1 1735-4463 ACECR at Tarbiat Modares University 1121 Special On Total Edge Irregularity Strength of Staircase Graphs and Related Graphs Susanti Y. b Puspitasari Y. I. c Khotimah H. d b Dept. of Mathematics Universitas Gadjah Mada c Surakarta Indonesia d Department of Mathematics Universitas Muhammadiyah Pringsewu Lampung Indonesia 1 4 2020 15 1 1 13 26 07 2017 09 05 2019 Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G has an edge irregular total k-labeling is called the total edge irregularity strength of graph G and denoted by tes(G). In this paper, we determine the exact value of total edge irregularity strength for staircase graphs, double staircase graphs and mirror-staircase graphs.
1004 Special On the Diophantine Equation x^6+ky^3=z^6+kw^3 Shabani-Solt. H. e Yusefnejad N. f Janfada A. S. g e Urmia University f Urmia University g Urmia University 1 4 2020 15 1 15 21 07 01 2017 04 03 2020 Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is not greater than 500. We exhibit a collection of (probably infinitely many) rational numbers k for which this Diophantine equation is satisfied. Finally, appealing these observations, we conjecture that the above result is true for all rational numbers k. 1025 Special Sums of Strongly z-Ideals and Prime Ideals in ${mathcal{R}} L$ Estaji A. A. h Karimi Feizabadi A. i Robat Sarpoushi M. j h Hakim Sabzevari University i Islamic Azad University j Hakim Sabzevari University 1 4 2020 15 1 23 34 12 02 2017 07 11 2019 It is well-known that the sum of two $z$-ideals in $C(X)$ is either $C(X)$ or a $z$-ideal. The main aim of this paper is to study the sum of strongly $z$-ideals in ${mathcal{R}} L$, the ring of real-valued continuous functions on a frame $L$. For every ideal $I$ in ${mathcal{R}} L$, we introduce the biggest strongly $z$-ideal included in $I$ and the smallest strongly $z$-ideal containing $I$, denoted by $I^{sz}$ and $I_{sz}$, respectively. We study some properties of $I^{sz}$ and $I_{sz}$.   Also, it is observed that the sum of any family of minimal prime ideals in the ring ${mathcal{R}} L$ is either ${mathcal{R}} L$ or a prime strongly $z$-ideal in ${mathcal{R}} L$. In particular, we show that the sum of two prime ideals in ${mathcal{R}} L$ such that are not a chain, is a prime strongly $z$-ideal. 1061 Special Characterization of $mathrm{PSL}(5,q)$ by its Order and One Conjugacy Class Size Khalili Asboei A.R. k k Department of Mathematics, Farhangian University 1 4 2020 15 1 35 40 09 04 2017 14 08 2017 Let $p=(q^4+q^3+q^2+q+1)/(5,q-1)$ be a prime number, where $q$ is a prime power. In this paper, we will show $Gcong mathrm{PSL}(5,q)$ if and only if $|G|=|mathrm{PSL}(5,q)|$, and $G$ has a conjugacy class size $frac{| mathrm{PSL}(5,q)|}{p}$. Further, the validity of a conjecture of J. G. Thompson is generalized to the groups under consideration by a new way. 1064 General The Banach Type Contraction for Mappings on Algebraic Cone Metric Spaces Associated with An Algebraic Distance and Endowed with a Graph Fallahi K. l Soleimani Rad Gh. m l Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran m Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran 1 4 2020 15 1 41 52 14 04 2017 08 05 2019 In this work, we define the notion of an algebraic distance in algebraic cone metric spaces defined by Niknam et al. [A. Niknam, S. Shamsi Gamchi and M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Infor. 9 (1) (2014), 71--80] and introduce some its elementary properties. Then we prove the existence and uniqueness of fixed point for a Banach contractive type mapping in algebraic cone metric spaces associated with an algebraic distance and endowed with a graph. 1070 Special On the Prime Spectrum of Torsion Modules Hassanzadeh-lelekaami D. n n Arak University of Technology 1 4 2020 15 1 53 63 19 04 2017 30 07 2018 The paper uses a new approach to investigate prime submodules and minimal prime submodules of certain modules such as Artinian and torsion modules. In particular, we introduce a concrete formula for the radical of submodules of Artinian modules. 