Georgian National Georgian Mathematical Ivane Javakhishvili Academy of Sciences Union Tbilisi State University Caucasian Mathematics Conference CMC I BOOK OF ABSTRACTS Tbilisi, September 5 – 6 2014 Organizers: European Mathematical Society Armenian Mathematical Union Azerbaijan Mathematical Union Georgian Mathematical Union Iranian Mathematical Society Moscow Mathematical Society Turkish Mathematical Society Sponsors: Georgian National Academy of Sciences Ivane Javakhishvili Tbilisi State University Steering Committee: Carles Casacuberta (ex officio; Chair of the EMS Committee for European Solidarity), Mohammed Ali Dehghan (President of Iranian Mathematical Society), Roland Duduchava (President of the Georgian Mathematical Union), Tigran Harutyunyan (President of the Armenian Mathematical Union), Misir Jamayil oglu Mardanov (Representative of the Azerbaijan Mathematical Union), Marta Sanz-Sole (ex officio; President of the European Mathematical Society), Armen Sergeev (Representative of the Moscow Mathematical Society and EMS), Betül Tanbay (President of the Turkish Mathematical Society). Local Organizing Committee: Tengiz Buchukuri (IT Responsible), Tinatin Davitashvili (Scientific Secretary), Roland Duduchava (Chairman), David Natroshvili (Vice chairman), Levan Sigua (Treasurer). Editors: Guram Gogishvili, Vazha Tarieladze, Maia Japoshvili Cover Design: David Sulakvelidze Contents Abstracts of Invited Talks 13 Maria J. Esteban, Symmetry and Symmetry Breaking for Optimizers of Functional Inequalities . 15 Mohammad Sal Moslehian, Recent Developments in Operator Inequalities . 15 Garib N. Murshudov, Some Application of Mathematics to Structural Biology 16 Dmitri Orlov, Categories in Geometry and Physics: Mirror Symmetry, D- Branes and Landau–Ginzburg Models . 17 Samson Shatashvili, Supersymmetric Gauge Theories and the Quantisation of Integrable Systems . 18 Leon A. Takhtajan, On Bott–Chern and Chern–Simons Characteristic Forms 19 Cem Yalçin Yildirim, Small Gaps Between Primes: the GPY Method and Recent Advancements Over it . 19 Abstracts of Invited Talks by Young Mathematicians (under 40) 21 Rovshan Bandaliyev, On a Two-Weighted Inequality for Certain Sublinear Operator in Weighted Musielak-Orlicz Spaces . 23 Iuliya Beloshapka, Twistor Approach for Harmonic 2-Spheres in a Loop Space 24 Kazim Buyukboduk, The Birch and Swinnerton-Dyer Conjecture: p-Adic VS Complex . 24 R. Duduchava, M. Tsaava, T. Tsutsunava, Mixed Boundary Value Prob- lem on Hypersurfaces . 25 Sergey Gorchinskiy, Loday Symbol, Countou-Carrère Symbol, and Reciprocity 26 Alireza Amini Harandi, Fixed Point Theory for Generalized Nonexpansive Mappings . 26 Ali Huseynli, On Basis Properties of Root Functions of a Nonselfadjoint Boundary Value Problem . 27 3 4 Tbilisi, September 5–6, 2014 A. Kh. Kobelyan, Some Property of Fourier Series with Respect by Ortho- gonal Systems . 28 Majid Soleimani-damaneh, Moslem Zamani, On Compromise Solutions and Scalarization in Multiobjective Optimization . 28 George Tephnadze, On the Cesàro Means of Walsh-Fourier Series . 30 Vardan Tepoyan, Isometric Representations of Abelian Semigroups . 30 Özgün Ünlü, Free Group Actions on Products of Spheres . 