Journal•ISSN: 0025-5734
Mathematics of The Ussr-sbornik
IOP Publishing
About: Mathematics of The Ussr-sbornik is an academic journal. The journal publishes majorly in the area(s): Boundary value problem & Bounded function. It has an ISSN identifier of 0025-5734. Over the lifetime, 2399 publications have been published receiving 45449 citations.
Topics: Boundary value problem, Bounded function, Function (mathematics), Boundary (topology), Mixed boundary condition
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TL;DR: In this article, the authors studied the distribution of eigenvalues for two sets of random Hermitian matrices and one set of random unitary matrices in the energy spectra of disordered systems.
Abstract: In this paper we study the distribution of eigenvalues for two sets of random Hermitian matrices and one set of random unitary matrices. The statement of the problem as well as its method of investigation go back originally to the work of Dyson [i] and I. M. Lifsic [2], [3] on the energy spectra of disordered systems, although in their probability character our sets are more similar to sets studied by Wigner [4]. Since the approaches to the sets we consider are the same, we present in detail only the most typical case. The corresponding results for the other two cases are presented without proof in the last section of the paper. §1. Statement of the problem and survey of results We shall consider as acting in iV-dimensiona l unitary space ///v, a selfadjoint operator BN (re) of the form
2,594 citations
TL;DR: In this paper, a theory of generalized solutions in the large Cauchy's problem for the equations in the class of bounded measurable functions is constructed, and the existence, uniqueness and stability theorems for this solution are proved.
Abstract: In this paper we construct a theory of generalized solutions in the large of Cauchy's problem for the equations in the class of bounded measurable functions. We define the generalized solution and prove existence, uniqueness and stability theorems for this solution. To prove the existence theorem we apply the "vanishing viscosity method"; in this connection, we first study Cauchy's problem for the corresponding parabolic equation, and we derive a priori estimates of the modulus of continuity in of the solution of this problem which do not depend on small viscosity.Bibliography: 22 items.
1,799 citations
TL;DR: In this paper, a study of infinite Hankel matrices and approximation problems connected with them is presented, with a focus on the problem of finding the optimal solution to a given problem.
Abstract: This article is a study of infinite Hankel matrices and approximation problems connected with them. Bibliography: 22 items.
685 citations
TL;DR: In this paper, a sequence of new knot invariants is constructed by using the relationship between the theory of distributive groupoids and knot theory, and the invariants are used to construct new knots.
Abstract: A sequence of new knot invariants is constructed by using the relationship between the theory of distributive groupoids and knot theory.Bibliography: 3 titles.
581 citations
TL;DR: In this paper, an algorithm for recognizing the solvability of arbitrary equations in a free semigroup is presented, and the algorithm is shown to be efficient in the presence of arbitrary variables.
Abstract: In this paper we construct an algorithm recognizing the solvability of arbitrary equations in a free semigroup.Bibliography: 4 titles.
569 citations