section 1: department of mathematics, inter-discipline …eprints.tsu.ge/251/1/2015_eng.pdf ·...
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SECTION 1: DEPARTMENT OF MATHEMATICS, INTER-DISCIPLINE (MATHEMATICS, COMPUTER SCIENCES) ....................................................................................................................... 13
On the approximation of conjugate functions by the Cesáro means of conjugate Fourier series ......................... 14 Teimuraz Akhobadze ............................................................................................................................................... 14
On some local properties of the conjugate function and the modulus of continuity of k-th order ....................... 15 A.Danelia ................................................................................................................................................................. 15
Nonemptiness of intersection of sets and existence of Chebyshev’s center ......................................................... 16 G. Chelidze............................................................................................................................................................... 16
On the summability of series with respect to rearranged block-orthonormal systems ........................................ 17 Givi Nadibaidze ........................................................................................................................................................ 17
On the constancy of signs and range of Fourier–Haar coefficients ....................................................................... 18 L.Gogoladze and V.Tsagareishvili ........................................................................................................................ 18
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Fourier coefificients of some classes of function with respect to general ortonormal systems ............................ 19 L.Gogoladze and V.Tsagareishvili ........................................................................................................................ 19
On the absolute convergence of the coeficients of double Fourie -Haar series ............................................. 20 Rusudan Meskhia ................................................................................................................................................... 20
Estimates for imaginary powers of the Laplace operator in variable Lebesgue spaces ......................................... 21 Tengiz Kopaliani
a, Amiran Gogatishvili
b, Alberto Fiorenza
g ..................................................................................... 21
On the number of representations of a positive integer by Gaussian binary quadratic forms .............................. 22 Teimuraz Vepkhvadze ............................................................................................................................................. 22
On Schur’s polynomials for isotropy irreducible homogeneous Riemann space .................................................. 23 R.M. Surmanidze ..................................................................................................................................................... 23
On the space of generalized theta-series with quadratic forms of five variables ................................................. 24 KetevanShavgulidze ................................................................................................................................................ 24
Differential equations defined by algebraic functions.......................................................................................... 25 Vakhtang Lomadze .................................................................................................................................................. 25
Some properties OF r-maximal sets and Q1,N- reducibility ................................................................................ 26 Roland Omanadze ................................................................................................................................................... 26
Three-Valued Multi Modal Epistemic Lukasiewicz logics ...................................................................................... 27 Revaz Grigolia
a, Antonio Di Nola
b .......................................................................................................................... 27
Some Combinatorial Problems Connected with the Functions Defined on the Infinite Sets ................................. 28 Archil Kipiani............................................................................................................................................................ 28
On one Problem of Reduction .............................................................................................................................. 29 PetreBabilua,BesarionDochviri, VakhtangJaoshvili ................................................................................................. 29
Limit Distribution of the Integral Square Deviation of Two Bernoulli RegressionFunctions .................................. 30 Elizbar Nadaraya
a, Petre Babilua
b............................................................................................................................ 30
European option hedging in the financial model with disorder moment ............................................................. 32 Khechinashvili Zaza.................................................................................................................................................. 32
On the Well-Posedness of the Cauchy Problem for One Class of Neutral Functional Differential Equation with Distributed Prehistory ......................................................................................................................................... 34
Tamaz Tadumadze .................................................................................................................................................. 34
On Asymptotic Behavior of Solution of Emden-Fowler Differential Equations with Deviating Argument ............ 35 Koplatadze Roman .................................................................................................................................................. 35
About structure of the bulk links wich appear after cutting of Generalized Mobius-Listings bodies .................... 36 Ilia Tavkhelidze ........................................................................................................................................................ 36
On a Model of Cusped (Tapered) Micropolar Prismatic Shells ............................................................................. 37 George Jaiani ........................................................................................................................................................... 37
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On a Cusped Double-Layered Prismatic Shell ....................................................................................................... 38 Natalia Chinchaladze ............................................................................................................................................... 38
On Myasnikov-Remeslennikov problem in the class of nilpotent R-groups .......................................................... 39 Mikheil Amaglobeli .................................................................................................................................................. 39
The cycle -symmetric problem of plane elasticity theory with partially unknown boundary. .............................. 40 Nana Odishelidze..................................................................................................................................................... 40
On one dimensional reduction algorithm for elastic multi-structure containing multilayer shell ......................... 41 Gia Avalishvili
a, Mariam Avalishvili
b ....................................................................................................................... 41
On Some Parallel Algorithms for Numerical Solving of Multidimensional Linear Problems of Mathematical Physics ................................................................................................................................................................. 42
Hamlet Meladzea,TinatinDavitashvili
b ..................................................................................................................... 42
About splitting four-layer semi-discrete scheme for an evolutionary equation into two-layer schemes ............. 43 Jemal Rogava
a , Romeo Galdava
b, David Gulua
c...................................................................................................... 43
A method of solution of a nonlinear integro-differential equation ...................................................................... 44 Jemal Peradze.......................................................................................................................................................... 44
The existence of a solution and the convergence of the approximate method for the nonlinear Timoshenko system ................................................................................................................................................................. 45
V.Odisharia .............................................................................................................................................................. 45
SECTION 2 - DEPARTMENT OF COMPUTER SCIENCES ............................................................ 46
The Automatic Synthesis of the Functional Programming Language Haskell's Programs ..................................... 47 Natela Archvadze .................................................................................................................................................... 47
Bicategorial Calculus and Logic-Topological Nets ................................................................................................. 50
for Massively Parallel Systems ............................................................................................................................. 50 Alexander Gamkrelidze
a, Revaz Kurdiani
b ............................................................................................................. 50
Bi-criteria Vehicle Routing Problem for Extreme Environment ............................................................................ 51 Bezhan Ghvaberidze ................................................................................................................................................ 51
Overview of supporting business decision-making systems ................................................................................. 52 Archil Varshanidze ................................................................................................................................................... 52
Decision Making Aggregation Operators for Intuitionistic and Hesitant Fuzzy Environments .............................. 53 Gvantsa Tsulaia ....................................................................................................................................................... 53
Continuous Dependence of the minimum of the Bolza type functional on the initial data in nonlinear optimal control problems with distributed delay ............................................................................................................. 54
Phridon Dvalishvili ................................................................................................................................................... 54
APPLICANT'S TEMPERAMENT AND NATURE’S TYPE RECOGNITIONBY USING FUZZY INFORMATION TECHNOLOGY ............................................................................................................................................................................ 55
Teimuraz Manjafarashvili ........................................................................................................................................ 55
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Business start-up Decision Making in OB-IDSS system ......................................................................................... 56 Otar Badagadze ....................................................................................................................................................... 56
