@article{ 
author = {Shiu, W.-Ch. and Lau, G.-Ch. and Ng, H.-K.},  
title = {Edge-coloring Vertex-weightings of Graphs}, 
abstract ={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.},  
Keywords = {Edge coloring, Vertex weightings.},
volume = {16},
Number = {1}, 
pages = {1-13}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1033-en.html},  
eprint = {http://ijmsi.ir/article-1-1033-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {kimiaei, M. and esmaeili, H. and rahpeymaii, F.},  
title = {A Trust-region Method using Extended Nonmonotone Technique for Unconstrained Optimization}, 
abstract ={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.},  
Keywords = {Unconstrained optimization, Trust-region framework, Nonmonotone technique, Theoretical convergence},
volume = {16},
Number = {1}, 
pages = {15-33}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1188-en.html},  
eprint = {http://ijmsi.ir/article-1-1188-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Nazari, E. and Heydari, A.},  
title = {On Contact and Symplectic Lie Algeroids}, 
abstract ={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.},  
Keywords = {Lie algebroid, Symplectic Lie algebroid, Contact Lie algebroid, Poisson structure},
volume = {16},
Number = {1}, 
pages = {35-53}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1220-en.html},  
eprint = {http://ijmsi.ir/article-1-1220-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Dundar, E. and Nuray, F. and Ulusu, U.},  
title = {Wijsman Statistical Convergence of Double Sequences of Sets}, 
abstract ={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.},  
Keywords = {Statistical convergence, Double sequence of sets, Wijsman convergence, Hausdorff convergence.},
volume = {16},
Number = {1}, 
pages = {55-64}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1172-en.html},  
eprint = {http://ijmsi.ir/article-1-1172-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Mohammadi, R.},  
title = {One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes}, 
abstract ={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).},  
Keywords = {Algebraic geometric codes, Maximal curves, Minimum distance, Goppa bound, Quantum error-correcting codes},
volume = {16},
Number = {1}, 
pages = {65-76}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1284-en.html},  
eprint = {http://ijmsi.ir/article-1-1284-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Guo, B. -N. and Qi, F.},  
title = {Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials}, 
abstract ={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.},  
Keywords = {Viewpoint, Ordinary differential equation, Solution, Derivative polynomial, Identity, Stirling numbers, Bernoulli number, Bernoulli polynomial, Frobenius-Euler polynomial},
volume = {16},
Number = {1}, 
pages = {77-95}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1275-en.html},  
eprint = {http://ijmsi.ir/article-1-1275-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Kourehpaz, A. and Nikandish, R.},  
title = {On Eulerianity and  Hamiltonicity in Annihilating-ideal Graphs}, 
abstract ={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.},  
Keywords = {Annihilating-ideal graph, Eulerian graphs, Hamiltonian graphs},
volume = {16},
Number = {1}, 
pages = {97-104}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1251-en.html},  
eprint = {http://ijmsi.ir/article-1-1251-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Sadeghian, A. and ShahzadehFazeli, S. A.l and Karbassi, S. M.},  
title = {Graph Clustering by Hierarchical Singular Value Decomposition with Selectable Range for Number of Clusters Members}, 
abstract ={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.},  
Keywords = {Graph Clustering, Singular Value Decomposition, Hierarchical Clustering, Selectable Clusters Number.},
volume = {16},
Number = {1}, 
pages = {105-121}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1274-en.html},  
