$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 1 Issue 4

December 2003

Issue of Open Mathematics

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Journal Overview

Open Access December 1, 2003

Schur and Schubert polynomials as Thom polynomials—cohomology of moduli spaces

László Fehér, Richárd Rimányi

Page range: 418-434

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Abstract

The theory of Schur and Schubert polynomials is revisited in this paper from the point of view of generalized Thom polynomials. When we apply a general method to compute Thom polynomials for this case we obtain a new definition for (double versions of) Schur and Schubert polynomials: they will be solutions of interpolation problems.

Open Access December 1, 2003

On subadditive functions and ψ-additive mappings

Janusz Matkowski

Page range: 435-440

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Abstract

In [4], assuming among others subadditivity and submultiplicavity of a function ψ: [0, ∞)→[0, ∞), the authors proved a Hyers-Ulam type stability theorem for “ψ-additive” mappings of a normed space into a normed space. In this note we show that the assumed conditions of the function ψ imply that ψ=0 and, consequently, every “ψ-additive” mapping must be additive

Open Access December 1, 2003

K-subanalytic rectilinearization and uniformization

Artur Piękosz

Page range: 441-456

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Abstract

We prove rectilinearization and uniformization theorems for K-subanalytic (∝anK-definable) sets and functions using the Lion-Rolin formula. Parallel reasoning gives standard results for the subanalytic case.

Open Access December 1, 2003

Domestic iterated one-point extensions of algebras by two-ray modules

Grzegorz Bobiński, Andrzej Skowroński

Page range: 457-476

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Abstract

In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the Auslander-Reiten translation. Moreover, we exhibit a wide class of almost sincere domestic simply connected algebras of large global dimensions.

Open Access December 1, 2003

Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field

Michael Melgaard

Page range: 477-509

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Abstract

For fixed magnetic quantum number m results on spectral properties and scattering theory are given for the three-dimensional Schrödinger operator with a constant magnetic field and an axisymmetrical electric potential V. In various, mostly singular settings, asymptotic expansions for the resolvent of the Hamiltonian H m+Hom+V are deduced as the spectral parameter tends to the lowest Landau threshold. Furthermore, scattering theory for the pair (H m, H om) is established and asymptotic expansions of the scattering matrix are derived as the energy parameter tends to the lowest Landau threshold.

Open Access December 1, 2003

Variation of the reduction type of elliptic curves under small base change with wild ramification

Masanari Kida

Page range: 510-560

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Abstract

We study the variation of the reduction type of elliptic curves under base change. A complete description of the variation is given when the base field is the p-adic field and the base change is of small degree.

Open Access December 1, 2003

Representation of Hilbert algebras and implicative semilattices

Sergio Celani

Page range: 561-572

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Abstract

In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.

Open Access December 1, 2003

The closure diagram for nilpotent orbits of the split real form of E8

Dragomir Đoković

Page range: 573-643

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Abstract

Let $$\mathcal{O}_1 $$ and $$\mathcal{O}_2 $$ be adjoint nilpotent orbits in a real semisimple Lie algebra. Write $$\mathcal{O}_1 $$ ≥ $$\mathcal{O}_2 $$ if $$\mathcal{O}_2 $$ is contained in the closure of $$\mathcal{O}_1 $$ . This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the split real form of the simple complex Lie algebra, E 8. The proof is based on the fact that the Kostant-Sekiguchi correspondence preserves the closure ordering. We also present a comprehensive list of simple representatives of these orbits, and list the irreeducible components of the boundaries $$\partial \mathcal{O}_1^i $$ and of the intersections $$\overline {\mathcal{O}_l^i } \cap \overline {\mathcal{O}_l^j } $$ .

Open Access December 1, 2003

On the Hilbert function of curvilinear zero-dimensional subschemes of projective spaces

E. Ballico, R. Notari, M. Spreafico

Page range: 644-649

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Abstract

Here we show the existence of strong restrictions for the Hilbert function of zerodimensional curvilinear subschemes of P n with one point as support and with high regularity index.

Open Access December 1, 2003

Stable vector bundles over cuspidal cubics

Lesya Bodnarchuk, Yuriy Drozd

Page range: 650-660

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Abstract

We give a complete classification of stable vector bundles over a cuspidal cubic and calculate their cohomologies. The technique of matrix problems is used, similar to [2, 3].

Open Access December 1, 2003

On representation theory and the cohomology rings of irreducible compact hyperkähler manifolds of complex dimension four

Daniel Guan

Page range: 661-669

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Abstract

In this paper, we continue the study of the possible cohomology rings of compact complex four dimensional irreducible hyperkähler manifolds. In particular, we prove that in the case b 2=7, b 3=0 or 8. The latter was achieved by the Beauville construction.

Open Access December 1, 2003

On quasistatic inelastic models of gradient type with convex composite constitutive equations

Krzysztof Chełmiński

Page range: 670-689

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Abstract

This article defines and presents the mathematical analysis of a new class of models from the theory of inelastic deformations of metals. This new class, containing so called convex composite models, enlarges the class containing monotone models of gradient type defined in [1]. This paper starts to establish the existence theory for models from this new class; we restrict our investigations to the coercive and linear self-controlling case.

Open Access December 1, 2003

Absolutely continuous functions of several variables and diffeomorphisms

Stanislav Hencl, Jan Malý

Page range: 690-705

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Abstract

In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an example of a function which is absolutely continuous with respect cubes but not with respect to balls.

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.