eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 1 8 article R. Abu-dawwas rrashid@yu.edu.jo 1 M. Bataineh msbataineh@just.edu.jo 2 Department of Mathematics, Yarmouk University, Jordan. Department of Mathematics and Statistics, Jordan University of Science and Technology, Jordan. Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero unity $1$. In this article, we introduce the concept of graded $r$-ideals. A proper graded ideal $P$ of a graded ring $R$ is said to be graded $r$-ideal if whenever $a, bin h(R)$ such that $abin P$ and $Ann(a)={0}$, then $bin P$. We study and investigate the behavior of graded $r$-ideals to introduce  several results. We introduced several characterizations for graded $r$-ideals;  we proved that $P$ is a graded $r$-ideal of $R$ if and only if $aP=aRbigcap P$  for all $ain h(R)$ with $Ann(a)={0}$. Also, $P$ is a graded $r$-ideal of $R$  if and only if $P=(P:a)$ for all $ain h(R)$ with $Ann(a)={0}$. Moreover,  $P$ is a graded $r$-ideal of $R$ if and only if whenever $A, B$ are graded ideals of   $R$ such that $ABsubseteq P$ and $Abigcap r(h(R))neqphi$, then $Bsubseteq P$. In this article, we introduce the concept of $huz$-rings. A graded ring $R$ is said to be $huz$-ring if every homogeneous element of $R$ is either a zero divisor or a unit. In fact, we proved that $R$ is a $huz$-ring if and only if every graded ideal of $R$ is a graded $r$-ideal. Moreover, assuming that $R$ is a graded domain, we proved that ${0}$ is the only graded $r$-ideal of $R$. http://ijmsi.ir/article-1-984-en.pdf Graded prime ideals Graded r-ideals. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 9 18 article S. P. sinimecheri@gmail.com 1 Department of Mathematics, University of Calicut, Kerala, India. In this paper we study hereditarily homogeneous generalized topological spaces. Various properties of hereditarily homogeneous generalized topological spaces are discussed. We prove that a generalized topological space is hereditarily homogeneous if and only if every transposition of $X$ is a $mu$-homeomorphism on $X$. http://ijmsi.ir/article-1-964-en.pdf $mu$-Open $mu$-Closed Generalized topology Homogeneous Hereditarily homogeneous GTS Highly transitive permutation groups Bihomogeneous eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 19 32 article F. Nikbakhtsarvestani Nikbakhf@myumanitoba.ca 1 S. M. Vaezpour vaez@aut.ac.ir 2 M. Asadi masadi@iauz.ac.ir 3 Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada. Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran. The purpose of this paper is to obtain the common fixed point results for two pair of weakly compatible mapping by using common (CLR) property in partial metric space. Also we extend the very recent results which are presented in [17,  Muhammad Sarwar, Mian Bahadur Zada and Inci M. Erhan, Common Fixed Point Theorems of Integral type on Metric Spaces and application to system of functional equations, Fixed point theory and applications, 2015, 2015:217] with proofing a new version of the continuity of partial metric. http://ijmsi.ir/article-1-970-en.pdf Fixed point Partial metric space (CLR)-Property. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 33 42 article A. Sadeghi : a-sadeghi@phdstu.scu.ac.ir 1 M. Saraj msaraj@scu.ac.ir 2 N. Mahdavi Amiri nezaam@sharif.edu 3 Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Iran. Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Iran. Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran. We consider a fractional program with both linear and quadratic equation in numerator and denominator  having second order cone (SOC) constraints. With a suitable change of variable, we transform the problem into a  second order cone programming (SOCP)  problem.  For the quadratic fractional case, using a relaxation, the problem is reduced to a semi-definite optimization (SDO) program. The problem is solved with SDO relaxation and the obtained results are compared with the interior point method (IPM), a sequential quadratic programming (SQP) approach, an active set strategy and a genetic algorithm. It is observed that the SDO relaxation method is much more accurate and faster than the other methods. Finally,a few numerical examples are worked through to demonstrate the applicability of the procedure. http://ijmsi.ir/article-1-1314-en.pdf Fractional Programming Second Order Cone SDP Relaxation. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 43 60 article A. Khan asifjnu07@gmail.com 1 V. Sharma vinita.sha23@gmail.com 2 Department of Mathematics, Aligarh Muslim University, Aligarh–202002, India. Department of Mathematics, Aligarh Muslim University, Aligarh–202002, India. In this paper, $(p,q)$-Lupas Bernstein Stancu operators are constructed. Statistical as well as other approximation properties of $(p,q)$-Lupac{s} Stancu operators are studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated. http://ijmsi.ir/article-1-1012-en.pdf $(p q)$-Integers Lupac{s} $(p q)$-Bernstein Stancu operators Statistical approximation Korovkin's type approximation. