$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 12 Issue 1

January 2014

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Contents
Journal Overview

Open Access October 30, 2013

Invariant connections and invariant holomorphic bundles on homogeneous manifolds

Indranil Biswas, Andrei Teleman

Page range: 1-13

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Abstract

Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when X has an α-invariant complex structure).

Open Access October 30, 2013

The Mukai conjecture for log Fano manifolds

Kento Fujita

Page range: 14-27

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Abstract

For a log Fano manifold (X,D) with D ≠ 0 and of the log Fano pseudoindex ≥2, we prove that the restriction homomorphism Pic(X) → Pic(D 1) of Picard groups is injective for any irreducible component D 1 ⊂ D. The strategy of our proof is to run a certain minimal model program and is similar to Casagrande’s argument. As a corollary, we prove that the Mukai conjecture (resp. the generalized Mukai conjecture) implies the log Mukai conjecture (resp. the log generalized Mukai conjecture).

Open Access October 30, 2013

Milnor fibration at infinity for mixed polynomials

Ying Chen

Page range: 28-38

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Abstract

We study the existence of Milnor fibration on a big enough sphere at infinity for a mixed polynomial f: ℝ2n → ℝ2. By using strongly non-degenerate condition, we prove a counterpart of Némethi and Zaharia’s fibration theorem. In particular, we obtain a global version of Oka’s fibration theorem for strongly non-degenerate and convenient mixed polynomials.

Open Access October 30, 2013

On the number of terms in the middle of almost split sequences over cycle-finite artin algebras

Piotr Malicki, José Peña, Andrzej Skowroński

Page range: 39-45

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Abstract

We prove that the number of terms in the middle of an almost split sequence in the module category of a cycle-finite artin algebra is bounded by 5.

Open Access October 30, 2013

Boolean algebras admitting a countable minimally acting group

Aleksander Błaszczyk, Andrzej Kucharski, Sławomir Turek

Page range: 46-56

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Abstract

The aim of this paper is to show that every infinite Boolean algebra which admits a countable minimally acting group contains a dense projective subalgebra.

Open Access October 30, 2013

Left-right noncommutative Poisson algebras

José Casas, Tamar Datuashvili, Manuel Ladra

Page range: 57-78

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Abstract

The notions of left-right noncommutative Poisson algebra (NPlr-algebra) and left-right algebra with bracket AWBlr are introduced. These algebras are special cases of NLP-algebras and algebras with bracket AWB, respectively, studied earlier. An NPlr-algebra is a noncommutative analogue of the classical Poisson algebra. Properties of these new algebras are studied. In the categories AWBlr and NPlr-algebras the notions of actions, representations, centers, actors and crossed modules are described as special cases of the corresponding wellknown notions in categories of groups with operations. The cohomologies of NPlr-algebras and AWBlr (resp. of NPr-algebras and AWBr) are defined and the relations between them and the Hochschild, Quillen and Leibniz cohomologies are detected. The cases P is a free AWBr, the Hochschild or/and Leibniz cohomological dimension of P is ≤ n are considered separately, exhibiting interesting possibilities of representations of the new cohomologies by the well-known ones and relations between the corresponding cohomological dimensions.

Open Access October 30, 2013

Classification of solvable groups possessing a unique nonlinear non-faithful irreducible character

Amin Saeidi

Page range: 79-83

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Abstract

In this note, we study finite groups possessing exactly one nonlinear non-faithful irreducible character. Our main result is to classify solvable groups that satisfy this property. Also, we give examples to show that these groups need not to be solvable in general.

Open Access October 30, 2013

Ordinal ultrafilters versus P-hierarchy

Andrzej Starosolski

Page range: 84-96

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Abstract

An earlier paper [Starosolski A., P-hierarchy on βω, J. Symbolic Logic, 2008, 73(4), 1202–1214] investigated the relations between ordinal ultrafilters and the so-called P-hierarchy. The present paper focuses on the aspects of characterization of classes of ultrafilters of finite index, existence, generic existence and the Rudin-Keisler-order.

