$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 12 Issue 5

May 2014

Issue of Open Mathematics

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Contents
Journal Overview

Open Access February 15, 2014

Abelian varieties over fields of finite characteristic

Yuri Zarhin

Page range: 659-674

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Abstract

The aim of this paper is to extend our previous results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.

Open Access February 15, 2014

On Cohen-Macaulay modules over non-commutative surface singularities

Yuriy Drozd, Volodymyr Gavran

Page range: 675-687

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Abstract

We generalize the results of Kahn about a correspondence between Cohen-Macaulay modules and vector bundles to non-commutative surface singularities. As an application, we give examples of non-commutative surface singularities which are not Cohen-Macaulay finite, but are Cohen-Macaulay tame.

Open Access February 15, 2014

A bound for the Milnor number of plane curve singularities

Arkadiusz Płoski

Page range: 688-693

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Abstract

Let f = 0 be a plane algebraic curve of degree d > 1 with an isolated singular point at 0 ∈ ℂ2. We show that the Milnor number μ0(f) is less than or equal to (d−1)2 − [d/2], unless f = 0 is a set of d concurrent lines passing through 0, and characterize the curves f = 0 for which μ0(f) = (d−1)2 − [d/2].

Open Access February 15, 2014

Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety

Vitaly Tarasov, Alexander Varchenko

Page range: 694-710

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Abstract

We describe hypergeometric solutions of the quantum differential equation of the cotangent bundle of a $$\mathfrak{g}\mathfrak{l}_n$$ partial flag variety. These hypergeometric solutions manifest the Landau-Ginzburg mirror symmetry for the cotangent bundle of a partial flag variety.

Open Access February 15, 2014

On the asymptotic form of convex hulls of Gaussian random fields

Youri Davydov, Vygantas Paulauskas

Page range: 711-720

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Abstract

We consider a centered Gaussian random field X = {X t : t ∈ T} with values in a Banach space $$\mathbb{B}$$ defined on a parametric set T equal to ℝm or ℤm. It is supposed that the distribution of X t is independent of t. We consider the asymptotic behavior of closed convex hulls W n = conv{X t : t ∈ T n}, where (T n) is an increasing sequence of subsets of T. We show that under some conditions of weak dependence for the random field under consideration and some sequence (b n)n≥1 with probability 1, (in the sense of Hausdorff distance), where the limit set is the concentration ellipsoid of . The asymptotic behavior of the mathematical expectations Ef(W n), where f is some function, is also studied.

Open Access February 15, 2014

The Carathéodory topology for multiply connected domains II

Mark Comerford

Page range: 721-741

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Abstract

We continue our exposition concerning the Carathéodory topology for multiply connected domains which we began in [Comerford M., The Carathéodory topology for multiply connected domains I, Cent. Eur. J. Math., 2013, 11(2), 322–340] by introducing the notion of boundedness for a family of pointed domains of the same connectivity. The limit of a convergent sequence of n-connected domains which is bounded in this sense is again n-connected and will satisfy the same bounds. We prove a result which establishes several equivalent conditions for boundedness. This allows us to extend the notions of convergence and equicontinuity to families of functions defined on varying domains.

Open Access February 15, 2014

Properties of derivations on some convolution algebras

Thomas Pedersen

Page range: 742-751

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Abstract

For all convolution algebras L 1[0, 1); L loc1 and A(ω) = ∩n L 1(ωn), the derivations are of the form D μ f = Xf * μ for suitable measures μ, where (Xf)(t) = tf(t). We describe the (weakly) compact as well as the (weakly) Montel derivations on these algebras in terms of properties of the measure μ. Moreover, for all these algebras we show that the extension of D μ to a natural dual space is weak-star continuous.

Open Access February 15, 2014

The cone of nonnegative polynomials with nonnegative coefficients and linear operators preserving this cone

Olga Katkova, Anna Vishnyakova

Page range: 752-760

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Abstract

Let be the cone of real univariate polynomials of degree ≤ 2n which are nonnegative on the real axis and have nonnegative coefficients. We describe the extremal rays of this convex cone and the class of linear operators, acting diagonally in the standard monomial basis, preserving this cone.

Open Access February 15, 2014

Boundary vs. interior conditions associated with weighted composition operators

Kei Izuchi, Yuko Izuchi, Shûichi Ohno

Page range: 761-777

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Abstract

Associated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk $$\mathbb{D}$$, we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior $$\mathbb{D}$$ and on the boundary $$\partial \mathbb{D}$$ respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators.

Open Access February 15, 2014

Characterization of intermediate values of the triangle inequality II

Hiroki Sano, Tamotsu Izumida, Ken-Ichi Mitani, Tomoyoshi Ohwada, Kichi-Suke Saito

Page range: 778-786

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Abstract

In [Mineno K., Nakamura Y., Ohwada T., Characterization of the intermediate values of the triangle inequality, Math. Inequal. Appl., 2012, 15(4), 1019–1035] there was established a norm inequality which characterizes all intermediate values of the triangle inequality, i.e. C n that satisfy 0 ≤ C n ≤ Σj=1n ‖x j‖ − ‖Σj=1n x j‖, x 1,...,x n ∈ X. Here we study when this norm inequality attains equality in strictly convex Banach spaces.

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.