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 MATHEMATICS The existence of invariant tori in the neighborhodd of a state of equilbrium of a system of differential equationsYu. N. Bibikov 9 Stabilization of a solution of the heat equationYu. N. Drozhzhinov 13 A game-theoretic version of an optimal stopping problemE. B. Dynkin 16 Infinite spectra of topological spaces and their limit spacesV. Zaitsev 20 Two methods of finding equilibrium points of concave $n$-person gamesS. I. Zukhovitskii, R. A. Polyak, M. E. Primak 24 On the solution of Cauchy iteration problems in basis seriesM. B. Kapilevich 28 Some syntactic theorems on Ju. T. Medvedev's calculus of finite problemsL. A. Levin 32 Continuity of metric projection and some geometric properties of the unit sphere in a Banach spaceE. V. Oshman 34 The algorithms which are connected with predicates and with Boolean functionsN. V. Petri 37 An exterior inverse problem of volume potential of variable density for a body which is close to a given oneA. I. Prilepko 40 The asymptotics of the prediction error in the multi-dimensional caseV. N. Solev 43 On the Tauberian theorem of M. V. KeldysM. A. Subkhankulov, F. I. An 47 Gauss and Cauchy measures and $\varepsilon$-entropyV. N. Sudakov 51 Mappings which do not lower the dimensionV. V. Fedorchuk 54 CYBERNETICS AND THE REGULATION THEORY Functional equivalence of automata with a final stateA. A. Letichevskii 58 MATHEMATICAL PHYSICS The discrete and continuous spectra of the radial Dirac equationL. A. Sakhnovich 61 PHYSICS Conformally plane gravitational fields generated by dustlike matterV. I. Vashchuk 65 Excitation of vibrations and the disintegration of biatomic molecules when they collide with atoms in a high-temperature gasB. V. Kuksenko, S. A. Losev 69 Configurational representation of nucleonic interaction in a superfluid nucleus modelV. Rybarska 73 Durability of solids as dependent on temperatureR. L. Salganik 76 GEOPHYSICS Transient processes in a convective system modelS. V. Pshenay-Severin 87