$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 11 Issue 10

October 2013

Issue of Open Mathematics

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Contents
Journal Overview

Open Access July 20, 2013

On orbits of the automorphism group on an affine toric variety

Ivan Arzhantsev, Ivan Bazhov

Page range: 1713-1724

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Abstract

Let X be an affine toric variety. The total coordinates on X provide a canonical presentation $$\bar X \to X$$ of X as a quotient of a vector space $$\bar X$$ by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.

Open Access July 20, 2013

Completely normal elements in some finite abelian extensions

Ja Koo, Dong Shin

Page range: 1725-1731

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Abstract

We present some completely normal elements in the maximal real subfields of cyclotomic fields over the field of rational numbers, relying on the criterion for normal element developed in [Jung H.Y., Koo J.K., Shin D.H., Normal bases of ray class fields over imaginary quadratic fields, Math. Z., 2012, 271(1–2), 109–116]. And, we further find completely normal elements in certain abelian extensions of modular function fields in terms of Siegel functions.

Open Access July 20, 2013

The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group

Leonid Kurdachenko, Javier Otal

Page range: 1732-1741

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Abstract

We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.

Open Access July 20, 2013

Groups where each element is conjugate to its certain power

Pál Hegedűs

Page range: 1742-1749

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Abstract

This paper deals with a rationality condition for groups. Let n be a fixed positive integer. Suppose every element g of the finite solvable group is conjugate to its nth power g n. Let p be a prime divisor of the order of the group. We conclude that the multiplicative order of n modulo p is small, or p is small.

Open Access July 20, 2013

The one-point Lindelöfication of an uncountable discrete space can be surlindelöf

Oleg Okunev

Page range: 1750-1754

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Abstract

We prove that the one-point Lindelöfication of a discrete space of cardinality ω 1 is homeomorphic to a subspace of C p (X) for some hereditarily Lindelöf space X if the axiom holds.

Open Access July 20, 2013

Remarks on absolutely star countable spaces

Yan-Kui Song

Page range: 1755-1762

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Abstract

We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed subspace which is not star countable (hence not absolutely star countable); (4) assuming $$2^{\aleph _0 } = 2^{\aleph _1 }$$, there exists an absolutely star countable normal space having a regular closed subspace which is not star countable (hence not absolutely star countable).

Open Access July 20, 2013

The Lindelöf principle in ℂn

Peter Dovbush

Page range: 1763-1773

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Abstract

Let D be a bounded domain in ℂn. A holomorphic function f: D → ℂ is called normal function if f satisfies a Lipschitz condition with respect to the Kobayashi metric on D and the spherical metric on the Riemann sphere ̅ℂ. We formulate and prove a few Lindelöf principles in the function theory of several complex variables.

Open Access July 20, 2013

Abstract Korovkin-type theorems in modular spaces and applications

Carlo Bardaro, Antonio Boccuto, Xenofon Dimitriou, Ilaria Mantellini

Page range: 1774-1784

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Abstract

We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results with respect to an axiomatic convergence, including almost convergence. An extension to non positive operators is also studied. Finally, we give some examples and applications to moment and bivariate Kantorovich-type operators, showing that our results are proper extensions of the corresponding classical ones.

Open Access July 20, 2013

Closure of dilates of shift-invariant subspaces

Moisés Soto-Bajo

Page range: 1785-1799

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Abstract

Let V be any shift-invariant subspace of square summable functions. We prove that if for some A expansive dilation V is A-refinable, then the completeness property is equivalent to several conditions on the local behaviour at the origin of the spectral function of V, among them the origin is a point of A*-approximate continuity of the spectral function if we assume this value to be one. We present our results also in a more general setting of A-reducing spaces. We also prove that the origin is a point of A*-approximate continuity of the Fourier transform of any semiorthogonal tight frame wavelet if we assume this value to be zero.

Open Access July 20, 2013

Tricyclic graphs with exactly two main eigenvalues

Xiaoxia Fan, Yanfeng Luo, Xing Gao

Page range: 1800-1816

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Abstract

An eigenvalue of a graph G is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. Let G 0 be the graph obtained from G by deleting all pendant vertices and δ(G) the minimum degree of vertices of G. In this paper, all connected tricyclic graphs G with δ(G 0) ≥ 2 and exactly two main eigenvalues are determined.

Open Access July 20, 2013

Gromov hyperbolicity of planar graphs

Alicia Cantón, Ana Granados, Domingo Pestana, José Rodríguez

Page range: 1817-1830

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Abstract

We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ℝ2 with convex tiles is non-hyperbolic; it is shown that in order to prove this conjecture it suffices to consider tessellation graphs of ℝ2 such that every tile is a triangle and a partial answer to this question is given. A weaker version of this conjecture stating that every tessellation graph of ℝ2 with rectangular tiles is non-hyperbolic is given and partially answered. If this conjecture were true, many tessellation graphs of ℝ2 with tiles which are parallelograms would be non-hyperbolic.

Open Access July 20, 2013

On the minimal length of the longest trail in a fixed edge-density graph

Vajk Szécsi

Page range: 1831-1837

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Abstract

A nearly sharp lower bound on the length of the longest trail in a graph on n vertices and average degree k is given provided the graph is dense enough (k ≥ 12.5).

Open Access July 20, 2013

Real linear isometries between function algebras. II

Osamu Hatori, Takeshi Miura

Page range: 1838-1842

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Abstract

We describe the general form of isometries between uniformly closed function algebras on locally compact Hausdorff spaces in a continuation of the study by Miura. We can actually obtain the form on the Shilov boundary, rather than just on the Choquet boundary. We also give an example showing that the form cannot be extended to the whole maximal ideal space.

Open Access July 20, 2013

Thin sequences in the corona of H ∞

Dimcho Stankov, Tzonio Tzonev

Page range: 1843-1849

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Abstract

In this paper we consider several conditions for sequences of points in M(H ∞) and establish relations between them. We show that every interpolating sequence for QA of nontrivial points in the corona $$M(H^\infty )\backslash \mathbb{D}$$ of H ∞ is a thin sequence for H ∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H ∞ necessarily satisfy the same condition.

Open Access July 20, 2013

Einstein-Weyl structures on lightlike hypersurfaces

Cyriaque Atindogbe, Lionel Bérard-Bergery, Carlos Ogouyandjou

Page range: 1850-1862

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Abstract

We study Weyl structures on lightlike hypersurfaces endowed with a conformal structure of certain type and specific screen distribution: the Weyl screen structures. We investigate various differential geometric properties of Einstein-Weyl screen structures on lightlike hypersurfaces and show that, for ambient Lorentzian space ℝ1n+2 and a totally umbilical screen foliation, there is a strong interplay with the induced (Riemannian) Weyl-structure on the leaves.

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.