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 MATHEMATICS Estimates of the derivatives of a solution of linear equations of elliptic and parabolic type with discontinuous coefficientsV. V. Basha 11 Random walks on groups: boundary, entropy, uniform distributionA. M. Vershik, V. A. Kaimanovich 15 On the solution of the Dirichlet problem by expansion in a Fourier seriesV. I. Vlasov 19 On the theory of systems of singular integral equations over a bounded plane domainA. Dzhuraev 22 Equations of Liouville typeA. V. Zhiber, N. H. Ibragimov, A. B. Shabat 26 Jordan nil-algebras of bounded indexE. I. Zel'manov 30 On approximation of solutions of some singular elliptic boundary value problemsA. A. Katrahova 34 Optimality conditions for a quasilinear problem with partial differential equations in the presence of phase constraintsYu. P. Krivenkov 37 Classes of objects having normal forms in the system of $\lambda$-conversion with logical operatorsA. S. Kuzichev 41 A generalization of the second theorem of N. N. Bogolyubov's averaging principleA. A. Martynyuk 46 On the optimality of the quadrature formula with equidistant nodes on classes of periodic functionsK. I. Oskolkov 49 On Lebesgue functions for some interpolation polynomials in two variablesL. M. Pimenova 52 A basic formula for the representation of subharmonic functions in the classical case of an arbitrary integral orderB. K. Pchelin 55 On the representation of analytic functions by series of Laguerre polynomialsP. K. Rusev 57 The synthesis of schemes and formulas in incomplete basesA. B. Ugol'nikov 60 On the imbedding of a strictly pseudoconvex domain in a polyhedronB. L. Fridman 63 The inverse scattering problem for difference equationsI. T. Habibullin 67 A generalized residual principle in reflexive spacesA. G. Yagola 71 FLUID MECHANICS On homobaric (uniform pressure) flows of suspensions of matter in gas under conditions of physicochemical transformationsP. B. Vainshtein, R. I. Nigmatulin 74 ASTRONOMY Determination of the Martian and Earth's orbits based on the radiolocation observations of Mars in 1964–1971M. D. Kislik, Yu. F. Kolyuka, V. A. Kotel'nikov, G. M. Petrov, V. F. Tikhonov 78 MATHEMATICAL PHYSICS The Schrödinger operator with a singular attractive potentialV. M. Adamyan, N. S. Pushek 81 Tensor description of half-integer spin fieldsV. A. Zhelnorovich 85 A new sufficient condition for the existence of phase transition in a classical system with long-range interactionV. I. Kolomytsev, A. V. Rokhlenko 90 Asymptotic solutions of elliptic boundary value problems when the domain is varied close to conical pointsV. G. Maz'ya, S. A. Nazarov, B. A. Plamenevskii 94 PHYSICS An elementary theory of explosions for soil ejection and their simulation using artificial gravityS. B. Barsanaev, V. Ts. Gurovich, K. A. Rasshikhin, K. P. Stanyukovich 97 Resonance acceleration of channeled particles in a field of powerful light waveV. V. Beloshitskii, M. A. Kumakhov 100 CRYSTALLOGRAPHY Crystal structure of potassium zinc beryllium silicate $\mathrm{K}_2\mathrm{Zn}_2\mathrm{Be}_2(\mathrm{SiO}_4)(\mathrm{Si}_2\mathrm{O}_7)$V. P. Balko, V. V. Bakakin, Yu. V. Gatilov, V. S. Pavlyuchenko 103