ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 Edge-coloring Vertex-weightings of Graphs 1 13 EN W.-Ch. Shiu Hong Kong Baptist University wcshiu@hkbu.edu.hk N G.-Ch. Lau Universiti Teknologi MARA Malaysia geeclau@yahoo.com Y H.-K. Ng San Jose State University, USA ho-kuen.ng@sjsu.edu N Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. A $k$-vertex weightings of a graph $G$ is a mapping $w: V(G) to {1, ldots, k}$. A $k$-vertex weighting induces an edge labeling $f_w: E(G) to N$ such that $f_w(uv)=w(u)+w(v)$. Such a labeling is called an {it edge-coloring k-vertex weightings} if $f_{w}(e)not= f_{w}(e')$ for any two adjacent edges $e$ and $e'$. Denote by $mu'(G)$ the minimum $k$ for $G$ to admit an edge-coloring $k$-vertex weightings. In this paper, we determine $mu'(G)$ for some classes of graphs. Edge coloring, Vertex weightings. http://ijmsi.ir/article-1-1033-en.html http://ijmsi.ir/article-1-1033-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 A Trust-region Method using Extended Nonmonotone Technique for Unconstrained Optimization 15 33 EN M. kimiaei Vienna University kimiaeim83@univie.ac.at Y H. esmaeili Bu Ali University esmaeili47@yahoo.com N F. rahpeymaii Payame Noor rahpeyma_83@yahoo.com N In this paper, we present a nonmonotone trust-region algorithm for unconstrained optimization. We first introduce a variant of the nonmonotone strategy proposed by Ahookhosh and Amini cite{AhA 01} and incorporate it into the trust-region framework to construct a more efficient approach. Our new nonmonotone strategy combines the current function value with the maximum function values in some prior successful iterates. For iterates far away from the optimizer, we give a very strong nonmonotone strategy. In the vicinity of the optimizer, we have a weaker nonmonotone strategy. It leads to a medium nonmonotone strategy when iterates are not far away from or close to the optimizer. Theoretical analysis indicates that the new approach converges globally to a first-order critical point under classical assumptions. In addition, the local convergence is also studied. Extensive numerical experiments for unconstrained optimization problems are reported. Unconstrained optimization, Trust-region framework, Nonmonotone technique, Theoretical convergence http://ijmsi.ir/article-1-1188-en.html http://ijmsi.ir/article-1-1188-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 On Contact and Symplectic Lie Algeroids 35 53 EN E. Nazari Tarbiat Modares University e.nazari@modares.ac.ir N A. Heydari Tarbiat Modares University aheydari@modares.ac.ir Y In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by means of the induced Poisson structures on the integral submanifolds. Moreover, for any compatible triple with invariant metric and admissible almost complex structure, we show that the bracket annihilates on the kernel of the anchor map. Lie algebroid, Symplectic Lie algebroid, Contact Lie algebroid, Poisson structure http://ijmsi.ir/article-1-1220-en.html http://ijmsi.ir/article-1-1220-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 Wijsman Statistical Convergence of Double Sequences of Sets 55 64 EN E. Dundar Department of Mathematics, Faculty of Science and Literature, Afyon Kocatepe University edundar@aku.edu.tr Y F. Nuray Department of Mathematics, Faculty of Science and Literature, Afyon Kocatepe University fnuray@aku.edu.tr N U. Ulusu Department of Mathematics, Faculty of Science and Literature, Afyon Kocatepe University ulusu@aku.edu.tr N In this paper, we study the concepts of Wijsman statistical convergence, Hausdorff statistical convergence and  Wijsman statistical Cauchy double sequences of sets and investigate the relationship between them. Statistical convergence, Double sequence of sets, Wijsman convergence, Hausdorff convergence. http://ijmsi.ir/article-1-1172-en.html http://ijmsi.ir/article-1-1172-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes 65 76 EN R. Mohammadi Department of Mathematics, Tarbiat Modares University. rasool.mohammadi@modares.ac.ir Y We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of minimum distance in several cases and get many records that don’t exist in MinT tables (tables of optimal parameters for linear codes), such as codes over F72 of dimension less than 36. Moreover, using maximal Hermitian curves and their sub-covers, we obtain a necessary and sufficient condition for self-orthogonality and Hermitian self-orthogonally of CL(D, G). Algebraic geometric codes, Maximal curves, Minimum distance, Goppa bound, Quantum error-correcting codes http://ijmsi.ir/article-1-1284-en.html