eprint = {http://ijmsi.ir/article-1-1274-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Karacan, M. and Çakmak, A. and Kızıltuğ, S. and Es, H.},  
title = {Surfaces Generated by Translation Surfaces of Type 1 in I^1_3}, 
abstract ={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.},  
Keywords = {Simply isotropic space, Translation surfaces, Surface at a constant distance from the edge of regression on a surface.},
volume = {16},
Number = {1}, 
pages = {123-135}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1256-en.html},  
eprint = {http://ijmsi.ir/article-1-1256-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {SalehiAmiri, S. S. and KhaliliAsboei, A.R.},  
title = {Recognition of $L_{2}(q)$ by the Main Supergraph}, 
abstract ={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 $L_{2}(q)$.},  
Keywords = {Graph, Main supergraph, Thompson's problem},
volume = {16},
Number = {1}, 
pages = {137-144}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1273-en.html},  
eprint = {http://ijmsi.ir/article-1-1273-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Pourgholi, R. and Tahmasbi, A. and Azimi, R.},  
title = {Application of Tau Approach for Solving Integro-Differential Equations with a Weakly Singular Kernel}, 
abstract ={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.},  
Keywords = {Shifted Legendre tau method, Weakly singular kernel, Integro-differential equation, Convection-diffusion equation.},
volume = {16},
Number = {1}, 
pages = {145-168}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1266-en.html},  
eprint = {http://ijmsi.ir/article-1-1266-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {DehghaniZadeh, F. and Jahangiri, M.},  
title = {Tame Loci of Generalized Local Cohomology Modules}, 
abstract ={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.},  
Keywords = {Graded modules, Generalized local cohomology modules, Associated prime ideals, Tame loci.},
volume = {16},
Number = {1}, 
pages = {169-180}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1079-en.html},  
eprint = {http://ijmsi.ir/article-1-1079-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Ziaaddini, M. and Erfanian, A.},  
title = {Relative non-Normal Graphs of a Subgroup of Finite Groups}, 
abstract ={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.},  
Keywords = {Non-normal graph, Relative Non-normal graph, Normality degree, Outer planar.},
volume = {16},
Number = {1}, 
pages = {181-189}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1198-en.html},  
eprint = {http://ijmsi.ir/article-1-1198-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {M.Robati, S.},  
title = {Nearly Rational Frobenius Groups}, 
abstract ={In this paper, we study the structure of nite Frobenius groups whose non-rational or non-real irreducible characters are linear.},  
Keywords = {Frobenius groups, Rational groups, Real groups.},
volume = {16},
Number = {1}, 
pages = {191-194}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1287-en.html},  
eprint = {http://ijmsi.ir/article-1-1287-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Budak, H. and Usta, F. and Sarikaya, M. Z.},  
title = {Some Weighted Integral Inequalities for Generalized Conformable Fractional Calculus}, 
abstract ={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.},  
Keywords = {Ostrowski inequality, Čebysev inequality, Grüss inequality, Conformable fractional integrals.},
volume = {16},
Number = {1}, 
pages = {195-212}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-1234-en.html},  
eprint = {http://ijmsi.ir/article-1-1234-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {inthisVolume, The Name of Authors},  
title = {ABSTRACTS IN PERSIAN Vol.16, No.1}, 
abstract ={Please see the full text contains the pesian abstracts of this volume.},  
Keywords = {ABSTRACTS, PERSIAN, Vol. 16, No. 1},
volume = {16},
Number = {1}, 
pages = {213-228}, 
publisher = {ACECR at Tarbiat Modares University},
url = {http://ijmsi.ir/article-1-2172-en.html},  
