ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
On Beck\'s Coloring for Measurable Functions
1
10
EN
A.
Assari
Jundi-Shapur University of Technology
amirassari@jsu.ac.ir
M.
Rahimi
University of Qom
m10.rahimi@gmail.com
10.52547/ijmsi.16.2.1
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.
Zero divisor graph, Domination number, Measurable function, Clique number, Coloring.
http://ijmsi.ir/article-1-1138-en.html
http://ijmsi.ir/article-1-1138-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
Fixed Point in Semi-linear Uniform Spaces and Convex Metric Spaces
11
23
EN
A.
Rawshdeh
Assis. Prof.
a_rawashdeh85@yahoo.com
A.
Tallafha
Prof.
a.tallafha@ju.edu.jo
10.52547/ijmsi.16.2.11
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.
Uniform spaces, Semi-linear uniform spaces, Contractions, metric spaces, types of metric spaces.
http://ijmsi.ir/article-1-1167-en.html
http://ijmsi.ir/article-1-1167-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
Erratum " Some result on simple hyper K- algebras ", Iranian Journal of Mathematical Sciences and Informatics Vol. 3, No. 2 (2008), pp. 29-48
25
29
EN
S.
Madadi- Dargahi
Shahed University
s.madadi@shahed.ac.ir
M. A.
Nasr-Azadani
Shahed University
nasr@shahed.ac.ir
10.52547/ijmsi.16.2.25
In this manuscript we show that the Theorem 3.28cite{C} is not correct in generally and modify it.
Simple hyper K- algebras, Positive implicative hyper K-ideal.
http://ijmsi.ir/article-1-1152-en.html
http://ijmsi.ir/article-1-1152-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
Topological Rings and Modules Via Operations
31
48
EN
H.
Ibrahim
Department of Mathematics, Faculty of Education, University of Zakho
hariwan_math@yahoo.com
A.
Khalaf
Department of Mathematics, College of Science, University of Duhok
aliasbkhalaf@gmail.com
10.52547/ijmsi.16.2.31
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.
Operations, $alpha_{beta}$-Open set, Rins, $alpha_{(beta, beta)}$-Topological rings, $alpha_{(beta, gamma)}$-Topological $R$-modules
http://ijmsi.ir/article-1-1208-en.html
http://ijmsi.ir/article-1-1208-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
Second Hankel Determinant for a Certain Subclass of 𝝀-Pseudo-Starlike Bi-Univalent Functions
49
59
EN
A. K.
Wanas
Department of Mathematics, College of Computer Science and Information Technology, University of Al-Qadisiyah
abbas.kareem.w@qu.edu.iq
A. M.
Majeed
Department of Mathematics, College of Science, University of Baghdad
abbas.alshareefi@yahoo.com
10.52547/ijmsi.16.2.49
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.
Analytic functions, Bi-univalent functions, 𝜆- Pseudo-starlike functions, Upper bounds, Second Hankel determinant.
http://ijmsi.ir/article-1-1224-en.html
http://ijmsi.ir/article-1-1224-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
Some Convergence Theorems of the pul-Stieltjes Integral
61
72
EN
G. B.
Flores
Mindanao State University - Buug Campus
greigbates.flores@gmail.com
J.
Benitez
Iligan Institute of Techonology of the Mindanao State University
jbenitez@gmail.com
10.52547/ijmsi.16.2.61
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.
PUL-Stieltjes Integral, Uniform Convergence, Equi-integrability.
http://ijmsi.ir/article-1-1240-en.html
http://ijmsi.ir/article-1-1240-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
The Number of Subgroups of a Given Type in Certain Finite Groups
73
87
EN
H. B.
Shelash
Kufa University, Iraq
ameen.hayder81@gmail.com
A. R.
Ashrafi
University of Kashan, Iran
ashrafi@kashanu.ac.ir
10.52547/ijmsi.16.2.73
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.
Subgroup, Normal subgroup, Characteristic subgroup.
http://ijmsi.ir/article-1-1751-en.html
http://ijmsi.ir/article-1-1751-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
On the Representation and the Uniform Polynomial Approximation of Polyanalytic Functions of Gevrey Type on the Unit Disk
89
115
EN
S.
Kabbaj
Department of Mathematics, Ibn Tofail University, Faculty of Sciences.
samirkabbaj59@gmail.com
H.
