Second International Conference Mathematics in Armenia Advances and Perspectives 24 - 31 August 2013, Tsaghkadzor, Armenia Dedicated to the 70th Anniversary of Foundation of Armenian National Academy of Sciences ABSTRACTS Yerevan, 2013 SECOND INTERNATIONAL CONFERENCE MATHEMATICS IN ARMENIA ADVANCES AND PERSPECTIVES Dedicated to the 70th Anniversary of Foundation of Armenian National Academy Of Sciences 24{31 August, 2013, Tsaghkadzor, Armenia Yerevan, 2013 Organizers • Institute of Mathematics of the National Academy of Sciences • Yerevan State University • American University of Armenia • State Engineering University of Armenia • Russian-Armenian (Slavonic) University Programme Committee • Sergei Adian (Moscow State University) • Norair Arakelian (Institute of Mathematics, NAS Armenia) • Bruce Boghosian (American University of Armenia) • Paul Gauthier (Universit´ede Montr´eal) • Hayk Ghazaryan (Yerevan State University) • Arshag Hajian (Northeastern University) • Rouben Ambartzumian (Institute of Mathematics, NAS Armenia) • Ildar Ibragimov (Steklov Mathematical Institute) • Boris Kashin (Steklov Mathematical Institute) • Yury Kutoyants (Universit´edu Maine) • Wolfgang Luh (Universit¨atTrier) • Yuri Movsisyan (Yerevan State University) • Henrik Shahgholian (KTH Royal Institute of Technology) • Alexandr Talalyan (Institute of Mathematics, NAS Armenia) • Norair Yengibaryan (Institute of Mathematics, NAS Armenia) • Vanik Zakaryan (State Engineering University of Armenia) Organizing Committee • Pargev Avetisyan (Russian-Armenian (Slavonic) University) • Rafayel Barkhudaryan (Institute of Mathematics, NAS Armenia) • Sergo Episkoposyan (State Engineering University of Armenia) • Gegham Gevorkyan (Yerevan State University) • Aram Hajian (American University of Armenia) • Aram Hakobyan (Yerevan State University) • Michael Poghosyan (Yerevan State University) • Artur Sahakian (Yerevan State University) Sponsors • The Research Mathematics Fund • Prometey Science Foundation, Armenia • State Committee of Science MES RA • \Hyur Service" LLC Contents Invited Lectures Adian S.I. The Burnside Problem on periodic groups for odd exponents n > 100............................................... 11 Arakelian N. On some problems and results in the Weierstrass theory of analytic functions . 12 Bilyk D. Discrepancy theory and analysis . 12 Hedenmalm H. Gauss-type operators, intertwining with Hilbert transform, and the Klein-Gordon equation . 12 Ibragimov I. and Zaporozhets D. Asymptotic behaviour of zeros of random polynomials and analytic functions . 13 Konyagin S. On Freiman's theorem . 13 Krikorian R. Kicked quasi-periodic Schrodinger cocycles and operators . 14 Laptev A. Spectral inequalities for Partial Differential Equations and their applications . 14 Lewis J.L. Hausdorff dimension and σ-finiteness of some p-harmonic measures. 14 Mundici D. Rational polyhedra, unital abelian l-groups, and MV -algebras . 15 Olevskii A. Wiener's conjecture on cyclic vectors . 16 Razborov A. Flag algebras . 16 Rodrigues J.F. Variations on a problem of Fichera and Stampacchia . 17 Takhtajan L. On functional-difference operators related to the modular double . 17 Talalyan A.A. On martingales and integrability criteria of trigonometric series . 17 Wojtaszczyk P. Performance of greedy algorithm in estimating Kolmogorov diameters . 19 Real and Complex Analysis Aleksanyan S. Optimal uniform and tangential approximation by entire and meromorphic functions . 21 Arestov V.V. Approximation of the differentiation operator by bounded operators in the space L2 on a half-line . 22 Avetisyan K. and Tonoyan Y. On Bergman type projections over Besov and mixed norm spaces . 24 Avetisyan R.A. On one singular set for absolute convergence . 24 Berezhnoi E. Banach-Steinhaus theorem for subspaces . 25 Chobanyan S.A. and Tarieladze V.I. Signs and permutations: Two problems of the function theory . 27 Christodoulides Y. Averaging of spectral measures associated with the Weyl-Titchmarsh m-function. 27 Danielyan A. Polynomial approximations on the closed subsets of the unit circle and applications . 28 Deikalova M.V. Nikol'skii inequality for algebraic polynomials on a sphere and an interval . 29 Episkoposian S.A. L1 and uniform convergence of series by the generalized Walsh system . 30 Galoyan L.N. On the negative order Cesaro means of the Fourier series in the trigonometric and Walsh systems . 32 Gevorgyan L.Z. On self-commutators of some operators. 33 Gevorkyan G.G. General Franklin periodic systems as bases in B1 .............................................................. 34 Gevorkyan G.G. and Keryan K.A. On general Franklin systems on R1 ................................................... 35 Glazyrina P.Yu. On fractional derivatives of trigonometric polynomials. 