Possibilistic OWA Aggregations in the Investment Decision Making .................................................................... 57 Otar Badagadze ....................................................................................................................................................... 57
The algorithm of the behavior of endless automaton in random medium ........................................................... 58 Tariel Khvedelidze ................................................................................................................................................... 58
Monte-Carlo Simulation Method for Generation of Possibility Distribution in Fuzzy Vehicle Routing Problem ... 59 Gia Sirbiladze ........................................................................................................................................................... 59
Using of Modified Version of the Hill’s Algorithm in Symmetrical Cryptography ................................................. 60 Zurab Kochladze ...................................................................................................................................................... 60
Matrix One-Way Function and Tropical Cryptography ........................................................................................ 61 Richard Megrelishvili ............................................................................................................................................... 61
Using User Behavior Data in Retrieval Algorithm Improvement .......................................................................... 62 Gela Besiashvilia
a, Maia Archuadze
b, Manana Khachidze
c ................................................................................... 62
Modern Retrieval Methods in Data Base ............................................................................................................. 63 Maia Archuadze
a, Manana Khachidze
b .................................................................................................................. 63
Calculating PageRank Using the Matrix Method .................................................................................................. 64 Manana Khachidze
a, Maia Archuadze
b, Gela Besiashvili
c ..................................................................................... 64
On Web Servic e Programming Issue ................................................................................................................... 65 Magda Tsintsadze .................................................................................................................................................... 65
Artificial Neural Network Model for Recovery of Nerve Signals Using Dijkstra’s Algorithm ................................. 66 Lela Mirtskhulava, Gillian Pearce ............................................................................................................................ 66
PERFORMANCE ANALISYSIS OF MULTICAST ROUTING PROTOCOLS ..................................................................... 67 Irma Aslanishvili ...................................................................................................................................................... 67
Application of Virtual Computers at the Process of Training in Network Technology and Operation Systems ..... 68 Maka Odiladze, Mery gegechkori, Nino narimanidze, Vano bakhtadze, Maia archuadze, Tamar burchuladze ..... 68
Ms Office Solutions Development (office2013, office365) ................................................................................... 69 Julieta Gagloshvili .................................................................................................................................................... 69
About Addressing in IPv6 Network ...................................................................................................................... 70 Papuna Qarchava, G.Asanishvili .............................................................................................................................. 70
Software package ANSYS 15.0 for some problems of mechanics ......................................................................... 71 Bidzina Midodashvili ............................................................................................................................................... 71
Meaning of georgian word-building in search engines for indexing ..................................................................... 72 Lasha Maraneli, Ana Sikharulidze ............................................................................................................................ 72
Hybrid Data Structures ........................................................................................................................................ 73
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Nikoloz Grdzelidze ................................................................................................................................................... 73
Modeling of some mathematical programming problemsand their solution via AMPL interface ......................... 74 Koba Gelashvili
a, Irina Khutsishvili
b ....................................................................................................................... 74
AMPL in Excel via SolverStudio ............................................................................................................................ 75 Koba Gelashvili
a, Julieta Gagloshvili
b .................................................................................................................... 75
Georgian Corpus Syntactic Tagger ........................................................................................................................ 76 Liana Lortkipanidze ................................................................................................................................................. 76
MADM Approach in hesitant fuzzy environment to making Optimal Investment Decisions................................. 77 Irina Khutsishvili ...................................................................................................................................................... 77
SECTION 3- DEPARTMENT OF GEOGRAPHY ............................................................................... 78
Georgian Geographical School: Modern Challenges ............................................................................................. 79 Nodar Elizbarashvili ................................................................................................................................................. 79
ZONING OF SOME CITRUS CULTURE - FROST RESISTANT TANGERINE TYPES IN WEST GEORGIA USING LANDSCAPE-MULTIFACTOR METHOD .................................................................................................................. 80
Zurab Seperteladze1, Eter Davitaia
1, Tamar Aleksidze
1, Nino Rukhadze
1, Giorgi Gaprindashvili
1,2 ....................... 80
ZONING OF FROST RESISTANT TANGERINE TYPES IN WES GEORGIA USING LANDSCAPE-MULTIFACTOR METHOD 81 Eter Davitaia ............................................................................................................................................................ 81
Climate Change and Frequency, Duration and Intensity of Extreme Weather and Climate Events Over Georgia . 82 Mariam Elizbarashvili
1 I.Keggenhoff
2, N.Kutaladze
3, E.Elizbarashvili
4, M.Tatishvili
4, L.King
2, R.Meskhia
3, N.Gogia
1,
B.Kikvadze5, D.Mikava
5 ............................................................................................................................................ 82
Topical issues of geography of mountain regions of Georgia ............................................................................... 83 Nodar Elizbarashvili ................................................................................................................................................. 83
Deforestation issues in Georgia ........................................................................................................................... 84 Neli Jamaspashvili N.N. Beruchashvili, L. Beruchashvili ........................................................................................ 84
Forest resources reproduction methods at the modern stage ............................................................................. 85 Neli Jamaspashvili N.N. Beruchashvili, L. Beruchashvili ......................................................................................... 85
Aspects of Sex Secondary Ratio in Georgia .......................................................................................................... 86 Giorgi Meladze ........................................................................................................................................................ 86
Samtskhe-Javakheti vegetation and related some of the current issue................................................................ 87 Robert Maglakelidze ............................................................................................................................................... 87
Ecological Indices of Winter Wheat under Climate Change .................................................................................. 88 Maia Meladze .......................................................................................................................................................... 88
The Historical Transformations of Dariali Section of Georgia's State Border According to the Cartographic Sources ............................................................................................................................................................................ 89
Dali Nikolaishvili1, Tevaz Tolordava
2 ........................................................................................................................ 89
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The Influence of Geographic Factors on the Assessment of the Georgia's Landscapes Sensitivity ....................... 90 Lia Matchavariani, Dali Nikolaishvili ........................................................................................................................ 90
Waste of stable organic substances (TransPOP) and their pollutants in agricultural plots of field (on the example of Kakheti region) ................................................................................................................................................ 91
Besik Kalandadze1, Rolf -Alexander Düring
2, Elbai Babaev
3 .................................................................................. 91
Degraded agricultural land mapping, GIS analysis and pine groves recovery (the example of Tusheti) ................ 92 Tengiz Gordeziani
1, Tsiala bekuraidze
1, David Svanidze
1, Manana Sharashenidze
1, Rusudan Elizbarashvili
1,
Nikoloz Inashvili 1 .................................................................................................................................................... 92
The possible reform of the calendar: is the result of geographical regulatories? ................................................. 93 Tsetsilia Donadze ..................................................................................................................................................... 93
The natural features of Georgia: problems and perspectives ............................................................................... 94 Giorgi Dvalashvili ..................................................................................................................................................... 94
Some Aspects about Geoecological Conditions of Kakheti Region ....................................................................... 95 Tinatin Nanobashvili ................................................................................................................................................ 95
Probabilistic assessment of vulnerability of riverside ......................................................................................... 96 Davit Kereselidze
1, Vazha Trapaidze
1 ...................................................................................................................... 96
The Marine Strategy Framework Directive (MSFD) implementation in the Black Sea for improving the monitoring of the marine environment ( Project – EMBLAS, first phase) ............................................................................... 97
