program and abstracts - Georgian Mathematical Union

Humboldt Kolleg
„SCIENCE IN GEORGIA: PERSPECTIVES OF DEVELOPMENT
AND THE ROLE OF HUMBOLDT FOUNDATION“
July 4-6, 2015, Tbilisi, Georgia
PROGRAM AND ABSTRACTS
ლ
ოს
ჰუმბოლ
დტ
BO
Georgian
Mathematical Union,
Georgian National
Academy of Sciences
Georgian
National Museum
SPONSOR:
Alexander von Humboldt Foundation,
Germany
LD
RG
UM
IA
*H
*
ბი
კლუ
ის
საქართ
ვე
ORGANIZERS:
T CLUB OF G
EO
Humboldt Club of
Georgia
Georgian National
Academy of Sciences
Georgian National
Museum
Georgian Mathematical
Union
Humboldt Club
of Georgia
HUMBOLDT KOLLEG
Science In Georgia:
Perspectives of Development and
the Role of Humboldt Foundation
ABSTRACTS & PROGRAM
July 4-6, 2015, Tbilisi, Georgia
Organizers:
Georgian Mathematical Union
Georgian National Academy of Sciences,
Georgian National Museum
Humboldt Club of Georgia
Sponsor:
Alexander von Humboldt Foundation, Germany
Venue:
Georgian National Academy of Sciences, Rustaveli Av. 52, Tbilisi
Georgian National Museum, Rustaveli Av. 52, Tbilisi
Organizing Committee:
Joni Apakidze (Co-Chairman), Tengiz Buchukuri, Tinatin Davitashvili (Scientific secretary),
Roland Duduchava (Chairman), David Kapanadze, Alexander Kartosia (Co-Chairman), David
Lordkipanidze (Co-Chairman), Levan Sigua
Web page: http://gmu.ge/HK2015/
Editors:
R. Duduchava, M. Kvinikadze
Cover Design:
D. Sulakvelidze
Contents
Program
5
Abstracts
9
Maia Akhalkatsi, Mariam Kimeridze, Natura 2000 Sensitive Forest Habitats of
Georgia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
Joni Apakidze, Neue Archäologische Ausgrabungen in Georgien (am Beispiel der
Tellsiedlung Tabakoni) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
Giorgi Bedianashvili, The Koban necropolis: The Late Bronze-Early Iron Age collections from the Caucasus stored at French museums . . . . . . . . . . . . .
13
Zurab Berezhiani, Dark Side of the Universe: Opening Windows to Parallel Worlds)
13
George Chkadua, Mixed Type Interaction Problem of Acoustic Waves and Piezoelectric Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
Nino Doborjginidze, Language and Technologies: Problems and Challenges of Modern Academic Georgian . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
Nino Gogelia, Zur linguistischen Erforschung rhetorischer Strategien im politischen
Diskurs von Marion Gräfin Dönhoff . . . . . . . . . . . . . . . . . . . . . . .
16
Valerij Gretchko, Cultural Communication in the Framework of Yuri Lotmans Semiotic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
Joseph Gubeladze, Quantum Analysis of Normal Polytopes . . . . . . . . . . . . .
18
Max Florian Hertsch, Serenade for Nadia by Zülfü Livaneli - A modern Turkish
Ring Parable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
Vugar Ismailov, Hilbert’s 13-th Problem and Approximation by Neural
Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
Marian Jaskuła, Internationalization & Globalization of Science . . . . . . . . . . .
21
Tornike Kadeishvili, Homotopy Algebras, Applications in Mathematics and Physics
22
3
4
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
Tornike Kadeishvili, How to Attract Young People to Science in Georgia . . . . . .
22
Irakli Kardava, Georgian Speech Recognizer in Famous Searching Systems and
Management of Software Package by Voice Commands in Georgian Language
23
Alexander Kartosia, The Fantastic City: The Linguistic Shaping and Re-shaping of
the Georgian Cultural Scene in the first Third of the 20th Century . . . . . . .
23
Mariana Malard, George I. Japaridze, Henrik Johannesson, Synthesizing Majorana Zero Modes in a Quantum Wire using a Modulated Electric Field . . . . .
24
Yurii Naidyuk, Scientific Two-Way Collaboration with German Colleagues: from
Personal Contacts through Intermediary of Alexander von Humboldt Foundation to European Research Programs . . . . . . . . . . . . . . . . . . . . . . .
25
Teimuraz Pirashvili, Goodwillie–Taylor Tower via Relative Homological Algebra.
Abelian Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
Nino Popiashvili, National and Intercultural Frontiers of Literature (on the Example
of Georgian Literature) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
Jaydeb Sarkar, Invariant and Wandering Subspaces of Reproducing Kernel Hilbert
Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
Frank-Olme Speck, Sommerfeld Problems in Rn . . . . . . . . . . . . . . . . . . .
27
Ilya M. Spitkovsky, On Some Numerical Range Related Results Obtained while
Working with Students in the USA and UAE . . . . . . . . . . . . . . . . . . .
28
Manana Tandashvili, Kartvelology and the Challenges of the 21st Century . . . . .
29
Zurab Tavartkiladze, Luka Megrelidze, Radiative Neutrino Masses Generation via
‘Soft’ Lepton Number Violation . . . . . . . . . . . . . . . . . . . . . . . . .
30
Frank Uhlig, Holistic Teaching and Learning Holistically . . . . . . . . . . . . . .
30
Kai Wang, Dixmier Trace of Quotient Module on Bounded Symmetric Domains . .
31
List of Participants
33
Index
36
Humboldt Kolleg Tbilisi, Georgia July 4-6, 2015
Science in Georgia: Perspectives of development
and the role of Humboldt Foundation
PROGRAM
July 3, Friday
Arrival day to Tbilisi
1500-1900 –
Registration at the National Academy of Sciences (NAS)
00
19
–
Welcome party at NAS
July 4, Saturday
Venue: National Academy of Sciences of Georgia
830 : 900
Registration
Room 1
900 : 1000
Opening ceremony of the Humboldt Kolleg
Audience will be addressed by R.Duduchava, T. Gamkrelidze, A. Kartosia, J.
Apakidze, Representatives of NAS, Ministry of Education and Science, AvH
foundation, Embassy of Germany in Georgia, National Humboldt Clubs.
Room 1
1000 : 1040
1040 : 1110
Chairman: Teimuraz Pirashvili
Maria Esteban- Programs supporting mathematical research in Europe
Coffee break
Room 1
1110 : 1150
Chairman: Teimuraz Pirashvili
Marian Jaskula – Internationalization and globalization of science (in
German)
Joseph Gubeladze – Quantum analysis of normal polytopes
Lunch
1150 : 1230
1230 : 1400
Rooms 1,2,3
1400 : 1600
1600 : 1630
1630: 1800
Room 1
1800
Interdisciplinary Sessions with 30 minute talks. The sessions are organized for those participants who did not participate in IWOTA. Deadline of submission of abstracts is May 15. Program of sessions will be announced on May
20.
Coffee break
Continuation of the Interdisciplinary Sessions.
Moderator: Roland Duduchava
Panel discussion: “Reform of Science in Georgia: Perspectives and
consequences” Participants: representative of the Ministry of Education and
Science, Representative of the Parliaments commission on Science and
Education, National Academy of Sciences, Shota Rustaveli National Science
Foundation, National Humboldt Clubs etc.