http://ijmsi.ir/article-1-1284-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials 77 95 EN B. -N. Guo Henan Polytechnic University bai.ni.guo@hotmail.com N F. Qi Tianjin Polytechnic University qifeng618@gmail.com Y In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds. Viewpoint, Ordinary differential equation, Solution, Derivative polynomial, Identity, Stirling numbers, Bernoulli number, Bernoulli polynomial, Frobenius-Euler polynomial http://ijmsi.ir/article-1-1275-en.html http://ijmsi.ir/article-1-1275-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 On Eulerianity and Hamiltonicity in Annihilating-ideal Graphs 97 104 EN A. Kourehpaz Department of Mathematics, Jundi-Shapur University of Technology asma_korehpaz@jsu:ac:ir N R. Nikandish Department of Mathematics, Jundi-Shapur University of Technology r.nikandish@jsu.ac.ir Y Let $R$ be a commutative ring with identity, and $ mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ mathrm{A}(R)^{*}=mathrm{A}(R)setminuslbrace 0rbrace $ and two distinct vertices $ I $ and $ J $ are adjacent if and only if $ IJ=0 $. In this paper, conditions under which $AG(R)$ is either Eulerian or Hamiltonian are given. Annihilating-ideal graph, Eulerian graphs, Hamiltonian graphs http://ijmsi.ir/article-1-1251-en.html http://ijmsi.ir/article-1-1251-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 Graph Clustering by Hierarchical Singular Value Decomposition with Selectable Range for Number of Clusters Members 105 121 EN A. Sadeghian Yazd University a_sadeghian@stu.yazd.ac.ir N S. A.l Shahzadeh Fazeli Yazd University fazeli@yazd.ac.ir Y S. M. Karbassi Yazd University smkarbassi@yazd.ac.ir N Graphs have so many applications in real world problems. When we deal with huge volume of data, analyzing data is difficult or sometimes impossible. In big data problems, clustering data is a useful tool for data analysis. Singular value decomposition(SVD) is one of the best algorithms for clustering graph but we do not have any choice to select the number of clusters and the number of members in each cluster. In this paper, we use hierarchical SVD to cluster graphs with it's adjacency matrix. In this algorithm, users can select a range for the number of members in each cluster. The results show in hierarchical SVD algorithm, clustering measurement parameters are more desirable and clusters are as dense as possible. The complexity of this algorithm is less than the complexity of SVD clustering method. Graph Clustering, Singular Value Decomposition, Hierarchical Clustering, Selectable Clusters Number. http://ijmsi.ir/article-1-1274-en.html http://ijmsi.ir/article-1-1274-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 Surfaces Generated by Translation Surfaces of Type 1 in I^1_3 123 135 EN M. Karacan Usak University murat.karacan@usak.edu.tr N A. Çakmak Bitlis Eren University acakmak@beu.edu.tr Y S. Kızıltuğ Erzincan University skiziltug@erzincan.edu.tr N H. Es Gazi Universiy hasanes@gazi.edu.tr N In this paper, we classify surface at a constant distance from the edge of regression on translation surfaces of Type 1 in the three dimensional simply isotropic space I^1_3 satisfying some algebraic equations in terms of the coordinate functions and the Laplacian operators with respect to the first, the second and the third fundamental form of the surface. We also give explicit forms of these surfaces. Simply isotropic space, Translation surfaces, Surface at a constant distance from the edge of regression on a surface. http://ijmsi.ir/article-1-1256-en.html http://ijmsi.ir/article-1-1256-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 Recognition of $L_{2}(q)$ by the Main Supergraph 137 144 EN S. S. Salehi Amiri Islamic Azad University, Babol salehisss@baboliau.ac.ir N A.R. Khalili Asboei Farhangian University khaliliasbo@yahoo.com Y Let $G$ be a finite group. The main supergraph $mathcal{S}(G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o(x) mid o(y)$ or $o(y)mid o(x)$. In this paper, we will show that $Gcong L_{2}(q)$ if and only if $mathcal{S}(G)cong mathcal{S} (L_{2}(q))$, where $q$ is a prime power. This work implies that Thompson's problem holds for the simple group $L_{2}(q)$. Graph, Main supergraph, Thompson's problem http://ijmsi.ir/article-1-1273-en.html http://ijmsi.ir/article-1-1273-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 Application of Tau Approach for Solving Integro-Differential Equations with a Weakly Singular Kernel 145 168 EN R. Pourgholi School of Mathematics and Computer Science, pourgholi@du.ac.ir Y A. Tahmasbi School of Mathematics and Computer