Journal•ISSN: 0025-5726

# Mathematics of The Ussr-izvestiya

IOP Publishing

About: Mathematics of The Ussr-izvestiya is an academic journal. The journal publishes majorly in the area(s): Group (mathematics) & Bounded function. Over the lifetime, 1479 publications have been published receiving 40342 citations.

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TL;DR: In this paper, the authors developed a duality method in the theory of averaging of nonlinear variational problems with stochastic Lagrangians and derived duality formulas that take account of the regularity problem.

Abstract: Duality methods in the theory of averaging of nonlinear variational problems are developed. The questions of a general nature that are discussed include a detailed analysis of the concept of regularity, an example of a nonregular Lagrangian, and the derivation of duality formulas that take account of the regularity problem. The main content is concerned with the averaging of variational problems with stochastic Lagrangians. Three groups of questions are investigated: 1) averaging of Lagrangians of a general form; 2) averaging of the Lagrangians of plasticity (the theory of the limit load); and 3) averaging of degenerate Lagrangians (problems with random soft or rigid inclusions). Bibliography: 13 titles.

1,128 citations

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TL;DR: In this article, the discriminant-form technique is used to transfer many results for unimodular symmetric bilinear forms to the non-unimodular case and is convenient in calculations.

Abstract: We set up the technique of discriminant-forms, which allows us to transfer many results for unimodular symmetric bilinear forms to the nonunimodular case and is convenient in calculations. Further, these results are applied to Milnor's quadratic forms for singularities of holomorphic functions and also to algebraic geometry over the reals. Bibliography: 57 titles.

896 citations

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TL;DR: In this paper, a general operator K-functor is constructed, depending on a pair A, B of C*-algebras, and the results (homotopy invariance, Bott periodicity, exact sequences) permit one to compute effectively in concrete examples.

Abstract: In this paper a general operator K-functor is constructed, depending on a pair A, B of C*-algebras. Special cases of this functor are the ordinary cohomological K-functor K*(B) and the homological K-functor K*(A). The results (homotopy invariance, Bott periodicity, exact sequences, etc.) permit one to compute effectively in concrete examples. The main result, concerning extensions of C*-algebras, consists in a description of a stable type of extensions of the most general form: . It is shown that the sum of such an extension with a fixed decomposable extension of the form is uniquely determined by an element of the group . Bibliography: 25 titles.

687 citations

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TL;DR: In this article, a negative solution to the problem of Milnor concerning the degrees of growth of groups was given, which also answers a question of Day concerning amenable groups and a number of other results are obtained on residually finite finitely generated infinite 2-groups.

Abstract: This paper gives a negative solution to the problem of Milnor concerning the degrees of growth of groups. The construction also answers a question of Day concerning amenable groups. A number of other results are obtained on residually finite finitely generated infinite 2-groups. Bibliography: 51 titles.

557 citations

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TL;DR: In this article, the realization of certain types of Chevalley groups as the Galois group of extensions of cyclotomic fields is studied, and a criterion for algebraic curve to be defined over an algebraic number field is given.

Abstract: This paper is devoted to the realization of certain types of Chevalley groups as the Galois group of extensions of certain cyclotomic fields. In addition, a criterion for an algebraic curve to be defined over an algebraic number field is given. Bibliography: 11 titles.

551 citations