5
July 5, Sunday
Venue: National Museum of Georgia
Conf. Hall
900 : 940
940 : 1020
1020 : 1050
Conf. Hall
1050 : 1110
1110 : 1140
1140
1200
1240
1400
1500
1900
: 1200
: 1240
: 1400
: 1500
: 1830
: 2300
Chairman: Josef Gubeladze
Zurab Berezhiani – Dark side of the Universe-Opening windows to parallel
worlds
Teimuraz Pirashvili – Goodwillie-Taylor tower via relative homological
algebra. Abelian case
Coffee break
Chairwoman: Maria Esteban
Thomas Gamkrelidze – “Paradigms” in Linguistics
Alexander Kartosia Die "phantastische Stadt". Sprachliche Gestaltung und
Umgestaltung der georgischen Kulturszene im ersten Drittel des 20. Jahrhunderts
(in German)
Marilyn Kelly-Buccellati – Excavations at Urkesh, Syria
David Lortkipanidze – Prehistory of Georgia
Lunch
Excursion in the National Museum
Excursion to Djvari & Mtsketa
Conference Dinner
July 6, Monday
Venue: National Academy of Sciences of Georgia
Room 1
900 : 930
930 : 1010
Opening ceremony of IWOTA 2015 and presentation of Humboldt
Kolleg
Audience will be addressed by R. Duduchava, M. Kaashoek, G. Kvesitadze (National Academy), V. Papava (I.Javakhishvili State University), Representativse of
Embassy of Germany, Ministry of Education and Science, , etc.
Joni Apakidze, Roland Duduchava, Alexander Kartosia-Support programs of Alexander von Humboldt Foundation and activities of Humboldt Club
Georgia
Room 1
1010 : 1110
Chairman: Marinus Kaashoek
Albrecht Boettcher – Toeplitz determinants and lattice theory (IWOTA
program)
Room 2
1010 : 1050
1050 : 1140
1100 : 1900
Chairman: David Lortkipanidze
Jony Apakidze – On recent excavations in Georgia (HK Prog.; in German)
Coffee break
Optional: Excursion to Kakheti (Signagi). Recommended for those
participants of Humboldt Kolleg, who did not attend IWOTA. For IWOTAparticipants the same excursion is scheduled on July 8
Room 1
1140 : 1220
1220 : 1310
Chairman: Albrecht Boettcher
Frank Speck – Operator relations in boundary value problems (IWOTA prog.)
Andre Ran – Recent progress in operator theory (IWOTA program)
6
Room 2
1140 : 1220
Chairman: Roland Duduchava
Dorothee Knees Global spatial regularity results for elasticity models with
cracks, damage, contact and other nonsmooth constraints (IWOTA program)
Ilya Spitkowsky – Factorization of semi almost periodic matrices (IWOTA
program)
Lunch
1220 : 1310
1310 : 1500
Rooms 1 - 11
1500 : 1700
1700 : 1730
Rooms 1- 11
1730 : 1900
Afternoons parallel sessions. Venue: Iv. Javakhishvili Tbilisi State
University
11 Parallel Sessions in IWOTA program. 30 minute talks
Coffee break
Afternoons parallel sessions. Venue: Iv. Javakhishvili Tbilisi State
University
11 Parallel Sessions in IWOTA program. 30 minute talks
July 7, Tuesday
Departure of those participants of Humboldt Kolleg who did not attend IWOTA Conference
Interdiciplinary sessions (HK program)
July 4, Saturday
Venue: National Academy of Sciences of Georgia
Room 1
1400 : 1430’
1430 : 1500
1500 : 1530
1530 : 1600
1600 : 1630
Room 1
1630 : 1700
1700 : 1730
Session “Role of science and technology in society and public
policy”
Chairman: Marian Jaskula
Andre Ran – Support for science, in particular mathematics, in The
Netherlands
Frank Uhlig – Holistic Teaching and Learning Holistically
Yuri Naidyuk – Scientific two-way collaboration with German colleagues:
from personal contacts through intermediary of Alexander von Humboldt
Foundation to European Research Programs
Lika Gablishvili – The role of globalization in Georgia-China's relations (in
German)
Coffee break
Session “Role of informatic, science and technology in society”
Chairman: Zurab Berezhiani
Tornike Kadeishvili – How to attract young people to science in Georgia
Irakli Kardava –Georgian Speech Recognizer in Famous Searching Systems and
Management of Software Package by Voice Commands in Georgian Language
7
Room 1
1700 : 1730
1730 : 1800
Room 2
1400 : 1430
1430 : 1500
1500 : 1530
1530 : 1600
1600 : 1630
1630 : 1700
1700 : 1730
1730 : 1800
Room 3
1400 : 1430
1430 : 1500
1500 : 1530
1530 : 1600
1600 : 1630
1630 : 1700
1700 : 1730
1730 : 1800
Session “Physics”
Chairman: Zurab Berezhiani
Mariana Malard, George I. Japaridze and Henrik Johannesson,
Synthesizing Majorana zero modes in a quantum wire using a modulated electric
field
Luka Megrelidze, Zurab Tavartkiladze, Radiative Neutrino Masses
Generation via ‘Soft’ Lepton Number Violation
Session “Mathematics”
Chairman: Ilya Spitkovsky
Tornike Kadeishvili – Homotopy Algebras, Applications in Topology and
Physics
Kai Wang – Dixmier trace of quotient module on bounded symmetric domains
Jaydeb Sarkar – Invariant and wandering subspaces of reproducing kernel
Hilbert spaces
Vugar Ismailov – Hilbert's 13-th problem and approximation by neural
networks
Coffee break
Chairman: Alexander Strasburger
Ilya Spitkovsky – On some numerical range related results obtained while
working with student in the USA and UAE
Frank Olme Speck– Sommerfeld problems in Rn
George Chkadua, Mixed Type Interaction Problem of Acoustic Waves and
Piezoelectric Structures
Session “Humanitarin subjects”
Chairman: Alexander Kartosia
Manana Tandaschwili – Kartvelology and the challenges of 21-th century (in
German)
Nino Doborjginidze – Language and Technologies: Problems and Challenges
of Modern Academic Georgian (in German)
Max Florian Hertsch – Serenade for Nadia by Zülfü Livaneli - A modern
Turkish Ring Parable. An attempt to verify Lessing’s idea of Enlightenment in
Livaneli’s novel
Nino Gogelia – Zur linguistischen Erforschung rhetorischer Strategien im
politischen Diskurs von Marion Gräfin Dönhoff (in German)
Coffee break
Chairman: Manana Tandaschwili
Maia Akhalkatsi & Mariam Kimeridze – Natura 2000 sensitive forest
habitats of Georgia
Ketevan Esebua, Pikria Noniashvili – Grakliani Gora, Agriculture of
Grakliani Gora in V-IV cc. bc
Giorgi Bedianashvili – The Koban necropolis: The Late Bronze-Early Iron Age
collections from the Caucasus stored at French museums
8
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
Abstracts
9
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
11
Natura 2000 Sensitive Forest Habitats of Georgia
M AIA A KHALKATSI1 , M ARIAM K IMERIDZE2
1
Institute of Botany, Ilia State University, Tbilisi, Georgia
2
GSNE “Orchis”, Tbilisi, Georgia
email: maia− [email protected]
Natura 2000 forest habitat’s Directive is a Community legislative instrument in the field of
nature conservation that establishes a common framework for the conservation of wild species
and natural habitats of Community importance. Natura 2000 sites cover about 20% of the
European territory. Furthermore, it is the EU contribution to the Emerald network (ASCIs)
set up under the Bern Convention. Natura 2000 is also a key contribution to the Program of
Work of Protected Areas of the Convention on Biological Diversity. The Directive is developed on the bases of CORINE biotope classification determining codes and habitat types of
Europe, in particular involving the division of the latter into sub-types. According to Interpretation Manual habitat classification is based on plant community types. This information
is obtained from literature data of botanists of Georgia. 24 forest habitat types are identified
for Georgia. 18 belong to the biogeographical region – Forests of Temperate Europe. 6 habitat types belong to Mediterranean deciduous forests. There are habitats, which are identical
to related European habitats by species composition on generic level, but species are different.
