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 MATHEMATICS Orthogonal systems of elements in smooth Banach spacesB. E. Veits 9 The finding of saddle points on polyhedraV. F. Dem'yanov 13 The simulation according to realizability of pseudo-Boolean algebrasF. A. Kabakov 16 A certain class of nonlinear operator equations, and certain equations of mechanicsR. I. Kachurovskii 19 Repetition of two-person games in long intervals of timeA. Yu. Levin 23 Two examples for the theory of the dimension of bicompactaI. K. Lifanov, V. V. Filippov 26 Families of homeomorphisms that are uniformly equicontinuous with respect to metricsV. P. Luferenko, G. D. Suvorov 30 A certain inverse spectral analysis problem for Hill's equationI. V. Stankevich 34 Homological properties of minimal compacta in the multidimensional Plateau problemA. T. Fomenko 38 Coercive boundary value problems for difference operatorsL. S. Frank 42 On a theorem of M. V. Keldysh and M. A. Lavrent’evB. N. Khimchenko 46 FLUID MECHANICS Lagrangian invariants in the dynamics of nonviscous compressible fluidsB. L. Gavrilin, M. M. Zaslavskii 48 THEORY OF ELASTICITY Periodic convolution equations and properties of their solutionsV. A. Babeshko 52 MATHEMATICAL PHYSICS Model of the neutrino in the general theory of relativity with groups of motion $G_3$ on $V_2$A. N. Golubyatnikov 55 Construction of solutions of Dirichlet and Neumann problems for an unclosed surfaceI. M. Polishchuk 59 PHYSICS The orientation dependence of line parameters of the characteristic X-ray spectrum of the atoms of elements in monocrystals. Basic parameters of $K$- and $L$-series $\mathrm{V}$ line in $\mathrm{V}_2\mathrm{O}_5$ monocristalI. B. Borovskii, V. I. Matyskin 63 Short-wave radio-emission and blast wave of an explosionA. P. Boronin, Yu. A. Medvedev, B. M. Stepanov 67 On Compton's mechanism of electron gas heating by means of lasersF. V. Bunkin, A. E. Kazakov 71 Instability of inhomogeneous high-pressure plasma in a homogeneous magnetic fieldA. B. Mikhailovskii 74 CRYSTALLOGRAPHY On details of Paterson's syntheses directly connected with structure symmetry elementsÈ. A. Kuz'min, V. P. Golovachev, N. V. Belov 86