booklet of program and abstracts

Humboldt Kolleg „SCIENCE IN GEORGIA: PERSPECTIVES OF DEVELOPMENT

AND THE ROLE OF HUMBOLDT FOUNDATION“July 4-6, 2015, Tbilisi, Georgia

PROGRAM AND ABSTRACTS

ORGANIZERS:

საქ

ართ

ველოს ჰუმბოლდტის კლ

უბი

* H

UM

BOLDT CLUB OF GEORGIA

*

Georgian Mathematical Union,

Georgian National Academy of Sciences

Georgian National Museum

Humboldt Club of Georgia

SPONSOR:

Alexander von Humboldt Foundation, Germany

Georgian NationalAcademy of Sciences

Georgian NationalMuseum

Georgian MathematicalUnion

Humboldt Clubof Georgia

HUMBOLDT KOLLEG

Science In Georgia:Perspectives of Development andthe Role of Humboldt Foundation

ABSTRACTS & PROGRAM

July 4-6, 2015, Tbilisi, Georgia

Organizers: Georgian Mathematical UnionGeorgian National Academy of Sciences,Georgian National MuseumHumboldt Club of Georgia

Sponsor: Alexander von Humboldt Foundation, Germany

Venue: Georgian National Academy of Sciences, Rustaveli Av. 52, TbilisiGeorgian 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), DavidLordkipanidze (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 ofGeorgia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Joni Apakidze, Neue Archaologische Ausgrabungen in Georgien (am Beispiel derTellsiedlung Tabakoni) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Giorgi Bedianashvili, The Koban necropolis: The Late Bronze-Early Iron Age col-lections 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 Piezo-electric Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Nino Doborjginidze, Language and Technologies: Problems and Challenges of Mod-ern Academic Georgian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Nino Gogelia, Zur linguistischen Erforschung rhetorischer Strategien im politischenDiskurs von Marion Grafin Donhoff . . . . . . . . . . . . . . . . . . . . . . . 16

Valerij Gretchko, Cultural Communication in the Framework of Yuri Lotmans Semi-otic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Joseph Gubeladze, Quantum Analysis of Normal Polytopes . . . . . . . . . . . . . 18

Max Florian Hertsch, Serenade for Nadia by Zulfu Livaneli - A modern TurkishRing Parable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Vugar Ismailov, Hilbert’s 13-th Problem and Approximation by NeuralNetworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Marian Jaskuła, Internationalization & Globalization of Science . . . . . . . . . . . 21

Tornike Kadeishvili, Homotopy Algebras, Applications in Mathematics and Physics 22

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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 andManagement of Software Package by Voice Commands in Georgian Language 23

Alexander Kartosia, The Fantastic City: The Linguistic Shaping and Re-shaping ofthe Georgian Cultural Scene in the first Third of the 20th Century . . . . . . . 23

Mariana Malard, George I. Japaridze, Henrik Johannesson, Synthesizing Majo-rana Zero Modes in a Quantum Wire using a Modulated Electric Field . . . . . 24

Yurii Naidyuk, Scientific Two-Way Collaboration with German Colleagues: fromPersonal Contacts through Intermediary of Alexander von Humboldt Founda-tion 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 Exampleof Georgian Literature) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Jaydeb Sarkar, Invariant and Wandering Subspaces of Reproducing Kernel HilbertSpaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Frank-Olme Speck, Sommerfeld Problems in Rn . . . . . . . . . . . . . . . . . . . 27

Ilya M. Spitkovsky, On Some Numerical Range Related Results Obtained whileWorking 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

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Humboldt Kolleg Tbilisi, Georgia July 4-6, 2015 Science in Georgia: Perspectives of development

and the role of Humboldt Foundation

P R O G R A M

July 3, Friday

Arrival day to Tbilisi

1500-1900 – Registration at the National Academy of Sciences (NAS) 1900 – 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 Chairman: Teimuraz Pirashvili 1000 : 1040 Maria Esteban- Programs supporting mathematical research in Europe

1040 : 1110 Coffee break

Room 1 Chairman: Teimuraz Pirashvili 1110 : 1150 Marian Jaskula – Internationalization and globalization of science (in

German) 1150 : 1230 Joseph Gubeladze – Quantum analysis of normal polytopes 1230 : 1400 Lunch

Rooms 1,2,3 1400 : 1600

Interdisciplinary Sessions with 30 minute talks. The sessions are orga-nized for those participants who did not participate in IWOTA. Deadline of sub-mission of abstracts is May 15. Program of sessions will be announced on May 20.

1600 : 1630 Coffee break 1630: 1800

Room 1 1800

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.

6

July 5, Sunday

Venue: National Museum of Georgia

Conf. Hall Chairman: Josef Gubeladze

900 : 940 Zurab Berezhiani – Dark side of the Universe-Opening windows to parallel worlds

940 : 1020 Teimuraz Pirashvili – Goodwillie-Taylor tower via relative homological algebra. Abelian case


Conf. Hall Chairwoman: Maria Esteban 1050 : 1110 Thomas Gamkrelidze – “Paradigms” in Linguistics 1110 : 1140 Alexander Kartosia Die "phantastische Stadt". Sprachliche Gestaltung und

Umgestaltung der georgischen Kulturszene im ersten Drittel des 20. Jahrhunderts (in German)

1140 : 1200 Marilyn Kelly-Buccellati – Excavations at Urkesh, Syria

1200 : 1240 David Lortkipanidze – Prehistory of Georgia 1240 : 1400 Lunch 1400 : 1500 Excursion in the National Museum 1500 : 1830 Excursion to Djvari & Mtsketa 1900 : 2300 Conference Dinner

July 6, Monday


Room 1 900 : 930

Opening ceremony of IWOTA 2015 and presentation of Humboldt Kolleg

Audience will be addressed by R. Duduchava, M. Kaashoek, G. Kvesitadze (Nat-ional Academy), V. Papava (I.Javakhishvili State University), Representativse of Embassy of Germany, Ministry of Education and Science, , etc.