The similarity between European and Caucasian plant species is mainly congeneric and not
conspecific. Therefore, some habitats, which are similar to the European habitat types, should
be considered as sub-types: 1) Beech forests without understory (Fageta sine fruticosa); 2)
Dark-coniferous forest (Piceetaorientale-Abietanordmanniana); 3) Pine forest (Pinuskochiana);
4) Yew forest (Taxusbaccata); 5) Hornbeam forest (Carpinuscaucasica); 6) Boxwood Forest
(Buxuscolchica). As priority sensitive habitats might be considered: 1) Beech forests with
Kolkhic understory (Fagetafruticosacolchica); 2) Kolhketi broad-leaved mixed forest; 3) Bog
woodland Tilio-Acerionforests of slopes, screes and ravines; 4) Alluvial forests; 5) Alluvial
forest with Adler trees (Alnusglutinosa)and ash tree (Fraxinus excelsior); 6) Riparian mixed
forests; 7) Yew forest (Taxusbaccata); 8) Zelkova forest (Zelkovacarpinifolia); 9) Boxwood
Forest (Buxuscolchica); 10) Sub-alpine birch krummholz. These conclusions could be considered as recommendations of the national experts to the commission to add sensitive habitats to
nature protection laws.
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Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
Neue Archäologische Ausgrabungen in Georgien
(am Beispiel der Tellsiedlung Tabakoni)
J ONI A PAKIDZE
Sokhumi State University, Institute of Archaeology, Tbilisi, Georgia
email: [email protected]
Die Tellsiedlung Tabakoni befindet sich in Westgeorgien im Bezirk Zugdidi. Die Siedlung
liegt ca. 15 Km von Schwarzmeerküste entfernt in einem Wald. Die Landschaft, in der diese
Siedlung liegt, gehört zur Kolchis Niederung. Diese mehrschichtige, künstliche Siedlung hat
einen Durchmesser von 45 m und eine Höhe von 2,90 m. Sie ist von einem Wasserkanal umschlossen, dies ist aufgrund der geo-klimatischen Bedingungen der kolchischen Tiefebene typisch für solche Siedlungen. Das Archäologische Institut der Staatlichen Universität Sokhumi
und die Eurasien Abteilung des Deutschen Archäologischen Instituts führen hier im Rahmen
einer Institutspartnerschaft, welche von der Alexander von Humboldt-Stiftung gefördert und
auch finanziell unterstützt wird, seit 2011 archäologische Ausgrabungen durch.
Während der Grabungskampagnen 2011 bis 2014 wurde die Tellsiedlung in den Arealen A,
B, C, D, E, F und G ausgegraben. Im Laufe der Arbeiten wurde festgestellt, dass die Siedlung
aus mittelbronzezeitlichen und zum Teil auch späten frühbronzezeitlichen frühkolchischen (sogenannten protokolchischen), Spätbronze- und Früheisenzeitlichen kolchischen und aus frühantiken kolchischen Kulturschichten besteht. Die ersten Ergebnisse von 14C-Daten bestätigen
gut die chronologische Gliederung dieser mehrschichtigen Tellsiedlung. 2014 kamen in den
Arealen C und G relativ gut erhaltene Holzkonstruktionen der kolchischen Architektur zu Tage.
Im nördlichen Teil des Areals G wurden in horizontaler Lage erhaltene Holzkonstruktionsreste
gefunden. Im übrigen Teil waren die Holzreste schräg in den Boden eingesetzt. Im gesamten
Areal C wurden ebenfalls Reste von Holzkonstruktionen gefunden.
Den Hauptanteil der Funde aus der Tellsiedlung Tabakoni stellt die Keramik. Frühkolchische
Keramik ist meistens in Form der sogenannten schwarzpolierten und “groben” Keramik vertreten. Keramik dieser Zeit weist am Boden oft Textilabdrücke auf. Die kolchische Keramik
der Spätbronze- und Früheisenzeit hat meistens eine runde Form, sie ist meist braun oder
schwarz, zum Teil auch grau. Das übliche Dekor sind Rillen und Kreise. Diese Motive sind
manchmal auch mit Kammstempelmuster kombiniert. Typisch sind sogenannte “Vogelbrusthenkel”, “Kniehenkel” und “zoomorphe” Henkel. Nicht selten fanden sich auch Kleinfunde
wie Sicheleinsätze aus Silex, Pfeilspitzen aus Silex, Spinnwirtel aus Ton, Anhänger aus Keramik, Klopfsteine und Mahlsteine. Es wurden auch einige Artefakte aus Bronze und Eisen gefunden.
Die Tellsiedlung Tabakoni, die in auch diesem Jahr (2015) archäologisch und naturwissenschaftlich weiter untersucht wird, hat für die Erforschung, sowie die kulturelle und neue
chronologische Interpretation der Siedlungen der Kolchis-Kultur eine wichtige Bedeutung als
gut stratifizierte Siedlung, die nach modernen Grabungsmethoden ausgegraben wird.
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
13
The Koban necropolis:
The Late Bronze-Early Iron Age collections
from the Caucasus stored at French museums
G IORGI B EDIANASHVILI
Georgian National Museum
Tbilisi, Georgia
email: [email protected]
In this presentation there will be discussed Ernest Chantres archaeological collections from
the Koban necropolis, stored at the National Archaeological Museum of France, at SaintGermain-en-Laye and the Confluences Museum in Lyon. The Koban necropolis, which was
excavated by Chantre in 1881, is located in the North Caucasus. It has given its name to one of
the Late Bronze and Early Iron Age cultures of the Caucasus.
The aim of presented research is to bring to the light Koban objects, both published and
unpublished, and organizes them in a systematic fashion. Typological classification of each
group of objects is examined and presented. These data are then compared with materials
from other parts of the Caucasus. The focus of presented research determines the cultural
environment of the Koban necropolis in the Caucasus region, as objects from this site reflect
certain characteristic features of different regions of the Caucasus such as Colchis and Shida
Kartli.
Dark Side of the Universe:
Opening Windows to Parallel Worlds
Z URAB B EREZHIANI
Dipartimento di Fisica, Universitá di L’Aquila, 67100 Coppito, L’Aquila, and
INFN, Laboratori Nazionali del Gran Sasso, 67010 Assergi, L’Aquila, Italy
email: [email protected], [email protected]
I shall talk on a hypothesis that dark matter in the Universe exists in the form of a hidden
parallel world (or worlds) with exactly identical content of particles and their interactions that
we have in ordinary particle sector. I shall discuss the scenarios how both ordinary and dark
matter fractions can be generated both simultaneously by the B − L and CP violating particle
processes between ordinary and parallel worlds and possibilities of transformation of the ordinary particles into their twins from a hidden parallel sector in today’s laboratory experiments.
An amusing introduction to this subject can be found in Ref. [1].
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Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
References
[1] Z. Berezhiani, Through the Looking-Glass: Alice’s Adventures in Mirror World. In:
I. Kogan Memorial Colection “From Fields to Strings: Circumnavigating Theoretical
Physics”, Eds. M. Shifman et al., 3 (2005), 2147–2195 [arXiv:hep-ph/0508233].
Mixed Type Interaction Problem of Acoustic Waves and
Piezoelectric Structures
G EORGE C HKADUA
King’s College London, Strand, London, United Kingdom
email: [email protected]
We investigate the mixed type transmission problem arising in the model of fluid-solid
acoustic interaction when a piezo-ceramic elastic body (Ω+ ) is embedded in an unbounded
fluid domain (Ω− ). The corresponding physical process is described by boundary-transmission
problem for second order partial differential equations. In particular, in the bounded domain Ω+
we have 4 × 4 dimensional matrix strongly elliptic second order partial differential equation,
while in the unbounded complement domain Ω− we have a scalar Helmholtz equation describing acoustic wave propagation. The physical kinematic and dynamic relations mathematically
are described by appropriate boundary and transmission conditions. With the help of the potential method and theory of pseudodifferential equations based on the Wiener–Hopf factorization
method the uniqueness and existence theorems are proved in Sobolev–Slobodetskii spaces and
on the basis of asymptotic analysis, we establish almost the best Hölder smoothness results for
solutions.