31 Abstracts of Participants’ Talks 33 Ali Abolhasani, Maryam Abolhasani, Two Different Approaches in Pre- diction of Infinite Variance ARMA(1,1) . 35 Nasser Aghazadeh, Solving Volterra Integro-Differential Equations by Using an Expansion Method . 36 Karim Ahmadidelir, On the Characterization of Finite Moufang Loops by their Non-Commuting Graph . 37 Asghar Ahmadkhanlu, Mohammad Jahanshahi, Existence Results for Non-Linear Fractional Integro-Differential Equation with Non-Local Bo- undary Conditions . 38 G. Akhalaia, N. Manjavidze, On Boundary Value Problems of the theory of Generalized Analytic Vectors . 39 D. B. Akhmetova, S. T. Alieva, K. B. Mansimov, On a Problem of Optimal Control Described by a Difference Analogue of Barbashin Type Integro-Differential Equation . 39 Akbar Aliev, Global Existence, Asymptotic Behavior and Blow-up of Solu- tions to Cauchy Problem of the System of Klein-Gordon Equations with Damping Terms . 40 Saeid Alikhani, Counting the Number of Some Kind of Dominating Sets of Graphs . 41 Yagub Aliyev, Sturm-Liouville Problems with Eigenparameter Dependent Boundary Conditions . 42 A. Alizadeh, H. R. Marasi, Numerical Solution of the Interrelated Differen- tial Equation of Motion in Phonon Engineering . 42 Mikheil Amaglobeli, Tengiz Bokelavadze, Some Results of the Theory of Exponential R-Groups . 44 R. V. Ambartzumian, Lifting Hilbert’s Fourth Problem to Three Dimensions 45 Caucasian Mathematics Conference, CMC I 5 V. Amikishiyev, T. Mehdiyev, J. Shabiyev, G. N. Murshudov, A Search for a Fragment Space: Organization and use of Prior Structural Knowledge 46 Maryam Amyari, Generalized Fredholm Operator in Locally m-Convex H∗- Algebras . 48 Rafik Aramyan, A Representation for Convex Bodies . 48 Ali Armandnejad, g-Tridiagonal Majorization and Circulant Majorization on Mn;m ....................................... 49 Fatemah Ayatollah Zadeh Shirazi, On Induced Hyperspace Topological Transformation Semigroups . 50 Mahdieh Azari, Ali Iranmanesh, Various Versions of Zagreb Indices Under Some Local Graph Operators . 50 Petre Babilua, Besarion Dochviri, Omar Purtukhia, On the Reduc- tion and Convergence of Payoffs for Partially Observable Stationary Se- quences . 51 Ali Bajravani, A Prym Torelli Theorem for General Prym-Canonical Curves of Genus g = 7 ................................. 52 Vladimer Baladze, The (co)Shape and (co)Homological Properties of Con- tinuous Maps . 53 Mehdi Bastani, Nasser Aghazadeh, On the Generalized Hermitian and Skew-Hermitian Splitting Iterative Method for Image Restoration . 55 Özlem Beyarslan, Geometric Representation of Groups in Pseudo-finite Fields 56 Bilal Bilalov, Aida Guliyeva, Bases in Morrey-Lebesgue and Morrey- Hardy Spaces . 56 Bilal Bilalov, Sabina Sadigova, Frame Properties of the Part of a System of Exponents with Degenerate Coefficient in Hardy Classes . 58 Rusudan Bitsadze, Marine Menteshashvili, On One Mixed Characteris- tic Problem . 59 Tengiz Buchukuri, Roland Duduchava, Laplace-Beltrami Equation on Hypersurfaces and Γ-Convergence . 59 Alexander Bufetov, Infinite Determinantal Measures . 60 Victor Burenkov, Vladimir Gol’dshtein, Alexander Ukhlov, Spec- tral Stability of the Dirichlet-Laplace Operator in Plane Domains . 