Published by De Gruyter

Volume 58 Issue 5

October 2008

Issue of Mathematica Slovaca

Contents
Journal Overview

Open Access August 27, 2008

Formations of lattice ordered groups and of GMV-algebras

Ján Jakubík

Page range: 521-534

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Abstract

A class of lattice ordered groups is called a formation if it is closed with respect to homomorphic images and finite subdirect products. Analogously we define the formation of GMV-algebras. Let us denote by ℱ1 and ℱ2 the collection of all formations of lattice ordered groups or of GMV-algebras, respectively. Both ℱ1 and ℱ2 are partially ordered by the class-theoretical inclusion. We prove that ℱ1 satisfies the infinite distributivity law and that ℱ2 is isomorphic to a principal ideal of ℱ1.

Open Access August 27, 2008

Note on a subgroup of Levy’s group

Milan Paštéka

Page range: 535-540

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Abstract

In the paper, there are proved some properties of the asymptotic density using the permutations.

Open Access August 27, 2008

Equivalence and symmetries of second-order differential equations

V. Tryhuk, O. Dlouhý

Page range: 541-566

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Abstract

In this article we investigate the equivalence of underdetermined differential equations and differential equations with deviations of second order with respect to the pseudogroup of transformations $$ \bar x $$ = φ(x), ȳ = ȳ($$ \bar x $$) = L(x) + y(x), $$ \bar z $$ = $$ \bar z $$($$ \bar x $$) = M(x) + z(x). Our main aim is to determine such equations that admit a large pseudogroup of symmetries. Instead the common direct calculations, we use some more advanced tools from differential geometry, however, our exposition is self-contained and only the most fundamental properties of differential forms are employed.

Open Access August 27, 2008

Maximum principle and existence of solutions for non necessarily cooperative systems involving Schrödinger operators

H. Serag, A. Qamlo

Page range: 567-580

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Abstract

In this paper, we obtain the necessary and sufficient conditions for having the maximum principle and existence of positive solutions for some cooperative systems involving Schrödinger operators defined on unbounded domains. Then, we deduce the existence of solutions for semi-linear systems. Finally we discuss the generalized maximum principle (gf q-positivity) for non cooperative systems.

Open Access August 27, 2008

Oscillation of fourth order nonlinear neutral difference equations-II

A. Tripathy

Page range: 581-604

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Abstract

Oscillatory and asymptotic behaviour of solutions of a class of fourth order nonlinear neutral difference equations of the form $$ \Delta ^2 (r(n)\Delta ^2 (y(n) + p(n)y(n - m))) + q(n)G(y(n - k)) = 0 $$ and $$ (E) \Delta ^2 (r(n)\Delta ^2 (y(n) + p(n)y(n - m))) + q(n)G(y(n - k)) = f(n) $$ are studied under the assumption $$ \sum\limits_{n = 0}^\infty {\tfrac{n} {{r(n)}}} $$ < ∞, for different ranges of p(n). Sufficient conditions are obtained for the existence of positive bounded solutions of (E).

Open Access August 27, 2008

I and I*-convergence of double sequences

Pratulananda Das, Pavel Kostyrko, Władysław Wilczyński, Prasanta Malik

Page range: 605-620

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Abstract

The idea of I-convergence was introduced by Kostyrko et al (2001) and also independently by Nuray and Ruckle (2000) (who called it generalized statistical convergence) as a generalization of statistical convergence (Fast (1951), Schoenberg(1959)). For the last few years, study of these convergences of sequences has become one of the most active areas of research in classical Analysis. In 2003 Muresaleen and Edely introduced the concept of statistical convergence of double sequences. In this paper we consider the notions of I and I*-convergence of double sequences in real line as well as in general metric spaces. We primarily study the inter-relationship between these two types of convergence and then investigate the category and porosity position of bounded I and I*-convergent double sequences.

Open Access August 27, 2008

Sequence spaces of fuzzy real numbers defined by Orlicz functions

Binod Tripathy, Bipul Sarma

Page range: 621-628

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Abstract

In this article we study different properties of convergent, null and bounded sequence spaces of fuzzy real numbers defined by an Orlicz function, like completeness, solidness, symmetricity, convergence free etc. We prove some inclusion results, too.

Open Access August 27, 2008

Extensions of homogeneous polynomials on c 0(l 2i)

M. Lourenço, L. Pellegrini

Page range: 629-634

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Abstract

We show that a 2-homogeneous polynomial on the complex Banach space c 0 l 2i) is norm attaining if and only if it is finite (i.e, depends only on finite coordinates). As the consequence, we show that there exists a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on c 0(l 2i).

Open Access August 27, 2008

Approximation of multivariate distribution functions

Margus Pihlak

Page range: 635-652

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Abstract

In the paper the unknown distribution function is approximated with a known distribution function by means of Taylor expansion. For this approximation a new matrix operation — matrix integral — is introduced and studied in [PIHLAK, M.: Matrix integral, Linear Algebra Appl. 388 (2004), 315–325]. The approximation is applied in the bivariate case when the unknown distribution function is approximated with normal distribution function. An example on simulated data is also given.

About this journal

Objective
Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca.

It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.

Topics

Algebra and number theory
Analysis
Graph theory
Probability theory and mathematical statistics
Topology, measure theory and integration
Many-valued logic and quantum structures
Differential equations and dynamic systems
Physics
Soft computing
Cryptography
Biology
Economy
Measuring

Article formats
Original research articles, short notes

Information on submission process