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.