OTHERS_CITABLE 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. http://ijmsi.ir/article-1-1121-en.pdf 2020-04-10 1 13 10.29252/ijmsi.15.1.1 Total edge irregularity strength Staircase graphs Double staircase graphs Mirror-staircase graphs Y. Susanti inielsusan@yahoo.com 1 Dept. of Mathematics Universitas Gadjah Mada AUTHOR Y. I. Puspitasari yuliaindahp.mail@gmail.com 2 Surakarta Indonesia AUTHOR H. Khotimah husnul.khotimah18@mail.ugm.ac.id 3 Department of Mathematics Universitas Muhammadiyah Pringsewu Lampung Indonesia AUTHOR

OTHERS_CITABLE 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. http://ijmsi.ir/article-1-1004-en.pdf 2020-04-10 15 21 10.29252/ijmsi.15.1.15 Diophantine equation Elliptic curve. H. Shabani-Solt. h.shabani.solt@gmail.com 1 Urmia University AUTHOR N. Yusefnejad yusefnejadnazanin@yahoo.com 2 Urmia University AUTHOR A. S. Janfada asjanfada@gmail.com 3 Urmia University AUTHOR

OTHERS_CITABLE 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. http://ijmsi.ir/article-1-1025-en.pdf 2020-04-10 23 34 10.29252/ijmsi.15.1.23 Frame Ring of real-valued continuous functions z-Ideal Strongly z-ideal. A. A. Estaji aaestaji@gmail.com 1 Hakim Sabzevari University AUTHOR A. Karimi Feizabadi akarimi@gorganiau.ac.ir 2 Islamic Azad University AUTHOR M. Robat Sarpoushi M.sarpooshi@yahoo.com 3 Hakim Sabzevari University AUTHOR

OTHERS_CITABLE 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. http://ijmsi.ir/article-1-1061-en.pdf 2020-04-10 35 40 10.29252/ijmsi.15.1.35 Conjugacy class size Prime graph Thompson's conjecture. A.R. Khalili Asboei khaliliasbo@yahoo.com 1 Department of Mathematics, Farhangian University AUTHOR

OTHERS_CITABLE 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. http://ijmsi.ir/article-1-1064-en.pdf 2020-04-10 41 52 10.29252/ijmsi.15.1.41 Algebraic cone metric space Algebraic distance Banach contraction Orbitally G-continuous mapping K. Fallahi fallahi1361@gmail.com 1 Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran AUTHOR Gh. Soleimani Rad gh.soleimani2008@gmail.com 2 Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran AUTHOR

OTHERS_CITABLE 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. http://ijmsi.ir/article-1-1070-en.pdf 2020-04-10 53 63 10.29252/ijmsi.15.1.53 Torsion modules Artinian module Prime submodules. D. Hassanzadeh-lelekaami lelekaami@gmail.com 1 Arak University of Technology AUTHOR

OTHERS_CITABLE ‎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. http://ijmsi.ir/article-1-809-en.pdf 2020-04-10 65 78 10.29252/ijmsi.15.1.65 Harmonic vector fields‎ ‎Harmonic maps‎ ‎Einstein metrics‎ ‎Lie group‎ ‎Pseudo-Riemannian homogeneous spaces. Y. Aryanejad y.keshavarzi@pnu.ac.ir 1 Payame noor University AUTHOR

OTHERS_CITABLE Abstract. In this note, we give some estimates of the generalized quadrature formula of Gauss-Jacobi type for phi-preinvex functions. http://ijmsi.ir/article-1-1057-en.pdf 2020-04-10 79 83 10.29252/ijmsi.15.1.79 Integral inequality $varphi $-preinvex function H ̈older inequality power mean inequality B. Meftah badrimeftah@yahoo.fr 1 Laboratoire des Télécommunications, Faculté des Sciences et de la Technologie, University of 8 May 1945 Guelma, P.O. Box 401, 24000 Guelma, Algeria. AUTHOR

OTHERS_CITABLE 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. http://ijmsi.ir/article-1-1082-en.pdf 2020-04-10 85 97 10.29252/ijmsi.15.1.85 n-ary Semihypergroup G-system Greens relations. S. Ostadhadi-Dehkordi ostadhadi-dehkordi@hotmail.com 1 Department of Mathematics, Hormozgan University, Bandar Abbas, Iran. AUTHOR K. P. Shum kpshum@ynu.edu.cn 2 Institute of Mathematics,Yunnan University, Kunming,650091, P.R. China AUTHOR

OTHERS_CITABLE ‎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. http://ijmsi.ir/article-1-1080-en.pdf 2020-04-10 99 109 10.29252/ijmsi.15.1.99 Shape‎ ‎Clustering‎ ‎K-means‎ ‎Model-based‎ ‎Landmark‎. M. Golalizadeh golalizadeh@modares.ac.ir 1 Department of Statistics, Faculty of Mathematical Sciences, Tarbiat Modares University AUTHOR H. Jafari ‎hamed.jafari@modares.ac.ir 2 Department of Statistics, Faculty of Mathematical Sciences, Tarbiat Modares University AUTHOR

OTHERS_CITABLE 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. http://ijmsi.ir/article-1-1102-en.pdf 2020-04-10 111 124 10.29252/ijmsi.15.1.111 Fixed point Weak contraction Partially ordered space Modular metric space. K. Chaira chaira_karim@yahoo.fr 1 University of Casablanca AUTHOR A. Eladraoui a.adraoui@live.fr 2 University of Casablanca AUTHOR M. Kabil kabilfstm@gmail.com 3 University of Casablanca AUTHOR

OTHERS_CITABLE 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} http://ijmsi.ir/article-1-1051-en.pdf 2020-04-10 125 133 10.29252/ijmsi.15.1.125 Prime (Semiprime) ring Additive mappings Generalized (Jordan) left derivations Generalized (Jordan) derivations (Jordan)Centralizers. A. Z. ansari ansari.abuzaid@gmail.com 1 Department of Mathematics, Faculty of Science, Islamic University of Madinah, K.S.A AUTHOR

OTHERS_CITABLE 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. http://ijmsi.ir/article-1-1116-en.pdf 2020-04-10 135 159 10.29252/ijmsi.15.1.135 Delayed Prey - Predator System Stage- Structure Refuge Stability Hop f Bifurcation. R. Naji rknaji@gmail.com 1 Baghdad university AUTHOR S. Majeed sm.salammajeed@yahoo.com 2 Thi-Qar University AUTHOR

OTHERS_CITABLE Please see the full text contains the Pesian abstracts for this volume. http://ijmsi.ir/article-1-1958-en.pdf 2020-08-21 161 174 ABSTRACTS PERSIAN Vol. 15 No. 1 IJMSI IJMSI 1 Academic Center for Education, Culture and Research (ACECR) Tarbiat Modares University (TMU) AUTHOR