Zoubeir
Department of Mathematics, Ibn Tofail University, Faculty of Sciences.
hzoubeir2014@gmail.com
10.52547/ijmsi.16.2.89
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.
Polyanalytic functions, Gevrey classes, Degree of polynomial approximation.
http://ijmsi.ir/article-1-1288-en.html
http://ijmsi.ir/article-1-1288-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
On the Graded Primal Avoidance Theorem
117
124
EN
Kh.
Al-Zoubi
Jordan University of Science and Technology
kfzoubi@just.edu.jo
10.52547/ijmsi.16.2.117
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.
Graded primal submodules, Graded primal avoidance, Graded $P_{L}$-compactly packed modules
http://ijmsi.ir/article-1-1291-en.html
http://ijmsi.ir/article-1-1291-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
WENO-Z Schemes with Legendre Basis for non-Linear Degenerate Parabolic Equations
125
143
EN
R.
Abedian
University of Tehran
rabedian@ut.ac.ir
10.52547/ijmsi.16.2.125
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.
WENO schemes, Legendre orthogonal polynomials, multidimensional non-linear degenerate parabolic equations, porous medium equation.
http://ijmsi.ir/article-1-1292-en.html
http://ijmsi.ir/article-1-1292-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
Ordered Γ-Semigroups and Fuzzy Γ-ideals
145
162
EN
A.
Mahboob
Madanapalle Institute of Technology & Science, Angallu, Madanapalle-517325, Andhra Pradesh, India
khanahsan56@gmail.com
B.
Davvaz
Yazd University, Yazd, Iran
davvaz@yazd.ac.ir
N. M.
Khan
Aligarh Muslim University
nm_khan123@yahoo.co.in
10.52547/ijmsi.16.2.129
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.
Ordered Γ-semigroup, right weakly regular ordered Γ-semigroup, Fuzzy set, Fuzzy Γ-ideals.
http://ijmsi.ir/article-1-1295-en.html
http://ijmsi.ir/article-1-1295-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
On Nonlinear Random Approximation of 3-variable Cauchy Functional Equation
163
177
EN
Y.
Je Cho
Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea
yjcho@gnu.ac.kr
Sh.-m.
Shin-min
Department of Mathematics and the RINS, Gyeongsang National University, Jinju 52828, Korea
smkang@gnu.ac.kr
T. M.
Rassias
Department of Mathematics National Technical University of Athens Zografou Campus, 157 80, Athens GREECE
trassias@math.ntua.gr
R.
Saadati
Department of Mathematics, Iran University of Science and Technology, Tehran, Iran
rsaadati@eml.cc
10.52547/ijmsi.16.2.147
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.
Approximation, Functional equations, $RC^*$-algebras, Random space
http://ijmsi.ir/article-1-1296-en.html
http://ijmsi.ir/article-1-1296-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
N-subalgebras of BCK=BCI-Algebras which are Induced from Hyperfuzzy Structures
179
195
EN
H.
Bordbar
Shahid Beheshti University
Bordbar.amirh@gmail.com
M. R.
Bordbar
Qom University
mbordbar@qom.ac.ir
R. A.
Borzooei
Shahid Beheshti University
Borzooei@sbu.ac.ir
Y. B.
Jun
Gyeongsang Natinal University
Skywine@gmail.com
10.52547/ijmsi.16.2.163
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.
hyperfuzzy set, hyperfuzzy structure, hyperfuzzy subalgebra, N-subalgebra, induced N- function.
http://ijmsi.ir/article-1-1301-en.html
http://ijmsi.ir/article-1-1301-en.pdf
ACECR at Tarbiat Modares University
Iranian Journal of Mathematical Sciences and Informatics
1735-4463
2008-9473
16
2
2021
10
1
A Geometric Numerical Integration of Lie-Poisson System for Ideal Compressible Isentropic Fluid
197
208
EN
E.
Nobary
Department of Mathematics, University of Science and Technology of Mazandaran
e.nobari@mazust.ac.ir
S. M.
Hosseini
Department of Mathematics, Tarbiat Modares University
hossei_m@modares.ac.ir
10.52547/ijmsi.16.2.181
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.
Ideal compressible isentropic fluid, Lie-Poisson system, Semidirect product, Geometric integration, Coadjoint orbit.
http://ijmsi.ir/article-1-1313-en.html
http://ijmsi.ir/article-1-1313-en.pdf