Such type of interaction problems of different dimensional fields appear in the mathematical
model of piezoelectric transducers. Further examples of similar models are related to phased
array microphones, ultrasound equipment, inkjet droplet actuators, drug discovery, sonar transducers, bioimaging, immunochemistry and acousto-biotherapeutics (see [1–3]).
In the paper [4] uniqueness and existence theorems of mixed type interaction problem of
acoustic waves and piezoelectric structures are stated without proof. The Dirichlet type and
Neumann type interaction problems of acoustic waves and piezoelectric structures are studied
in [5].
References
[1] T. R. Gururaja, Piezoelectric transducers for medical ultrasonic imaging. Proceedings of
the Eighth IEEE International Symposium on Applications of Ferroelectrics, 1992, 259–
265.
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
15
[2] F. Josse, Z.A. Shana, D. E. Radtke, and D. T. Haworth, Analysis of piezoelectric bulkacoustic-wave resonators as detectors in viscous conductive liquids. IEEE Trans Ultrason
Ferroelectr Freq Control 37 (1990), No. 5, 359–68.
[3] M. Thompson, C. L. Arthur, and G. K. Dhaliwal, Liquid-phase piezoelectric and acoustic
transmission studies of interfacial immunochemistry. Anal. Chem. 58 (1986), No. 6,
1206-1209; doi:10.1021/ac00297a051.
[4] G. Chkadua, Mathematical problems of interaction of different dimensional physical
fields. J. Phys.: Conf. Ser. 451 (2013), 012025; doi:10.1088/1742-6596/451/1/012025.
[5] G. Chkadua and D. Natroshvili, Interaction of Acoustic Waves and Piezoelectric Structures. Math. Methods Appl. Sci., 2014; doi:10.1002/mma.3210.
Language and Technologies: Problems and
Challenges of Modern Academic Georgian
N INO D OBORJGINIDZE
Institute of Linguistic Studies, Ilia State University
Tbilisi, Georgia
email: nino [email protected]
The development of scholarship in Georgia largely depends on the ability of academic Georgian to receive and process relevant information, generate new knowledge and export it, i.e.
internationalize academic or other type of generated in Georgian language.
To streamline these processes, the rich textual heritage available in the Georgian language
needs to be documented to meet modern linguistic and technological standards. We need to create Georgian language modeling applications, morphology and syntactic modules and software
for parallel corpus and machine translation.
In this paper I aim to present the Georgian Language Corpus (GLC) developed at the Institute of Linguistic Studies of Ilia State University during 2009-2014 (corpora.iliauni.edu.ge). At
present the corpus contains over 100 000 000 word forms and has two main sections, monolingual and bilingual. The monolingual section consists of a) Old and Middle Georgian Corpus,
and b) New and Modern Georgian Corpus. The Old Georgian Corpus on its part contains a
translation corpus structured according to translation schools, i.e. the chronological and stylistic principle (pre-Athonite, Athonite, Antiochian, etc.) and source texts (cf. Greek - Georgian,
Syriac - Georgian Christian Arabic Georgian, Armenian Georgian). The bilingual section includes parallel corpora of Kartlis Tskhovreba (The Georgian Chronicle, a Georgian-Armenian
corpus) and Vepkhistkaosani (The Knight in the Panthers Skin, a Georgian-English corpus).
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Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
The rich language legacy is presented in the GLC not only from the perspective of historical
grammar but also of social and public functions and relations with other languages and cultures.
Such projects are indispensable for maintaining and supporting public and social functions
of the Georgian language, for integrating into contemporary academic discourses and in general,
for developing the humanities in Georgia.
Zur linguistischen Erforschung rhetorischer
Strategien im politischen Diskurs von Marion
Gräfin Dönhoff
N INO G OGELIA
Staatliche Universität Suchumi
Assistenz-Professorin der Fachrichtung “Deutsche Philologie”
Tbilisi, Georgien
email: [email protected]
Seit es gesellschaftliche Institutionen gibt, die das Miteinander innerhalb einer sozialen
Gemeinschaft festlegen, gibt es auch politische Kommunikation, in einem weiteren Sinne auch
öffentliche Kommunikation. Historisch betrachtet zeigt sich politische Kommunikation vor
allem mündlich, als unmittelbare Kommunikation über politische Themen und Sachverhalte.
Man versteht unter “politischer Sprache” als Oberbegriff alle Arten öffentlichen, institutionellen
und privaten Sprechens über politische Fragen, alle politiktypischen Textsorten sowie jede
für das Sprechen über politische Zusammenhänge charakteristische Weise der Verwendung
lexikalischer und stilistischer Sprachmittel.
“Sprache der Politik” ist ein ernstzunehmender Gegenstand linguistischer Analyse. Als
kennzeichnend für die Sprache der Politik können genannt werden: Metaphernreichtum, häufige
Verwendung rhetorischer Figuren, pathetische Sprechweise, Diskursivität, außerdem die reichhaltige Verwendung von Schlagwörtern.
“Sprache der Politik” verfügt über die sprachliche Inhalte, die im gemeinten Sprachgebrauchsbereich ausschlaggebend sind. Argumentationsanalytisch feststellbare Merkmale politischen Sprachgebrauchs finden ihre Entsprechung überall da, wo Sprache auch außerhalb der
Politik zu argumentativen Zwecken eingesetzt wird. Viele scheinbar spezifische politische
Textsorten finden Entsprechungen im außersprachlichen Bereich. Dies gilt vor allem für alle
rechtsförmigen Textsorten, aber auch für Reden, programmatische Texte, Werbetexte oder Texte
im publizistischen Bereich.
In meinem Vortrag handelt es sich um Formen argumentativen Sprachgebrauchs, die im
politischen Diskurs von Marion Gräfin Dönhoff in besonderer Intensität auftreten. Anhand
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
17
exemplarischer Analyse einer ihrer Rede wird gezeigt, dass “der politische Diskurs” von Marion Gräfin Dönhoff durch ein spezifisches Zusammenwirken von textgestalterischen Elementen
charakterisiert ist, dass sich rhetorische Strategien als dominant erweisen und die gewünschte
Wirkung auf Öffentlichkeit erzielen können.
Cultural Communication in the Framework
of Yuri Lotman’s Semiotic Theory
VALERIJ G RETCHKO
Kobe University, Faculty of Intercultural Studies
Kobe, Japan
email: [email protected]
The term “communication” occupies a central place in the semiotic theory of Yuri Lotman.
In this theory, communication is regarded not as a mere exchange of texts, but proves instead
to be a translation in which the texts of the culture are being coded and decoded in (at least)
two different types of ways. Because of the basic incompatibility of these codes, an exact
translation is not possible. However, precisely this difference is of exceptional significance.
New texts that develop within this process of nontrivial translation represent the basis for a
creative development of culture.
My paper investigates the question of the genesis and formation of Yuri Lotman’s model of
communication, discussing its theoretical implications for cultural research. I will show how
the basic idea that the semiotic, communicative, and cultural processes manifest themselves in
two principally different forms, runs like a red thread through the whole Lotman’s scholarship.