36 Gogatishvili A. Boundedness of Stein's spherical maximal function in variable Lebesgue space and application to the wave equation . 37 Goginava U. and Gogoladze L. Convergence of logarithmic means of Multiple Fourier series. 38 Harutyunyan A. Toeplitz operators on weighted Besov spaces of holomorphic functions on the polydisk . 38 Heidarirad Z. and Pryde A. Uniform continuity and weak almost periodicity on locally compact quantum groups . 38 Jiang M. Phase unwrapping problem. 39 Karagulyan G. A. On the divergence sets of Walsh-Fourier series of continuous functions . 40 1 Karakhanyan M.I. On β-uniform algebras Hβ (∆). 41 Karapetyan A.H. Weighted integral representations in tube domain over real unit ball . 42 Khachatryan R.A. On directionally differentiable selections of set-valued mappings . 43 Kobelyan A. and Grigoryan M. On the convergence of hard sampling operators. 45 Lechner R. An interpolatory estimate for the UMD{valued directional Haar projection. 46 Martirosyan Anush Equivalence of the absolute and unconditional convergences for wavelet systems. 47 Martirosyan M.S. On a representation of interpolating functions for biorthogonal systems of exponents . 48 Mkrtchyan A.D. Analytically nonextendable multidimensional power series. 49 Passenbrunner M. Pointwise estimates for spline Gram matrix inverses . 50 Petrosyan A.I. Duality in some spaces of functions harmonic in the unit ball . 51 Poghosyan L. and Poghosyan A. Convergence acceleration of the quasi-periodic interpolation by rational and polynomial corrections . 52 Sahakian A. On multiple Fourier series of functions of bounded partial generalized variation. 54 Sahakyan K.P. Hermite type quadrature and cubature formulas 54 Sargsyan S.A. On the divergence of Fourier-Walsh series . 55 Serrano E.P., Troparevsky M.I. and Fabio M.A. Solving deconvolution problems by wavelet decomposition methods . 55 Surnachev M.D. On density of smooth functions in weighted Sobolev-Orlicz spaces . 57 Tephnadze G. On partial sums and Fejer means of Walsh-Fourier series . 59 Vagharshakyan A. Lower bounds for L1 discrepancy. 59 Vigovskaya I., Zelinskyi Yu. and Mkrtchyan H. Generalized convex sets in the hypercomplex space . 59 Differential and Integral Equations Aleksanyan H., Shahgholian H. and Sjolin¨ P. Homogenization of Dirichlet problem for divergence type elliptic systems . 61 Arakelyan A. Numerical approximation for a variational problem of the spatial segregation of Reaction-Diffusion system . 62 Babayan A.O. On the Dirichlet problem for the fourth order partial differential equation when characteristic equation has only double roots . 63 Bibikov P.V. On differential invariants and contact equivalence of ordinary differential equations . 64 Dumanyan V.Zh. On solvability of Dirichlet problem for general second order elliptic equation . 65 Dymarskii Y.M. and Evtushenko Y. On manifolds of periodic eigenvalue problems with selected double eigenvalue . 68 Ghazaryan H.G. The density of the smooth compactly supported functions in a weighted multi - anisotropic Sobolev space . 69 Harutyunyan T. The inverse problem for a family of Sturm- Liouville operators . 69 Harutyunyan T. and Ashrafyan Yu. On the \movement" of the zeros of eigenfunctions of the Sturm-Liouville problem. 70 Hayrapetyan H. M. and Hayrapetyan A. R. On the Dirichlet boundary value problem in the half-space in weighted spaces . 71 Hayrapetyan H.M. and Babayan V.A. On the Riemann Boundary Value Problem in the space of continuous functions . 72 Kamalyan A.G. and Spitkovsky I.M. On partial indices of triangular matrix functions. 73 Karapetyan G. and Saribekyan N. Spectral stability of higher order semi-elliptic operators. 74 Koplatadze R. Essentially nonlinear functional differential equation with advanced argument . 75 Mikayelyan H. Asymptotic of the minimizers of the two- dimensional Mumford-Shah functional near the crack-tip . 76 Pahlevanyan A. The isospectral Sturm-Liouville problems. 76 Petrosyan A.A. and Hakobyan G.S. Variational inequalities for a class of nonlinear pseudoparabolic operators . 77 Saks R.S. H.Weil orthogonal decomposition of the L2(G) space and eigenfunctions of the curl operator. 78 Tadumadze T. and Gorgodze N. Variation formulas of solution for functional differential equations taking into account delay function perturbation and initial data optimization problems . 79 Teymurazyan R. A steady glacier flow as an obstacle problem. 80 Probability and Statistics Aharonyan N.G. Orientation-dependent chord length distribution function for a convex domain . 81 Aramyan R. A solution of the generalized cosine equation in Hilbert's fourth problem . 82 Aryasova O. and Pilipenko A. On differentiability of a flow for an SDE with discontinuous drift . 83 Basirat M. Inference for stress-strength parameter of Levy distribution based on type-II progressive censoring . 84 Bezhaeva Z.I. and Oseledets V.I. The.