1 1735-4463 ACECR at Tarbiat Modares University 1033 Special Edge-coloring Vertex-weightings of Graphs Shiu W.-Ch. b Lau G.-Ch. c Ng H.-K. d b Hong Kong Baptist University c Universiti Teknologi MARA Malaysia d San Jose State University, USA 1 4 2021 16 1 1 13 23 02 2017 10 04 2021 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.
1188 General A Trust-region Method using Extended Nonmonotone Technique for Unconstrained Optimization kimiaei M. e esmaeili H. f rahpeymaii F. g e Vienna University f Bu Ali University g Payame Noor 1 4 2021 16 1 15 33 22 10 2017 26 03 2020 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. 1220 Special On Contact and Symplectic Lie Algeroids Nazari E. h Heydari A. i h Tarbiat Modares University i Tarbiat Modares University 1 4 2021 16 1 35 53 26 11 2017 26 05 2018 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. 1172 General Wijsman Statistical Convergence of Double Sequences of Sets Dundar E. j Nuray F. k Ulusu U. l j Department of Mathematics, Faculty of Science and Literature, Afyon Kocatepe University k Department of Mathematics, Faculty of Science and Literature, Afyon Kocatepe University l Department of Mathematics, Faculty of Science and Literature, Afyon Kocatepe University 1 4 2021 16 1 55 64 05 10 2017 25 07 2018 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. 1284 General One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes Mohammadi R. m m Department of Mathematics, Tarbiat Modares University. 1 4 2021 16 1 65 76 20 02 2018 25 04 2018 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). 1275 General Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials Guo B. -N. n Qi F. o n Henan Polytechnic University o Tianjin Polytechnic University 1 4 2021 16 1 77 95 06 02 2018 26 05 2018 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. 1251 General On Eulerianity and Hamiltonicity in Annihilating-ideal Graphs Kourehpaz A. p Nikandish R. p Department of Mathematics, Jundi-Shapur University of Technology Department of Mathematics, Jundi-Shapur University of Technology 1 4 2021 16 1 97 104 30 12 2017 09 07 2019 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. 1274 General Graph Clustering by Hierarchical Singular Value Decomposition with Selectable Range for Number of Clusters Members Sadeghian A. Shahzadeh Fazeli S. A.l Karbassi S. M. Yazd University Yazd University Yazd University 1 4 2021 16 1 105 121 04 02 2018 08 08 2019 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. 1256 Special Surfaces Generated by Translation Surfaces of Type 1 in I^1_3 Karacan M. Çakmak A. Kızıltuğ S. Es H. Usak University Bitlis Eren University Erzincan University Gazi Universiy 1 4 2021 16 1 123 135 10 01 2018 15 08 2020 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. 1273 General Recognition of $L_{2}(q)$ by the Main Supergraph Salehi Amiri S. S. Khalili Asboei A.R. Islamic Azad University, Babol Farhangian University 1 4 2021 16 1 137 144 02 02 2018 21 07 2018 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 $L_{2}(q)$. 1266 General Application of Tau Approach for Solving Integro-Differential Equations with a Weakly Singular Kernel Pourgholi R. Tahmasbi A. Azimi R. School of Mathematics and Computer Science, School of Mathematics and Computer Science, School of Mathematics and Computer Science, 1 4 2021 16 1 145 168 27 01 2018 19 02 2020 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. 1079 Special Tame Loci of Generalized Local Cohomology Modules Dehghani Zadeh F. Jahangiri M. Islamic Azad University, Yazd branch Kharazmi university 1 4 2021 16 1 169 180 07 05 2017 24 10 2020 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. 1198 Special Relative non-Normal Graphs of a Subgroup of Finite Groups Ziaaddini M. Erfanian A. Department of Pure Mathematics, Ferdowsi University of Mashhad Department of Pure Mathematics and the Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad 1 4 2021 16 1 181 189 03 11 2017 12 07 2019 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. 1287 Special Nearly Rational Frobenius Groups M. Robati S. Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran. 1 4 2021 16 1 191 194 28 02 2018 08 10 2018 In this paper, we study the structure of nite Frobenius groups whose non-rational or non-real irreducible characters are linear. 1234 General Some Weighted Integral Inequalities for Generalized Conformable Fractional Calculus Budak H. Usta F. Sarikaya M. Z. Department of Mathematics, Faculty of Science and Arts, Düzce University Department of Mathematics, Faculty of Science and Arts, Düzce University Department of Mathematics, Faculty of Science and Arts, Düzce University 1 4 2021 16 1 195 212 08 12 2017 08 05 2018 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. 2172 General ABSTRACTS IN PERSIAN Vol.16, No.1 in this Volume The Name of Authors Academic Center for Education, Culture and Research (ACECR) 1 4 2021 16 1 213 228 02 08 2021 02 08 2021 Please see the full text contains the pesian abstracts of this volume.