Kakhaber Bilashvili1, David Kereselidze
1, Vazha Trapasidze
1 ,Vakhtang Gvakharia
2, Nino Machitadze
2 ........ 97
Methodology of calculation of sanitary-ecological discharge of the river ............................................................ 98 Vazha Trapaidze
1, Davit Kereselidze
1, Kakhaber Bilashvili
1, Giorgi Bregvadze
1 ...................................................... 98
The impact of the geographical environment on distribution of radio waves (Case of the South Caucasus) ....... 99 Lamzira Lagidze 1, Nino Paichadze 1 ....................................................................................................................... 99
Influence of the beginning of the year on relation and trend between the river flow and precipitations .......... 100 Giorgi Bregvadze ................................................................................................................................................... 100
Calculation of the sediment load of the river Dzirula (Ubisa) by using the energetical priciples......................... 101 Merab Alaverdashvili
1, Darejan Kiknadze
1, Nunu Tsintsadze
1, Nestan Khupenia
1, Nana Kokaia
1 ........................ 101
The reservoirs ecological problems and their solution on the example of Tbilisi sea ......................................... 102 Nodar Tsivtsivadze1, Lamzira Lagidze1, Nargizi Motsonelidze1, Giorgi Ivanovi1 ................................................ 102
SECTION 4- DEPARTMENT OF ELECTRIC AND ELECTRONIC ENGINEERING ................ 103
Extension of the method of auxiliary sources for the eigenvalue problem of the Laplace operator in case of space periodic boundaries ........................................................................................................................................... 104
David Kakulia a Giorgi Ghvedashvili
b ..................................................................................................................... 104
Modern Electronic Measurement Devices Design and Application for Uznadze Psychological Set Theory Experimental Investigations .............................................................................................................................. 105
Lev Gheonjian1, Maya Kalahdarishvili
2, Dmitry Nadirashvili
2, David Imnadze1, George Kapanadze
1 ................... 105
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Effect of NMR Echo Enhancement of Nuclei of Half-Metalli Compound in Applied Magnetic Fields .................. 106 Ts. Gavasheli
a , G. Mamniashvili
b , А. Аkhalkatsi
c , G. Ghvedashvili
a , Т. Gegechkori
b ....................................... 106
Modeling of Elelctronic System for Fuel Pressure Control .................................................................................. 107 Gheonjian , I. Oganezova , B. Khvitia, R. Jobava .................................................................................................... 107
Dielectrophoresis - based cnt technology for fets .............................................................................................. 108 Giorgi Aroshvili
a .................................................................................................................................................... 108
SECTION 5- DEPARTMENT OF GEOLOGY .................................................................................. 110
Hydrothermal mineralization process and geological conditions of its occurrence in Javakheti plateau late Cenozoic dolerites ............................................................................................................................................. 111
Bezhan Tutberidze, Mariam Akhalkatsishvili ........................................................................................................ 111
Sedimentological and Paleoichnological Study of the Lower Cretaceous Sediments of the River Aragvi Basin .. 112 Zurab Lebanidze .................................................................................................................................................... 112
Studying of the Stability of Supportive Gravimetric Point Pedestal of Tbilisi ..................................................... 113 Guram Kutelia
1, Evgeni Sakvarelide
2 ..................................................................................................................... 113
Petrology of Early Jurassic Volcanism Products in Kakheti over the Alazani River and Prospects of their Utilization as Building- and Face-Stone Material (by the Example of the Stori River Basin) ............................... 114
Karlo Aqimidze, Bezhan Tutberidze, masters: Temur Jgushia, Aleksandre Skhiladze, Giorgi Khachapuridze ....... 114
SECTION 6-DEPARTMENT OF CHEMISTRY .............................................................................. 116
Catalytic synthesis of amides from aldoximes .................................................................................................... 117 A.Koridze*, O. Lekashvili, N. Batiashvili ................................................................................................................. 117
Our studies on chirality, chiral recognition mechanisms and separation of enantiomers in 2014 ...................... 118 B. Chankvetadze .................................................................................................................................................... 118
Siloxane based solid polymer electrolyte membranes ....................................................................................... 120
O.Mukbaniani a,b
, J.Aneli b
, E. Markarashvili a,b
, T. Tatrishvili a,b
, I. Esartia a,b
, N. Jalagonia a,b
, D.Otiashvili a,b
............................................................................................................................................................................... 120
Study of Thermophysical Properties of Antibiocorrosive Coatings Based on Modified Polymeric Matrices..... 121 N.Lekishvili, Kh. Barbakadze, M.Kobiashvili, N.Kokiashvili, D.Petviashvili, T.Machaladze ......................................... 121
Some new findings in the field of syntheses of indole-containing systems. ................................................... 122 I. Chikvaidze, Sh. Samsonya, N. Chikvaidze, D.Kadzrishvili, T.Giorgadze. ........................................................ 122
Study of Structural Changes of Water Droplets Confined in the Polyoxyethylen (4)Lauril Ether Reverse Micelles .......................................................................................................................................................................... 123
M.Rukhadze........................................................................................................................................................... 123
Kinetics of heterogeneous oxidation of methane ....................................................................................... 124 G. Bezarashvili, M. Tsotniashvili, M.Kekenadze ................................................................................................... 124
Characterization of Izomers from Point of View of Mathematical chemistry .................................................. 125
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M. Gverdtsiteli ....................................................................................................................................................... 125
Obtaining of Barium hydroarsenate on the basis of Arsenic-containing wastes ............................................... 126 K. Giorgadze .......................................................................................................................................................... 126
Some new data in condensed four nuclear indole systems ................................................................................ 127 M.Trapaidze, T.Iashvili, A. Gurgrnidze, K. Museridze .......................................................................................... 127
Sulfur and Chlorine in Tkibuli hard coal ............................................................................................................. 128
N.Takaishvilia, G. Supatashvilia............................................................................................................................. 128
Study on Separation of Enantiomers of Antimycotic Drugs by Using Polysaccharide-Based Chiral Columns under polar-organic and reversed-phase conditions .................................................................................................... 129
M.Karchkhadze A. Mskhiladze 2,L.Chankvtadze 1, A. Dadianidze1, B.Chankvetadze 1 .......................................... 129
Synthesis of Nitroso Group Containing N-Glycosilamines ............................................................................... 130 N.Sidamonidze, R. Gakhokidze, R. Vardiashvili, M.Nutsubidze ............................................................................. 130
Synthesis and Study of Antimony (V) Containing Borates .................................................................................. 132 L.Turiashvili, B.Jioshvili .......................................................................................................................................... 132
Tribological Properties of Antibacterial Polymer Materials ........................................................................... 133
W.Brostow 1
, S.Brumbley 2
, M. Gakhutishvili 1, 4
, N.Hnatchuk 1
, J. Youngblood 3 ,
S.Pokharel 3
. .................... 133
Processes in the fuel cell working on the hydrogen sulfide .............................................................................. 134 E. Tskhakaia ............................................................................................................................................................ 134
Increasing the Concentrations of Hydrogen Sulphuride by Using of membrane Methods and technologies ...... 135 R.Khositashvii ......................................................................................................................................................... 135
Synthesis of some mono- and di-adamantane fragment containing dipeptides via Ugi- reaction. ..................... 136
D.Zurabishvili a, T. Bukia a, M. Lomidze a,U.Kazmaierb,S.msoniya a. ...................................................................... 136
Synthesis of novel chiral sulfoxides and investigation of relationships between enantioselectivity and chemical structure in high-performance liquid chromatography ....................................................................... 137
R. Kakava, B.Chankvetadze ................................................................................................................................... 137
Investigation of enantiomer separations in high-performance liquid chromatography with polysaccharide-based chiral selectors and reversed-phase eluents ........................................................................................... 138
Z. Shedania. B. Chankvetadze ................................................................................................................................. 138
Investigation of influence of nonionic additives on the water structure confined AOT reverse micelles .......... 139 T. Butkhuzi ............................................................................................................................................................. 139
Investigation of the Microenvironment in Reverse Micelles by Ultraviolet-Spectroscopy on the Basis of Molecular Probe ................................................................................................................................................ 140
N. Msareulishvili .................................................................................................................................................... 140
Synthesis some of 5(6)-(1-adamantyl)-2-ami no(aminomethyl)benzimidazoles, 5(6)-amino-, alk(aryl)oxy-2-(1-
adamantyl)benzimidazoles . .............................................................................................................................. 141
D.Zurabishvili a, M.Lomidze b, I.Gogolas hvili b, T. B uk ia b, M. Soselia b,M. Trapaidze b, S. Samsoniya b. ..................... 141
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Composites on the basis of wood waste products and polyorganosiloxanes ..................................................... 142
J.Aneli a
, G. Buzaladze b
, E.Markarashvili a,b
, T. Tatrishvili a,b
, I.Esartia a,b
, L. Kalatozishvili a
, D.Otiashvili a,b
, O.