930 : 1010 Joni Apakidze, Roland Duduchava, Alexander Kartosia-Support prog-rams of Alexander von Humboldt Foundation and activities of Humboldt Club Georgia

Room 1 Chairman: Marinus Kaashoek 1010 : 1110 Albrecht Boettcher – Toeplitz determinants and lattice theory (IWOTA

program)

Room 2 Chairman: David Lortkipanidze 1010 : 1050 Jony Apakidze – On recent excavations in Georgia (HK Prog.; in German) 1050 : 1140 Coffee break 1100 : 1900 Optional: Excursion to Kakheti (Signagi). Recommended for those

participants of Humboldt Kolleg, who did not attend IWOTA. For IWOTA-participants the same excursion is scheduled on July 8

Room 1 Chairman: Albrecht Boettcher 1140 : 1220 Frank Speck – Operator relations in boundary value problems (IWOTA prog.) 1220 : 1310 Andre Ran – Recent progress in operator theory (IWOTA program)

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Room 2

Chairman: Roland Duduchava

1140 : 1220 Dorothee Knees Global spatial regularity results for elasticity models with cracks, damage, contact and other nonsmooth constraints (IWOTA program)

1220 : 1310 Ilya Spitkowsky – Factorization of semi almost periodic matrices (IWOTA program)

1310 : 1500 Lunch

Rooms 1 - 11 1500 : 1700

Afternoons parallel sessions. Venue: Iv. Javakhishvili Tbilisi State University

11 Parallel Sessions in IWOTA program. 30 minute talks 1700 : 1730 Coffee break

Rooms 1- 11 1730 : 1900

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


Room 1 Session “Role of science and technology in society and public policy” Chairman: Marian Jaskula

1400 : 1430’ Andre Ran – Support for science, in particular mathematics, in The Netherlands

1430 : 1500 Frank Uhlig – Holistic Teaching and Learning Holistically 1500 : 1530 Yuri Naidyuk – Scientific two-way collaboration with German colleagues:

from personal contacts through intermediary of Alexander von Humboldt Foundation to European Research Programs

1530 : 1600 Lika Gablishvili – The role of globalization in Georgia-China's relations (in

German) 1600 : 1630 Coffee break

Room 1 Session “Role of informatic, science and technology in society” Chairman: Zurab Berezhiani

1630 : 1700 Tornike Kadeishvili – How to attract young people to science in Georgia 1700 : 1730 Irakli Kardava –Georgian Speech Recognizer in Famous Searching Systems and

Management of Software Package by Voice Commands in Georgian Language

https://plus.google.com/u/0/110698060991996840797?prsrc=4

8

Room 1 Session “Physics” Chairman: Zurab Berezhiani

1700 : 1730 Mariana Malard, George I. Japaridze and Henrik Johannesson,

Synthesizing Majorana zero modes in a quantum wire using a modulated electric field

1730 : 1800 Luka Megrelidze, Zurab Tavartkiladze, Radiative Neutrino Masses Generation via ‘Soft’ Lepton Number Violation

Room 2 Session “Mathematics” Chairman: Ilya Spitkovsky

1400 : 1430 Tornike Kadeishvili – Homotopy Algebras, Applications in Topology and Physics

1430 : 1500 Kai Wang – Dixmier trace of quotient module on bounded symmetric domains

1500 : 1530 Jaydeb Sarkar – Invariant and wandering subspaces of reproducing kernel Hilbert spaces

1530 : 1600 Vugar Ismailov – Hilbert's 13-th problem and approximation by neural networks


Chairman: Alexander Strasburger 1630 : 1700 Ilya Spitkovsky – On some numerical range related results obtained while

working with student in the USA and UAE

1700 : 1730 Frank Olme Speck– Sommerfeld problems in Rn

1730 : 1800 George Chkadua, Mixed Type Interaction Problem of Acoustic Waves and Piezoelectric Structures

Room 3 Session “Humanitarin subjects” Chairman: Alexander Kartosia

1400 : 1430 Manana Tandaschwili – Kartvelology and the challenges of 21-th century (in

German) 1430 : 1500 Nino Doborjginidze – Language and Technologies: Problems and Challenges

of Modern Academic Georgian (in German)

1500 : 1530 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

1530 : 1600 Nino Gogelia – Zur linguistischen Erforschung rhetorischer Strategien im politischen Diskurs von Marion Gräfin Dönhoff (in German)

1600 : 1630 Coffee break Chairman: Manana Tandaschwili

1630 : 1700 Maia Akhalkatsi & Mariam Kimeridze – Natura 2000 sensitive forest habitats of Georgia

1700 : 1730 Ketevan Esebua, Pikria Noniashvili – Grakliani Gora, Agriculture of Grakliani Gora in V-IV cc. bc

1730 : 1800 Giorgi Bedianashvili – The Koban necropolis: The Late Bronze-Early Iron Age collections from the Caucasus stored at French museums

Humboldt Kolleg Tbilisi, Georgia, July 4-6, 2015 9

A b s t r a c t s


Natura 2000 Sensitive Forest Habitats of GeorgiaMAIA AKHALKATSI1, MARIAM KIMERIDZE2

1 Institute of Botany, Ilia State University, Tbilisi, Georgia2 GSNE “Orchis”, Tbilisi, Georgia

email: maia−[email protected]