eprint = {http://ijmsi.ir/article-1-2172-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Assari, A. and Rahimi, M.},  
title = {On Beck\'s Coloring for Measurable Functions}, 
abstract ={We study Beck-like coloring of measurable functions on a measure space $Omega$ taking values in a measurable semigroup $Delta$‎. ‎To any‎ ‎measure space $Omega$ and any measurable semigroup $Delta$ we assign a graph (called a zero-divisor graph) whose vertices are labelled by‎ ‎the classes of measurable functions defined on $Omega$ and having values in $Delta$‎, ‎with two vertices $f$ and $g$ adjacent if $f.g=0$ a.e.‎. ‎We show that‎, ‎if $Omega$ is atomic‎, ‎then not only the Beckchr('39')s conjecture holds but also the domination number coincide to the clique number and chromatic number as well‎. ‎We also determine some other graph properties of such a graph‎.},  
Keywords = {Zero divisor graph‎, ‎Domination number‎, ‎Measurable function‎, ‎Clique number‎, ‎Coloring‎.},
volume = {16},
Number = {2}, 
pages = {1-10}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.1},
url = {http://ijmsi.ir/article-1-1138-en.html},  
eprint = {http://ijmsi.ir/article-1-1138-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Rawshdeh, A. and Tallafha, A.},  
title = {Fixed Point in Semi-linear Uniform Spaces and Convex Metric Spaces}, 
abstract ={Tallafha, A. and Alhihi S. in [15], asked the following question. If f is a contraction from a complete semi-linear uniform space (X,Γ) to it self, is f has a unique fixed point. In this paper, we shall answer this question negatively and we shall show that convex metric space and M-space are equivalent except uniqueness. Also we shall characterize convex metric spaces and use this characterization to give some application using semi-linear uniform spaces.},  
Keywords = {Uniform spaces, Semi-linear uniform spaces, Contractions, metric spaces, types of metric spaces.},
volume = {16},
Number = {2}, 
pages = {11-23}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.11},
url = {http://ijmsi.ir/article-1-1167-en.html},  
eprint = {http://ijmsi.ir/article-1-1167-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Madadi-Dargahi, S. and Nasr-Azadani, M. A.},  
title = {Erratum‎ " ‎Some result on simple hyper K‎- ‎algebras‎ ", ‎Iranian Journal of Mathematical Sciences and Informatics‎ ‎Vol‎. ‎3‎, ‎No‎. ‎2 (2008)‎, ‎pp‎. ‎29-48}, 
abstract ={‎‎In this manuscript we show that the Theorem 3.28cite{C} is not correct in generally and modify it‎.},  
Keywords = {Simple hyper K‎- ‎algebras‎, Positive implicative hyper K-ideal.},
volume = {16},
Number = {2}, 
pages = {25-29}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.25},
url = {http://ijmsi.ir/article-1-1152-en.html},  
eprint = {http://ijmsi.ir/article-1-1152-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Ibrahim, H. and Khalaf, A.},  
title = {Topological Rings and Modules Via Operations}, 
abstract ={The structure of an $alpha_{(beta, beta)}$-topological ring is richer in comparison with the structure of an $alpha_{(beta, beta)}$-topological group. The theory of $alpha_{(beta, beta)}$-topological rings has many common features with the theory of $alpha_{(beta, beta)}$-topological groups. Formally, the theory of $alpha_{(beta, beta)}$-topological abelian groups is included in the theory of $alpha_{(beta, beta)}$-topological rings. The purpose of this paper is to introduce and study the concepts of $alpha_{(beta, beta)}$-topological rings and $alpha_{(beta, gamma)}$-topological $R$-modules. we show how they may be introduced by specifying the neighborhoods of zero, and present some basic constructions.  We provide fundamental concepts and basic results on $alpha_{(beta, beta)}$-topological rings and $alpha_{(beta, gamma)}$-topological $R$-modules.},  
Keywords = {Operations, $alpha_{beta}$-Open set, Rins,  $alpha_{(beta, beta)}$-Topological rings, $alpha_{(beta, gamma)}$-Topological $R$-modules},
volume = {16},
Number = {2}, 
pages = {31-48}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.31},