The paper traces the origin and development of dual models in the semiotic theory of Lotman. It
demonstrates that the field of application of these models was gradually extended from the level
of text to the level of the individual consciousness, and the culture as a whole. The static model,
where two different codes merely oppose each other, has been enhanced through the dynamic
aspect which presupposes such forms of interaction as translation and dialogue. For possible
sources from which this approach has been developed, we can draw on both the theoretical
conception of dialogicity (Bakhtin) as well as neurophysiologic work on the asymmetry of the
brain hemispheres.
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Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
Quantum Analysis of Normal Polytopes
J OSEPH G UBELADZE
SFSU, Mathematics Department, San Francisco, USA
email: [email protected]
Polytopes have fascinated humans since antiquity. Examples include diamonds and the
pyramids of the ancient Egypt. In the contemporary natural sciences there is a ubiquity of
polytopal shapes – be it physics, chemistry, or biology. The natural habitat of polytopes is
obviously Euclidean geometry: polygons in the plane, Platonic solids in the space, and their
more complex and higher dimensional counterparts. In the post ww2 mathematics polytopes
have found new life as connecting links between algebra and geometry, in the form of toric
algebraic geometry. This field can loosely be described as ‘geometry of formulas’, a venue in
pure mathematics which eluded Hilbert’s vision of the future development of mathematics at the
dawn of the 20th century. In toric geometry, systems of high degree multivariate polynomials
are encoded in the configurations of lattice points (i.e., points with integer coordinates) inside
convex polytopes. A central notion in the field is that of a normal polytope – it is a correct
discrete version of the convex compact sets, like balls, prisms, pyramids etc.
Having worked in the field of toric algebraic geometry proper for over 30 years, which
employs techniques from commutative algebra and K-theory, we came to realize that the basic
continuous vs. discrete dichotomy, just touched upon in the definition of normal polytopes, is a
challenge in its own right. Systematic formal treatment of this dichotomy leads to a structurally
very rich new mathematical object – an infinite dynamical space, which can be explored from
various complementary perspectives: number theoretic, topological, geometric. The full blown
mathematical framework for exploring the continuous vs. discrete dichotomy is expected to
constitute a trilogy, of which the first is the recent joint preprint with my coauthors W. Bruns
and M. Michałek [1]. This work studies the extent of distortion of the suggested discretization
of the continuum of Euclidean geometry: local singularities of the resulting space. The next
anticipated step should reveal large scale emergent trends, exhibited by quantum processes in
this space. The 3rd step will conjecturally reveal underlying smooth differential structures,
controlling the ultimate fate of the mentioned processes. At present, the 2nd and 3rd steps
are rather speculative and may well be several years away from being fully implemented. But
already now one can ask whether this inquiry is confined exclusively to pure mathematics, or
it has potential to provide a new formalism for tackling challenges the physical world poses to
us. A possible fruitful interaction with experts in various fields, hinted at in [2], is still matter
of future experience, for which meetings as Humboldt Kolleg is a stage.
References
[1] W. Bruns, J. Gubeladze, M. Michałek, Quantum jumps of normal polytopes (2015).
Preprint: http://arxiv.org/abs/1504.01036.
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[2] J. Gubeladze, Normal polytopes, in Proceedings of 22nd International Conference on
Formal Power Series and Algebraic Combinatorics, San Francisco, 2010, pp. 4–8.
http://math.sfsu.edu/fpsac/local− proceedings.pdf
Serenade for Nadia by Zülfü Livaneli A Modern Turkish Ring Parable
M AX F LORIAN H ERTSCH
Institute of Literary Studies, Hacettepe University, Department of German Language and
Linguistics, Ankara, Turkey
email: [email protected]
Zülfü Livaneli’s novel: Serenade for Nadia provides a remarkable perspective in literary
analysis, especially by the ideal of Lessing’s vision of Enlightenment. Through its characters,
who have different ethnic backgrounds and struggle within them, the novel provides an analogy to the ideal of modern, Turkish Enlightenment. Livaneli’s novel indicates a clear link to
Lessings drama: Nathan the Wise which has its climax in the so called Ring Parable. Lessing
describes the equality of the main monotheistic religions in this famous parable. Even though,
these religions do not accept each other, although they have quite comparable roots, Livaneli
highlights the equality of different Turkish ethnic groups in a similar way within the help of
(actually) two Ring Parables in the novel. While Lessing defines the Ring Parable through the
main character Nathan the Wise, Livaneli initiates it through Professor Maximillian Wagner
who opens the novel with E. Saids statement: War to ignorance (Livaneli 2013:37).
This article examines Kaminsikis (2013) hypothesis, if Livaneli has truly created a modern
Turkish Ring Parable within the notion of Lessing’s Enlightenment.
References
[1] A. Kaminsiki, Zülfü Livanelis Roman “Serenade für Nadja” - Eine türkische Ringparabel. Qantara.de, Web: 8th of April 2015, http:
de.qantara.de/inhalt/zulfu-livanelis-roman-serenade-fur-nadja-eine-turkische-ringparabel.
[2] O. Z. Livaneli, Serenade für Nadja. Klett-Cotta Verlag, 2013.
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Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
Hilbert’s 13-th Problem and Approximation
by Neural Networks
V UGAR I SMAILOV
Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan
Baku, Azerbaijan
email: [email protected]
The past two decades have seen a tremendous growth of interest in the MLP (multilayer
feedforward perceptron) model of neural networks. The application areas of this model is as diverse as areas of computer science, medicine, finance, physics, engineering, petroleum science,
etc.
The solution of Hilbert’s 13-th problem given by Kolmogorov has been much discussed in
neural network literature. Hilbert’s problem reads as follows: Is the root of the equation
x7 + ax3 + bx2 + cx + 1 = 0
a superposition of continuous functions of two variables?
As a solution of this problem, Kolmogorov in the late 50’s proved that each continuous function of three and more variables can be represented by superpositions of continuous functions
of two variables.
Hecht-Nielsen was the first who noticed relationship of Hilbert’s 13-th problem to neural
network theory. He showed that an arbitrary function can be implemented by a three layer
neural network with appropriate activation functions. Girosi and Poggio pointed out that the
Kolmogorov’s solution is not useful, since the inner universal functions in the Kolmogorov superposition formula are highly nonsmooth and incomputable. This difficulty was overcome by
Kurkova by using staircase like functions of a sigmoidal type. These functions were constructed
in a way that they can approximate any continuous function on any compact subset of the real
line with an arbitrary accuracy. Kurkova’s results showed that an arbitrary continuous function
can be approximated arbitrarily well by two hidden layer neural networks with an arbitrary sigmoidal activation function. However, the number of units in hidden layers needed to realize
such approximation is exceedingly large. What if the hidden layers consist of a fixed number
of units? Is it possible to approximate every continuous function in this case? This question
was first answered by Maiorov and Pinkus. They showed that there exists a sigmoidal, strictly
increasing, analytic activation function such that two hidden layer neural networks with this activation function, d inputs, 3d neurons in the first hidden layer and 6d + 3 neurons in the second
hidden layer can approximate any continuous multivariate function over any compact subset of
Rd . Using the Kolmogorov superposition theorem and the ideas of Maiorov and Pinkus, we
prove that for some nonanalytic but infinitely differentiable activation functions these numbers
in the hidden layers can be reduced to d and 2d + 2 respectively.
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
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Internationalization & Globalization of Science
[Experiences of the Jagiellonian University in Cracow (Poland) and one of the Polish
non-governmental organization on the example of Societas Humboldtiana Polonorum on the
developing of excellence in research and education through Internationalization]
M ARIAN JASKUŁA
Department of Physical Chemistry & Electrochemistry, Faculty of Chemistry, Jagiellonian
University, Cracow, 30-060 Poland
email: [email protected]
The international cooperation is one of the most important factors deciding on global progress
in sciences. This dependence is especially strong to see in natural & life sciences where collaborate often big various groups of researchers coming from different countries. As a good
examples may be the papers published on the field of nuclear physics where the number of
authors is sometimes twenty or thirty. The science of today requires collaboration of many
specialists.