Mukbaniani a,b
...................................................................................................................................................... 142
Arsenic in Coal of Tkibuli ................................................................................................................................. 143 N. Labartkava , G. Supatashvili ............................................................................................................................ 143
Macrocyclic Receptor and Small Peptide Models in Neurodegenerative Diseases and New Bioactive Peptidomimetics ................................................................................................................................................ 144
L. Arabuli ............................................................................................................................................................... 144
HPLC de term ination o f p olyphenols i n wines a n d p arts o f c luster o f a u t o c h t h o n o u s Ge o r gi a n r e d gr a p e s ............................................................................................................................................................... 145
N. Beridze , A. Shalashvili, B. Chankvetadze .................................................................................................... 145
HPLC de termination o f p olyphenols i n wines a n d p a r t s o f c l u st e r o f a u t o c h t h o n o u s Ge o r gi a n wh i t e gr a p e s ............................................................................................................................................................... 146
E. Tsutsqiridze, A. Shalashvili, B. Chankvetadze ............................................................................................. 146
Synthesis of Di(2,9-benzimidazol-2-yl)benzo[e]pyrrolo[3,2-g] indole................................................................. 147
T.Shonia,,
Sh. Samsoniya; M. Trapaidze; A.Gurgenidzee ..................................................................................... 147
Separation of enantiomers of chiral sulfoxides with chloro-substituted tris phenylcarbamates of cellulose as chiral selectors in high-performance liquid chromatography ............................................................................. 148
M.-l. Konjaria, ( Supervisor: B. Chankvetadze ) ..................................................................................................... 148
Looking for Highest Possible Selectivity of Enantioseparations In High-Performance Liquid Chromatography .......................................................................................................................................................................... 149
T.Khatiashvili .......................................................................................................................................................... 149
Separation of enantiomers of chiral sulfoxides with methyl-and chloro-methyl-substitued tris-phenylcarbamate of cellulose as chiral selectors in high-performance liquid chromatography ...................................................... 150
N.Shashviashvili, (Supervisor: B. Chankvetadze ) ............................................................................................... 150
SECTION 7- DEPARTMENT OF BIOLOGY ................................................................................... 151
Nucleolus in Motion: Contraction of Intra- and Peri-nucleolar Condensed Chromatin Induces Relocalization of FC/DFC Assembly during the Selective Inhibition of rRNA Synthesis .................................................................. 152
P. Tchelidze1 , A. Benassarou2 , H. Kaplan2 , M-F. O’Donohue2 , E. Elias2 , L. Lucas2 , C. Terryn2 , L. Rusishvili1 , G. Mosidze1 , N. Lalun2 , D. Ploton2 ..................................................................................................................... 152
Immunohistochemical study of changes in rats hippocampus in condition of halothane anesthesia with midazolam premedication ................................................................................................................................. 153
E. Bakuradze1,2, I. Modebadze1,2, N. Bedineishvili1, M. Berulava3, Z. Vadachkoria4, L. Dzidziguri4, D. Dzidziguri1,2 .......................................................................................................................................................... 153
CMV seropositivity in different Ethnical Groups of Georgia ............................................................................... 154 N. Chikadze, N. Mitskevich, T. Tsertsvadze, N. Gachechiladze.............................................................................. 154
Has ever Brahmaea ledereri Rogenh. inhabited the Colchis refugium unlike the Hyrcan refugium? .................. 155
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Arnold Gegechkori................................................................................................................................................. 155
Botanical diversity of heidelbergcement's quarryes in georgia (dedoplitskaro, kavtiskhevi,bgardabani) ........... 156 Shamil Shetekauri .................................................................................................................................................. 156
Hydrobiological investigation of Sagarejo fishery ponds .................................................................................... 157 Zelimkhan Kereselidze ........................................................................................................................................... 157
Endemic and Caucaso-Anatolian Species of Genus Rosa (f. Rosaceae) of Flora Meskheti and Javakheti (Lesser Caucasus) ........................................................................................................................................................... 158
Nana Barnaveli ...................................................................................................................................................... 158
Determination of the level of Genome stability in atherosclerosis .................................................................... 159 Maia Gaiozishvili, Tamar Buadze, Teimuraz Lezhava ............................................................................................ 159
The influence of metalls on somatic recombination and chromosomal fragility in different aged individuals and correction of disorders with Epitalon ................................................................................................................. 160
Tinatin Jokhadze, Tamar Buadze, Nikoloz Baratashvili ......................................................................................... 160
Different approaches in treatment of prostate tumors ...................................................................................... 161 Nana Kotrikadze .................................................................................................................................................... 161
Plant conservation using in vitro technologies ................................................................................................... 162 Mariam Gaidamashvili, Eka Khurtsidze ................................................................................................................. 162
Developing of an optimal conditions for in vitro propagation of potato ............................................................ 163 Ana Gogichaishvili, Mariam Gaidamashvili ........................................................................................................... 163
The role of flavonoids from Saperavi in regulation of hippocampal-related functions .................................... 164 Nanuli Doreulee ..................................................................................................................................................... 164
Influence of orexin-A on epileptiform activity in the hippocampus of laboratory white rats ............................. 165 Nanuli Doreulee,
ა Butsiko Chkhartishvili,ა Manana Chikovani,ა Besarion Partsvaniaბ .......................................... 165
Early postnatal feeding of rats with flavonoids from Saperavi improves spatial memory and stimulates
neurogenesis in the dentata gyrus of the hippocampus. .................................................................................... 166 Mariam Kurasbediani, Roza Bukia, Ekaterine Mitaishvili, Nanuli Doreulee ............................................................... 166
SECTION 8- DEPARTMENT OF PHYSICS ,INTER-DISCIPLINE (PHYSICS, BIOLOGY ..... 167
Measurement of the analysing power in proton-proton elastic scattering at small angles ................................ 168 M.Tabidze
a,b, N.Lomidze
b, Z.Bagdasarian
b,c, D.Chiladze
a,c, A.Kacharava
c, G.Macharashvili
b,c, D.Mchedlishvili
b,c,
M.Nioradzeb .......................................................................................................................................................... 168
Self-adjoint extension procedure in the relativistic equations ........................................................................... 169 Teimuraz Nadareishvili
a,b Anzor Khelashvili
b ........................................................................................................ 169
Split Quaternions and Particles in (2+1)--Space ................................................................................................. 170 Merab Gogberashvili ............................................................................................................................................. 170
Matrix that saves written information by optical indication .............................................................................. 171
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Tengiz Kamushadze, Sh.Mirianashvili,N.Rtveleishvili,D.Machavariani,Z.Razmadze ............................................. 171 Semiconductor Physical Institute, Iv. Javakhishvili Tbilisi State University, ChavchavadzeAve. 3 ........................ 171
Obtaining of ZnMnTe/ZnMnTeO structures by RBQE technological method ...................................................... 172 M. Sharvashidze, T. Butkhuzi, N. Gapishvili, L. Trapaidze,T. Khulordava, E. Kekelidze, L. Aptsiauri ..................... 172
Novel Magnetic Resonance Technique to Detect Magnetoelectric Coupling in Multiferroic Materials .............. 174 A. Shengelaya, D. Daraselia, D. Japaridze .............................................................................................................. 174
