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 MATHEMATICS Extension of recursive hierarchies, and $R$-operationsV. I. Amstislavskii 1023 On the theory of the convergence of approximate solutions of an operator equationYu. E. Boyarintsev, V. G. Vasil'ev 1027 A remark on compact classes of algebraic systemsS. R. Kogalovskii 1029 Approximation of discontinuous functions by Fourier sumsG. I. Natanson 1033 A certain variational problem in parametric formA. V. Pogorelov 1037 The fundamental matrix of solutions of the system of the spectral problem of heat and mass transferM. L. Rasulov 1039 Asymptotic behavior of a periodic solution of an equation of neutral type with small lagV. I. Rozhkov 1041 The $k$stability of homeomorphisms and the union of cellsA. V. Chernavskii 1045 The minimax character of Hotelling's $T^2$ testO. V. Shalaevskii 1048 MECHANICS Speeding up of solid particles by cumulative explosionV. M. Titov, Yu. I. Fadeenko, N. S. Titova 1051 CYBERNETICS AND THE REGULATION THEORY Comparison of the complexities of realization of Boolean functions by automata and Turing machinesYu. Ya. Breitbart 1053 Problems of finite control of linear systems with lumped parametersA. G. Butkovskiy 1056 THEORY OF ELASTICITY Dynamic stability and vibrations of sandwich panels in a supersonic gas flowA. I. Smirnov 1060 ASTRONOMY The ellipticity of the trajectory of free motions of the earth poleV. P. Karklin 1064 On the possibility to evaluate the dimensions and masses of the ice nucleus of a comet. Photoluminescence of parent moleculesD. O. Mokhnach 1067 MATHEMATICAL PHYSICS Optimal solution to the problem of linear antenna synthesisA. G. Ramm 1071 PHYSICS Some features of secondary ionic emission from $\mathrm{W}$ – $\mathrm{Mo}$ alloy under the action of slow ionsU. A. Arifov, D. D. Gruich, Kh. M. Khamidova 1075 The possibility of stabilizing the flute-type instability of plasma by means of a feed-back systemV. V. Arsenin, V. A. Chuyanov 1078 Polarization phenomena observed when electrons are scattered by protons in the high-energy regionA. I. Akhiezer, M. P. Rekalo 1081 The internal energy of a solid, as dependent on the rate of temperature variationG. A. Gemmerling 1084 The $K_\alpha$ band of carbon X-ray emission in titanium carbides, in diamond and in graphiteE. A. Zhurakovskiy 1088 Investigation of the optical in the air with a mode – locked laser dischargeS. D. Kaitmazov, A. A. Medvedev, A. M. Prokhorov 1092 Resonance transfer of excitation and change in the superfine state of the atomM. I. Chibisov 1094 Einstein's spaces of the second order of immersionM. Sh. Yakupov 1096