Open Access October 30, 2013

Curvature properties of φ-null Osserman Lorentzian S-manifolds

Letizia Brunetti, Angelo Caldarella

Page range: 97-113

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Abstract

We expound some results about the relationships between the Jacobi operators with respect to null vectors on a Lorentzian S-manifold and the Jacobi operators with respect to particular spacelike unit vectors. We study the number of the eigenvalues of such operators on Lorentzian S-manifolds satisfying the φ-null Osserman condition, under suitable assumptions on the dimension of the manifold. Then, we provide in full generality a new curvature characterization for Lorentzian S-manifolds and we use it to obtain an algebraic decomposition for the Riemannian curvature tensor of φ-null Osserman Lorentzian S-manifolds.

Open Access October 30, 2013

Generalized n-Laplacian: boundedness of weak solutions to the Dirichlet problem with nonlinearity in the critical growth range

Robert Černý

Page range: 114-127

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Abstract

Let n ≥ 2 and let Ω ⊂ ℝn be an open set. We prove the boundedness of weak solutions to the problem $$u \in W_0^1 L^\Phi \left( \Omega \right) and - div\left( {\Phi '\left( {\left| {\nabla u} \right|} \right)\frac{{\nabla u}} {{\left| {\nabla u} \right|}}} \right) + V\left( x \right)\Phi '\left( {\left| u \right|} \right)\frac{u} {{\left| u \right|}} = f\left( {x,u} \right) + \mu h\left( x \right) in \Omega ,$$ where ϕ is a Young function such that the space W 01 L Φ(Ω) is embedded into an exponential or multiple exponential Orlicz space, the nonlinearity f(x, t) has the corresponding critical growth, V(x) is a continuous potential, h ∈ L Φ(Ω) is a non-trivial continuous function and µ ≥ 0 is a small parameter. We consider two classical cases: the case of Ω being an open bounded set and the case of Ω = ℝn.

Open Access October 30, 2013

Second order BVPs with state dependent impulses via lower and upper functions

Irena Rachůnková, Jan Tomeček

Page range: 128-140

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Abstract

The paper deals with the following second order Dirichlet boundary value problem with p ∈ ℕ state-dependent impulses: z″(t) = f (t,z(t)) for a.e. t ∈ [0, T], z(0) = z(T) = 0, z′(τ i+) − z′(τ i−) = I i(τ i, z(τ i)), τ i = γ i(z(τ i)), i = 1,..., p. Solvability of this problem is proved under the assumption that there exists a well-ordered couple of lower and upper functions to the corresponding Dirichlet problem without impulses.

Open Access October 30, 2013

Asymptotic behavior of a sixth-order Cahn-Hilliard system

Alain Miranville

Page range: 141-154

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Abstract

Our aim in this paper is to study the asymptotic behavior, in terms of finite-dimensional attractors, of a sixth-order Cahn-Hilliard system. This system is based on a modification of the Ginzburg-Landau free energy proposed in [Torabi S., Lowengrub J., Voigt A., Wise S., A new phase-field model for strongly anisotropic systems, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 2009, 465(2105), 1337–1359], assuming isotropy.

Open Access October 30, 2013

Approximation of solutions to second order nonlinear Picard problems with Carathéodory right-hand side

Jacek Gulgowski

Page range: 155-166

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Abstract

We present an approximation method for Picard second order boundary value problems with Carathéodory righthand side. The method is based on the idea of replacing a measurable function in the right-hand side of the problem with its Kantorovich polynomial. We will show that this approximation scheme recovers essential solutions to the original BVP. We also consider the corresponding finite dimensional problem. We suggest a suitable mapping of solutions to finite dimensional problems to piecewise constant functions so that the later approximate a solution to the original BVP. That is why the presented idea may be used in numerical computations.

Open Access October 30, 2013

The box parameter for words and permutations

Helmut Prodinger

Page range: 167-174

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Abstract

The box parameter for words counts how often two letters w j and w k define a “box” such that all the letters w j+1; ..., w k−1 fall into that box. It is related to the visibility parameter and other parameters on words. Three models are considered: Words over a finite alphabet, permutations, and words with letters following a geometric distribution. A typical result is: The average box parameter for words over an M letter alphabet is asymptotically given by 2n − 2n H M/M, for fixed M and n → ∞.

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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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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.