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In this article we present material relating to Lenin's activity as Head of the Soviet Government in the fields of soviet science, culture and education, without of course making any claim to completeness. In spite of the enormous difficulties which the Soviet country had lived through in the years of civil war and of outside intervention and, in particular, had experienced at the beginning of the period of reconstruction, in those very years the network of colleges grew, the network of scientific research institutes and other scientific establishments was started, and the necessary foundation for the further development of Soviet science was laid. Here we tell of the perspicacity of the founder of the Soviet state and of his faith in the future. The greater part of the documents quoted was written by Lenin; but numerous documents from the period in question signed by other statesmen, have a direct connection with Lenin, since any largescale measure in the fields of science, culture, and education was carried out with his approval. We present the material divided into sections, but chronological order is observed in each section. Every document we quote is given with its full title.

A great amount of information about the theory of games of very varied mathematical content has been accumulated in recent years. The account by Karlin in his monograph [64] of only some of the most highly developed branches of the theory of antagonistic games took up about 500 pages. A common approach to the theory of games as a whole has not yet been worked out. This article attempts to survey systematically the basic branches and directions of the theory of games in its present state. The general definition of a game as a formalized representation of a conflict is taken as a basis. All the "forms" of games considered earlier can be obtained from this definition as particular cases. A systematic look at the theory of games, as in the case of normative theory, enables us to place many of the results of the theory of games in fairly natural groupings. Without being able to give either an exhaustive or even a fairly full description of these results the author has restricted himself to an account of the most typical of them. The amount of detail is not uniform and is inversely proportional to the accessibility of the original material. Facts that can be found in Russian publications are merely noted or just mentioned. In particular, questions considered in the author's survey article [32] are only very briefly touched upon. Specific assertions given in this paper are mainly illustrative in character and some could be replaced by others without detriment. We consider practically all the significant branches of the theory of games with the exception of differential games. Although the theory of differential games has a well-defined place in a number of directions of the theory of games, its methods and problems are becoming increasingly independent. Detailed surveys of the theory of differential games are given in [59], [97]. The author does not touch upon the history of the theory of games and refers the interested reader to the addendum to the Russian edition of von Neumann and Morgenstern's basic monograph "The Theory of Games and Economic Behaviour" [82]. The present article is similar in concept to a paper of the same name given by the author at the First All-Union Conference on the Theory of Games at Erevan in November 1968 (see [123] and [37]), but there are essential differences in the selection of material and the presentation.

In this paper we consider dynamical systems resulting from the motion of a material point in domains with strictly convex boundary, that is, such that the operator of the second quadratic form is negative-definite at each point of the boundary, where the boundary is taken to be equipped with the field of inward normals. We prove that such systems are ergodic and are K-systems. The basic method of investigation is the construction of transversal foliations for such systems and the study of their properties.

We study "typical" metric (ergodic) properties of measure preserving homeomorphisms of regularly connected cellular polyhedra and of some other spaces. In 1941 Oxtoby and Ulam proved (for a narrower class of spaces) that ergodicity is such a property. Using a modification of their construction and the method of approximating metric automorphisms by periodic ones, we prove in this paper that almost all properties that are "typical" for the metric automorphisms of the Lebesgue spaces are also "typical" for the situation under discussion.

This paper presents an account of the mathematical foundations of the construction of game playing programs and methods of putting them on computers. We give a description of the principles used in organizing and processing information in the chess programs devised by the authors during the years 1961-6 for the electronic computer M-20. We also give some games played according to these programs.