Iranian Journal of Mathematical Sciences and Informatics
Volume:16 Issue: 2, Nov 2021

We study Beck-like coloring of measurable functions on a measure space Ω taking values in a measurable semigroup ∆. To any measure space Ω and any measurable semigroup ∆, we assign a graph (called a zero-divisor graph) whose vertices are labeled by the classes of measurable functions defined on Ω and having values in ∆, with two vertices f and g adjacent if f · g = 0 a.e.. We show that, if Ω is atomic, then not only the Beck’s conjecture holds but also the domination number coincides to the clique number and chromatic number as well. We also determine some other graph properties of such a graph.

Tallafha, A. and Alhihi S. in [15], asked the following question. If f is a contraction from a complete semi-linear uniform space (X,Γ) to it self, is f has a unique fixed point. In this paper, we shall answer this question negatively and we shall show that convex metric space and M-space are equivalent except uniqueness. Also we shall characterize convex metric spaces and use this characterization to give some application using semi-linear uniform spaces.

‎‎In this manuscript we show that the Theorem 3.28cite{C} is not correct in generally and modify it‎.

The structure of an α(β,β) -topological ring is richer in comparison with the structure of an α(β,β) -topological group. The theory of α(β,β) -topological rings has many common features with the theory of α(β,β) -topological groups. Formally, the theory of α(β,β) -topological abelian groups is included in the theory of α(β,β) -topological rings. The purpose of this paper is to introduce and study the concepts of α(β,β) -topological rings and α(β,γ) -topological R-modules. we show how they may be introduced by specifying the neighborhoods of zero, and present some basic constructions. We provide fundamental concepts and basic results on α(β,β) -topological rings and α(β,γ) -topological Rmodules.

In this paper, we discuss the upper bounds for the second Hankel determinant 𝐻2(2) of a new subclass of 𝜆-pseudo-starlike bi-univalent functions defined in the open unit disk 𝑈.

The PUL integral is an integration process, similar to the Kurzweil-Henstock integral, which uses the notion of partition of unity. Boonpogkrong discussed the Kurzweil-Henstock integral on manifolds. The PUL-Stieltjes integral, established by Flores and Benitez, is an extension of the PUL Integral. In this paper, we present some Convergence Theorems for the PUL-Stieltjes integral. Notions on the equi-integrability of this integral are also presented in the paper.

The number of subgroups, normal subgroups and characteristic subgroups of a finite group G are denoted by Sub(G), NSub(G) and CSub(G), respectively. The main goal of this paper is to present a matrix model for computing these positive integers for dicyclic groups, semi-dihedral groups, and three sequences U6n, V8n and H(n) of groups that can be presented as follows: U6n = ⟨a, b | a 2n = b 3 = e, bab = a⟩, V8n = ⟨a, b | a 2n = b 4 = e, aba = b −1 , ab−1a = b⟩, H(n) = ⟨a, b, c | a 2 n−2 = b 2 = c 2 = e, [a, b] = [b, c] = e, ac = ab⟩. For each group, a matrix model containing all information is given.