p-type CuCrO2: theoretical and experimental study of defect creation ............................................................. 175 M. Boshta
1 , T. Tchelidze
2 , M. Neumann-Spallart
3 , E. Chikoidze
3 .................................................................... 175
Amiran Bibilashvili, Zurab Kushitashvili, Zurab Jibuti ............................................................................................ 176
Determination of the magnetic anisotropy constant of nanoparticles using measurements of the low-temperature heat capacity ................................................................................................................................ 177
Archil Ugulava, S. Chkhaidze, Sh. Kekutia, M. Verulashvili .................................................................................... 177
Investigation of the magnetization process of the strong anizotropic nanoparticles in the solid-state matrix ... 178 Simon Chkhaidze, A. Ugulava, M. Verulashvili ...................................................................................................... 178
Investigation ion waves in quantum Fermi liquid using Novel quantum kinetic equation .................................. 179 Grigol Peradze ....................................................................................................................................................... 179
The magnetorotational instability in differentially rotating plasma flows ......................................................... 180 George Mamatsashvili
a ........................................................................................................................................ 180
Plasma physics of condensed matter ................................................................................................................. 181 Nodar Tsintsadze ................................................................................................................................................... 181
Some aspects of the statistical thermodynamics of magnetized Fermi gas ........................................................ 182 Nodar Tsintsadze
a,b , Levan Tsintsadze
b , Ketino Sigua
b ...................................................................................... 182
Investigation of the processe realized in closed electron shall Particle collisioins. ............................................ 183 R. Lomsadze
a, M. Gochitashvili, N. Mosulishvili
a, D.Kuparashvili
a and R. Kezerashvili
b,c....................................... 183
Ionization and ionic fragmentation precision measurements of the components of a sample using chromatograph mass - spectrometric device ..................................................................................................... 184
R. Lomsadze, M. Gochitashvili, D.Kuparashvili, N.Tsiskarishvili and G. Takadze ................................................... 184
Dissociation, dissociative excitation end ionization processes for N2 and O2 molecules by electron bombardment ................................................................................................................................................... 185
M. Gochitashvilia, R. Lomsazde
a, O.Taboridze
a, D. Kuparashvili
a, N.Mosulishvili
a, R. Kezerashvilib .................... 185
Optical Properties of the Particle Trapped by Ellipsoidal Confinement Potential ............................................... 186 Z.S. Machavariani .................................................................................................................................................. 186
Exciton confined in the potential well of ellipsoidal shape ................................................................................ 187 T. Kereselidze ........................................................................................................................................................ 187
Nonlinear generation of zonal flows and large scale magnetic fields by ULF waves and modeling of mutual transformation of these waves in the ionosphere, analysis of satellite data ...................................................... 189
Oleg Kharshiladze a , Khatuna Chargazia
b , Revaz Chanishvili
b ............................................................................ 189
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Annual Report of the “Computational Physics” Institute’s scientific activity (2014) ........................................... 190 Revaz Zaridze ......................................................................................................................................................... 190
Scaling laws of convective perturbations in astrophysical shear flows ............................................................... 191 A. G. Tevzadze
a,R. G. Chanishvili
b,c, G. D. Chagelishvili
b,c, E. S. Uchava
a,b,c, and G. R. Khujadze
d ....................... 191
Elene Uchava and Alexander Tevzadze ................................................................................................................. 192
Chromosphere spicule Doppler velocities and half width asymmetry of variation ............................................. 193 D. Khutsishvili
a,b, Nana Shatashvili
a , Vazha Kulidzanishvili
b ................................................................................. 193
Beltrami-Bernoulli Equilibria in Astrophysical Plasmas with Degenerate Electrons............................................ 194 Nana Shatashvili
a,b and V.I. Berezhiani
b,c , S.M. Mahajan
d .................................................................................. 194
Effect of Ascorbin Acid (Vitamin C) on the ESR spectra of the red and black hair: pheomelanin free radicals are not always present in the red hair ..................................................................................................................... 195
Eduard Chikvaidze, Maia Topeshashvili ................................................................................................................ 195
Progress of the nanophasic and quantum biophysics in Georgia: Research results for the period of 2003–2014 196 D.E. Khoshtariya, M. Makharadze, T. Dolidze, M. Shushanyan, S. Uchaneishvili, T. Tretyakova, N. Shengelia, T. Partskhaladze, D. Waldeck, S. Rondinini, R. van Eldik ........................................................................................... 196
Biophysical Mechanisms of Impact of antibiotics on bacteria. Nanotechnology of cooking nanoparticles with drugs.................................................................................................................................................................. 198
Tamaz Mdzinarashvili, Irina Papukashvili, M. Khvedelidze, N. Shengelia, E. Shekiladze, N. Turkadze ................. 198
The biophysical investigation of the same chemical composition of phospholipids made by liposomes ............ 200 Eka shekiladze, Tamaz Mdzinarashvili, Mariam Khvedelidze ................................................................................ 200
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Section 1: Department of Mathematics, Inter-discipline
(Mathematics, Computer Sciences)
Mathematical Analysis Theory of Probability and Mathematical Statistics Algebra-Geometry Differential Equations Mechanics Math. Logic and Discrete Structures Numerical Analysis and Computing technologies
http://conference.ens-2015.tsu.ge/en/page/program/4http://conference.ens-2015.tsu.ge/en/page/program/5http://conference.ens-2015.tsu.ge/en/page/program/6http://conference.ens-2015.tsu.ge/en/page/program/7http://conference.ens-2015.tsu.ge/en/page/program/14http://conference.ens-2015.tsu.ge/en/page/program/15
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Mathematical Analysis
On the approximation of conjugate functions by the Cesáro means of conjugate Fourier
series
Teimuraz Akhobadze
e-mail:[email protected]
Departament of mathematics, Faculty of exact and natural sciences,
Ivane Javakhishvili Tbilisi state university,
Address: 1, Chavchavadze Ave., 0179 Tbilisi, Georgia
It is well known that if the deviation from f of partial sums of trigonometric Fourier series of a function
f in the space [0,2 ]pL (1 )p has a certain order, then the same order has the deviation from f
of its conjugates. In general, this fact is not true in the case 1p or .p
In thеadditional conditions the assessments of the deviations of Cesaro means of conjugate trigonometric
Fourier series from the corresponding conjugate functions in the spaces of continuous and locally
integrable functions are given.
Analogous problems are considered for the multiple cases.
References
[1]Ch.J.Vallee-Poussin, Lesons sur l’approximation des fonctions d’une variable reelle, Paris, (1919).
[2]I.Nisimura, On the approximation by Casáro mean of Fourier series, Bull.Kyushu Inst. Tech.(1955),
11-18
mailto:[email protected]
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On some local properties of the conjugate function and the modulus of continuity of k-th
order
A.Danelia
e-mail:[email protected]
Departament of mathematics, Faculty of exact and natural sciences,
Ivane Javakhishvili Tbilisi state university,
Address: 1, Chavchavadze Ave., 0179 Tbilisi, Georgia
In this paper we study a local smoothness of the conjugate functions of several variables in the space of
continuous functions. The direct estimates are obtained and exactness of these estimates are established
by proper examples.
mailto:[email protected]
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Nonemptiness of intersection of sets and existence of Chebyshev’s center
G. Chelidze
e-mail:[email protected]
Departament of mathematics, Faculty of exact and natural sciences,
Ivane Javakhishvili Tbilisi state university,
Address: 1, Chavchavadze Ave., 0179 Tbilisi, Georgia
Chebyshev center of a bounded set of Banach space is defined as the center of the radius of smallest ball
which contains given set. For the bounded set of Banach space it was defined the numerical parameter,
which describes the deviation of the shape of the set from spherical one. In the present paper we prove the
following theorem: If Banach space is such that for every bounded set there exists a Chebyshev center of
it, then the intersection of embedded bounded closed sets is nonempty if the upper limit of numerical
parameters of sets is grater then 1/2 .
mailto:[email protected]
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On the summability of series with respect to rearranged block-orthonormal systems
Givi Nadibaidze
Department of Mathematics, Iv. Javakhishvili Tbilisi State University, University str. 13
Below a question connected with the problems of almost everywhere summability of series with respect
to rearranged block-orthonormal systems are considered.