809 General Harmonicity and Minimality of Vector Fields on Lorentzian Lie Groups Aryanejad Y. o o Payame noor University 1 4 2020 15 1 65 78 30 11 2015 20 10 2019 ‎We consider four-dimensional lie groups equipped with‎ ‎left-invariant Lorentzian Einstein metrics‎, ‎and determine the harmonicity properties ‎of vector fields on these spaces‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional ‎restricted to vector fields‎. ‎We also classify vector fields defining harmonic maps‎, ‎and calculate explicitly the energy of these vector ‎fields‎. ‎Then we study the minimality of critical points for the energy functional‎. 1057 General New Integral Inequalities Through the phi-Preinvexity Meftah B. p p Laboratoire des Télécommunications, Faculté des Sciences et de la Technologie, University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria. 1 4 2020 15 1 79 83 02 04 2017 11 03 2018 Abstract. In this note, we give some estimates of the generalized quadrature formula of Gauss-Jacobi type for phi-preinvex functions. 1082 General Quotient G-systems and Green's Relations Ostadhadi-Dehkordi S. Shum K. P. Department of Mathematics, Hormozgan University, Bandar Abbas, Iran. Institute of Mathematics,Yunnan University, Kunming,650091, P.R. China 1 4 2020 15 1 85 97 10 05 2017 08 09 2017 In this paper, we first introduce the concepts of G-systems, quotient G-systems and isomorphism theorems on G-systems of n-ary semihypergroups . Also we consider the Green's equivalences on G-systems and further in-vestigate some of their properties. A number of n-ary semihypergroups are constructed and presented as examples in this paper. 1080 Special Comparing Model-based Versus K-means Clustering for the Planar Shapes Golalizadeh M. Jafari H. Department of Statistics, Faculty of Mathematical Sciences, Tarbiat Modares University Department of Statistics, Faculty of Mathematical Sciences, Tarbiat Modares University 1 4 2020 15 1 99 109 09 05 2017 06 03 2018 ‎In some fields‎, ‎there is an interest in distinguishing different geometrical objects from each other‎. ‎A field of research that studies the objects from a statistical point of view‎, ‎provided they are‎ ‎invariant under translation‎, ‎rotation and scaling effects‎, ‎is known as the statistical shape analysis‎. ‎Having some objects that are registered using key points on the outline of the objects‎, ‎the main purpose‎ ‎of this paper is to compare two popular clustering procedures to cluster objects‎. ‎We also use some indexes‎ ‎to evaluate our clustering application‎. ‎The proposed methods are applied to the real life data. 1102 General Extensions of Some Fixed Point Theorems for Weak-Contraction Mappings in Partially Ordered Modular Metric Spaces Chaira K. Eladraoui A. Kabil M. University of Casablanca University of Casablanca University of Casablanca 1 4 2020 15 1 111 124 12 06 2017 29 05 2019 The purpose of this paper is to establish fixed point results for a single mapping in a partially ordered modular metric space, and to prove a common fixed point theorem for two self-maps satisfying some weak contractive inequalities. 1051 Special On Identities with Additive Mappings in Rings ansari A. Z. Department of Mathematics, Faculty of Science, Islamic University of Madinah, K.S.A 1 4 2020 15 1 125 133 22 03 2017 25 09 2017 begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract} 1116 Special The Dynamical Analysis of a Delayed Prey-Predator Model with a Refuge-Stage Structure Prey Population Naji R. Majeed S. Baghdad university Thi-Qar University 1 4 2020 15 1 135 159 14 07 2017 07 07 2018 A mathematical model describing the dynamics  of a  delayed  stage structure prey - predator  system  with  prey  refuge  is  considered.  The  existence,  uniqueness  and bounded- ness  of  the  solution  are  discussed.    All  the  feasibl e  equilibrium  points  are determined.  The   stability  analysis  of  them  are  investigated.  By  employ ing  the time delay as the bifurcation parameter, we observed  the existence of Hopf bifurcation at the positive equilibrium. The stability and direction of the Hopf bifurcation are determined by  utilizing  the  normal  form  method  and  the  center  manifold  reduction.  Numerical simulations are given to support the analytic results. 1958 General ABSTRACTS IN PERSIAN Vol.15, No.1 IJMSI IJMSI Academic Center for Education, Culture and Research (ACECR) Tarbiat Modares University (TMU) 1 4 2020 15 1 161 174 21 08 2020 21 08 2020 Please see the full text contains the Pesian abstracts for this volume.