Statistically convergent difference double sequence spaces

In this article we define the notion of statistically convergent difference double sequence spaces. We examine the spaces 2l∞（△, q）, 2c（△, q）, 2cB（△, q）, 2cR（△, q）, 2cBR（△,q） etc. being symmetric, solid, monotone, etc. We prove some inclusion results too.     

New double sequence spaces of fuzzy numbers

Abstract

In this paper we introduce some new double sequence spaces of fuzzy numbers using Orlicz function and also we examine that if a sequence of fuzzy numbers is double strongly convergent with respect to an Orlicz function then it is double statistical convergent.     

Vector valued paranormed statistically convergent double sequence spaces

In this article we introduce the vector valued paranormed sequence spaces and defined over a seminormed space (X,q). We study their different properties like completeness, solidness, symmetry, convergence freeness etc. We prove some inclusion results.      

Independence equivalence classes of cycles

The independence equivalence class of a graph G is the set of graphs that have the same independence polynomial as G. Beaton, Brown and Cameron (2019) found the independence equivalence classes of even cycles, and raised the problem of finding the independence equivalence class of odd cycles. The problem is completely solved in this paper.     

Independence equivalence classes of paths

The independence equivalence class of a graph G is the set of graphs that have the same independence polynomial as G. A graph whose independence equivalence class contains only itself, up to isomorphism, is independence unique. Beaton, Brown and Cameron [2] showed that paths with an odd number of vertices are independence unique and raised the problem of finding the independence equivalence class of paths with an even number of vertices. The problem is completely solved in this paper.     

Vector valued double sequence spaces defined by Orlicz function

In this article we introduce some vector valued double sequence spaces defined by Orlicz function. We study some of their properties like solidness, symmetricity, completeness etc. and prove some inclusion results.     

Two valued measure and some new double sequence spaces in 2-normed spaces

The purpose of this paper is to introduce some new generalized double difference sequence spaces using summability with respect to a two valued measure and an Orlicz function in 2-normed spaces which have unique non-linear structure and to examine some of their properties. This approach has not been used in any context before.     

On enumeration of polynomial equivalence classes

The isomorphism of polynomials(IP),one of the hard problems in multivariate public key cryptography induces an equivalence relation on a set of systems of polynomials.Then the enumeration problem of IP consists of counting the numbers of different classes and counting the cardinality of each class that is highly related to the scale of key space for a multivariate public key cryptosystem.In this paper we show the enumeration of the equivalence classes containing ∑n-1 i=0 aiX2qi when char(Fq) = 2,which implies that these polynomials are all weak IP instances.Moreover,we study the cardinality of an equivalence class containing the binomial aX 2q i + bX 2qj(i=j) over Fqn without the restriction that char(Fq) = 2,which gives us a deeper understanding of finite geometry as a tool to investigate the enumeration problem of IP.     

Some double sequence spaces of interval numbers defined by Orlicz function

In this paper we introduce some interval valued double sequence spaces defined by Orlicz function and study different properties of these spaces like inclusion relations, solidity, etc. We establish some inclusion relations among them. Also we introduce the concept of double statistical convergence for interval number sequences and give an inclusion relation between interval valued double sequence spaces.     

The number of equivalence classes of nondegenerate bilinear and sesquilinear forms over a finite field

Generating functions in the form of infinite products are given for the number of equivalence classes of nondegenerate sesquilinear forms of rank n over GF(q²) and for the number of equivalence (or congruence) classes of nondegenerate bilinear forms of rank n over GF(q).     

Some multiplier generalized difference sequence spaces over n-normed spaces defined by a Musielak-Orlicz function

In the present paper, we introduce some multiplier sequence spaces over n-normed spaces defined by a Musielak-Orlicz functionM = (M _k ). We also study some topological properties and some inclusion relations between these spaces.     

Coverings by classes of permutable equivalence relations

Supported by the Russian Foundation for Fundamental Research, grant No. 93-01-16011.