Let kN be increasing sequences of natural numbers and
1,k k kN N , )1( k .
Let n be a system of functions from 2 0,1L . The system n will be called a k -orthonormal
system if 2
1n , 1,2,...n and , 0i j , for , ki j , i j , )1( k .
In this paper the conditions are established for te sequence kN when there exists a rearrangement of
functions of the block-orthonormal system n such that in certain conditions on na we have
summability a. e. of series 1
( )nn
n
a x
with respect to rearranged k -orthonormal system n .
mailto:[email protected]
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On the constancy of signs and range of Fourier–Haar coefficients
L.Gogoladze and V.Tsagareishvili
e-mail: [email protected] , [email protected]
Department of Mathematics of Iv. Javakhishvili state university
University str. 2 Georgia, Tbilisi 0186
We investigate the relation between the properties of functions and their Fourier–Haar coefficients. We show that for some classes of functions Fourier–Haar coefficients have constancy signs and ranges. In 1964, B. I. Golubov proved that if f (x) ∈ C(0, 1), then its Fourier–Haar coefficients have constant signs, when f(x) is a nonincreasing function on [0, 1] and in some cases those coefficients have certain range. We continue investigation of the properties of functions which follow from the behaviour of their
Fourier–Haar Coefficients.
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Fourier coefificients of some classes of function with respect to general ortonormal systems
L.Gogoladze and V.Tsagareishvili
e-mail: [email protected] , [email protected]
Department of Mathematics of Iv. Javakhishvili state university
University str. 2 Georgia, Tbilisi 0186
It is well known that if f(x) ∈ L(0; 1) is an arbitrary function then its Fourier coefficients with respect to general orthonormal systems (ONS) may belong only to . Thus in the general case it is impossible to estimate these coefficients by moduli of continuity or moduli of smoothness of the given functions. The
conditions are found which should be satisfied by ONS so that the coefficients of some classes of
functions can be estimated by module of continuity or module of smoothness of these functions.
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On the absolute convergence of the coeficients of double Fourie -Haar series
Rusudan Meskhia
e-mail : [email protected]
Department of Mathematics. Faculty of Exact and Natural Sciences
.I.Javakhishvi li Tbilisi State University, 2.University str. ,Tbilisi 0186,Georgia
The absolute convergence of the coefficients of double Fourier-Haar series is considered.The
sufficient conditions for the absolute convergence of double Fourier-Haar series are
established in terms of the modulus of variation of a function.
mailto:[email protected]
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Estimates for imaginary powers of the Laplace operator in variable Lebesgue spaces
Tengiz Kopaliania, Amiran Gogatishvilib, Alberto Fiorenzag
e-mail: [email protected]
a Department of Mathematics of Iv. Javakhishvili Tbilisi State University
2, University Str., Tbilisi 0146, Georgia
b
Institute of Mathematics of the Academy of Sciences of the Czech Republic
Zitna 25 , 115 67 Prague 1, Czech Republic g
Dipartimento di Costruzioni e Metodi Matematici in Architettura
Universit di Napoli Via Monteoliveto, 3 I-80134 Napoli, Italy
We study some estimates of norms in variable exponent Lebesgue spaces for singular integral
operators that are imaginary powers of the Laplace operator in ℝ n . Using the Mellin transform argument, fromthese estimates we obtain the boundedness for a family of maximal operators in
variable exponent Lebesgue spaces, which are closely related to the (weak) solution of the wave
equation.
References
A. Fiorenza, A. Gogatishvili, T. Kopaliani, Estimates for imaginary powers of the Laplace operator in variable
Lebesgue spaces and applications, J. Contemp. Math. Anal. 49 (2014), no. 5, 232–240
mailto:[email protected]://www.ams.org/mathscinet/search/journaldoc.html?cn=J_Contemp_Math_Analhttp://www.ams.org/mathscinet/search/publications.html?pg1=ISSI&s1=326877
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On the number of representations of a positive integer by Gaussian binary quadratic forms
Teimuraz Vepkhvadze
e-mail: [email protected]
Department of Mathematics, Faculty of Exact and Natural Sciences,
Iv.Javakhishvili Tbilisi State University, 3.Chavchavadze Av., Tbilisi 0179
Using modular properties of generalized theta functions with characteristics by means of the analytical
theory of quadratic forms, we obtain formulae for the number of representations of a positive integer by
certain primitive Gaussian binary quadratic forms.
mailto:[email protected]
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23
On Schur’s polynomials for isotropy irreducible homogeneous Riemann space
R.M. Surmanidze
e-mail: [email protected]
Mathematics department, Ivane Javakhishvili Tbilisi State University
We consider one class of isotropy irreducible homogeneous Riemann spaces M , where the
subgroup is of the type simple Lie algebra 1, nAn [1]. Studied the Schur’s polynomials for tensor
squared and cube of irreducible representations connected with given [2], [3].
References
[1]. O. V. Manturov, Homogeneous Riemannian spaces with an irreducible rotation group. (Russian)
Trudy Sem. Vektor. Tenzor. Anal. 13 (1966), 68-145.
[2]. A. Barut, R. Raczka, Theory of Group Representations and Applications. Polish scientific publishers,
Warszawa 1977.
[3]. W. Fulton, Young Tableaux with Applications to Representation Theory and Geometry. Cambridge
University Press, 1997.
[4]. R. M. Surmanidze, Tensor invariants and homogeneous Riemann spaces, Journal of Mathematical
Sciences, November, 2013, Vol. 195, Issue 2, pp 245-257.
mailto:[email protected]
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On the space of generalized theta-series with quadratic forms of five variables
KetevanShavgulidze
e-mail: [email protected]
Department of Mathematics
Faculty of exact and natural sciences
Iv. Javakhishvili Tbilisi State University
The spherical polynomial with quadratic form of five variables is constructed. The basis of the space of
this spherical polynomial is established.The space of generalized theta-seriesis considered.
REFERENCES
1. F. Gooding, Modular forms arising from spherical polynomials and positive definite quadratic forms, J.
Number Theory 9, pp.36-47, 1977.
2. K. Shavgulidze, On the dimensions of some spaces of generalized theta-series, Lithuanian
Mathematical J. 53, pp.235-240, 2013
mailto:[email protected]
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Differential equations defined by algebraic functions
Vakhtang Lomadze
e-mail: [email protected]
Mathematics Department, I. Javakhishvili Tbilisi State University, Georgia
The class of ordinary linear constant coefficient differential equations is naturally embedded into a wider
class by associating differential equations to algebraic curves.
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Some properties OF r-maximal sets and Q1,N- reducibility
Roland Omanadze
e-mail: [email protected]
Department of Mathematics, I.Javakhishvili Tbilisi State University
1, Chavchavdze Ave., 0218 Tbilisi, Georgia
Tennenbaum (see, [3, p.159]) defined the notion of -reducibility on stes of natural numbers as follows: a set is -redusible to a set (in symbols: ) if there exists a computable function such that for
every (where denotes the set of natural numbers),
( ) .
We say in this case that via . If via a computable function such that for all ,
( ) ( ) and ⋃ ( ) is computable, then we say that is -reducible to
, and denoted . The notion of -reducibility was introduced by Bulitko in [1].
Our notation and terminology are standard and can be found in [3 ].
Theorem 1. There exists two c.e. sets having no c.e. least upper bound on the -reducibility ordering.
If is any noncomputable c.e. set, a nontrivial splitting of is a pair of disjoint noncomputable c.e. sets
such that .