Natura 2000 forest habitat’s Directive is a Community legislative instrument in the field ofnature conservation that establishes a common framework for the conservation of wild speciesand natural habitats of Community importance. Natura 2000 sites cover about 20% of theEuropean 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 ofWork of Protected Areas of the Convention on Biological Diversity. The Directive is devel-oped on the bases of CORINE biotope classification determining codes and habitat types ofEurope, in particular involving the division of the latter into sub-types. According to Inter-pretation Manual habitat classification is based on plant community types. This informationis obtained from literature data of botanists of Georgia. 24 forest habitat types are identifiedfor Georgia. 18 belong to the biogeographical region – Forests of Temperate Europe. 6 habi-tat types belong to Mediterranean deciduous forests. There are habitats, which are identicalto 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 notconspecific. Therefore, some habitats, which are similar to the European habitat types, shouldbe 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 withKolkhic understory (Fagetafruticosacolchica); 2) Kolhketi broad-leaved mixed forest; 3) Bogwoodland Tilio-Acerionforests of slopes, screes and ravines; 4) Alluvial forests; 5) Alluvialforest with Adler trees (Alnusglutinosa)and ash tree (Fraxinus excelsior); 6) Riparian mixedforests; 7) Yew forest (Taxusbaccata); 8) Zelkova forest (Zelkovacarpinifolia); 9) BoxwoodForest (Buxuscolchica); 10) Sub-alpine birch krummholz. These conclusions could be consid-ered as recommendations of the national experts to the commission to add sensitive habitats tonature protection laws.


Neue Archaologische Ausgrabungen in Georgien(am Beispiel der Tellsiedlung Tabakoni)

JONI APAKIDZE

Sokhumi State University, Institute of Archaeology, Tbilisi, Georgia

email: [email protected]

Die Tellsiedlung Tabakoni befindet sich in Westgeorgien im Bezirk Zugdidi. Die Siedlungliegt ca. 15 Km von Schwarzmeerkuste entfernt in einem Wald. Die Landschaft, in der dieseSiedlung liegt, gehort zur Kolchis Niederung. Diese mehrschichtige, kunstliche Siedlung hateinen Durchmesser von 45 m und eine Hohe von 2,90 m. Sie ist von einem Wasserkanal um-schlossen, dies ist aufgrund der geo-klimatischen Bedingungen der kolchischen Tiefebene typ-isch fur solche Siedlungen. Das Archaologische Institut der Staatlichen Universitat Sokhumiund die Eurasien Abteilung des Deutschen Archaologischen Instituts fuhren hier im Rahmeneiner Institutspartnerschaft, welche von der Alexander von Humboldt-Stiftung gefordert undauch finanziell unterstutzt wird, seit 2011 archaologische Ausgrabungen durch.

Wahrend 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 Siedlungaus mittelbronzezeitlichen und zum Teil auch spaten fruhbronzezeitlichen fruhkolchischen (so-genannten protokolchischen), Spatbronze- und Fruheisenzeitlichen kolchischen und aus fruhan-tiken kolchischen Kulturschichten besteht. Die ersten Ergebnisse von 14C-Daten bestatigengut die chronologische Gliederung dieser mehrschichtigen Tellsiedlung. 2014 kamen in denArealen C und G relativ gut erhaltene Holzkonstruktionen der kolchischen Architektur zu Tage.Im nordlichen Teil des Areals G wurden in horizontaler Lage erhaltene Holzkonstruktionsrestegefunden. Im ubrigen Teil waren die Holzreste schrag in den Boden eingesetzt. Im gesamtenAreal C wurden ebenfalls Reste von Holzkonstruktionen gefunden.

Den Hauptanteil der Funde aus der Tellsiedlung Tabakoni stellt die Keramik. FruhkolchischeKeramik ist meistens in Form der sogenannten schwarzpolierten und “groben” Keramik vert-reten. Keramik dieser Zeit weist am Boden oft Textilabdrucke auf. Die kolchische Keramikder Spatbronze- und Fruheisenzeit hat meistens eine runde Form, sie ist meist braun oderschwarz, zum Teil auch grau. Das ubliche Dekor sind Rillen und Kreise. Diese Motive sindmanchmal auch mit Kammstempelmuster kombiniert. Typisch sind sogenannte “Vogelbrus-thenkel”, “Kniehenkel” und “zoomorphe” Henkel. Nicht selten fanden sich auch Kleinfundewie Sicheleinsatze aus Silex, Pfeilspitzen aus Silex, Spinnwirtel aus Ton, Anhanger aus Kera-mik, Klopfsteine und Mahlsteine. Es wurden auch einige Artefakte aus Bronze und Eisen ge-funden.

Die Tellsiedlung Tabakoni, die in auch diesem Jahr (2015) archaologisch und naturwis-senschaftlich weiter untersucht wird, hat fur die Erforschung, sowie die kulturelle und neuechronologische Interpretation der Siedlungen der Kolchis-Kultur eine wichtige Bedeutung alsgut stratifizierte Siedlung, die nach modernen Grabungsmethoden ausgegraben wird.


The Koban necropolis:The Late Bronze-Early Iron Age collections

from the Caucasus stored at French museumsGIORGI BEDIANASHVILI

Georgian National MuseumTbilisi, Georgia


In this presentation there will be discussed Ernest Chantres archaeological collections fromthe Koban necropolis, stored at the National Archaeological Museum of France, at Saint-Germain-en-Laye and the Confluences Museum in Lyon. The Koban necropolis, which wasexcavated by Chantre in 1881, is located in the North Caucasus. It has given its name to one ofthe 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 andunpublished, and organizes them in a systematic fashion. Typological classification of eachgroup of objects is examined and presented. These data are then compared with materialsfrom other parts of the Caucasus. The focus of presented research determines the culturalenvironment of the Koban necropolis in the Caucasus region, as objects from this site reflectcertain characteristic features of different regions of the Caucasus such as Colchis and ShidaKartli.