In the lecture the experiences of Jagiellonian University, the oldest Polish university with
long 650 years history are mentioned. The international cooperation played very important role
in middle ages that was unfortunately forgotten and only in recent decades, is undergoing a
renaissance. The internalization of sciences starts with the internationalization of teaching and
exchange of students. The very important role play here the numerous programmes of European Community like as Erasmus or Leonardo. The author of the lecture who is a professor
for chemistry at the Jagiellonian University is the best personal example of importance of scientific international contacts: to be fellowship holder abroad and to host foreign students and
researchers in Poland.
The Jagiellonian University has today more than 184 bilaterale agreements concerning the
international cooperation on the field of science and 1404 agreements connected with exchange
of the students (mainly ERASMUS). Four percent of our staff are foreigners and this number is
growing.
Very important role play in the process of internationalization various scientific societies
and non governmental organizations. The may be directly or indirectly connected with the financing of science and exchange. As the examples should be here mentioned the Foundation for
Polish Science (as organization which support financially the common projects and exchange),
and for example Societas Humboldtiana Polonorum, that joined over 1300 Polish recipients of
Humboldt fellowship and try to inspire Humboldtians for developing and deepening of such
contacts. The author of the lecture was many years the general secretary of this society as well
as ambassador scientist of the Humboldt-Foundation and in the talk his experiences will be
presented.
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Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
Homotopy Algebras, Applications in Mathematics
and Physics
T ORNIKE K ADEISHVILI
TSU A. Razmadze Mathematical Institute
email: [email protected]
Homotopy Algebra is the general title for algebraic objects for which classical axioms are
satisfied just up to certain homotopies which also are included in the structure. Particular examples of such objects are: A∞ -algebra with measured nonassociativity, B∞ -algebra with measured noncommutativity, L∞ -algebra with measured deviation from Jacobi identity etc. These
algebras show up in various problems and are more informative than classical objects. That
is why now a days they are intensively used in various problems of topology, geometry, algebra. Last years homotopy algebras become useful in physics, namely in string theory and
quantization problems.
How to Attract Young People to Science in Georgia
T ORNIKE K ADEISHVILI
TSU A. Razmadze Mathematical Institute
email: [email protected]
The problem mentioned in the title becomes more and more actual in our country. We are
going to present various examples showing that now a days the involvement in international
scientific community is most attractive argument for talented yang people.
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
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Georgian Speech Recognizer in
Famous Searching Systems and Management of
Software Package by Voice Commands in Georgian Language
I RAKLI K ARDAVA
Sokhumi State University, Department of Computer Science Tbilisi, Georgia
email: [email protected]
The speech recognition system and creation of program Software based on it is one of
the important components of natural language computer modelling. For example, the popular
Google Voice system, by which the word or sentence pronounced by a person is automatically
written in textual form, in Google’s Search system field for given language by using already
realized speech recognition systems. The trial Software program has been developed by us,
which is able to solve the problems, as for the Google search system, also for YouTube, Yahoo,
Bing, Yandex and Wikipedia in Georgian language. Also, it is possible to translate automatically Georgian words or sentences pronounced individually and get texts in the appropriate
language by using Google Translate. Program management is performed with Georgian voice
commands.
The ‘Fantastic City’: The Linguistic Shaping
and Re-shaping of the Georgian Cultural Scene
in the first Third of the 20th Century
A LEXANDER K ARTOSIA
Ivane Javakhishvili Tbilisi State University
email: [email protected]
Following the Revolution 1917 and the outbreak of Civil War in Russia, many Russian
artists found refuge in Georgia. The Georgian capital became a ‘Fantastic City’. The most
influential Georgian author of that period, Grigol Robakidze, wrote 1919: “Tiflis is pervaded by
an aesthetical perception of the world. ... People coming from different nations and cultures are
brothers in art. We believe in that new International. Here in Tiflis must be laid the foundations
for its construction.”
The literary life of the ‘Fantastic City’ took a multilingual form. The meaning of ‘multilingual’ is two-fold. On the one hand books appeared with texts in Georgian, Russian and
Armenian; on the other hand the so-called ‘Zaum language’ of Futurism developed, whose
main aim was the alienation from ‘normal’ language.
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Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
After the occupation of Georgia by the Russian Red Army in 1921, the protest against the
occupation and annexation led to a linguistic re-shaping of the cultural scene in the ‘Fantastic City’. Again in two respects: firstly all Georgian authors including those who previously
sometimes pleased their Russian colleagues by writing in Russian now used only Georgian.
Secondly, the futurist alienation from the normal language was replaced by a new more traditional (archaic) form.
Synthesizing Majorana Zero Modes in a Quantum
Wire Using a Modulated Electric Field
M ARIANA M ALARDa , G EORGE I. JAPARIDZEb,c , H ENRIK J OHANNESSONd
a
University of Brasilia, 70904-910 Brasilia-DF, Brazil
Andronikashvili Institute of Physics, Tbilisi, Georgia
c
Ilia State University, Center for Study of the Optically Trapped Quantum Matter,
Tbilisi, Georgia
d
Department of Physics, University of Gothenburg, SE 412 96 Gothenburg, Sweden
b
email: [email protected]
We explore a scheme for engineering a one-dimensional spinless p-wave superconductor
hosting Majorana zero modes, using an all-electric setup with a spin-orbit coupled quantum
wire in proximity to an s-wave superconductor. The crossing of the Fermi level with only a
single spin-split quasiparticle band is ensured by employing a periodically modulated electric
field, which, assisted by the electron-electron interaction in the wire, opens a gap at two of the
spin-orbit shifted Fermi momenta. While the smallness of the gap makes the scheme impractical
for present-day semiconductor devices, it may be realized using spin-orbit coupled fermionic
cold atoms.
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
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Scientific Two-Way Collaboration with German
Colleagues: from Personal Contacts through
Intermediary of Alexander von Humboldt
Foundation to European Research Programs
Y URII NAIDYUK
B.Verkin Institute for Low Temperature Physics and Engineering of the National Academy of
Sciences of Ukraine, Kharkiv, Ukraine
email: [email protected]
International scientific cooperation plays a key role in basic and applied science. New partnership usually starts with personal contacts, however, to intensify and extend collaboration
help of some foundations and institutions are of particular importance. Alexander von Humboldt foundation plays this role, strengthening regional and interdisciplinary links between the
scientists. Along with individual financial support, diverse Alexander von Humboldt foundation
awards and projects (i.e. Institutspartnerschaft program), organizing Humboldt-Kolloquien and
Humboldt-Kollegs are significant to broaden ones outlook and to find new research directions
and partners. My report will contain an overview of scientific cooperation of our Department
at the Institute of Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine mainly with German partners supported by Alexander von Humboldt foundation. The cooperation led to recognition of our original point-contact spectroscopy method in
Germany and other western countries and finally in participation in the European Framework
Program 7.
Finally, in my talk, I will represent to your Humboldt Club Ukraine, which plays a significant role in number of activities to intensify collaboration with German scientists. Humboldt
Club Ukraine distributes actual information, which helps Ukrainian scientists to start and maintain collaborative projects with German scientists and find a proper way for funding. Humboldt
Club Ukraine organizes various events with Alumni, participation in the meetings, Humboldt
lectures, Humboldt Kollegs etc.
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Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
Goodwillie–Taylor Tower via Relative Homological
Algebra. Abelian Case
T EIMURAZ P IRASHVILI
University of Leicester, UK
email: [email protected]
Based on basic properties of relative homological algebra, we give very simple construction
of Goodwillie–Taylor tower for functors T : C → Ch. Here C is a category with zero object
and finite coproduct, while Ch is the category of chain complexes over a ring.