url = {http://ijmsi.ir/article-1-1208-en.html},  
eprint = {http://ijmsi.ir/article-1-1208-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Wanas, A. K. and Majeed, A. M.},  
title = {Second Hankel Determinant for a Certain Subclass of 𝝀-Pseudo-Starlike Bi-Univalent Functions}, 
abstract ={In this paper, we discuss the upper bounds for the second Hankel determinant 𝐻2(2) of a new subclass of 𝜆-pseudo-starlike bi-univalent functions defined in the open unit disk 𝑈.},  
Keywords = {Analytic functions, Bi-univalent functions, 𝜆- Pseudo-starlike functions, Upper bounds, Second Hankel determinant.},
volume = {16},
Number = {2}, 
pages = {49-59}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.49},
url = {http://ijmsi.ir/article-1-1224-en.html},  
eprint = {http://ijmsi.ir/article-1-1224-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Flores, G. B. and Benitez, J.},  
title = {Some Convergence Theorems of the pul-Stieltjes Integral}, 
abstract ={The PUL integral is an integration process, similar to the Kurzweil-Henstock integral, which uses the notion of partition of unity. Boonpogkrong discussed the Kurzweil-Henstock integral on manifolds. The PUL-Stieltjes integral, established by Flores and Benitez, is an extension of the PUL Integral. In this paper, we present some Convergence Theorems for the PUL-Stieltjes integral. Notions on the equi-integrability of this integral are also presented in the paper.},  
Keywords = {PUL-Stieltjes Integral, Uniform Convergence, Equi-integrability.},
volume = {16},
Number = {2}, 
pages = {61-72}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.61},
url = {http://ijmsi.ir/article-1-1240-en.html},  
eprint = {http://ijmsi.ir/article-1-1240-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Shelash, H. B. and Ashrafi, A. R.},  
title = {The Number of Subgroups of a Given Type in Certain Finite Groups}, 
abstract ={The number of subgroups, normal subgroups and characteristic subgroups of a finite group $G$ are denoted by $Sub(G)$, $NSub(G)$ and $CSub(G)$, respectively. The main goal of this paper is to present a matrix model for computing these positive integers for dicyclic groups, semi-dihedral groups,  and three sequences $U_{6n}$, $V_{8n}$ and $H(n)$ of groups that can be presented as follows: begin{eqnarray*} U_{6n} &=& langle a, b mid a^{2n} = b^{3} = e, bab = arangle, V_{8n} &=& langle a, b mid a^{2n} = b^{4} = e, aba = b^{-1}, ab^{-1}a = brangle, H(n)&=&langle a,b,c mid a^{2^{n-2}}=b^{2}=c^{2}=e, [x,y]=[y,z]=e, x^{z}=xy rangle. end{eqnarray*} For each group, a matrix model containing all information is given.},  
Keywords = {Subgroup, Normal subgroup, Characteristic subgroup.},
volume = {16},
Number = {2}, 
pages = {73-87}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.73},
url = {http://ijmsi.ir/article-1-1751-en.html},  
eprint = {http://ijmsi.ir/article-1-1751-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Kabbaj, S. and Zoubeir, H.},  
title = {On the Representation and the Uniform Polynomial Approximation of Polyanalytic Functions of Gevrey Type on the Unit Disk}, 
abstract ={ In this paper we deÖne Gevrey polyanalytic classes of order N on the unit disk D and we characterize these classes by a speciÖc expansion into Nanalytic polynomials on suitable neighborhoods of D. As an application of our main theorem, we perform for the Gevrey polyanalytic classes of order N on the unit disk D, an analogue to E. M. Dyníkinís theorem. We derive also, for these classes, their characteristic degree of the best uniform approximation on D by Nanalytic polynomials. Keywords: Polyanalytic functions, Gevrey classes, Degree of polynomial approximation. 2000 Mathematics subject classiÖcation: 30D60, 26E05, 41A10. 