A nontrivial splitting of is a Friedberg splitting (see, [2]) if for every c.e. is not c.e., then each of , is not c.e. .
A c.e. set is -maximal if ̅ is infinite and for every computable , either ̅ or ̅ ̅ is finite.
Theorem 2. Suppose that , is a Friedberg splitting of r-maximal set, a (A) and
b ( ) . Then for all c.e. sets C, D a (C, D b) we have C D.
A set is hemi r-maximal (see, [2]) if there are a -maximal set and a nontrivial splitting of
such that .
Theorem 3. The
References
[1] V.K.Bulitko, On ways of characterizing complete sets, Math. USSR, Izv. 38 (1992), 2.
[2] R.G.Downey and M.Stob, Automorphisms of the lattice of recursively enumerable sets: Orbits.
Advances in Mathematics, 92 (1992).
[3] H.Rogers, Theory of recursive functions and effective computability. McGraw-Hill Book Co., New
York, 1967.
mailto:[email protected]
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Three-Valued Multi Modal Epistemic Lukasiewicz logics
Revaz Grigolia a, Antonio Di Nola
b
e-mail: [email protected]. [email protected] a Mathematical logic and discrete structures, Faculty of Exact and Natural Sciences, Iv,
Javakhishvili Tbilisi State university, Chavchavadze av., 1 b Department of mathematics, University of Salerno, Via Giovanni Paolo II, 132, Italy
We introduce new logics - multimodal epistemic three-valued Lukasiewicz logics EŁ3(n), the langu-age
of which contains the following connectives: , , , , , and □i , ◊i (i = 1, ... , n). We suggest the
following schemata of axioms for EŁ3(n): to the schemata of axioms of three-valued Lukasiewicz logic
Ł3 [1]
(L1) ( )
(L2) ( ) (( ) ( )),
(L3) ( ) ( ),
(L4) (( ) ) (( ) ).
(L5) ( & ) ( & & )
we add
1) □i , i = 1, ... , n,
2) □i □i□i, i = 1, ... , n,
3) □i ( ) (□i □i ), i = 1, ... , n,
4) □i ( & ) (□i & □i ), i = 1, ... , n,
5) □i ( ) (□i □i ), i = 1, ... , n,
6) ◊i □i ◊i , i = 1, ... , n,
7) □i ( ) (□i □i ), i = 1, ... , n,
inference rules: , / , /□i , i = 1, ... , n.
A 3-valued Kripke frame for agent i is a pair Ji = (Wi,Ri), i = 1, … , n, consisting of a non-empty set Wi of
elements called the states of the agent i (or possible worlds of the agent i); Ri Wi Wi is a binary
reflexive and transitive relation on Wi (called the accessibility relation for agent i).
A 3-valued descriptive Kripke frame is a pair J = (W, R), W = {W1, … , Wn} is the set of n agents (or
possible worlds); R W W is a binary reflexive and transitive relation on W (called the accessibility
relation between agents i (= Wi)).
Theorem. Multimodal epistemic three-valued Lukasiewicz logic EŁ3(n) is complete with respect to 3-
valued descriptive Kripke frames.
References
[1] R. Grigolia, Algebraic analysis of Lukasiewicz-Tarski n-valued logical systems, Selected papers on
Lukasiewicz Sentential Calculi, Wroclaw, 81-91 (1977).
mailto:[email protected]
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Some Combinatorial Problems Connected with the Functions Defined on the Infinite Sets
Archil Kipiani
e-mail:[email protected]
Department of Mathematics Iv. Javakhishvili Tbilisi State University, Georgia
It is proved that for any infinite set E, there exists a sequence ( ) ∈ , in which each member has the following properties:
;
| ;
∈ There are exactly n permutations of the set E , such that each permutation commutes with .
mailto:[email protected]
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On one Problem of Reduction
PetreBabilua,BesarionDochviri, VakhtangJaoshvili
e-mail: [email protected]
Faculty Exact and Natural Sciences of I. Javakhishvili Tbilisi State University, Tbilisi, Georgia
We consider the following system of partially observable stochastic process in the conditional-Gaussian
scheme:
0 1 1
0 1 2
, , , ,
, , ,
t t
t t
d a t a t dt b t dw t
d A t A t dt dw t
where 1w and 2w are independent Wiener process, 0 , 0 t T [1]. Consider the following
gain function g x x , xR , and introduce the payoffs [2]:
0 sup , supT T
T TS E S E
M M
.
Suppose that the conditions (11.4)-(11.11) [1] are fulfilled. Let us introduce the following notations
t t tm E J , 2
t t tE m .
T h e o r e m 1 . The payoff TS
has the following form
supT
TS E m
M
.
Theorem of reduction [2]:
T h e o r e m 2 . The payoff TS
has the following form
supT
TS E
M
,
where
0 1 0 10 0
1, , ,
t t
t s sa s a s ds A s dw s
.
This talk is partially supported by the ShotaRustaveli National Science Foundation (Project # FR/308/5-
104/12).
References
R. Liptser, A. N. Shiryaev, Statistics of random processes. (Russian) Nauka, Moscow, 1974.
P. Babilua, I. Bokuchava, and B. Dochviri, The optimal stopping problem for the Kalman-Bucy scheme.
(Russian) Teor. Veroyatn. Primen. 55 (2010), no. 1, 133-142; translation in Theory Probab.
Appl. 55 (2011), no. 1, 110-119.
mailto:[email protected]
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Limit Distribution of the Integral Square Deviation of Two Bernoulli RegressionFunctions
Elizbar Nadarayaa, Petre Babiluab
e-mail: [email protected]
a Academy member, Faculty Exact and Natural Sciences of I. Javakhishvili Tbilisi State
University, Tbilisi, Georgia
b Faculty Exact and Natural Sciences of I. Javakhishvili Tbilisi State University, Tbilisi, Georgia
Let random variables iY , 1,2i , take two values 1and 0 with probabilities ip (success) and1 ip
(failure), 1,2i , respectively. Assume that the probability of success ip is the function of an independent
variable 0,1x ,i.e. 1ii ip p x P Y x , 1,2i ([1]-[3]). Let jt , 1, ,j n ,be the division points of the interval 0,1
2 1, 1, ,
2j
jt j n
n
.
Let further 1
iY and 2
iY , 1, ,j n , be mutually independent random Bernoulli variables with
1 , 0 1 , 1, , , 1,2k ki i k i i i k iP Y t p t P Y t p t i n k . Using the samples
1 11 , , nY Y and
2 21 , , nY Y we want to check the hypothesis
0 1 2: , 0,1H p x p x p x x , against the sequence of “close” alternatives of the form
1 : u o , 1,2n k n k nH p x p x x k ,
where 0n relevantly, 1 2u x u x , 0,1x ,and no uniformly in 0,1x . The problem of comparing two bernoulli regression functuions arises in some applications, for example in
quantal biossays in pharmacology. There x denotes the dose of a drung and p x the probability of response to the dose x .
We consider the criterion of testing the hypothesis 0H based on the statistic function
2 22
1 2 1 2
1 1ˆ ˆ ,
2 2
, 1 , 0,
n n
n n n n n n n n
n n n
T nb p x p x p x dx nb p x p x dx
b b
where
11
1ˆ , , 1,2
nj i
in in n in jjn n
x tp x p x p x p x K Y i
nb b
,
1
1 n in
in n
x tp x K
nb b
,
K x is some distribution density and 0nb is a sequence of positive numbers, ˆ inp is the kernel estimator of the regression function ([4], [5]).
mailto:[email protected]
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T h e o r e m . Let K x H and 11 2, , 0,1p x u x u x C .If2
nnb , 1 2 0n nb and
1 2 2
0n n nb c , 00 c , then for the hypothesis 1nH
1 2 1 ,1dn nb T p p N a ,
ddenotes convergence in distribution and ,1N a is a random variable having the standard normal
distribution with parameters ,1a ,
12
01 2
02
ca u x u x dx
p ,
where
0, 0 for 0, 1H k x K x x K x dx ,
1
2
0
1x
p p x p x K u du
,
22 2 2
0
2
2 1x
p p x p x dx K x dx
, 0K K K .
