$Open Mathematics$

Open Access Published by De Gruyter Open Access

Volume 1 Issue 3

September 2003

Issue of Open Mathematics

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Journal Overview

Open Access September 1, 2003

Nonadaptive search problem with sets of equal sum

Emil Kolev

Page range: 272-283

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Abstract

Consider the set A={1,2,3,…,2n}, n≥3 and let x∈ A be unknown element. For given natural number S we are allowed to ask whether x belongs to a subset B of A such that the sum of the elements of B equals S. We investigate for which S it is possible to find x using a nonadaptive search.

Open Access September 1, 2003

Smooth approximations without critical points

Petr Hájek, Michal Johanis

Page range: 284-291

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Abstract

In any separable Banach space containing c 0 which admits a C k-smooth bump, every continuous function can be approximated by a C k-smooth function whose range of derivative is of the first category. Moreover, the approximation can be constructed in such a way that its derivative avoids a prescribed countable set (in particular the approximation can have no critical points). On the other hand, in a Banach space with the RNP, the range of the derivative of every smooth bounded bump contains a set residual in some neighbourhood of zero.

Open Access September 1, 2003

Almost periodic solutions of neutral impulsive systems with periodic time-dependent perturbed delays

Valéry Covachev, Zlatinka Covacheva, Haydar Akça, Eada Al-Zahrani

Page range: 292-314

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Abstract

A neutral impulsive system with a small delay of the argument of the derivative and another delay which differs from a constant by a periodic perturbation of a small amplitude is considered. If the corresponding system with constant delay has an isolated ω-periodic solution and the period of the delay is not rationally dependent on ω, then under a nondegeneracy assumption it is proved that in any sufficiently small neighbourhood of this orbit the perturbed system has a unique almost periodic solution.

Open Access September 1, 2003

On the secant varieties to the osculating variety of a Veronese surface

E. Ballico, C. Fontanari

Page range: 315-326

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Abstract

In this paper we study the k-th osculating variety of the order d Veronese embedding of P n. In particular, for k=n=2 we show that the corresponding secant varieties have the expected dimension except in one case.

Open Access September 1, 2003

Decompositions of the category of noncommutative sets and Hochschild and cyclic homology

Jolanta Słomińska

Page range: 327-331

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Abstract

In this note we show that the main results of the paper [PR] can be obtained as consequences of more general results concerning categories whose morphisms can be uniquely presented as compositions of morphisms of their two subcategories with the same objects. First we will prove these general results and then we will apply it to the case of finite noncommutative sets.

Open Access September 1, 2003

On a family of vector space categories

Grzegorz Bobiński, Andrzej Skowroński

Page range: 332-359

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Abstract

In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten quivers.

Open Access September 1, 2003

On the torsion of linear higher order connections

Ivan Kolář

Page range: 360-366

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Abstract

For a linear r-th order connection on the tangent bundle we characterize geometrically its integrability in the sense of the theory of higher order G-structures. Our main tool is a bijection between these connections and the principal connections on the r-th order frame bundle and the comparison of the torsions under both approaches.

Open Access September 1, 2003

A pathwise solution for nonlinear parabolic equations with stochastic perturbations

Bogdan Iftimie, Constantin Varsan

Page range: 367-381

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Abstract

We analyse here a semilinear stochastic partial differential equation of parabolic type where the diffusion vector fields are depending on both the unknown function and its gradient ∂ xu with respect to the state variable, ∈ ℝn. A local solution is constructed by reducing the original equation to a nonlinear parabolic one without stochastic perturbations and it is based on a finite dimensional Lie algebra generated by the given diffusion vector fields.

Open Access September 1, 2003

The prime and maximal spectra and the reticulation of BL-algebras

Laurenťiu Leuštean

Page range: 382-397

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Abstract

In this paper we study the prime and maximal spectra of a BL-algebra, proving that the prime spectrum is a compact T 0 topological space and that the maximal spectrum is a compact Hausdorff topological space. We also define and study the reticulation of a BL-algebra.

Open Access September 1, 2003

An essay on model theory

Ludomir Newelski

Page range: 398-410

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Abstract

Some basic ideas of model theory are presented and a personal outlook on its perspectives is given.

Open Access September 1, 2003

A necessary and sufficient condition for the existence of an exponential attractor

Dalibor Pražák

Page range: 411-417

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Abstract

We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction. As an application, we show that the evolution operator for the wave equation with nonlinear damping has an exponential attractor.

About this journal

Open Mathematics is a fully peer-reviewed open access journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, no space constraints and quick publication after the acceptance.
Open Mathematics is listed inter alia by Clarivate Analytics (formerly Thomson Reuters) - Current Contents/Physical, Chemical and Earth Sciences, JCR and SCIE. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind.

The journal aims at presenting high-impact and relevant research 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

Special Issues:

Fractional Problems with Variable-Order or Variable Exponents
GUEST EDITORS:
Jiabin Zuo, Guangzhou University, China
Debajyoti Choudhuri, National Institute of Technology Rourkela, India
ADVISORY EDITOR:
J. Vanterler da C. Sousa, University of Campinas, Campinas, Brazil