Dark Side of the Universe:Opening Windows to Parallel Worlds

ZURAB BEREZHIANI

Dipartimento di Fisica, Universita di L’Aquila, 67100 Coppito, L’Aquila, andINFN, 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 hiddenparallel world (or worlds) with exactly identical content of particles and their interactions thatwe have in ordinary particle sector. I shall discuss the scenarios how both ordinary and darkmatter fractions can be generated both simultaneously by the B − L and CP violating particleprocesses between ordinary and parallel worlds and possibilities of transformation of the ordi-nary 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].


References[1] Z. Berezhiani, Through the Looking-Glass: Alice’s Adventures in Mirror World. In:

I. Kogan Memorial Colection “From Fields to Strings: Circumnavigating TheoreticalPhysics”, Eds. M. Shifman et al., 3 (2005), 2147–2195 [arXiv:hep-ph/0508233].

Mixed Type Interaction Problem of Acoustic Waves andPiezoelectric Structures

GEORGE CHKADUA

King’s College London, Strand, London, United Kingdom


We investigate the mixed type transmission problem arising in the model of fluid-solidacoustic interaction when a piezo-ceramic elastic body (Ω+) is embedded in an unboundedfluid domain (Ω−). The corresponding physical process is described by boundary-transmissionproblem 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 describ-ing acoustic wave propagation. The physical kinematic and dynamic relations mathematicallyare described by appropriate boundary and transmission conditions. With the help of the poten-tial method and theory of pseudodifferential equations based on the Wiener–Hopf factorizationmethod the uniqueness and existence theorems are proved in Sobolev–Slobodetskii spaces andon the basis of asymptotic analysis, we establish almost the best Holder smoothness results forsolutions.

Such type of interaction problems of different dimensional fields appear in the mathematicalmodel of piezoelectric transducers. Further examples of similar models are related to phasedarray microphones, ultrasound equipment, inkjet droplet actuators, drug discovery, sonar trans-ducers, bioimaging, immunochemistry and acousto-biotherapeutics (see [1–3]).

In the paper [4] uniqueness and existence theorems of mixed type interaction problem ofacoustic waves and piezoelectric structures are stated without proof. The Dirichlet type andNeumann type interaction problems of acoustic waves and piezoelectric structures are studiedin [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.


[2] F. Josse, Z.A. Shana, D. E. Radtke, and D. T. Haworth, Analysis of piezoelectric bulk-acoustic-wave resonators as detectors in viscous conductive liquids. IEEE Trans UltrasonFerroelectr Freq Control 37 (1990), No. 5, 359–68.

[3] M. Thompson, C. L. Arthur, and G. K. Dhaliwal, Liquid-phase piezoelectric and acoustictransmission 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 physicalfields. 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 Struc-tures. Math. Methods Appl. Sci., 2014; doi:10.1002/mma.3210.

Language and Technologies: Problems andChallenges of Modern Academic Georgian

NINO DOBORJGINIDZE

Institute of Linguistic Studies, Ilia State UniversityTbilisi, Georgia

email: nino [email protected]

The development of scholarship in Georgia largely depends on the ability of academic Geor-gian 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 languageneeds to be documented to meet modern linguistic and technological standards. We need to cre-ate Georgian language modeling applications, morphology and syntactic modules and softwarefor parallel corpus and machine translation.

In this paper I aim to present the Georgian Language Corpus (GLC) developed at the Insti-tute of Linguistic Studies of Ilia State University during 2009-2014 (corpora.iliauni.edu.ge). Atpresent the corpus contains over 100 000 000 word forms and has two main sections, monolin-gual 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 atranslation corpus structured according to translation schools, i.e. the chronological and stylis-tic principle (pre-Athonite, Athonite, Antiochian, etc.) and source texts (cf. Greek - Georgian,Syriac - Georgian Christian Arabic Georgian, Armenian Georgian). The bilingual section in-cludes parallel corpora of Kartlis Tskhovreba (The Georgian Chronicle, a Georgian-Armeniancorpus) and Vepkhistkaosani (The Knight in the Panthers Skin, a Georgian-English corpus).


The rich language legacy is presented in the GLC not only from the perspective of historicalgrammar 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 functionsof the Georgian language, for integrating into contemporary academic discourses and in general,for developing the humanities in Georgia.

Zur linguistischen Erforschung rhetorischerStrategien im politischen Diskurs von Marion

Grafin DonhoffNINO GOGELIA

Staatliche Universitat SuchumiAssistenz-Professorin der Fachrichtung “Deutsche Philologie”

Tbilisi, Georgien


Seit es gesellschaftliche Institutionen gibt, die das Miteinander innerhalb einer sozialenGemeinschaft festlegen, gibt es auch politische Kommunikation, in einem weiteren Sinne auchoffentliche Kommunikation. Historisch betrachtet zeigt sich politische Kommunikation vorallem mundlich, als unmittelbare Kommunikation uber politische Themen und Sachverhalte.Man versteht unter “politischer Sprache” als Oberbegriff alle Arten offentlichen, institutionellenund privaten Sprechens uber politische Fragen, alle politiktypischen Textsorten sowie jedefur das Sprechen uber politische Zusammenhange charakteristische Weise der Verwendunglexikalischer und stilistischer Sprachmittel.

“Sprache der Politik” ist ein ernstzunehmender Gegenstand linguistischer Analyse. Alskennzeichnend fur die Sprache der Politik konnen genannt werden: Metaphernreichtum, haufigeVerwendung rhetorischer Figuren, pathetische Sprechweise, Diskursivitat, außerdem die reich-haltige Verwendung von Schlagwortern.

“Sprache der Politik” verfugt uber die sprachliche Inhalte, die im gemeinten Sprachge-brauchsbereich ausschlaggebend sind. Argumentationsanalytisch feststellbare Merkmale poli-tischen Sprachgebrauchs finden ihre Entsprechung uberall da, wo Sprache auch außerhalb derPolitik zu argumentativen Zwecken eingesetzt wird. Viele scheinbar spezifische politischeTextsorten finden Entsprechungen im außersprachlichen Bereich. Dies gilt vor allem fur allerechtsformigen Textsorten, aber auch fur Reden, programmatische Texte, Werbetexte oder Texteim publizistischen Bereich.

