$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 5 Issue 1

March 2007

Issue of Open Mathematics

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Contents
Journal Overview

Open Access March 1, 2007

A family of regular vertex operator algebras with two generators

Dražen Adamović

Page range: 1-18

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Abstract

For every m ∈ ℂ ∖ {0, −2} and every nonnegative integer k we define the vertex operator (super)algebra D m,k having two generators and rank $$\frac{{3m}}{{m + 2}}$$ . If m is a positive integer then D m,k can be realized as a subalgebra of a lattice vertex algebra. In this case, we prove that D m,k is a regular vertex operator (super) algebra and find the number of inequivalent irreducible modules.

Open Access March 1, 2007

Perturbation index of linear partial differential-algebraic equations with a hyperbolic part

Lutz Angermann, Joachim Rang

Page range: 19-49

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Abstract

This paper deals with linear partial differential-algebraic equations (PDAEs) which have a hyperbolic part. If the spatial differential operator satisfies a Gårding-type inequality in a suitable function space setting, a perturbation index can be defined. Theoretical and practical examples are considered.

Open Access March 1, 2007

Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussian and Freund distributions

Khadiga Arwini, Christopher Dodson

Page range: 50-83

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Abstract

We provide explicit information geometric tubular neighbourhoods containing all bivariate distributions sufficiently close to the cases of independent Poisson or Gaussian processes. This is achieved via affine immersions of the 4-manifold of Freund bivariate distributions and of the 5-manifold of bivariate Gaussians. We provide also the α-geometry for both manifolds. The Central Limit Theorem makes our neighbourhoods of independence limiting cases for a wide range of bivariate distributions; the topological character of the results makes them stable under small perturbations, which is important for applications in models of stochastic processes.

Open Access March 1, 2007

Integrable three-dimensional coupled nonlinear dynamical systems related to centrally extended operator Lie algebras and their Lax type three-linearization

J. Golenia, O. Hentosh, A. Prykarpatsky

Page range: 84-104

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Abstract

The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integro-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Bäcklund transformation. The connection of this hierarchy with integrable by Lax two-dimensional Davey-Stewartson type systems is studied.

Open Access March 1, 2007

Differential invariants of generic hyperbolic Monge-Ampère equations

Michal Marvan, Alexandre Vinogradov, Valery Yumaguzhin

Page range: 105-133

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Abstract

In this paper basic differential invariants of generic hyperbolic Monge-Ampère equations with respect to contact transformations are constructed and the equivalence problem for these equations is solved.

Open Access March 1, 2007

Scattering properties for a pair of Schrödinger type operators on cylindrical domains

Michael Melgaard

Page range: 134-153

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Abstract

Strong asymptotic completeness is shown for a pair of Schrödinger type operators on a cylindrical Lipschitz domain. A key ingredient is a limiting absorption principle valid in a scale of weighted (local) Sobolev spaces with respect to the uniform topology. The results are based on a refined version of Mourre’s method within the context of pseudo-selfadjoint operators.

Open Access March 1, 2007

Comparison theorems for noncanonical third order nonlinear differential equations

Ivan Mojsej, Ján Ohriska

Page range: 154-163

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Abstract

The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with quasiderivatives. We prove comparison theorems on property A between linear and nonlinear equations. Some integral criteria ensuring property A for nonlinear equations are also given. Our assumptions on the nonlinearity of f are restricted to its behavior only in a neighborhood of zero and a neighborhood of infinity.

Open Access March 1, 2007

Slice modules over minimal 2-fundamental algebras

Zygmunt Pogorzały, Karolina Szmyt

Page range: 164-180

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Abstract

We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard. For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism) a slice module is a tilting module.

Open Access March 1, 2007

On homological classification of pomonoids by regular weak injectivity properties of S-posets

Xia Zhang, Valdis Laan

Page range: 181-200

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Abstract

If S is a partially ordered monoid then a right S-poset is a poset A on which S acts from the right in such a way that the action is compatible both with the order of S and A. By regular weak injectivity properties we mean injectivity properties with respect to all regular monomorphisms (not all monomorphisms) from different types of right ideals of S to S. We give an alternative description of such properties which uses systems of equations. Using these properties we prove several so-called homological classification results which generalize the corresponding results for (unordered) acts over (unordered) monoids proved by Victoria Gould in the 1980’s.

Open Access March 1, 2007

A short proof of Eilenberg and Moore’s theorem

Maria Nogin

Page range: 201-204

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Abstract

In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.

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.