In this paper we deÖne Gevrey polyanalytic classes of order N on the unit disk D and we characterize these classes by a speciÖc expansion into Nanalytic polynomials on suitable neighborhoods of D. As an application of our main theorem, we perform for the Gevrey polyanalytic classes of order N on the unit disk D, an analogue to E. M. Dyníkinís theorem. We derive also, for these classes, their characteristic degree of the best uniform approximation on D by Nanalytic polynomials. Keywords: Polyanalytic functions, Gevrey classes, Degree of polynomial approximation. 2000 Mathematics subject classiÖcation: 30D60, 26E05, 41A10. 1. Introduction The polyanalytic functions of order 2, the so-called bianalytic functions, originates from mechanics where they played a fundamental role in solving the problems of the planar theory of elasticity. Their usefulness in mechanics was illustrated by the pioneering works of Kolosso§, Muskhelishvili and their followers (([15])-([17]), [24], [25], [27]). By the systematic use of complex variable techniques these authors have greatly simpliÖed and extended the mathematicalmethods of the elasticity theory. The class of polyanalytic functions of order Corresponding Author 1analytic polynomials on suitable neighborhoods of  D. As an application of our main theorem, we perform for the Gevrey polyanalytic classes of order N on the unit disk D, an analogue to E. M. Dyníkinís theorem. We derive also, for these classes, their characteristic degree of the best uniform approximation on D by Nanalytic polynomials. Keywords: Polyanalytic functions, Gevrey classes, Degree of polynomial approximation. 2000 Mathematics subject classiÖcation: 30D60, 26E05, 41A10. 1. Introduction The polyanalytic functions of order 2, the so-called bianalytic functions, originates from mechanics where they played a fundamental role in solving the problems of the planar theory of elasticity. Their usefulness in mechanics was illustrated by the pioneering works of Kolosso§, Muskhelishvili and their followers (([15])-([17]), [24], [25], [27]). By the systematic use of complex variable techniques these authors have greatly simpliÖed and extended the mathematicalmethods of the elasticity theory. The class of polyanalytic functions of order Corresponding Author 1analytic
polynomials.

Let G be an abelian group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we generalize the graded primary avoidance theorem for modules to the graded primal avoidance theorem for modules. We also introduce the concept of graded PL-compactly packed modules and give a number of its properties

This paper provides a fourth-order scheme for approximating solutions of non-linear degenerate parabolic equations that their solutions may contain discontinuity. In the reconstruction step, a fourth-order weighted essentially non-oscillatory (WENO) reconstruction in Legendre basis, written as a convex combination of interpolants based on different stencils, is constructed. In the one-dimensional case, the new fourth-order reconstruction is based on a four-point stencil. The most important subject is that one of these interpolation polynomials is taken as a quadratic polynomial, and the linear weights of the symmetric and convex combination are set as to get fourth-order accuracy in smooth areas. Following the methodology of the traditional WENO-Z reconstruction, the non-oscillatory weights is calculated by the linear weights. The accuracy, robustness, and high-resolution properties of the new procedure are shown by extensive numerical examples.

We prove that every fuzzy generalized bi-Γ-ideal and every fuzzy interior Γ-ideal in a right weakly regular ordered Γ-semigroup is a fuzzy Γ-ideal. We also show that every fuzzy generalized bi-Γ-ideal in a duo right weakly regular ordered Γ-semigroup is a fuzzy interior Γ-ideal. Then, by using fuzzy Γ-ideals, fuzzy bi-Γ-ideals, fuzzy generalized bi-Γ-ideals and fuzzy interior Γ-ideals, left simple, right simple and simple ordered Γ-semigroups have been characterized. Finally we characterize right weakly regular ordered Γ-semigroup by its fuzzy Γ-ideals, fuzzy bi-Γ-ideals, fuzzy generalized bi-Γ-ideals and fuzzy interior Γ-ideals.

In this paper, we study to approximate the homomorphisms and derivations for 3-variable Cauchy functional equations in RC∗-algebras and Lie RC∗-algebras by the fixed point method..

In the paper [J. Ghosh and T.K. Samanta, Hyperfuzzy sets and hyperfuzzy group, Int. J. Advanced Sci Tech. 41 (2012), 27–37], Ghosh and Samanta introduced the concept of hyperfuzzy sets as a generalization of fuzzy sets and interval-valued fuzzy sets, and applied it to group theory. The aim of this manuscript is to study N -structures in BCK/BCI-algebras induced from hyperfuzzy structures.

In this paper we apply a geometric integrator to the problem of Lie-Poisson system for ideal compressible isentropic fluids (ICIF) numerically. Our work is based on the decomposition of the phase space, as the semidirect product of two infinite dimensional Lie groups. We have shown that the solution of (ICIF) stays in coadjoint orbit and this result extends a similar result for matrix group discussed in [6]. By using the coadjoint action of the Lie group on the dual of its Lie algebra to advance the numerical flow, we (as in [2]) devise methods that automatically stay on the coadjoint orbit. The paper concludes with a concrete example.