References
S. Efremovich, Nonparametric curve estimation – methods, theory, and applications. Springer-Verlag,
New York, 1999.
J. B. Copas, Regression, prediction and shrinkage. J. R. Stat. Soc., Ser. B45 (1983), 311-354.
H. Okumura and K. Naito, Weighted kernel estimators in nonparametric binomial regression. The
International Conference on Recent Trends and Directions in Nonparametric Statistics. J. Nonparametr.
Stat. 16 (2004), no. 1-2, 39-62.
E. A. Nadaraya, On estimating regression. (Russian) Teor. Veroyatn. Primen.9 (1964), 157-159.
G. S. Watson, Smooth regression analysis. Sankhyā Ser. A 26 (1964), 359-372.
https://zbmath.org/authors/?q=ai:copas.john-bhttps://zbmath.org/journals/?q=se:00001602https://zbmath.org/authors/?q=ai:nadaraya.eh-ahttps://zbmath.org/journals/?q=se:00000211
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European option hedging in the financial model with disorder moment
Khechinashvili Zaza
e-mail: [email protected]
Department of Probability and Statistics, Faculty of Exact and Natural Sciences,
Tbilisi State University, University st. 2.
On the probability space ),)(,,( 0 PFF Nnn we consider the model of risky asset price evolution
,00},)2(
)()1(
)(exp{1 SnMnInMnInSnS where, )1(nM and
)2(nM are independent Gaussian martingales, is the random variable which takes values
,,...,2,1 Nn with probabilities NiiPi ,...,2,1),( . )1(
nM and)2(
nM are jointly independent of ,
)(AI is the indicator of .A
Consider ),( SB financial market and European contingent claim ).( NSf
In the special class of
admissible strategies we find hedging strategy optimal in the mean square sense. So, we construct strategy
),( nn which minimizes the following expression
,])([ 2NN XSfE
where NNNNN BSX
is the corresponding capital value at terminal moment .N
We study this problem for the GF strategies, for which
.11 nnnnn GSB
It means, that for 0 nG there is some operating expenses and for 0 nG -investment.
References
[1] A.N. Shiryaev. Essentials of Stochastic Finance. Facts, Models, Theory. World Scientific, Singapure,
1999.
[2] Glonti, O., Khechinashvili, Z. Geometric Gaussian Martingales With Disorder. Theory of Stochastic
Processes,
Vol. 16(32), no. 1, 2010, pp. 44-48.
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Hedging of European Option of Exotic Type Omar Glonti, Omar Purtukhia
e-mail: [email protected], [email protected]
Department of Mathematics, Faculty of Exact and Natural Sciences,
Ivane Javakhishvili Tbilisi State University,
3 Chavtchavadze Ave, Tbilisi 0179, Georgia
The payoff functions of derivative securities with more complicated forms than standard European or
American call and put options are known as exotic options. One of such kind exotic option is so-called
Binary Option. It is an option with discontinuous payoff function. The simplest examples of the Binary
Options are call and putoptions "cash or nothing". The payoff function of the call option has the form
}{ KT
SQI
TBC
, and for the put option _ }{ KTS
QITBP , where K isthe strike price at the
time of executionT . It is also common the Binarny Option "an asset or nothing". There are same conditionsas in "cash or nothing" option,but the difference is that owner of the call option receives price
of the asset TS
instead of amountQ . The Standard European Call Option ( )( KTS ) is equivalent to a
long position (the bought asset) in the "asset or nothing" option and short position (the sold asset) in the
"cash or nothing" option, when KQ .
Moreover, so-called Asian Options also are type of Exotic Option. The payoff function of this option
depends on average value of the price of an asset during the certain period of option life time. The payoff
function of the Asian Option by definition has the following representation: )),0(( KTTsA
ATC ,
where
T
TtdtS
TTTTsA
00
1),0( is arithmetic mean of the prices of asset at time interval ],0[ TT , K is
a strike and )( tSS ( Tt 0 )is geometrical Brownian motion. The main difficulty in pricing and
hedging of the Asian Option is that the random variable ),0( TTsA is no lognormal distributed and
therefore, it is rather difficult to obtain explicit formulas of pricing of this option.
We consider an Exotic Option which is a certain combination of the Binary and Asian Options and
investigate the hedging problem. In particular, we study the European Option with payoff function
T
bSa dtIQ t0
}{ and for this purpose we give the Clark stochastic integral representation of such kind
payoff function with the explicit form of integrand. For instance, the following Clark representation is
fulfilled:
u
TT
u
uTT
KS wddtut
wrtK
utQdt
t
rtKQdtIQ
t
000}{ )
1(
1)
1(
,
where is the standard normal distribution function and is its density function, w is the innovation
Wiener process.
The work is partially supported by the Shota Rustaveli National Science Foundation, project no.
FR/308/5-104/12, FR/69/5-104/12.
mailto:[email protected]
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34
On the Well-Posedness of the Cauchy Problem for One Class of Neutral Functional
Differential Equation with Distributed Prehistory
Tamaz Tadumadze
e-mail: [email protected]
Department of Mathematics, Iv. Javakhishvili Tbilisi State University, 13 University St., 0186 Tbilisi, Georgia
The functional differential equation is considered
],[,))(),(,()()()( 10000
tttdssxtxtftxtAtx
t
t
(1)
with the initial condition
00000000 )(,,)()(),()( xtxttthtxttx (2)
and with distributed prehistory on the interval ],[],,[ 10000 ttttt , where 0,0 0 are fixed
numbers. A theorem on the continuous dependence of solution of the problem (1),(2) is proved with
respect to perturbations of the initial data ))(),(,,,( 000000 thtxt and the integrand f of the right
hand side of equation. Perturbation of the initial data is small in the standard norm and perturbation of
the integrand is small in the integral sense. Such type theorems are used in proving of the variation
formulas and necessary optimality conditions [1, 2] .
References
[1] G. L. Kharatishvili, T. A. Tadumadze, Variation formulas of solutions and optimal control
problems for differential equations with retarded argument. J. Math. Sci. ( NY) , 104, 1(2007), 1-175 .
[2] T. Tadumadze, N. Gorgodze, Variation formulas of a solution and initial data optimization problems
for quasi-linear neutral functional differential equations with discontinuous initial condition. Memoirs on
Differential Equations and Mathematical Physics , 63 (2014), 1-77.
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35
On Asymptotic Behavior of Solution of Emden-Fowler Differential Equations with
Deviating Argument
Koplatadze Roman
e-mail: [email protected]
Department of Mathematics of Iv. Javakhishvili Tbilisi State University
2, University Str., Tbilisi 0146, Georgia
The Emden-Fowler differential equation
,0))(())(()()()( tusigntutptu n
is considered, where 2n , 0 , 1 , );( RRLp loc , );( RRC ,
)(lim tt .
Oscillatory properties of solution of the equation are studied. In particular, sufficient (necessary and
sufficient) conditions are established for this equation to have Properties A and B.
mailto:[email protected]
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36
About structure of the bulk links wich appear after cutting of Generalized Mobius-Listings