Abstract

In this paper, we study some basic properties of the zero-divisor graph of ring $F_{p^l} \times F_{q^m} \times F_{r^n}$, where $F_{p^l}$, $F_{q^m}$ and $F_{r^n}$ are fields of order $p^l$, $q^m$ and $r^n$, respectively, $p, q$ and $r$ are primes (not necessarily distinct) and $l, m, n \geq 1$ are positive numbers. Also, we discuss some topological indices of the graph $\Gamma(F_{p^l} \times F_{q^m} \times F_{r^n})$.

Keywords: Zero-divisor graph; direct product of rings; graph parameters..

MSC: 05C10, 05C12, 05C25

Abstract

In this paper, we characterized the matrices of operators that transform the generalized Cesàro sequence space to the convergence sequence space in Banach spaces. Our results generalize the characterization of the sequence space in $L_p$, $1

Keywords: Matrices of operators; Cesàro sequence spaces; Orlicz function.

MSC: 40A30, 40J05

Abstract

In this article, we discuss the curvature properties of statistical submanifolds in cosymplectic statistical manifolds with constant curvature. We also establish some pinching results for such submanifolds and hypersurfaces in cosymplectic statistical manifolds having constant curvature. As an application of the main result we also obtain an obstruction condition for such immersion.

Keywords: Chen-Ricci inequality; dual connections; statistical manifolds; cosymplectic statistical manifolds.

MSC: 53B05, 53B20, 53C40

Abstract

Following the generalization of Moore-Smith convergence of nets to fuzzy topological spaces which was given in Pu Pao-Ming, Liu Ying-Ming, \emph{Fuzzy topology I. Neighborhood structure of a fuzzy point and Moore-Smith convergence}, J. Math. Anal. Appl., \textbf{76} (1980), 571--599, a characterization theorem between fuzzy topologies and fuzzy convergence classes was introduced in Ying-Ming Liu, \emph{On fuzzy convergence classes}, Fuzzy Sets and Systems, \textbf{30} (1989), 47--51. Our goal in this paper is to provide modified versions of this characterization. Specifically, we will introduce the concept of fuzzy semi-convergence class to give an alternative characterization of fuzzy topology, in relation to the ordinary convergence of fuzzy nets, and then we will introduce the concept of fuzzy ideal convergence class to obtain analogous results, in relation to the ideal convergence of fuzzy nets.

Keywords: Fuzzy set; fuzzy topology; fuzzy convergence class; fuzzy ideal convergence class.

MSC: 54A20

Abstract

In this paper, we study the relation between a space $X$ satisfying certain generalized metric properties and the Pixley-Roy hyperspace $\mathcal F[X]$ over $X$ satisfying the same properties. We prove that if $X$ has a $\sigma$-point-finite $cn$-network (resp., $ck$-network), then $\mathcal F[X]$ also has a $\sigma$-point-finite $cn$-network (resp., $ck$-network).

Keywords: Pixley-Roy; hyperspace; $cn$-network; $ck$-network; $\sigma$-point-finite.

MSC: 54B20, 54D20

Abstract

In this paper, by some group action, we introduce a new type of weighted Orlicz spaces $L^\Phi_{w,v}(\Omega)$, where $w$ and $v$ are weights on $\Omega$ and $\Phi$ is a Young function. We study conditions under which $L^\Phi_{w,v}(G)$ is a convolution Banach algebra, where $G$ is a locally compact group.

Keywords: Locally compact group; weighted Orlicz algebra; Young function; convolution; spaceablity; inclusion.

MSC: 46E30, 47B37, 43A15