1. Introduction The polyanalytic functions of order 2, the so-called bianalytic functions, originates from mechanics where they played a fundamental role in solving the problems of the planar theory of elasticity. Their usefulness in mechanics was illustrated by the pioneering works of Kolosso§, Muskhelishvili and their followers (([15])-([17]), [24], [25], [27]). By the systematic use of complex variable techniques these authors have greatly simpliÖed and extended the mathematicalmethods of the elasticity theory. The class of polyanalytic functions of order Corresponding Author 1analytic polynomials on suitable neighborhoods of  D. As an application of our main theorem, we perform for the Gevrey polyanalytic classes of order N on the unit disk D, an analogue to E. M. Dyníkinís theorem. We derive also, for these classes, their characteristic degree of the best uniform approximation on D by Nanalytic polynomials. Keywords: Polyanalytic functions, Gevrey classes, Degree of polynomial approximation. 2000 Mathematics subject classiÖcation: 30D60, 26E05, 41A10. 1. Introduction The polyanalytic functions of order 2, the so-called bianalytic functions, originates from mechanics where they played a fundamental role in solving the problems of the planar theory of elasticity. Their usefulness in mechanics was illustrated by the pioneering works of Kolosso§, Muskhelishvili and their followers (([15])-([17]), [24], [25], [27]). By the systematic use of complex variable techniques these authors have greatly simpliÖed and extended the mathematicalmethods of the elasticity theory. The class of polyanalytic functions of order Corresponding Author 1analytic polynomials.},  
Keywords = {Polyanalytic functions, Gevrey classes, Degree of polynomial approximation.},
volume = {16},
Number = {2}, 
pages = {89-115}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.89},
url = {http://ijmsi.ir/article-1-1288-en.html},  
eprint = {http://ijmsi.ir/article-1-1288-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Al-Zoubi, Kh.},  
title = {On the Graded Primal Avoidance Theorem}, 
abstract ={ Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we generalize the graded primary avoidance theorem for modules to the graded primal avoidance theorem for modules. we also introduce the concept of graded $P_{L}$-compactly packed modules and give a number of its properties.},  
Keywords = {Graded primal submodules, Graded primal avoidance, Graded $P_{L}$-compactly packed modules},
volume = {16},
Number = {2}, 
pages = {117-124}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.117},
url = {http://ijmsi.ir/article-1-1291-en.html},  
eprint = {http://ijmsi.ir/article-1-1291-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Abedian, R.},  
title = {WENO-Z Schemes with Legendre Basis for non-Linear Degenerate Parabolic Equations}, 
abstract ={This paper provides a fourth-order scheme for approximating solutions of non-linear degenerate parabolic equations that their solutions may contain discontinuity. In the reconstruction step, a fourth-order weighted essentially non-oscillatory (WENO) reconstruction in Legendre basis, written as a convex combination of interpolants based on different stencils, is constructed. In the one-dimensional case, the new fourth-order reconstruction is based on a four-point stencil. The most important subject is that one of these interpolation polynomials is taken as a quadratic polynomial, and the linear weights of the symmetric and convex combination are set as to get fourth-order accuracy in smooth areas. Following the methodology of the traditional WENO-Z reconstruction, the non-oscillatory weights is calculated by the linear weights. The accuracy, robustness, and high-resolution properties of the new procedure are shown by extensive numerical examples.},  
Keywords = {WENO schemes, Legendre orthogonal polynomials, multidimensional non-linear degenerate parabolic equations, porous medium equation.},
volume = {16},
Number = {2}, 
pages = {125-143}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.125},
url = {http://ijmsi.ir/article-1-1292-en.html},  
eprint = {http://ijmsi.ir/article-1-1292-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Mahboob, A. and Davvaz, B. and Khan, N. M.},  
