$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 2 Issue 2

April 2004

Issue of Open Mathematics

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Contents
Journal Overview

Open Access April 1, 2004

Hochschild Cohomology of skew group rings and invariants

E. Marcos, R. Martínez-Villa, Ma. Martins

Page range: 177-190

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Abstract

Let A be a k-algebra and G be a group acting on A. We show that G also acts on the Hochschild cohomology algebra HH ⊙ (A) and that there is a monomorphism of rings HH ⊙ (A) G→HH ⊙ (A[G]). That allows us to show the existence of a monomorphism from HH ⊙ (Ã) G into HH ⊙ (A), where Ã is a Galois covering with group G.

Open Access April 1, 2004

A numerical solution of a two-dimensional transport equation

Olga Martin

Page range: 191-198

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Abstract

In this paper we present a variational method for approximating solutions of the Dirichlet problem for the neutron transport equation in the stationary case. Error estimates from numerical examples are used to evaluate an approximation of the solution with respect to the steps of two grids.

Open Access April 1, 2004

Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients

Dana Piciu

Page range: 199-217

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Abstract

The aim of this paper is to define the notions of pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (taking as a guide-line the elegant construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambek-see [14], p.36). For some informal explanations of the notion of fraction see [14], p. 37. In the last part of this paper the existence of the maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (Theorem 4.5) is proven and I give explicit descriptions of this MV-algebra for some classes of pseudo MV-algebras.

Open Access April 1, 2004

Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold

Masahito Toda

Page range: 218-249

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Abstract

The paper studies the first homology of finite regular branched coverings of a universal Borromean orbifold called B 4,4,4ℍ3. We investigate the irreducible components of the first homology as a representation space of the finite covering transformation group G. This gives information on the first betti number of finite coverings of general 3-manifolds by the universality of B 4,4,4. The main result of the paper is a criterion in terms of the irreducible character whether a given irreducible representation of G is an irreducible component of the first homology when G admits certain symmetries. As a special case of the motivating argument the criterion is applied to principal congruence subgroups of B 4,4,4. The group theoretic computation shows that most of the, possibly nonprincipal, congruence subgroups are of positive first Betti number.

Open Access April 1, 2004

Quasilinearization for the periodic boundary value problem for hybrid differential equation

L. Hall, S. Hristova

Page range: 250-259

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Abstract

The method of quasilinearization for a periodic boundary value problem for nonlinear hybrid differential equations is studied. It is shown that the convergence is quadratic.

Open Access April 1, 2004

The Dirichlet problem for Baire-one functions

Jiří Spurný

Page range: 260-271

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Abstract

Let X be a compact convex set and let ext X stand for the set of all extreme points of X. We characterize those bounded function defined on ext X which can be extended to an affine Baire-one function on the whole set X.

Open Access April 1, 2004

Generalized Mukai conjecture for special Fano varieties

Marco Andreatta, Elena Chierici, Gianluca Occhetta

Page range: 272-293

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Abstract

Let X be a Fano variety of dimension n, pseudoindex i X and Picard number ρX. A generalization of a conjecture of Mukai says that ρX(i X−1)≤n. We prove that the conjecture holds for a variety X of pseudoindex i X≥n+3/3 if X admits an unsplit covering family of rational curves; we also prove that this condition is satisfied if ρX> and either X has a fiber type extremal contraction or has not small extremal contractions. Finally we prove that the conjecture holds if X has dimension five.

Open Access April 1, 2004

Cycles of polynomial mappings in two variables over rings of integers in quadratic fields

T. Pezda

Page range: 294-331

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Abstract

We find all possible cycle-lengths for polynomial mappings in two variables over rings of integers in quadratic extensions of rationals.

Open Access April 1, 2004

Affinely equivalent complete flat manifolds

Michal Sadowski

Page range: 332-338

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Abstract

Let E Aff(Γ,G, m) be the set of affine equivalence classes of m-dimensional complete flat manifolds with a fixed fundamental group Γ and a fixed holonomy group G. Let n be the dimension of a closed flat manifold whose fundamental group is isomorphic to Γ. We describe E Aff(Γ,G, m) in terms of equivalence classes of pairs (ε, ρ), consisting of epimorphisms of Γ onto G and representations of G in ℝm-n. As an application we give some estimates of card E Aff(Γ,G, m).

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.