$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 13 Issue 1

January 2015

Issue of Open Mathematics

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Contents
Journal Overview

In the present article we define W-paths of elements in a W-perfect group as a useful tools and obtain their basic properties.

We study the problem of computing the maximal and minimal possible eigenvalues of a symmetric matrix when the matrix entries vary within compact intervals. In particular, we focus on computational complexity of determining these extremal eigenvalues with some approximation error. Besides the classical absolute and relative approximation errors, which turn out not to be suitable for this problem, we adapt a less known one related to the relative error, and also propose a novel approximation error. We show in which error factors the problem is polynomially solvable and in which factors it becomes NP-hard.

The symmetry of the Bagley–Torvik equation is investigated by using the Lie group analysis method. The Bagley–Torvik equation in the sense of the Riemann–Liouville derivatives is considered. Then we prove a Noetherlike theorem for fractional Lagrangian densities with the Riemann-Liouville fractional derivative and few examples are presented as an application of the theory.

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.

Volume 13 Issue 1

Issue of Open Mathematics

On the use of semi-closed sets and functions in convex analysis

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Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces

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Absolutely strongly star-Hurewicz spaces

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On the strong metric dimension of the strong products of graphs

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Erratum to “On the strong metric dimension of the strong products of graphs”

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Pointwise density topology

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Invariance groups of finite functions and orbit equivalence of permutation groups

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Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition

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Dynamics of differentiation operators on generalized weighted Bergman spaces

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Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices

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Vietoris topology on spaces dominated by second countable ones

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Identities arising from higher-order Daehee polynomial bases

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A function space from a compact metrizable space to a dendrite with the hypo-graph topology

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Solutions of minus partial ordering equations over von Neumann regular rings

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New interval oscillation criteria for second-order functional differential equations with nonlinear damping

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Notes on monotonically metacompact generalized ordered spaces

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The classification of modular Lie superalgebras of type M

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On the smoothness of the free boundary in a nonlocal one-dimensional parabolic free boundary value problem

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Two bounds on the noncommuting graph

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A new kind of the solution of degenerate parabolic equation with unbounded convection term

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A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings

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Properties of k-beta function with several variables

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Commuting Conditions of the k-th Cho operator with the structure Jacobi operator of real hypersurfaces in complex space forms

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Infinite dimension of solutions of the Dirichlet problem

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An extended Prony’s interpolation scheme on an equispaced grid

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Positivity and contractivity in the dynamics of clusters’ splitting with derivative of fractional order

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On Poincaré duality for pairs (G,W)

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Some identities of degenerate special polynomials

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Chaotic and hypercyclic properties of the quasi-linear Lasota equation

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Semilinear problems for the fractional laplacian with a singular nonlinearity

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Existence, decay and blow up of solutions for the extensible beam equation with nonlinear damping and source terms

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On some ideal related to the ideal (v0)

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The Umbral operator and the integration involving generalized Bessel-type functions

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Mild solution of fractional order differential equations with not instantaneous impulses

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On graded P-compactly packed modules

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The classification of partially symmetric 3-braid links

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Linear and nonlinear abstract differential equations of high order

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Real Hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator

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Exact solutions of supersymmetric Burgers equation with Bosonization procedure

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On some ideal related to the ideal (v⁰)

Linear relations between modular forms for Г₀⁺(p)

Coupled fixed point theorems for (α, φ)_g-contractive type mappings in partially ordered G-metric spaces

On Vⁿ-semigroups

Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X^-1A=L