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 61 67 article M. Mortazavizadeh mortazavizadeh@mail.um.ac.ir 1 R. Raisi Tousi raisi@um.ac.ir 2 R. A. Kamyabi Gol kamyabi@um.ac.ir 3 Department of Mathematics, Ferdowsi University of Mashhad , P. O. Box 1159-91775, Mashhad, Islamic Republic of Iran. Department of Mathematics, Ferdowsi University of Mashhad , P. O. Box 1159-91775, Mashhad, Islamic Republic of Iran. Department of Mathematics, Ferdowsi University of Mashhad , P. O. Box 1159-91775, Mashhad, Islamic Republic of Iran, Centre of Ex cellence in Analysis on Algebraic Structures (CEAAS). In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space. http://ijmsi.ir/article-1-994-en.pdf Locally compact abelian group Translation invariant space Translation metric. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 69 77 article R. Hosseini ‎hosseini-k@azaruniv.edu 1 M. ‎Jahanshahi ‎Jahanshahi@azaruniv.edu 2 A.A. Pashavand ‎apashavand@yahoo.com 3 N. Aliev nihan@aliev.info 4 Department of Mathematics, Azarbaijan Shahid Madani University, 35 Km Tabriz-Maraghe Road, Tabriz, Iran. Department of Mathematics, Azarbaijan Shahid Madani University, 35 Km Tabriz-Maraghe Road, Tabriz, Iran. Institute of Mathematics and Mechanics of NAS of Azarbijan, Baku, Azarbijan. Institute of Mathematics and Mechanics of NAS of Azarbijan, Baku, Azarbijan. In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional derivative. The peresented solutions for these problems are as infinite series. ‎Convergence‎ of series solutions and uniqueness of them are stablished by general theory of mathematical analysis and theory of ODEs. http://ijmsi.ir/article-1-1040-en.pdf Mittag-Lefller function‎ Fractional partial differential equation‎ Non local boundary condition. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 79 92 article Zh.-B. Gao gaozhenbin@aliyun.com 1 R.-Y. Han 3213358692@qq.com 2 S.-M. Lee sinminlee@gmail.com 3 H.-N. Ren 1114912080@qq.com 4 G.-Ch. Lau geeclau@yahoo.com 5 College of Science, Harbin Engineering University, Harbin, 150001, P. R. China. College of Science, Harbin Engineering University, Harbin, 150001, P. R. China. 1403, North First Avenue, Upland, CA 91786,USA. College of Science, Harbin Engineering University, Harbin, 150001, P. R. China. Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (Segamat Campus), 85000 Johor, Malaysia. Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$.  For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G$ is said to be friendly if $| v_{f}(1)-v_{f}(0) | leq 1$. The friendly index set of the graph $G$, denoted by $FI(G)$, is defined as  ${|e_{f^+}(1) - e_{f^+}(0)|$ : the vertex labeling $f$ is friendly$}$. The full friendly index set of the graph $G$, denoted by $FFI(G)$, is defined as ${e_{f^+}(1) - e_{f^+}(0)$ : the vertex labeling $f$ is friendly$}$. A graph $G$ is cordial if $-1, 0$ or $1in FFI(G)$. In this paper, by introducing labeling subgraph embeddings method, we determine the cordiality of a family of cubic graphs which are double-edge blow-up of $P_2times P_n, nge 2$. Consequently, we completely determined friendly index and full product cordial index sets of this family of graphs. http://ijmsi.ir/article-1-925-en.pdf Vertex labeling Full friendly index set Cordiality $P_2$-embeddings $C_4$-embeddings. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 93 104 article F. Firuzi ffiruzi@gmail.com 1 Y. Alipour Fakhri y_alipour@pnu.ac.ir 2 E. Peyghan epeyghan@gmail.com 3 Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran. Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran. Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran. We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ( M, g ) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficient for the g-natural metric G̃ to be locally symmetric. http://ijmsi.ir/article-1-1014-en.pdf Almost contact structure B-metrics g-natural metrics Local symmetry Sphere bundle. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 105 125 article H. S. Ramane hsramane@yahoo.com 1 G. A. Gudodagi gouri.gudodagi@gmail.com 2 V. V. Manjalapur vinu.m001@gmail.com 3 A. Alhevaz a.alhevaz@shahroodut.ac.ir 4 Department of Mathematics, Karnatak University, Dahrwad- 580003, India. Department of Mathematics, KLE Societys, G. I. Bagewadi Arts, Science and Commerce College, Nipani 591237, Karnataka, India. Department of Mathematics, KLE Societys, Basavaprabhu Kore Arts, Science and Commerce College, Chikodi 591201, Karnataka, India. Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box: 316-3619995161, Shahrood, Iran. Let $D$ be a diameter and $d_G(v_i, v_j)$ be the distance between the vertices $v_i$ and $v_j$ of a connected graph $G$. The complementary distance signless Laplacian matrix of a graph $G$ is $CDL^+(G)=[c_{ij}]$ in which $c_{ij}=1+D-d_G(v_i, v_j)$ if $ineq j$ and $c_{ii}=sum_{j=1}^{n}(1+D-d_G(v_i, v_j))$. The complementary transmission $CT_G(v)$ of a vertex $v$ is defined as $CT_G(v)=sum_{u in V(G)}[1+D-d_G(u, v)]$. Let $CT(G)=diag[CT_G(v_1), CT_G(v_2), ldots, CT_G(v_n)]$. The complementary distance signless Laplacian matrix of $G$ is $CDL^+(G)=CT(G)+CD(G)$. If $rho_1, rho_2, ldots, rho_n$ are the eigenvalues of $CDL^+(G)$ then the complementary distance signless Laplacian energy of $G$ is defined as $E_{CDL^+}(G)=sum_{i=1}^{n}left| rho_i-frac{1}{n}sum_{j=1}^{n}CT_G(v_j)right|$. noindent In this paper we obtain the bounds for the largest eigenvalue of $CDL^+(G)$. Further we determine Nordhaus-Gaddum type results for the largest eigenvalue. In the sequel we establish the bounds for the complementary distance signless Laplacian energy.} http://ijmsi.ir/article-1-1017-en.pdf Complementary distance matrix Complementary distance signless Laplacian eigenvalues Complementary distance signless Laplacian energy Diameter. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 127 138 article R. Daskalov daskalovrn@gmail.com 1 E. Metodieva metodieva56@gmail.com 2 Department of Mathematics, Technical University of Gabrovo, Bulgaria. Department of Mathematics, Technical University of Gabrovo, Bulgaria.  An $(n, r)$-arc is a set of $n$ points of a projective plane such that some $r$, but no $r+1$ of them, are collinear. The maximum size of an $(n, r)$-arc in  PG(2, q) is denoted by $m_r(2,q)$. In this paper thirteen new $(n, r)$-arc in  PG(2,,29) and a table with the best known lower and upper bounds on $m_r(2,29)$ are presented. The results are obtained by non-exhaustive local computer search. http://ijmsi.ir/article-1-1020-en.pdf Finite projective plane $(n r)$-Arc in a projective plane $(l t)$-Blocking set in a projective plane Maximum size of an $(n r)$-arc eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 139 151 article M. Amini mamini1356@yahoo.com 1 F. Hassani ‎Hassani@pnu.ac.ir 2 Department of Mathematics, Payame Noor University, Tehran, Iran. Department of Mathematics, Payame Noor University, Tehran, Iran.  In this paper, a new homological dimension of modules, copresented dimension, is defined. We study some basic properties of this homological dimension. Some ring extensions are considered, too. For instance, we prove that if $Sgeq R$ is a finite normalizing extension and $S_R$ is a projective module, then for each right $S$-module $M_S$, the copresented dimension of $M_S$ does not exceed the copresented dimension of $Hom_{R}(S,M)$. http://ijmsi.ir/article-1-1036-en.pdf Coherent ring‎ ‎Copresented‎ ‎Dimension‎ ‎Projective module. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 153 156 article H. Safa hesam.safa@gmail.com 1 Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran. In the present paper, we prove that if L is a nilpotent Lie algebra whose proper subalge- bras are all nilpotent of class at most n, then the class of L is at most bnd=(d 􀀀 1)c, where b c denotes the integral part and d is the minimal number of generators of L. http://ijmsi.ir/article-1-1037-en.pdf Minimal number of generators Nilpotency class Nilpotent Lie algebra. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 157 171 article A. Rastegar rastegar1352@gmail.com 1 Department of Mathematics, Sharif University of Technology, Tehran, Iran. By Grothedieck's Anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number fields encode all arithmetic information of these curves. The goal of this paper is to develope and arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing the arithmetic information coming from all curves of the same topological type defined over number fields. We also introduce Hecke-Teichmuller Lie algebra which plays the role of Hecke algebra in the anabelian framework. http://ijmsi.ir/article-1-992-en.pdf Anabelian geometry Grothendieck conjectures Huperbolic curves Outer automorphism Galois representation. eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 173 184 article J. Kok kokkiek2@tshwane.gov.za 1 K. A. Germina srgerminaka@gmail.com 2 Center for Studies in Discrete Mathematics, Vidya Academy of Science & Technology,Thrissur, India. Department of Mathematics,School of Physical Sciences, Central University of Kerala, Kasargod, India. In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and certain derivative split graphs.  http://ijmsi.ir/article-1-1007-en.pdf Chromatic harmonic index Chromatic harmonic polynomial Split graph Derivative split graph eng ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 2019-10 14 2 185 200 article The Name of Authors In This Volume fatemeh.bardestani@gmail.com 1 All Affilliations Please see the full text contains the Pesian abstracts for this volume. http://ijmsi.ir/article-1-1918-en.pdf ABSTRACTS PERSIAN Vol. 14 No. 2