In meinem Vortrag handelt es sich um Formen argumentativen Sprachgebrauchs, die impolitischen Diskurs von Marion Grafin Donhoff in besonderer Intensitat auftreten. Anhand


exemplarischer Analyse einer ihrer Rede wird gezeigt, dass “der politische Diskurs” von Mar-ion Grafin Donhoff durch ein spezifisches Zusammenwirken von textgestalterischen Elementencharakterisiert ist, dass sich rhetorische Strategien als dominant erweisen und die gewunschteWirkung auf Offentlichkeit erzielen konnen.

Cultural Communication in the Frameworkof Yuri Lotman’s Semiotic Theory

VALERIJ GRETCHKO

Kobe University, Faculty of Intercultural StudiesKobe, Japan


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 insteadto 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 exacttranslation 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 acreative development of culture.

My paper investigates the question of the genesis and formation of Yuri Lotman’s model ofcommunication, discussing its theoretical implications for cultural research. I will show howthe basic idea that the semiotic, communicative, and cultural processes manifest themselves intwo 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. Itdemonstrates that the field of application of these models was gradually extended from the levelof 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 dynamicaspect which presupposes such forms of interaction as translation and dialogue. For possiblesources from which this approach has been developed, we can draw on both the theoreticalconception of dialogicity (Bakhtin) as well as neurophysiologic work on the asymmetry of thebrain hemispheres.


Quantum Analysis of Normal PolytopesJOSEPH GUBELADZE

SFSU, Mathematics Department, San Francisco, USA


Polytopes have fascinated humans since antiquity. Examples include diamonds and thepyramids of the ancient Egypt. In the contemporary natural sciences there is a ubiquity ofpolytopal shapes – be it physics, chemistry, or biology. The natural habitat of polytopes isobviously Euclidean geometry: polygons in the plane, Platonic solids in the space, and theirmore complex and higher dimensional counterparts. In the post ww2 mathematics polytopeshave found new life as connecting links between algebra and geometry, in the form of toricalgebraic geometry. This field can loosely be described as ‘geometry of formulas’, a venue inpure mathematics which eluded Hilbert’s vision of the future development of mathematics at thedawn of the 20th century. In toric geometry, systems of high degree multivariate polynomialsare encoded in the configurations of lattice points (i.e., points with integer coordinates) insideconvex polytopes. A central notion in the field is that of a normal polytope – it is a correctdiscrete 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, whichemploys techniques from commutative algebra and K-theory, we came to realize that the basiccontinuous vs. discrete dichotomy, just touched upon in the definition of normal polytopes, is achallenge in its own right. Systematic formal treatment of this dichotomy leads to a structurallyvery rich new mathematical object – an infinite dynamical space, which can be explored fromvarious complementary perspectives: number theoretic, topological, geometric. The full blownmathematical framework for exploring the continuous vs. discrete dichotomy is expected toconstitute a trilogy, of which the first is the recent joint preprint with my coauthors W. Brunsand M. Michałek [1]. This work studies the extent of distortion of the suggested discretizationof the continuum of Euclidean geometry: local singularities of the resulting space. The nextanticipated step should reveal large scale emergent trends, exhibited by quantum processes inthis 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 stepsare rather speculative and may well be several years away from being fully implemented. Butalready now one can ask whether this inquiry is confined exclusively to pure mathematics, orit has potential to provide a new formalism for tackling challenges the physical world poses tous. A possible fruitful interaction with experts in various fields, hinted at in [2], is still matterof 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.


[2] J. Gubeladze, Normal polytopes, in Proceedings of 22nd International Conference onFormal Power Series and Algebraic Combinatorics, San Francisco, 2010, pp. 4–8.http://math.sfsu.edu/fpsac/local−proceedings.pdf

Serenade for Nadia by Zulfu Livaneli -A Modern Turkish Ring Parable

MAX FLORIAN HERTSCH

Institute of Literary Studies, Hacettepe University, Department of German Language andLinguistics, Ankara, Turkey


Zulfu Livaneli’s novel: Serenade for Nadia provides a remarkable perspective in literaryanalysis, 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 anal-ogy to the ideal of modern, Turkish Enlightenment. Livaneli’s novel indicates a clear link toLessings drama: Nathan the Wise which has its climax in the so called Ring Parable. Lessingdescribes 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, Livanelihighlights 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 themain character Nathan the Wise, Livaneli initiates it through Professor Maximillian Wagnerwho 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 modernTurkish Ring Parable within the notion of Lessing’s Enlightenment.

References[1] A. Kaminsiki, Zulfu Livanelis Roman “Serenade fur Nadja” - Eine turkische Ringpara-

bel. 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 fur Nadja. Klett-Cotta Verlag, 2013.


Hilbert’s 13-th Problem and Approximationby Neural Networks

VUGAR ISMAILOV

Institute of Mathematics and Mechanics National Academy of Sciences of AzerbaijanBaku, Azerbaijan


The past two decades have seen a tremendous growth of interest in the MLP (multilayerfeedforward perceptron) model of neural networks. The application areas of this model is as di-verse 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 inneural 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 func-

tion of three and more variables can be represented by superpositions of continuous functionsof two variables.