title = {Ordered Γ-Semigroups and Fuzzy Γ-ideals}, 
abstract ={We prove that every fuzzy generalized bi-Γ-ideal and every fuzzy interior Γ-ideal in a right weakly regular ordered Γ-semigroup is a fuzzy Γ-ideal. We also show that every fuzzy generalized bi-Γ-ideal in a duo right weakly regular ordered Γ-semigroup is a fuzzy interior Γ-ideal. Then, by using fuzzy Γ-ideals, fuzzy bi-Γ-ideals, fuzzy generalized bi-Γ-ideals and fuzzy interior Γ-ideals, left simple, right simple and simple ordered Γ-semigroups have been characterized. Finally we characterize right weakly regular ordered Γ-semigroup by its fuzzy Γ-ideals, fuzzy bi-Γ-ideals, fuzzy generalized bi-Γ-ideals and fuzzy interior Γ-ideals.},  
Keywords = {Ordered Γ-semigroup, right weakly regular ordered Γ-semigroup, Fuzzy set, Fuzzy Γ-ideals.},
volume = {16},
Number = {2}, 
pages = {145-162}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.129},
url = {http://ijmsi.ir/article-1-1295-en.html},  
eprint = {http://ijmsi.ir/article-1-1295-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {JeCho, Y. and Shin-min, Sh.-m. and Rassias, T. M. and Saadati, R.},  
title = {On Nonlinear Random Approximation of 3-variable Cauchy Functional Equation}, 
abstract ={In the  $RC^*$-algebras and Lie $RC^*$-algebras, we approximate the homomorphisms and derivations   for the 3-variable Cauchy functional equation, by the fixed point method.},  
Keywords = {Approximation, Functional equations, $RC^*$-algebras, Random  space},
volume = {16},
Number = {2}, 
pages = {163-177}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.147},
url = {http://ijmsi.ir/article-1-1296-en.html},  
eprint = {http://ijmsi.ir/article-1-1296-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Bordbar, H. and Bordbar, M. R. and Borzooei, R. A. and Jun, Y. B.},  
title = {N-subalgebras of BCK=BCI-Algebras which are Induced from Hyperfuzzy Structures}, 
abstract ={In the paper [J. Ghosh and T.K. Samanta, Hyperfuzzy sets and hyperfuzzy group, Int. J. Advanced Sci Tech. 41 (2012), 27{37], Ghosh and Samanta introduced the concept of hyperfuzzy sets as a generalization of fuzzy sets and interval-valued fuzzy sets, and applied it to group theory. The aim of this manuscript is to study N-structures in BCK/BCI-algebras induced from hyperfuzzy structures.},  
Keywords = {hyperfuzzy set, hyperfuzzy structure, hyperfuzzy subalgebra, N-subalgebra, induced N- function.},
volume = {16},
Number = {2}, 
pages = {179-195}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.163},
url = {http://ijmsi.ir/article-1-1301-en.html},  
eprint = {http://ijmsi.ir/article-1-1301-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}

@article{ 
author = {Nobary, E. and Hosseini, S. M.},  
title = {A Geometric Numerical Integration of Lie-Poisson System for Ideal Compressible Isentropic Fluid}, 
abstract ={In this paper we apply a geometric integrator to the problem of Lie-Poisson system for ideal compressible isentropic fluids (ICIF) numerically. Our work is based on the decomposition of the phase space, as the semidirect product of two infinite dimensional Lie groups. We have shown that the solution of (ICIF)  stays in coadjoint orbit and this result extends a similar result for matrix group discussed in [6] (Hairer, et al). By using the coadjoint action of the Lie group on the dual of its Lie algebra to advance the numerical flow, we (as in Engo, et al. [2]) devise methods that automatically stay on the coadjoint orbit. The paper concludes with a concrete example.},  
Keywords = {Ideal compressible isentropic fluid, Lie-Poisson system, Semidirect product, Geometric integration, Coadjoint orbit.},
volume = {16},
Number = {2}, 
pages = {197-208}, 
publisher = {ACECR at Tarbiat Modares University},

doi = {10.52547/ijmsi.16.2.181},
url = {http://ijmsi.ir/article-1-1313-en.html},  
eprint = {http://ijmsi.ir/article-1-1313-en.pdf},  
journal = {Iranian Journal of Mathematical Sciences and Informatics},  
issn = {1735-4463}, 
eissn = {2008-9473}, 
year = {2021}  
}