60 Kazim Büyükboduk, The Birch and Swinnerton-Dyer Conjecture: p-Adicvs Complex . 62 6 Tbilisi, September 5–6, 2014 İsmail Naci Cangül, Subgroups of Some Discrete Groups and Some Useful Methods . 62 Luís Castro, David Kapanadze, Crack Impedance-Dirichlet Boundary Value Problems of Diffraction in a Half-Plane . 63 Vildan Çetkin, Halis Aygün, On L-Soft Merotopies . 63 Giorgi Chelidze, Badri Mamporia, Weakly Independent Random Ele- ments, Gaussian Case . 65 B. Chikvinidze, M. Mania, New Proofs of Some Results on BMO Martingales Using BSDEs . 66 Temur Chilachava, Nonlinear Mathematical Model of Bilateral Assimilation Taking Into Account Demographic Factor . 66 Otar Chkadua, David Natroshvili, Localized Boundary-Domain Integral Equations Approach for Problems of the Theory of Piezo-Elasticity for Inhomogeneous Solids . 68 İlhan Dagadur, Seyda Sezgek, Cλ-Rate Sequence Space Defined by a Mo- dulus Function . 69 S. H. Dalalyan, Hypergroups Over the Group and Applications . 70 Ana Danelia, Tengiz Kopaliani, Amiran Gogatishvili, Local Hardy- Littlewood Maximal Operator in Variable Lebesgue Spaces . 70 Majid Deafshpour, Some Fixed Point Results in Boolean Metric Spaces . 71 Rostislav Devyatov, Equivariant Infinitesimal Deformations of Algebraic Threefolds with an Action of an Algebraic Torus of Complexity 1 . 72 Nurhan Dundar, Necat Polat, Mathematical Behavior of a Modified Two- Component Shallow Water Equations . 73 Ali Ebadian, On T -Neighborhood on Univalent Functions . 74 Neda Ebrahimi, Mina Jamshidi, Homomorphism on Local Top Spaces . 75 Neda Ebrahimi, Mina Jamshidi, A New Causal Ladder in General Relativity 76 Neda Ebrahimi, Mina Jamshidi, Action of Fuzzy Top Spaces on Fuzzy Ma- nifolds . 77 Lasha Ephremidze, Nika Salia, Some Computational Aspects of Novel Ma- trix Spectral Factorization Algorithm . 78 Maryam Esmaeili, Ali Tavakoli, Construction of Multiple Knot B-Spline Wavelet with Ideal Knots . 78 Caucasian Mathematics Conference, CMC I 7 M. Faghfouri, A. Haji Badali, F. Gholami, A Note on General Kaluza- Klein Cosmology . 79 A. Fakharzadeh J., H. Alimorad D., A Theoretical Measure Technique for Determining 3-D Symmetric Optimal Shapes with a Given Center of Mass 81 Farzaneh Falahati Nezhad, Ali Iranmanesh, Abolfazl Tehranian, Mahdieh Azari, Lower Bounds on the Multiplicative Zagreb Indices of Graph Operations . 82 H. Rahmani Fazli, Modeling of a Fractional-Order Economic System . 83 Mortaza Gachpazan, Madjid Erfanian, A New Sequential Approach for Solving the Integro-Differential Equation Via Haar Wavelet Bases . 84 T. S. Gadjiev, S. A. Aliev, R. A. Rasulov, Blow-up Solutions Some Classes of the Nonlinear Parabolic Equations . 85 T. S. Gadjiev, M. N. Kerimova, G. Sh. Gasanova, The Solutions De- generate Nonlinear Elliptic-Parabolic Equations . 86 T. Gadjiev, Nigar Sadykhova, Removable Singularities of Solutions of De- generate Nonlinear Elliptic Equations . 86 Tamilla Gasanova, Sabina Sadigova, On Frames of Double and Unary Systems in Lebesgue Spaces . 88 Levon Gevorgyan, On Self-Commutators of Operators . 89 M. Ghanbari, D. A. Mojdeh, M. Ramezani, Algorithm for Maximum Independent Set in Wireless Network Graphs . 90 Yaser Gholizade