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The issue is dedicated to the 175th birthday of Pafnuti Lvovich Chebyshev

	To the 175th anniversary of P. L. Chebyshev's birth S. N. Kruzhkov		3
Plenary reports
	Some geometrical problems related to the flows on surfaces D. V. Anosov		5
	The application of Chebyshev’s ideas in modern numerical mathematics N. S. Bakhvalov		5
	Adele formulas for gamma- and beta-functions in algebraic number fields V. S. Vladimirov		11
	Nonlinear waves in solids N. I. Gvozdovskaya, A. G. Kulikovskii, E. I. Sveshnikova, A. P. Chugainova		12
	Asymptotic theory of localized solutions of Navier–Stokes equations with small viscosity V. P. Maslov, A. I. Shafarevich		16
Selected reports
	Mathematical study of sound waves propagation progress in mixtures N. S. Bakhvalov, G. V. Sandrakov, M. È. Èglit		19
	Extremal properties of multidimensional Chebyshev mappings I. V. Belyakov, A. M. Stepin		22
	A general approach to asymptotic nonlinear analysis A. D. Bruno		24
	Trajectory attractors of evolution equations without unique solvability of the Cauchy problem M. I. Vishik, V. V. Chepyzhov		27
	Highly precise results of the block method application E. A. Volkov, A. K. Kornoukhov, E. A. Yakovleva		30
	Solution of equations describing thin layer flow of heavy viscous liquid on a curvilinear surface S. S. Grigoryan, È. F. Khairetdinov		32
	On some methods of statistical data processing of medical and radiological measurements M. P. Dorofeeva, N. N. Chentsova		36
	A numerical method for solving an inverse problem of quantum scattering theory E. P. Zhidkov, R. G. Airapetyan		38
	Exact analysis of the error of locally one-dimensional methods for the heat equation with a right-hand side in $L_2$ S. B. Zaitseva, A. A. Zlotnik		40
	A priori estimates, convergence and stability of difference schemes for the solution of nonlinear evolution equations F. F. Ivanauskas		43
	On estimation of effective characteristics of porous materials under large deformations V. A. Levin, V. V. Lokhin, K. M. Zingerman		48
	Numerical-analytical study of aerodynamic pendulum behavior B. Ya. Lokshin, V. A. Samsonov		50
	Permanence of competing species Yu. Lopez-Gomez		52
	On the convergence time to equilibrium in large finite Markov chains A. D. Manita		56
	Computation of generalized Chebyshev polynomials on a computer Yu. V. Matiyasevich		59
	Invariant manifolds of a renormalization group, and critical behavior in a hierarchical fermion model M. D. Missarov		61
	Some refinements of probability inequalities S. V. Nagaev		64
	Modeling system for flight dynamics problems Yu. M. Okunev, V. A. Sadovnichii, V. A. Samsonov, G. G. Chernii		66
	Generalized solutions of the Cauchy problem for some classes of first-order hyperbolic systems E. Yu. Panov		75
	Optimization models in hydrodynamical problems of environment. V. V. Penenko		78
	Nonclassical initial-boundary value problems in the theory of unsteady internal waves Yu. D. Pletner, A. G. Sveshnikov		80
	Chebyshev nets and the development of net approaches in mathematical physics (on P. L. Chebyshev's “On cutting cloth”) A. G. Popov		82
	Stochastic differential equations with a randomly changing structure in Banach spaces V. Pougatcheff, I. N. Sinitsyn		86
	The volume of a polyhedron as a function of the lengths of its edges I. Kh. Sabitov		89
	On the “freezing” of inessential variables I. M. Sobol'		92
	On a class of degenerate nonuniformly parabolic equations A. S. Tersenov		94
	Additive problems for numbers having a given number of prime divisors N. M. Timofeev		98