Hecht-Nielsen was the first who noticed relationship of Hilbert’s 13-th problem to neuralnetwork theory. He showed that an arbitrary function can be implemented by a three layerneural network with appropriate activation functions. Girosi and Poggio pointed out that theKolmogorov’s solution is not useful, since the inner universal functions in the Kolmogorov su-perposition formula are highly nonsmooth and incomputable. This difficulty was overcome byKurkova by using staircase like functions of a sigmoidal type. These functions were constructedin a way that they can approximate any continuous function on any compact subset of the realline with an arbitrary accuracy. Kurkova’s results showed that an arbitrary continuous functioncan be approximated arbitrarily well by two hidden layer neural networks with an arbitrary sig-moidal activation function. However, the number of units in hidden layers needed to realizesuch approximation is exceedingly large. What if the hidden layers consist of a fixed numberof units? Is it possible to approximate every continuous function in this case? This questionwas first answered by Maiorov and Pinkus. They showed that there exists a sigmoidal, strictlyincreasing, analytic activation function such that two hidden layer neural networks with this ac-tivation function, d inputs, 3d neurons in the first hidden layer and 6d+ 3 neurons in the secondhidden layer can approximate any continuous multivariate function over any compact subset ofRd. Using the Kolmogorov superposition theorem and the ideas of Maiorov and Pinkus, weprove that for some nonanalytic but infinitely differentiable activation functions these numbersin the hidden layers can be reduced to d and 2d + 2 respectively.


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 thedeveloping of excellence in research and education through Internationalization]

MARIAN JASKUŁA

Department of Physical Chemistry & Electrochemistry, Faculty of Chemistry, JagiellonianUniversity, Cracow, 30-060 Poland


The international cooperation is one of the most important factors deciding on global progressin sciences. This dependence is especially strong to see in natural & life sciences where col-laborate often big various groups of researchers coming from different countries. As a goodexamples may be the papers published on the field of nuclear physics where the number ofauthors is sometimes twenty or thirty. The science of today requires collaboration of manyspecialists.

In the lecture the experiences of Jagiellonian University, the oldest Polish university withlong 650 years history are mentioned. The international cooperation played very important rolein middle ages that was unfortunately forgotten and only in recent decades, is undergoing arenaissance. The internalization of sciences starts with the internationalization of teaching andexchange of students. The very important role play here the numerous programmes of Euro-pean Community like as Erasmus or Leonardo. The author of the lecture who is a professorfor chemistry at the Jagiellonian University is the best personal example of importance of sci-entific international contacts: to be fellowship holder abroad and to host foreign students andresearchers in Poland.

The Jagiellonian University has today more than 184 bilaterale agreements concerning theinternational cooperation on the field of science and 1404 agreements connected with exchangeof the students (mainly ERASMUS). Four percent of our staff are foreigners and this number isgrowing.

Very important role play in the process of internationalization various scientific societiesand non governmental organizations. The may be directly or indirectly connected with the fi-nancing of science and exchange. As the examples should be here mentioned the Foundation forPolish Science (as organization which support financially the common projects and exchange),and for example Societas Humboldtiana Polonorum, that joined over 1300 Polish recipients ofHumboldt fellowship and try to inspire Humboldtians for developing and deepening of suchcontacts. The author of the lecture was many years the general secretary of this society as wellas ambassador scientist of the Humboldt-Foundation and in the talk his experiences will bepresented.


Homotopy Algebras, Applications in Mathematicsand Physics

TORNIKE KADEISHVILI

TSU A. Razmadze Mathematical Institute


Homotopy Algebra is the general title for algebraic objects for which classical axioms aresatisfied just up to certain homotopies which also are included in the structure. Particular ex-amples of such objects are: A∞-algebra with measured nonassociativity, B∞-algebra with mea-sured noncommutativity, L∞-algebra with measured deviation from Jacobi identity etc. Thesealgebras show up in various problems and are more informative than classical objects. Thatis why now a days they are intensively used in various problems of topology, geometry, al-gebra. Last years homotopy algebras become useful in physics, namely in string theory andquantization problems.

How to Attract Young People to Science in GeorgiaTORNIKE KADEISHVILI

TSU A. Razmadze Mathematical Institute


The problem mentioned in the title becomes more and more actual in our country. We aregoing to present various examples showing that now a days the involvement in internationalscientific community is most attractive argument for talented yang people.


Georgian Speech Recognizer inFamous Searching Systems and Management of

Software Package by Voice Commands in Georgian LanguageIRAKLI KARDAVA

Sokhumi State University, Department of Computer Science Tbilisi, Georgia


The speech recognition system and creation of program Software based on it is one ofthe important components of natural language computer modelling. For example, the popularGoogle Voice system, by which the word or sentence pronounced by a person is automaticallywritten in textual form, in Google’s Search system field for given language by using alreadyrealized 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 automat-ically Georgian words or sentences pronounced individually and get texts in the appropriatelanguage by using Google Translate. Program management is performed with Georgian voicecommands.

The ‘Fantastic City’: The Linguistic Shapingand Re-shaping of the Georgian Cultural Scene

in the first Third of the 20th CenturyALEXANDER KARTOSIA

Ivane Javakhishvili Tbilisi State University


Following the Revolution 1917 and the outbreak of Civil War in Russia, many Russianartists found refuge in Georgia. The Georgian capital became a ‘Fantastic City’. The mostinfluential Georgian author of that period, Grigol Robakidze, wrote 1919: “Tiflis is pervaded byan aesthetical perception of the world. ... People coming from different nations and cultures arebrothers in art. We believe in that new International. Here in Tiflis must be laid the foundationsfor its construction.”

The literary life of the ‘Fantastic City’ took a multilingual form. The meaning of ‘mul-tilingual’ is two-fold. On the one hand books appeared with texts in Georgian, Russian andArmenian; on the other hand the so-called ‘Zaum language’ of Futurism developed, whosemain aim was the alienation from ‘normal’ language.


After the occupation of Georgia by the Russian Red Army in 1921, the protest against theoccupation and annexation led to a linguistic re-shaping of the cultural scene in the ‘Fantas-tic City’. Again in two respects: firstly all Georgian authors including those who previouslysometimes 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 tradi-tional (archaic) form.