National and Intercultural Frontiers of Literature
(on the Example of Georgian Literature)
N INO P OPIASHVILI
Ivane Javakhishvili Tbilisi State University
Tbilisi, Georgia
email: [email protected], [email protected]
Literature in its essence is an intercultural and multicultural phenomenon. On the one hand,
literature is a narrative based on national identity and experience and, on the other hand, sharing
the existing experience and multicultural environment. The intercultural nature of literature
enables us to identify a number of layers in fiction. These layers might be felt and reflected in
a text equally or by various degrees of intensity Authors layer National layer Intercultural
layer.
The intensity of the above mentioned definitions may be completely individual in case of a
particular author and his texts. Intercultural layer might be of primary importance, whereas in
some cases national layer, or authors identity and texts created by personal experience (and not
inspiration provoked by national experience) might dominate.
Georgian literature has a long tradition, thus we can discuss national characteristic of the
literature as well as its intercultural one. The paper deals with national and intercultural issues
of literature on the example of Georgian literature.
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
27
Invariant and Wandering Subspaces of Reproducing
Kernel Hilbert Spaces
JAYDEB S ARKAR
Indian Statistical Institute, Statistics and Mathematics Unit,
Bangalore, India
email: [email protected], [email protected]
We discuss brie y recent and not so recent results about invariant subspaces (Beurling-LaxHalmos type theorem) and analytic models and operator positivity of bounded linear operators
on Hilbert spaces. We also discuss some related results on wandering subspaces in both one
and several variables.
Part of this talk is based on joint work with Monojit Bhattacharjee and Dinesh K. Keshar.
Sommerfeld Problems in Rn
F RANK -O LME S PECK
Técnico, Universidade de Lisboa, Departamento de Matemática, Portugal
email: [email protected]
Motivated by the classical Sommerfeld diffraction problem we consider interface problems
in weak formulation for the n-dimensional Helmholtz equation in Ω = Rn+ ∪ Rn− (due to xn > 0
or xn < 0, respectively), where the interface Γ = ∂Ω is identified with Rn−1 and divided into
two parts, Σ and Σ0 , with different transmission conditions of first and second kind. These two
parts are half-spaces of Rn−1 (half-planes for n = 3) and more general sets in the first part of the
paper. The aim of this work is to construct explicitly resolvent operators acting from the interface data into the energy space H 1 (Ω). The approach is based upon a factorization conception
for Wiener-Hopf operators (according to the interface equations), the so-called Wiener-Hopf
factorization through an intermediate space, that includes Simonenko’s well-known “generalized factorization of matrix functions in Lp spaces” and avoids an interpretation of the factors
as unbounded operators. In a natural way, we meet non-isotropic Sobolev spaces which reflect
the wedge asymptotic of diffracted waves.
References
[1] F.-O. Speck, A class of interface problems for the Helmholtz equation in Rn . Math. Meth.
Appl. Sciences, online publ. Feb. 2015, 13 p., DOI 10.1002/mma.3386.
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Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
[2] F.-O. Speck, Wiener-Hopf factorization through an intermediate space. Integral Equations Operator Theory 82 (2015), no. 3, 395–415.
On Some Numerical Range Related Results
Obtained while Working with Students
in the USA and UAE
I LYA M. S PITKOVSKY
New York University Abu Dhabi, UAE and
The College of William and Mary, Williamsburg, VA, USA
email: [email protected], [email protected], [email protected]
The numerical range, a.k.a. the field of values, or the Hausdorff set of an n-by-n matrix A is
the range F (A) of the quadratic form hAx, xi on the unit sphere of Cn . It is a convex compact
subset of C; more specifically, F (A) is the convex hull of a certain algebraic curve of class n
associated with A. For n = 2 this curve is an ellipse (degenerating into two points, when A is
normal), yielding the classical elliptical range theorem. The classification of possible resulting
shapes for n = 3 was provided by Kippenhahn [4], with the tests developed in [3]. A (somewhat
implicit) description of all admissible curves for arbitrary n is given in [2], but further research
of possible shapes of the numerical ranges in case of higher sizes is still of interest.
In this talk, I will describe several results obtained in this direction when A is a matrix of
arbitrary size but structured in a very specific way. They are partially published [1], and partially
still in preparation.
References
[1] R. T. Chien, I. M. Spitkovsky, On the Numerical Ranges of Some Tridiagonal Matrices.
Linear Algebra and Its Applications 470 (2015), 228–240.
[2] J. W. Helton, I. M. Spitkovsky, The Possible Shapes of Numerical Ranges. Operators
and Matrices 6 (2012), 607–611.
[3] D. Keeler, L. Rodman, I. M. Spitkovsky, The Numerical Range of 3 × 3 Matrices. Linear
Algebra and Its Applications 252 (1997), 115–139.
[4] R. Kippenhahn, Über den Wertevorrat einer Matrix. Mathematichse Nachrichten 6 (1951),
193–228.
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
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Kartvelology and the Challenges of the 21st Century
M ANANA TANDASHVILI
Institute of Empirical Linguistics, Goethe University Frankfurt, Germany
email: [email protected]
Kartvelology isprimarily understood as a subject of research in linguistics which represents
an interesting discipline with many peculiar facets especially for linguistic typology. On the
other hand, Kartvelology represents the nationalphilology of Georgia, thus requiring special
care and well-scheduled measures for its further development locally and abroad. Linguistics in
the 21st century is characterized by a more practical use of its research materials, i.e., language
data. Today, linguistic research results are converted with the help of modern technologies into
practically usable products such eLexicons, spell checkers, so-called smart technologies, etc. At
the same time, we witness a thorough technologisation of linguistic research processes in the
creation of large speech corpora, which enable modern linguists to explore issues much more
systematically than ever before and to make them useful for the challenges of the 21st century.
After Georgias independence, when the borders were abolished and access to the open European and even world-wide linguistic society became possible, Kartvelology still remained
enclosed in itself. Post-Soviet Georgia has not succeeded yet in a thorough abolition of Soviet
structures or in the modernization of the education system, let alone the establishment of modern research methods and themes. Instead, the country has remained stuck in the processes of
political, economic and societal transformation on its path towards a modern democratic state.
This is clearly reflected by the state of Kartvelology, too.
The survival of Kartvelology in the 21st century primarily requires measures of internationalization, namely a) the transfer of knowledge with respect to modern theoretical thought and
research methods, b) the creation of speech corpora for the Georgian language, c) scientific
exchange through international cooperation projects, d) the introduction of modern standards in
research and teaching, and e) the development of a promotion program for the new generation
of students in form of an international Graduate School in Kartvelology. Judging from 15 years
of experience, I may state that this should be possible through cooperation between Georgian
and foreign funding institutions.
In my paper, I will thematize the above mentioned aspects of the further development of
Kartvelology in the 21st century on the basis of activities that we have carried out at Goethe
University Frankfurt since 2000, summarizing the results of 12 international projects we have
undertaken in cooperation with 17 Georgian research institutes and universities, among them
the Georgian National Corpus project and the Batumi summer schools program.
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Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
Radiative Neutrino Masses Generation
via ‘Soft’ Lepton Number Violation
Z URAB TAVARTKILADZE , L UKA M EGRELIDZE
Center for Elementary Particle Physics, Ilia State University,
Tbilisi Georgia
email: [email protected]
Within SUSY framework, we propose neutrino mass generation via radiative mechanism.
Within considered mechanism, the lepton number violation is originating from the SUSY breaking sector. These require to have physics, beyond the MSSM, near the TeV scale. We give several explicit realizations of the proposed mechanism and besides some novelties discuss various
phenomenological implications.
