF@CE54Q8U>A4QJKPgJK@UBD;z6F=525@CBF@0pq Z+÷ U~åå!æj&÷ Yô þ ô:ãuèU÷7W ² Ì ª Ì ^ : Ì W
²µ Í q

C h ap ter Splines on Surfaces Marian Neamtu This chapter

Transcription

Similar documents