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 The present state of investigations in the foundations of mathematicsA. Mostowski 3 Some problems of the qualitative theory of differential equationsV. V. Nemytskii 39 Some problems of nonlinear analysisM. A. Krasnosel'skii 57 Scientific notes and problems On a method of integration of partial differential equations of the first orderI. S. Arzhanykh 115 Extension of the method of characteristics to simultaneous partial differential equations of the first orderI. S. Arzhanykh 119 On the method of iterationsV. M. Dubrovskii 127 The determination of a completely additive function by its values on half-spacesP. O. Kostelyanets, Yu. G. Reshetnyak 135 On the solution of Cauchy's problem for regular systems of linear partial differential equationsA. G. Kostyuchenko, G. E. Shilov 141 On an indeterminate equation in Hilbert space and its application in potential theoryS. G. Krein 149 On implicit functionsL. D. Kudryavtsev 155 On the ring of functions with absolutely convergent Fourier seriesZ. I. Leibenzon 157 On the signs of the solution of a system of linear equationsV. S. Mikhel'son 163 On the continuous dependence of the solution of Cauchy's problem upon the initial dataA. D. Myshkis, U. K. Grinfel'd 171 On the curves and two-dimensional surfaces along which a solution of the wave equation can have a discontinuityI. G. Petrovskii, L. A. Chudov 175 On some criteria of locally nilpotent groupsB. I. Plotkin 181 On the mutual disposition of the lines of regressionN. A. Sapogov 187 On the variation of lengths and directions in pseudo-conformal mappingsB. A. Fuks 193 On conditions of pseudo-conformality of a mapping of four-dimensional spaceB. A. Fuks 201 Determination of the value of the measure for a region of $n$-dimensional Euclidean space from its values for all half-spacesA. A. Khachaturov 205 Methodical notes A simple proof of the mean-value theorem for harmonic functionsB. P. Demidovich 213 In the Moscow Mathematical Society Meetings of the Moscow Mathematical Society 215 Mathematical Events in the USSR Sergei Pavlovich Finikov (photo) Sergei Pavlovich Finikov (on his seventieth birthday)G. F. Laptev 245 Meetings of the Town's Mathematical Seminar in Leningrad 253 XVI Moscow School Mathematical CompetitionD. E. Men'shov, I. R. Shafarevich, E. A. Morozova, V. M. Zolotarev 257 School Mathematical Competition in KishinevI. A. Itskovich, K. S. Sibirskii 263 Reviews and Bibliography Historical-Mathematical Investigations, vols. IV, V (review)V. F. Rogachenko 267 Sh.  E. Mikeladze, Numerical methods of mathematical analysis (review)B. L. Ginzburg 274 On book “Numerical methods of mathematical analysis” by Sh. E. MikeladzeA. I. Zhukov 276 V. A. Unkovskii, Theory of probability (review)V. V. Petrov, Yu. V. Linnik 278 Letters to the Editor Comments on the paper “A three- and a four-dimensional analogue of Pascal's theorem” by D. D. Mordukhai-BoltovskiiI. Metel'ka 283 CorrectionF. R. Gantmakher 284 CorrectionG. P. Tolstov 284 Correction 285 To the paper “Classification of three-dimensional Riemannian spaces according to groups of motions”G. I. Kruchkovich 285