1 1735-4463 ACECR at Tarbiat Modares University 1138 General On Beck's Coloring for Measurable Functions Assari A. b Rahimi M. c b Jundi-Shapur University of Technology c University of Qom 1 10 2021 16 2 1 10 27 08 2017 12 07 2021 We study Beck-like coloring of measurable functions on a measure space $Omega$ taking values in a measurable semigroup $Delta$‎. ‎To any‎ ‎measure space $Omega$ and any measurable semigroup $Delta$ we assign a graph (called a zero-divisor graph) whose vertices are labelled by‎ ‎the classes of measurable functions defined on $Omega$ and having values in $Delta$‎, ‎with two vertices $f$ and $g$ adjacent if $f.g=0$ a.e.‎. ‎We show that‎, ‎if $Omega$ is atomic‎, ‎then not only the Beckchr('39')s conjecture holds but also the domination number coincide to the clique number and chromatic number as well‎. ‎We also determine some other graph properties of such a graph‎.
1167 Special Fixed Point in Semi-linear Uniform Spaces and Convex Metric Spaces Rawshdeh A. d Tallafha A. e d Assis. Prof. e The University of Jordan, Department of Mathematics. Amman-Jordan 1 10 2021 16 2 11 23 01 10 2017 26 06 2018 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. 1152 Special Erratum‎ " ‎Some result on simple hyper K‎- ‎algebras‎ ", ‎Iranian Journal of Mathematical Sciences and Informatics‎ ‎Vol‎. ‎3‎, ‎No‎. ‎2 (2008)‎, ‎pp‎. ‎29-48 Madadi- Dargahi S. f Nasr-Azadani M. A. g f Shahed University g Shahed University 1 10 2021 16 2 25 29 16 09 2017 05 11 2018 ‎‎In this manuscript we show that the Theorem 3.28cite{C} is not correct in generally and modify it‎. 1208 Special Topological Rings and Modules Via Operations Ibrahim H. h Khalaf A. i h Department of Mathematics, Faculty of Education, University of Zakho i Department of Mathematics, College of Science, University of Duhok 1 10 2021 16 2 31 48 11 11 2017 30 04 2021 The structure of an $alpha_{(beta, beta)}$-topological ring is richer in comparison with the structure of an $alpha_{(beta, beta)}$-topological group. The theory of $alpha_{(beta, beta)}$-topological rings has many common features with the theory of $alpha_{(beta, beta)}$-topological groups. Formally, the theory of $alpha_{(beta, beta)}$-topological abelian groups is included in the theory of $alpha_{(beta, beta)}$-topological rings. The purpose of this paper is to introduce and study the concepts of $alpha_{(beta, beta)}$-topological rings and $alpha_{(beta, gamma)}$-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 $alpha_{(beta, beta)}$-topological rings and $alpha_{(beta, gamma)}$-topological $R$-modules. 1224 General Second Hankel Determinant for a Certain Subclass of 𝝀-Pseudo-Starlike Bi-Univalent Functions Wanas A. K. j Majeed A. M. k j Department of Mathematics, College of Computer Science and Information Technology, University of Al-Qadisiyah k Department of Mathematics, College of Science, University of Baghdad 1 10 2021 16 2 49 59 30 11 2017 08 05 2018 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. 1240 Special Some Convergence Theorems of the pul-Stieltjes Integral Flores G. B. l Benitez J. m l Mindanao State University - Buug Campus m Iligan Institute of Techonology of the Mindanao State University 1 10 2021 16 2 61 72 17 12 2017 29 05 2021 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. 1751 General The Number of Subgroups of a Given Type in Certain Finite Groups Shelash H. B. n Ashrafi A. R. o n Kufa University, Iraq o University of Kashan, Iran 1 10 2021 16 2 73 87 25 10 2019 18 09 2021 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 $U_{6n}$, $V_{8n}$ and $H(n)$ of groups that can be presented as follows: begin{eqnarray*} U_{6n} &=& langle a, b mid a^{2n} = b^{3} = e, bab = arangle, V_{8n} &=& langle a, b mid a^{2n} = b^{4} = e, aba = b^{-1}, ab^{-1}a = brangle, H(n)&=&langle a,b,c mid a^{2^{n-2}}=b^{2}=c^{2}=e, [x,y]=[y,z]=e, x^{z}=xy rangle. end{eqnarray*} For each group, a matrix model containing all information is given. 1288 General On the Representation and the Uniform Polynomial Approximation of Polyanalytic Functions of Gevrey Type on the Unit Disk Kabbaj S. p Zoubeir H. p Department of Mathematics, Ibn Tofail University, Faculty of Sciences. Department of Mathematics, Ibn Tofail University, Faculty of Sciences. 1 10 2021 16 2 89 115 03 03 2018 21 05 2020  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. 1291 General On the Graded Primal Avoidance Theorem Al-Zoubi Kh. Jordan University of Science and Technology 1 10 2021 16 2 117 124 06 03 2018 08 12 2018  Let $G$ be a 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 $P_{L}$-compactly packed modules and give a number of its properties. 1292 Special WENO-Z Schemes with Legendre Basis for non-Linear Degenerate Parabolic Equations Abedian R. University of Tehran 1 10 2021 16 2 125 143 07 03 2018 21 12 2020 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. 1295 General Ordered Γ-Semigroups and Fuzzy Γ-ideals Mahboob A. Davvaz B. Khan N. M. Madanapalle Institute of Technology & Science, Angallu, Madanapalle-517325, Andhra Pradesh, India Yazd University, Yazd, Iran Aligarh Muslim University 1 10 2021 16 2 145 162 20 03 2018 22 09 2019 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. 1296 General On Nonlinear Random Approximation of 3-variable Cauchy Functional Equation Je Cho Y. Shin-min Sh.-m. Rassias T. M. Saadati R. Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea Department of Mathematics National Technical University of Athens Zografou Campus, 157 80, Athens GREECE Department of Mathematics, Iran University of Science and Technology, Tehran, Iran 1 10 2021 16 2 163 177 21 03 2018 17 04 2021 In the  $RC^*$-algebras and Lie $RC^*$-algebras, we approximate the homomorphisms and derivations   for the 3-variable Cauchy functional equation, by the fixed point method. 1301 General N-subalgebras of BCK=BCI-Algebras which are Induced from Hyperfuzzy Structures Bordbar H. Bordbar M. R. Borzooei R. A. Jun Y. B. Shahid Beheshti University Qom University Shahid Beheshti University Gyeongsang Natinal University 1 10 2021 16 2 179 195 08 04 2018 16 02 2019 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. 1313 Special A Geometric Numerical Integration of Lie-Poisson System for Ideal Compressible Isentropic Fluid Nobary E. Hosseini S. M. Department of Mathematics, University of Science and Technology of Mazandaran Department of Mathematics, Tarbiat Modares University 1 10 2021 16 2 197 208 20 04 2018 26 09 2020 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] (Hairer, et al). By using the coadjoint action of the Lie group on the dual of its Lie algebra to advance the numerical flow, we (as in Engo, et al. [2]) devise methods that automatically stay on the coadjoint orbit. The paper concludes with a concrete example.