Science, tahmasbi@du.ac.ir N R. Azimi School of Mathematics and Computer Science, r.azimi@std.du.ac.ir N In this work, the convection-diffusion integro-differential equation with a weakly singular kernel is discussed. The  Legendre spectral tau method is introduced for finding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices. Also the convergence analysis for  shifted Legendre polynomials and error estimation for tau method have been discussed and approved with the exact solution. Finally, several numerical examples are given to demonstrate the high accuracy of the method. Shifted Legendre tau method, Weakly singular kernel, Integro-differential equation, Convection-diffusion equation. http://ijmsi.ir/article-1-1266-en.html http://ijmsi.ir/article-1-1266-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 Tame Loci of Generalized Local Cohomology Modules 169 180 EN F. Dehghani Zadeh Islamic Azad University, Yazd branch dehghanizadeh@iauyazd.ac.ir N M. Jahangiri Kharazmi university mjahangiri@ipm.ir Y Let $M$ and $N$ be two finitely generated graded modules over a standard graded Noetherian ring $R=bigoplus_{ngeq 0} R_n$. In this paper we show that if $R_{0}$ is semi-local of dimension $leq 2$ then, the set $hbox{Ass}_{R_{0}}Big(H^{i}_{R_{+}}(M,N)_{n}Big)$ is asymptotically stable for $nrightarrow -infty$ in some special cases. Also, we study the torsion-freeness of graded generalized local cohomology modules $H^{i}_{R_{+}}(M,N)$. Finally, the tame loci $T^{i}(M,N)$ of $(M,N)$ will be considered and some sufficient conditions are proposed for the openness of these sets in the Zariski topology. Graded modules, Generalized local cohomology modules, Associated prime ideals, Tame loci. http://ijmsi.ir/article-1-1079-en.html http://ijmsi.ir/article-1-1079-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 Relative non-Normal Graphs of a Subgroup of Finite Groups 181 189 EN M. Ziaaddini Department of Pure Mathematics, Ferdowsi University of Mashhad ma.ziyaaddini@stu.um.ac.ir N A. Erfanian Department of Pure Mathematics and the Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad erfanian@um.ac.ir Y Let G be a finite group and H,K be two subgroups of G. We introduce the relative non-normal graph of K with respect to H , denoted by NH,K, which is a bipartite graph with vertex sets HHK and KNK(H) and two vertices x ∈ H HK and y ∈ K NK(H) are adjacent if xy / ∈ H, where HK =Tk∈K Hk and NK(H) = {k ∈ K : Hk = H}. We determined some numerical invariants and state that when this graph is planar or outerplanar. Non-normal graph, Relative Non-normal graph, Normality degree, Outer planar. http://ijmsi.ir/article-1-1198-en.html http://ijmsi.ir/article-1-1198-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 Nearly Rational Frobenius Groups 191 194 EN S. M. Robati Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran. sajjad.robati@gmail.com Y In this paper, we study the structure of nite Frobenius groups whose non-rational or non-real irreducible characters are linear. Frobenius groups, Rational groups, Real groups. http://ijmsi.ir/article-1-1287-en.html http://ijmsi.ir/article-1-1287-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 Some Weighted Integral Inequalities for Generalized Conformable Fractional Calculus 195 212 EN H. Budak Department of Mathematics, Faculty of Science and Arts, Düzce University hsyn.budak@gmail.com Y F. Usta Department of Mathematics, Faculty of Science and Arts, Düzce University fuatusta@duzce.edu.tr N M. Z. Sarikaya Department of Mathematics, Faculty of Science and Arts, Düzce University sarikaymz@gmail.com N In this paper, we have obtained weighted versions of Ostrowski, Čebysev and Grüss type inequalities for conformable fractional integrals which is given by Katugompola. By using the Katugampola definition for conformable calculus, the present study confirms previous findings and contributes additional evidence that provide the bounds for more general functions. Ostrowski inequality, Čebysev inequality, Grüss inequality, Conformable fractional integrals. http://ijmsi.ir/article-1-1234-en.html http://ijmsi.ir/article-1-1234-en.pdf

ACECR at Tarbiat Modares University Iranian Journal of Mathematical Sciences and Informatics 1735-4463 2008-9473 16 1 2021 4 1 ABSTRACTS IN PERSIAN Vol.16, No.1 213 228 EN The Name of Authors in this Volume Academic Center for Education, Culture and Research (ACECR) fatemeh.bardestani@gmail.com Y Please see the full text contains the pesian abstracts of this volume. ABSTRACTS, PERSIAN, Vol. 16, No. 1 http://ijmsi.ir/article-1-2172-en.html http://ijmsi.ir/article-1-2172-en.pdf