$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 12 Issue 10

October 2014

Issue of Open Mathematics

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Journal Overview

Open Access June 21, 2014

Three solutions to discrete anisotropic problems with two parameters

Marek Galewski, Piotr Kowalski

Page range: 1403-1415

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Abstract

In this note we derive a type of a three critical point theorem which we further apply to investigate the multiplicity of solutions to discrete anisotropic problems with two parameters.

Open Access June 21, 2014

A classification of the torsion tensors on almost contact manifolds with B-metric

Mancho Manev, Miroslava Ivanova

Page range: 1416-1432

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Abstract

The space of the torsion (0,3)-tensors of the linear connections on almost contact manifolds with B-metric is decomposed in 15 orthogonal and invariant subspaces with respect to the action of the structure group. Three known connections, preserving the structure, are characterized regarding this classification.

Open Access June 21, 2014

Composition results for strongly summing and dominated multilinear operators

Dumitru Popa

Page range: 1433-1446

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Abstract

In this paper we prove some composition results for strongly summing and dominated operators. As an application we give necessary and sufficient conditions for a multilinear tensor product of multilinear operators to be strongly summing or dominated. Moreover, we show the failure of some possible n-linear versions of Grothendieck’s composition theorem in the case n ≥ 2 and give a new example of a 1-dominated, hence strongly 1-summing bilinear operator which is not weakly compact.

Open Access June 21, 2014

Near viability for fully nonlinear differential inclusions

Irina Căpraru, Alina Lazu

Page range: 1447-1459

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Abstract

We consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result.

Open Access June 21, 2014

Partial regularity of solution to generalized Navier-Stokes problem

Václav Mácha

Page range: 1460-1483

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Abstract

In the presented work, we study the regularity of solutions to the generalized Navier-Stokes problem up to a C 2 boundary in dimensions two and three. The point of our generalization is an assumption that a deviatoric part of a stress tensor depends on a shear rate and on a pressure. We focus on estimates of the Hausdorff measure of a singular set which is defined as a complement of a set where a solution is Hölder continuous. We use so-called indirect approach to show partial regularity, for dimension 2 we get even an empty set of singular points.

Open Access June 21, 2014

Ground states for asymptotically periodic Schrödinger-Poisson systems with critical growth

Hui Zhang, Junxiang Xu, Fubao Zhang, Miao Du

Page range: 1484-1499

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Abstract

For a class of asymptotically periodic Schrödinger-Poisson systems with critical growth, the existence of ground states is established. The proof is based on the method of Nehari manifold and concentration compactness principle.

Open Access June 21, 2014

A reverse engineering approach to the Weil representation

Anne-Marie Aubert, Tomasz Przebinda

Page range: 1500-1585

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Abstract

We describe a new approach to the Weil representation attached to a symplectic group over a finite or a local field. We dissect the representation into small pieces, study how they work, and put them back together. This way, we obtain a reversed construction of that of T. Thomas, skipping most of the literature on which the latter is based.

Open Access June 21, 2014

Quasi-minimal rotational surfaces in pseudo-Euclidean four-dimensional space

Georgi Ganchev, Velichka Milousheva

Page range: 1586-1601

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Abstract

In the four-dimensional pseudo-Euclidean space with neutral metric there are three types of rotational surfaces with two-dimensional axis — rotational surfaces of elliptic, hyperbolic or parabolic type. A surface whose mean curvature vector field is lightlike is said to be quasi-minimal. In this paper we classify all rotational quasi-minimal surfaces of elliptic, hyperbolic and parabolic type, respectively.

Open Access June 21, 2014

The behavior of domain decomposition methods when the overlapping length is large

Minh-Binh Tran

Page range: 1602-1614

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Abstract

In this paper, we introduce a new approach for the convergence problem of optimized Schwarz methods by studying a generalization of these methods for a semilinear elliptic equation. We study the behavior of the algorithm when the overlapping length is large.

About this journal

Open Mathematics is a fully peer-reviewed open access journal that publishes original and relevant works on topics across the full span of mathematics. The journal's primary goal is to maintain the high quality of its published content and to provide free, instant, and continued access to all content worldwide.

AIMS AND SCOPE
Open Mathematics aims to promote knowledge directly relevant to all fields of mathematics. Subject areas suitable for publication include, but are not limited to, the following:

Algebra, Algebraic Geometry, Category Theory, Complex Analysis, Control Theory and Optimization, Differential Equations, Differential Geometry, Discrete Mathematics, Dynamical Systems and Ergodic Theory, Functional Analysis, Geometry, Mathematical Logic and Foundations, Mathematical Physics, Number Theory, Numerical Analysis, Operator Theory, Probability Theory and Statistics, Real Analysis, and Topology.

The journal accepts submissions of research articles, reviews, and communications. Submission of a manuscript implies that the work described is not copyrighted, published or submitted elsewhere, except in abstract form. The corresponding author should ensure that all authors approve the manuscript before its submission.