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 Finite automata and models of simple forms of behaviourM. L. Tsetlin 3 Representations of a group of matrices of the second order with elements from a locally compact field, and special functions on locally compact fieldsI. M. Gel'fand, M. I. Graev 29 Some problems in the theory of linear and non-linear partial differential equationsL. Nirenberg 101 Arnol'd Zel'manovich Val'fish (photo) Arnol'd Zel'manovich Val'fish [Arnold Walfisz] (obituary)G. A. Lomadze, G. S. Chogoshvili 119 Scientific notes and problems Over-summability of a power series by Cesàro's methodsN. A. Davydov 129 The removability of singularities of analytic functionsE. P. Dolzhenko 135 On local convergence of basis seriesM. M. Dragilev 143 On Denjoy's conjectureL. D. Ivanov 147 A necessary and sufficient condition for the comparability of operatorsP. N. Knyazev 151 Free bimodules over a biregular ringZ. S. Lipkina 155 Operator norms of matricesYu. I. Lyubich 161 Dependence of volume and diameter of sets in an $n$-dimensional Banach spaceM. S. Mel'nikov 165 On the theory of integral equations of convolution typeL. S. Rakovshchik 171 An example of a completely continuous integral operator from $L_p$ to $L_p$ with positive kernel not belonging to $L_r$ $(r>1)$D. V. Salekhov 179 On the best linear methods of approximating functions of classes $B^r$ and $H^r$L. V. Taikov 183 On positive quadratic forms representing the same numbersV. N. Timofeev 191 On $k$-regular imbeddings of graphs in Euclidean spacesYu. A. Shashkin 195 Commutative semigroups of finite rankL. N. Shevrin 201 Mathematical Events in the USSR Meetings of the Moscow Mathematical Society 205 Abstracts of talks, presented to the Presidium of Moscow Mathematical Society and accepted by the Presidium The optimal control in Banach spaceYu. V. Egorov 211 Cauchy problem for equations of unsteady filtration in the class of unbounded solutionsA. S. Kalashnikov 213 A priori bounds and some properties for solutions of elliptic and parabolic equationsS. N. Kruzhkov 215 Simple subgroups of simple noncompact Lie groupsA. I. Sirota 216 Perturbation of eigenvalues and eigenfunctions for a second-order differential equation under perturbation of the boundaryZh. Ling 217 Semiclassical asymptotics of the Dirac equation solutionV. P. Maslov 220 Meetings of the Leningrad Mathematical Society 223 News Defence of Theses in Mathematics 229 Reviews and Bibliography New books on mathematics 233 Letters to the Editor Letter to the editorB. M. Levitan 239 Corrections 241