Journal•ISSN: 1072-3374

# Journal of Mathematical Sciences

Springer Science+Business Media

About: Journal of Mathematical Sciences is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Boundary value problem & Mathematics. It has an ISSN identifier of 1072-3374. Over the lifetime, 16519 publications have been published receiving 89072 citations.

Topics: Boundary value problem, Mathematics, Nonlinear system, Boundary (topology), Differential equation

##### Papers published on a yearly basis

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TL;DR: A survey of the theory of Kats-Moody algebras is given in this paper, which contains a description of the connection between the infinite-dimensional Lie algebra of Kats and systems of differential equations generalizing the Korteweg-de Vries and sine-Gordon equations and integrable by the inverse scattering problem.

Abstract: The survey contains a description of the connection between the infinite-dimensional Lie algebras of Kats-Moody and systems of differential equations generalizing the Korteweg-de Vries and sine-Gordon equations and integrable by the method of the inverse scattering problem. A survey of the theory of Kats-Moody algebras is also given.

1,288 citations

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TL;DR: In this paper, Kantorovich and Akad defined a translocation of masses as a function Ψ(e, e′) defined for pairs of (B)-sets e, e − ∈ R such that: (1) it is nonnegative and absolutely additive with respect to each of its arguments, (2) Φ (e, R) = Φ(e), Ψ (R, e−∆), Ω(R, E − ∆), e− ∆ = Π(e−∀ −∆ −

Abstract: ON THE TRANSLOCATION OF MASSES L. V. Kantorovich∗ The original paper was published in Dokl. Akad. Nauk SSSR, 37, No. 7–8, 227–229 (1942). We assume that R is a compact metric space, though some of the definitions and results given below can be formulated for more general spaces. Let Φ(e) be a mass distribution, i.e., a set function such that: (1) it is defined for Borel sets, (2) it is nonnegative: Φ(e) ≥ 0, (3) it is absolutely additive: if e = e1 + e2+ · · · ; ei∩ ek = 0 (i = k), then Φ(e) = Φ(e1)+ Φ(e2) + · · · . Let Φ′(e′) be another mass distribution such that Φ(R) = Φ′(R). By definition, a translocation of masses is a function Ψ(e, e′) defined for pairs of (B)-sets e, e′ ∈ R such that: (1) it is nonnegative and absolutely additive with respect to each of its arguments, (2) Ψ(e, R) = Φ(e), Ψ(R, e′) = Φ′(e′). Let r(x, y) be a known continuous nonnegative function representing the work required to move a unit mass from x to y. We define the work required for the translocation of two given mass distributions as W (Ψ,Φ,Φ′) = ∫

1,046 citations

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TL;DR: In this paper, the theory of strong solutions of Ito equations in Banach spaces is expounded, and the results of this theory are applied to the investigation of strongly parabolic Ito partial differential equations.

Abstract: The theory of strong solutions of Ito equations in Banach spaces is expounded. The results of this theory are applied to the investigation of strongly parabolic Ito partial differential equations.

793 citations

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TL;DR: Tangent spaces of a sub-Riemannian manifold are themselves sub-riemannians as mentioned in this paper, and they come with an algebraic structure: nilpotent Lie groups with dilations.

Abstract: Tangent spaces of a sub-Riemannian manifold are themselves sub-Riemannian manifolds. They can be defined as metric spaces, using Gromov’s definition of tangent spaces to a metric space, and they turn out to be sub-Riemannian manifolds. Moreover, they come with an algebraic structure: nilpotent Lie groups with dilations. In the classical, Riemannian, case, they are indeed vector spaces, that is, abelian groups with dilations. Actually, the above is true only for regular points. At singular points, instead of nilpotent Lie groups one gets quotient spaces G/H of such groups G.

749 citations

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TL;DR: A survey of computational methods in linear algebra can be found in this article, where the authors discuss the means and methods of estimating the quality of numerical solution of computational problems, the generalized inverse of a matrix, the solution of systems with rectangular and poorly conditioned matrices, and more traditional questions such as algebraic eigenvalue problems and systems with a square matrix.

Abstract: The authors' survey paper is devoted to the present state of computational methods in linear algebra. Questions discussed are the means and methods of estimating the quality of numerical solution of computational problems, the generalized inverse of a matrix, the solution of systems with rectangular and poorly conditioned matrices, the inverse eigenvalue problem, and more traditional questions such as algebraic eigenvalue problems and the solution of systems with a square matrix (by direct and iterative methods).

667 citations