$Open Mathematics$

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

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20 YEARS - 20 VOLUMES

Look back at the journal’s 20-year journey and browse its high-impact content. Visit the website

On this occasion seven papers of excellent and profound mathematics have been published to encourage reflection about further directions in the field.
See the content of the SPECIAL ISSUE ON "FUTURE DIRECTIONS OF FURTHER DEVELOPMENTS IN MATHEMATICS"　　　

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SPECIAL ISSUE PROPOSALS

If you have an idea for a prospective topical issue, please complete Special Issue proposal questionaire (in DOC), addressing your proposal to the Managing Editor (Dr. Justyna Zuk, Justyna.Zuk@degruyter.com).

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Open Mathematics is a fully peer-reviewed open access journal that publishes significant, original and relevant works on topics across the full span of mathematics. Coverage includes:

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, Topology.

In order to sustain the publishing process, each article accepted for publication in Open Mathematics is subject to an Article Processing Charge of €1000. This fee is used to cover the costs of the peer-review process, professional typesetting and copyediting, as well as online hosting, long-term preservation, and extensive promotion to potential readers. There is no submission fee. Information regarding payment of the charge will be provided following acceptance for publication. Inquiries concerning Article Processing Charges should be addressed to the Managing Editor (Dr. Justyna Zuk, Justyna.Zuk@degruyter.com) before or just after submission of a manuscript.

Detailed information on　Article Processing Charges, Editorial Policy, Instructions for Authors etc. can be found as documents (in PDF) in the Supplementary Materials below. Publishing Ethics, Open Access Services at DG, FAQ for Authors and Editors etc. can be directed from External Links.