Synthesizing Majorana Zero Modes in a QuantumWire Using a Modulated Electric Field

MARIANA MALARDa, GEORGE I. JAPARIDZEb,c, HENRIK JOHANNESSONd

a University of Brasilia, 70904-910 Brasilia-DF, Brazilb 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


We explore a scheme for engineering a one-dimensional spinless p-wave superconductorhosting Majorana zero modes, using an all-electric setup with a spin-orbit coupled quantumwire in proximity to an s-wave superconductor. The crossing of the Fermi level with only asingle spin-split quasiparticle band is ensured by employing a periodically modulated electricfield, which, assisted by the electron-electron interaction in the wire, opens a gap at two of thespin-orbit shifted Fermi momenta. While the smallness of the gap makes the scheme impracticalfor present-day semiconductor devices, it may be realized using spin-orbit coupled fermioniccold atoms.


Scientific Two-Way Collaboration with GermanColleagues: from Personal Contacts through

Intermediary of Alexander von HumboldtFoundation to European Research Programs

YURII NAIDYUK

B.Verkin Institute for Low Temperature Physics and Engineering of the National Academy ofSciences of Ukraine, Kharkiv, Ukraine


International scientific cooperation plays a key role in basic and applied science. New part-nership usually starts with personal contacts, however, to intensify and extend collaborationhelp of some foundations and institutions are of particular importance. Alexander von Hum-boldt foundation plays this role, strengthening regional and interdisciplinary links between thescientists. Along with individual financial support, diverse Alexander von Humboldt foundationawards and projects (i.e. Institutspartnerschaft program), organizing Humboldt-Kolloquien andHumboldt-Kollegs are significant to broaden ones outlook and to find new research directionsand partners. My report will contain an overview of scientific cooperation of our Departmentat the Institute of Low Temperature Physics and Engineering of the National Academy of Sci-ences of Ukraine mainly with German partners supported by Alexander von Humboldt founda-tion. The cooperation led to recognition of our original point-contact spectroscopy method inGermany and other western countries and finally in participation in the European FrameworkProgram 7.

Finally, in my talk, I will represent to your Humboldt Club Ukraine, which plays a signif-icant role in number of activities to intensify collaboration with German scientists. HumboldtClub Ukraine distributes actual information, which helps Ukrainian scientists to start and main-tain collaborative projects with German scientists and find a proper way for funding. HumboldtClub Ukraine organizes various events with Alumni, participation in the meetings, Humboldtlectures, Humboldt Kollegs etc.


Goodwillie–Taylor Tower via Relative HomologicalAlgebra. Abelian Case

TEIMURAZ PIRASHVILI

University of Leicester, UK


Based on basic properties of relative homological algebra, we give very simple constructionof Goodwillie–Taylor tower for functors T : C → Ch. Here C is a category with zero objectand 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)

NINO POPIASHVILI

Ivane Javakhishvili Tbilisi State UniversityTbilisi, Georgia


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, sharingthe existing experience and multicultural environment. The intercultural nature of literatureenables us to identify a number of layers in fiction. These layers might be felt and reflected ina text equally or by various degrees of intensity Authors layer National layer Interculturallayer.

The intensity of the above mentioned definitions may be completely individual in case of aparticular author and his texts. Intercultural layer might be of primary importance, whereas insome cases national layer, or authors identity and texts created by personal experience (and notinspiration provoked by national experience) might dominate.

Georgian literature has a long tradition, thus we can discuss national characteristic of theliterature as well as its intercultural one. The paper deals with national and intercultural issuesof literature on the example of Georgian literature.


Invariant and Wandering Subspaces of ReproducingKernel Hilbert Spaces

JAYDEB SARKAR

Indian Statistical Institute, Statistics and Mathematics Unit,Bangalore, India


We discuss brie y recent and not so recent results about invariant subspaces (Beurling-Lax-Halmos type theorem) and analytic models and operator positivity of bounded linear operatorson Hilbert spaces. We also discuss some related results on wandering subspaces in both oneand several variables.

Part of this talk is based on joint work with Monojit Bhattacharjee and Dinesh K. Keshar.

Sommerfeld Problems in Rn

FRANK-OLME SPECK

Tecnico, Universidade de Lisboa, Departamento de Matematica, Portugal


Motivated by the classical Sommerfeld diffraction problem we consider interface problemsin 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 intotwo parts, Σ and Σ′, with different transmission conditions of first and second kind. These twoparts are half-spaces of Rn−1 (half-planes for n = 3) and more general sets in the first part of thepaper. The aim of this work is to construct explicitly resolvent operators acting from the inter-face data into the energy space H1(Ω). The approach is based upon a factorization conceptionfor Wiener-Hopf operators (according to the interface equations), the so-called Wiener-Hopffactorization through an intermediate space, that includes Simonenko’s well-known “general-ized factorization of matrix functions in Lp spaces” and avoids an interpretation of the factorsas unbounded operators. In a natural way, we meet non-isotropic Sobolev spaces which reflectthe 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.


[2] F.-O. Speck, Wiener-Hopf factorization through an intermediate space. Integral Equa-tions Operator Theory 82 (2015), no. 3, 395–415.

On Some Numerical Range Related ResultsObtained while Working with Students

in the USA and UAEILYA M. SPITKOVSKY

New York University Abu Dhabi, UAE andThe 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 isthe range F (A) of the quadratic form 〈Ax, x〉 on the unit sphere of Cn. It is a convex compactsubset of C; more specifically, F (A) is the convex hull of a certain algebraic curve of class nassociated with A. For n = 2 this curve is an ellipse (degenerating into two points, when A isnormal), yielding the classical elliptical range theorem. The classification of possible resultingshapes for n = 3 was provided by Kippenhahn [4], with the tests developed in [3]. A (somewhatimplicit) description of all admissible curves for arbitrary n is given in [2], but further researchof 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 ofarbitrary size but structured in a very specific way. They are partially published [1], and partiallystill 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. Operatorsand Matrices 6 (2012), 607–611.

