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 On the fiftieth anniversary of the Siberian Branch of Russian Academy of Sciences 3 Optimal control of the flow of a viscous heat-conducting gasE. V. Amosova 5 A statistical model of an epidemic processA. I. Borodulin, B. M. Desiatkov, A. N. Shabanov, A. A. Yarigin 23 Construction of the $\delta$-homogeneous VES production functionE. V. Volnikh, A. V. Kutishkin, Yu. G. Nikonorov 31 An example of the spherically symmetric motion of a compressible fluidA. R. Garifullin 45 Application of the orthogonality properties of factors in a probabilistic recognition problemV. V. Goltiapin 53 A nonlocal boundary value problem with overdetermination for an elliptic equationA. A. Illarionov 64 Algebraic approach to the design of distributed computing systemsS. P. Kovalyov 70 Roots of the Luzin affairS. S. Kutateladze 85 On a modification of the Prony methodL. S. Maergoiz, B. N. Varava 93 Some questions concerning constructive methods in the theory of inverse problemsM. V. Neshchadim 101 An analysis of modifications of the Black-Scholes model of the dynamics of the pricing of financial derivativesI. E. Poloskov 110 Jensen's inequality in ideal spacesV. Ya. Prudnikov 119 Differential-invariant submodels of three-dimensional subalgebras for a compressible fluidL. Z. Urazbakhtina 128 Group-theoretic properties of a generalization of Bessel functionsM. D. Khriptun 138