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 MATHEMATICS The index of a pseudodifferential operator with a finite group of shiftsA. B. Antonevich 751 Spaces that can be defined by variation of local approximationsYu. A. Brudnyi 753 The partial orderability of rings and algebrasA. I. Veksler 756 A certain problem of optimal stabilizationV. I. Zubov 760 Decomposition of a tensor product of irreducible maximally degenerate representations of the group of complex matrices of order $n$ with determinant $1$È. V. Kissin 763 Proof of Fermat’s last theorem for all prime exponents less than 5500V. V. Kobelev 767 Group algebras of analytic functionals, and their representationsG. L. Litvinov 769 Quasianalyticity criterion for abstract operatorsYu. I. Lyubich, V. A. Tkachenko 772 The covering of $A$-sets, and multiple separabilityA. A. Lyapunov 775 Construction of a correct guiding function for a system of differential equationsÈ. Muhamadiev 777 Spectral synthesis for the shift operator, and zeros in certain classes of analytic functions that are smooth up to the boundaryN. K. Nikol'skii 780 Theorems on traces and extensions of functions from surfacesM. D. Ramazanov 784 Symmetric domains and Jordan algebrasV. I. Semyanistyi 788 Certain cases of the realization of elements of homotopy groups of homogeneous spaces by totally geodesic spheresA. T. Fomenko 792 The method of limit transformations in the problem of the existence of Poisson stable solutions of differential equationsB. A. Shcherbakov 796 THEORY OF ELASTICITY Method of solving certain boundary-value problems of the stability theory of cylindrical shellsL. I. Shkutin 800 ASTRONOMY Evaluation of the structure of solar corona from the rocket experiment made on February 15, 1961A. A. Dmitriev, R. G. Indzhgia, A. E. Mikirov, S. M. Poloskov 803 PHYSICS Invariance groups and differentiation in the matrix space theoryM. V. Gorbatenko, Yu. A. Romanov 805 Carbon dioxide laser in the regime of single impulsesA. V. Eletskii, B. M. Smirnov 809 Ultrasonic oscillations of radiation intensity of “moving medium” lasersB. L. Livshits, A. T. Trusunov 813 Some non-stationary problems of finite-amplitude wave theory in dissipative mediumsO. V. Rudenko, S. I. Soluyan 815 Generalization of Hartree–Fock's method for the case of nonperfect Bose gasYu. A. Tserkovnikov 819 GEOPHYSICS Indicatrices of light scattering by sea waterV. I. Voitov, O. V. Kopelevich 827 CRYSTALLOGRAPHY Crystalline structure of the $\mathrm{Y}=\mathrm{Ca}_6[\mathrm{Si}_2\mathrm{O}_7][\mathrm{SiO}_4](\mathrm{OH})_2$ phaseR. M. Ganiev, V. V. Ilyukhin, N. V. Belov 831 The relation between the shape of crystals and thermodynamic conditions during their growthV. I. Trubin 835