Holistic Teaching and Learning Holistically
F RANK U HLIG
Department of Mathematics and Statistics, Auburn University,
Auburn, AL 36849-5310, USA
email: [email protected]
We discuss ways to teach holistically.
The holistic method encourages student curiosity and respects student input fully – whether
qualified or not. This requires attitude changes in both teachers and students from the more
standard top-down approach to cooperative teaching and learning. The holistic approach leads
to, allows and favors open discussions and deep learning in class – by students and teacher alike.
Using the students’ innate ’desire to understand’ drives the course of a holistically taught
class. The teacher’s role is to guide and adjust a class’s course as the subject matter, experience
and - in mathematics courses - as the algebraic, geometric and logical rules of math dictate.
Holistic teaching respects and adheres to Piaget’s ’necessity principle’ of learning. And it uses
Savory’s ’holistic management principle’ for wide and comprehensive teaching and learning as
is necessitated in complex natural environments such as education and the human growth and
maturation process.
The practice of teaching holistically is exemplified by one extended undergraduate class
example that studies the definition and measurement of angles in Rn from first principles of
both Geometry and Linear Algebra.
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
31
Dixmier Trace of Quotient Module
on Bounded Symmetric Domains
K AI WANG
School of Mathematical Sciences, Fudan University,
Shanghai, China
email: [email protected]
In this talk we will concern quotient module of rank 1 on bounded symmetric domain. We
prove that the restriction operator with polynomial symbol is L n,∞ essentially normal, and
establish a Diximer trace formula on the quotient module. The talk is based on joint work with
Prof. Harald Upmeier.
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
Humboldt Kolleg, Tbilisi, Georgia July 4-6, 2015
Science in Georgia: Perspectives of development
and the role of Humboldt Foundation
List of Participants
Invited Humboldt Fellows
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Akhalkatsi Maia – Georgia – maia [email protected]
Apakidze Joni – Georgia – [email protected]
Balavadze Mikheil – Georgia – [email protected]
Berezhiani Zurab – Italy – [email protected]
Chanturia Lado – Georgia – [email protected]
Doborjginidze Nino – Georgia – nino [email protected]
Duduchava Roland – Georgia – [email protected]
Gamkrelidze Tamaz – Georgia – [email protected]
Gegelia Jambul – Germany – [email protected]–mainz.de
Goldstein Stanislaw Poland – [email protected]
Gretchko Valerij – Ukraine & Japan – [email protected]
Gubeladze Joseph – USA – [email protected]
Hryniv Rostyslav – Ukraine – [email protected]
Isoria Levan – Georgia – [email protected]
Jaskula Marian – Poland – [email protected]
Kadeishvili Tornike – Georgia – [email protected]
Kakabadze Mikheil – Georgia – [email protected]
Kartosia Alexander – Georgia – [email protected]
Kharanauli Anna – Georgia – [email protected]
Khujanov Ravshan – Uzbekistan – [email protected]
Kovtunenko Victor – Austria – [email protected]
Lordkipanidze David – Georgia – [email protected]
Naidyuk Yuri – Ukraine – [email protected]
Paichadze David – Georgia – [email protected]
Papikian Mihran – Armenia – [email protected]
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Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
26.
27.
28.
29.
30.
31.
Pirashvili Teimuraz – UK – [email protected]
Strasburger Aleksander – Poland – aleksander [email protected]
Tandaschwili Manana – Germany – [email protected]
Tarkhnishvili David – Georgia – david [email protected]
Tsurtsumia Olga – Georgia – [email protected]
Wang Kai – China & Germany – [email protected]
Invited Early Career Scientists
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
Bedianashvili Giorgi – Georgia – [email protected]
Chabashvili Levan – Georgia – [email protected]
Chikvinidze Besik – Georgia – [email protected]
Chkadua George – Georgia – [email protected]
Christian Michel – Georgia – [email protected]–sb.de
Esebua Ketevan – Georgia – qeti [email protected]
Gablishvili Lia – Georgia – [email protected]
Gogelia Lia – Georgia – [email protected]
Grzibovski Richard – Germany – [email protected]–sb.de
Hertsch Max Florian – Germany & Turkey – [email protected]
Inasaridze Niko – Georgia – [email protected]
Ismailov Vugar – Azerbaijan – [email protected]
Kantún-Montiel Gabriel – Mexico – [email protected]
Kardava Irakli – Georgia – [email protected]
Kobelyan Artur – Armenya – a [email protected]
Oleinikov Andriy – Uktraine – [email protected]
Palvelev Roman – Russia – [email protected]
Popiashvili Nino – Georgia – [email protected]
Sarkar Jayeb – India – [email protected]
Shukur Ali Alseraf – Belarus – [email protected]
Svanadze Maia – Georgia – [email protected]
Tavartkiladze Zurab – Georgia – [email protected]
Tephnadze George – Georgia – [email protected]
Tepoyan Vardan – Armenia – [email protected]
Tsaava Medea – Georgia – [email protected]
Tsutsunava Tamta – Georgia – [email protected]
Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015
27. Tutberidze Margarita – Georgia – [email protected]
28. Unlu Ozgun – Turkey – [email protected]
29. Zviadadze Shalva – Georgia – [email protected]
Other Invited Participants
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
Ashordia Malkhaz – Georgia – [email protected]
Boettcher Albrecht – Germany – [email protected]–chemnitz.de
Buchukuri Tengiz – Georgia – t [email protected]
Chagelishvili George – Georgia – [email protected]
Chitashvili Marine – Georgia – [email protected]
Chkadua Otar – Georgia – [email protected]
Curto Raul – USA – [email protected]
Davitashvili Tina – Georgia – t [email protected]
Epremidze Lasha – Georgia & US+AE – [email protected]
Esteban Maria – France – [email protected]
Inasaridze Hvedri – Georgia – [email protected]
Japaridze George – Georgia – [email protected]
Kaashoek Marinus – Netherlands – [email protected]
Kapanadze David – Georgia – [email protected]
Kereselidze Nugzar – Georgia – [email protected]
Kiguradze Ivan – Georgia – [email protected]
Knees Dorothee – Germany – [email protected]
Kokilashvili Vakhtang – Georgia – [email protected]
Kostenko Oleksiy – Ukraine & Austria – [email protected]
Kulikova Natalia – Russia – [email protected]
Kvesitadze George – Georgia – [email protected]
Kvinikhidze Alexander – Georgia – sasha [email protected]
Marsagishvili Tamaz – Georgia – [email protected]
Meskhi Alexander – Georgia – [email protected]
Ran Andre – Netherlands – [email protected]
Shargorodsky Eugene – UK – [email protected]
Sharvashidze George – Georgia – [email protected]
Shkalikov Andrey – Russia – [email protected]
Sigua Levan – Georgia – [email protected]
Speck Frank – Portugal – [email protected]
Spitkovsky Ilya – USA & UAE – [email protected]
Uhlig Frank – USA – [email protected]
Vasilevski Nikolai – Mexico – [email protected]
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Index
Akhalkatsi M., 11
Apakidze J., 12
Spitkovsky I. M., 28
Tandashvili M., 29
Tavartkiladze Z., 30
Bedianashvili G., 13
Berezhiani Z., 13
Uhlig F., 30
Chkadua G., 14
Wang K., 31
Doborjginidze N., 15
Gogelia N., 16
Gretchko V., 17
Gubeladze J., 18
Hertsch M. F., 19
Ismailov V., 20
Japaridze G.I., 24
Jaskuła M., 21
Johannesson H., 24
Kadeishvili T., 22
Kardava I., 23
Kartosia A., 23
Kimeridze M., 11
Malard M., 24
Megrelidze L., 30
Naidyuk Yu., 25
Pirashvili T., 26
Popiashvili N., 26
Sarkar J., 27
Speck F.-O., 27
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