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 Diophantine representation of enumerable predicatesYu. V. Matiyasevich 3 On $n$-dimensional canonically polarized varieties and varieties of fundamental typeS. G. Tankeev 31 Rings of definition of dense subgroups of semisimple linear groupsÈ. B. Vinberg 45 Semisimple algebraic groups which are split over a quadratic extensionB. Yu. Weisfeiler 56 Homology spheres and contractible compact manifoldsA. Z. Dymov 72 Metric properties of endomorphisms on homogeneous spaces of compact groupsS. A. Yuzvinskii 78 Approximation of periodic functions by Fejér sunsG. K. Lebed', A. A. Avdeenko 83 Extreme values of functionals and best approximation on classes of periodic functionsN. P. Korneichuk 93 Recovery of a function from its coefficients in a Dirichlet seriesA. F. Leont'ev 125 Integral characteristics of the growth of spectral functions for generalized second order boundary problems with boundary conditions at a regular endI. S. Kats 154 Correctly solvable boundary value problems in an infinite layer for systems of linear partial differential equationsV. M. Borok 185 Differential properties of solutions of elliptic boundary-value problems with power singularities on the right-hand sidesYu. P. Krasovskii 202 Bases in uniformly convex and uniformly flattened Banach spacesV. I. Gurarii, N. I. Gurarii 210 Coefficient sequences in Hilbert and Banach space expansionsN. I. Gurarii 216 Control of Markov processes and $W$-spacesN. V. Krylov 224