[3] D. Keeler, L. Rodman, I. M. Spitkovsky, The Numerical Range of 3× 3 Matrices. LinearAlgebra and Its Applications 252 (1997), 115–139.

[4] R. Kippenhahn, Uber den Wertevorrat einer Matrix. Mathematichse Nachrichten 6 (1951),193–228.


Kartvelology and the Challenges of the 21st CenturyMANANA TANDASHVILI

Institute of Empirical Linguistics, Goethe University Frankfurt, Germany


Kartvelology isprimarily understood as a subject of research in linguistics which representsan interesting discipline with many peculiar facets especially for linguistic typology. On theother hand, Kartvelology represents the nationalphilology of Georgia, thus requiring specialcare and well-scheduled measures for its further development locally and abroad. Linguistics inthe 21st century is characterized by a more practical use of its research materials, i.e., languagedata. Today, linguistic research results are converted with the help of modern technologies intopractically usable products such eLexicons, spell checkers, so-called smart technologies, etc. Atthe same time, we witness a thorough technologisation of linguistic research processes in thecreation of large speech corpora, which enable modern linguists to explore issues much moresystematically 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 Eu-ropean and even world-wide linguistic society became possible, Kartvelology still remainedenclosed in itself. Post-Soviet Georgia has not succeeded yet in a thorough abolition of Sovietstructures or in the modernization of the education system, let alone the establishment of mod-ern research methods and themes. Instead, the country has remained stuck in the processes ofpolitical, 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 internation-alization, namely a) the transfer of knowledge with respect to modern theoretical thought andresearch methods, b) the creation of speech corpora for the Georgian language, c) scientificexchange through international cooperation projects, d) the introduction of modern standards inresearch and teaching, and e) the development of a promotion program for the new generationof students in form of an international Graduate School in Kartvelology. Judging from 15 yearsof experience, I may state that this should be possible through cooperation between Georgianand foreign funding institutions.

In my paper, I will thematize the above mentioned aspects of the further development ofKartvelology in the 21st century on the basis of activities that we have carried out at GoetheUniversity Frankfurt since 2000, summarizing the results of 12 international projects we haveundertaken in cooperation with 17 Georgian research institutes and universities, among themthe Georgian National Corpus project and the Batumi summer schools program.


Radiative Neutrino Masses Generationvia ‘Soft’ Lepton Number Violation

ZURAB TAVARTKILADZE, LUKA MEGRELIDZE

Center for Elementary Particle Physics, Ilia State University,Tbilisi Georgia


Within SUSY framework, we propose neutrino mass generation via radiative mechanism.Within considered mechanism, the lepton number violation is originating from the SUSY break-ing sector. These require to have physics, beyond the MSSM, near the TeV scale. We give sev-eral explicit realizations of the proposed mechanism and besides some novelties discuss variousphenomenological implications.

Holistic Teaching and Learning HolisticallyFRANK UHLIG

Department of Mathematics and Statistics, Auburn University,Auburn, AL 36849-5310, USA


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 morestandard top-down approach to cooperative teaching and learning. The holistic approach leadsto, 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 taughtclass. The teacher’s role is to guide and adjust a class’s course as the subject matter, experienceand - 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 usesSavory’s ’holistic management principle’ for wide and comprehensive teaching and learning asis necessitated in complex natural environments such as education and the human growth andmaturation process.

The practice of teaching holistically is exemplified by one extended undergraduate classexample that studies the definition and measurement of angles in Rn from first principles ofboth Geometry and Linear Algebra.


Dixmier Trace of Quotient Moduleon Bounded Symmetric Domains

KAI WANG

School of Mathematical Sciences, Fudan University,Shanghai, China


In this talk we will concern quotient module of rank 1 on bounded symmetric domain. Weprove that the restriction operator with polynomial symbol is L n,∞ essentially normal, andestablish a Diximer trace formula on the quotient module. The talk is based on joint work withProf. Harald Upmeier.


Humboldt Kolleg, Tbilisi, Georgia July 4-6, 2015Science in Georgia: Perspectives of development

and the role of Humboldt Foundation

List of Participants

Invited Humboldt Fellows

1. 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

10. 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]


26. 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. 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.de6. Esebua Ketevan – Georgia – qeti [email protected]. Gablishvili Lia – Georgia – [email protected]. Gogelia Lia – Georgia – [email protected]. Grzibovski Richard – Germany – [email protected]–sb.de

10. Hertsch Max Florian – Germany & Turkey – [email protected]. Inasaridze Niko – Georgia – [email protected]. Ismailov Vugar – Azerbaijan – [email protected]. Kantun-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]


27. Tutberidze Margarita – Georgia – [email protected]. Unlu Ozgun – Turkey – [email protected]. Zviadadze Shalva – Georgia – [email protected]

Other Invited Participants1. Ashordia Malkhaz – Georgia – [email protected]. Boettcher Albrecht – Germany – [email protected]–chemnitz.de3. 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]

10. 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]

Index

Akhalkatsi M., 11Apakidze J., 12

Bedianashvili G., 13Berezhiani Z., 13

Chkadua G., 14

Doborjginidze N., 15

Gogelia N., 16Gretchko V., 17Gubeladze J., 18

Hertsch M. F., 19

Ismailov V., 20

Japaridze G.I., 24Jaskuła M., 21Johannesson H., 24

Kadeishvili T., 22Kardava I., 23Kartosia A., 23Kimeridze M., 11

Malard M., 24Megrelidze L., 30

Naidyuk Yu., 25

Pirashvili T., 26Popiashvili N., 26

Sarkar J., 27Speck F.-O., 27

Spitkovsky I. M., 28

Tandashvili M., 29Tavartkiladze Z., 30

Uhlig F., 30

Wang K., 31

36

booklet of program and abstracts

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