Damghan UniversityGlobal Analysis and Discrete Mathematics2476-53417120221101Some Results on c-Covers of A Pair of Groups1923310.22128/gadm.2022.430.1047ENHomayoonArabyaniDepartment of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran.Journal Article20210621Let G be a group and N be a normal subgroup of G. In this paper, we provide some results on c-covers of a pair of groups. Moreover, we prove that every c-perfect pair of groups (G, N) admits at least one c-cover and also we show that a c-cover of a pair of finite groups has a unique domain up to isomorphism under some assumptions. https://gadm.du.ac.ir/article_233_dac6b25e8100ae2b59c08fe4ad1d2808.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417120221101Legendre Spectral Tau Method for Solving the Fractional Integro-Differential Equations with A Weakly Singular Kernel113123410.22128/gadm.2022.490.1063ENRuhangizAzimiAssociate Professor, Mathematics and Computer Science Department, Adib mazandaran institute of higher education, Sari, Iran0000-0003-4926-6830MostafaMohagheghy NezhadAssociate Professor,Mathematica and Computer Science Department, Adib mazandaran institute of higher education, Sari, Iran0000-0001-8529-0673RezaPourgholiSchool of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran.0000-0003-4111-5130Journal Article20220112In this paper, the Tau method based on shifted Legendre polynomials has been introduced to approximate the numerical solutions of a class of fractional integro-differential equations with a weakly singular kernel . By using operational matrices we reduce the problem to a set of algebraic equations . Also the upper bound of the error of the shifted Legendre expansion is investigated. Finally, several numerical examples are given to illustrate the high accuracy of the method.https://gadm.du.ac.ir/article_234_b3cab2cf521ba19ee62921621913bf2a.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417120221101Solving Fredholm Integral Equations of the Second Kind Using an Improved Cuckoo Optimization Algorithm335223510.22128/gadm.2022.447.1051ENHassanDana MazraehSchool of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran.MaryamKalantariDepartment of Mathematics and Computer Science, Damghan University, Iran.Seyed HashemTabasischool of mathematics and computer science, Damghan universityAlirezaAfzal AghaeiDepartment of Mathematics and Computer Science, Damghan University, Iran.ZahraKalantariDepartment of Computer Sciences, Shahid Beheshti University, G.C. Tehran, Iran.FarhadFahimiDepartment of Computer Sciences, University of Tabriz, Tabriz, Iran.Journal Article20210915In this paper, we propose an improved cuckoo optimization algorithm (ICOA) to determine unknown function u(x) in the Fredholm integral equations of the second kind. To show utility and capability of the ICOA, we solve some Fredholm integral equations of the second kind using the ICOA and Adomian decomposition method and compare results each other. Also, by using the parallelization technique the running time of the algorithm was reduced significantly. Results obtained by implementing the ICOA on a computer with 2.2 GHz CPU and 14Gb RAM.https://gadm.du.ac.ir/article_235_33b8462e8eb6ffd4a0601eb0f7dae243.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417120221101Some Result on Weak-Tenacity of A Graph536225410.22128/gadm.2022.543.1073ENBehzadSalehian Matikolaeifaculties members / Damghan UniversityJournal Article20220521Connectivity has been used in the past to describe the stability of graphs. If two graphs, have the same connectivity, then it dose not distinguish between these graphs. That is, the connectivity is not a good measure of graph stability. Then we need other graph parameters to describe the stability. Suppose that two graphs have the same connectivity and the order (the number of vertices or edges) of the largest components of these graphs are not equal. Hence, we say that these graphs must be different in respect to stability and so we can define a new measure which distinguishes these graphs. In this paper, the Weak-Tenacity of graph G is introduced as a new measure of stability in this sense and it is defined as<br /><br /><em>T<sub>w</sub>(G) = min<sub>S<span id="MJXc-Node-6" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">⊆</span></span>V(G) </sub>{ (|S| + m<sub>e </sub>(G-S)) / ω(G-S) : ω(G-S) > 1},</em><br /><br />Where <em>m<sub>e</sub>(G-S)</em> denotes the number of, edges of the largest component of <em>G-S</em>. At last, We give the Weak-Tenacity of graphs obtained via various operations.https://gadm.du.ac.ir/article_254_15071ab72534e712d15d07d5fde5a66a.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417120221101Central Factor Groups of Locally Finite and Locally Nilpotent Groups636625310.22128/gadm.2022.518.1071ENMitraHassanzadehDepartment of pure Mathematics, Ferdowsi University of Mashhad,Mashhad, lranRasoulHatamianDepartment of Basic Sciences, School of Mathematical Sciences, Payame Noor University,
Tehran, Iran.SaeedKayvanfarDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article20220318Let <em>P</em> be a group property. A group <em>G</em> is called a locally Pgroup if each finite subset of <em>G</em> is contained in a <em>P</em>-subgroup of <em>G</em>. In this paper some relations between the central factor groups and commutator subgroups in locally nilpotent and locally finite groups are investigated.https://gadm.du.ac.ir/article_253_73dc03d9516124ee1395d36eabb26693.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417120221101On the Relative 2-Engel Degree of A Subgroup of A Finite Group677328510.22128/gadm.2022.602.1078ENHaniehGolmakaniDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.AbbasJafarzadehDepartment of Mathematics, Quchan University of Technology, Quchan, Iran.Journal Article20221004Let G be a finite group. The notion of n-Engel degree of G, denote by d<sub>n</sub>(G), is the probability of two randomely chosen elements x, y ∈ G satisfy the n-Engel condition [y<sub>,n </sub>x]=1. The case n=1 is the known commutativity degree of G. The aim of this paper, is to define and investigate the relative 2-Engel degree of a subgroup H of G as the probability of two randomely chosen elements x∈G and y∈H satisfy the 2-Engel condition [y<sub>,2 </sub>x]=1. https://gadm.du.ac.ir/article_285_a8ecfd77baa04af4f55e3fad3fe0e74f.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417120221101Some Remarks on c-Isoclinic Pairs of Filippov Algebras758828610.22128/gadm.2022.484.1059ENSedighehSheikh-MohseniDepartment of Mathematics, Faculty of Science, Higher
Education Center of Eghlid, Eghlid, Iran.Journal Article20211222In this paper, we study the notion of c-isoclinism for the pairs of Filippov algebras. Also, we give an equivalent condition for pairs of Filippov algebras to be c-isoclinic. In particular, it is shown that two Filippov algebras are c-isoclinic if and only if then each of them can be constructed from another by using the operations of forming direct sums, taking subalgebras, and factoring Filippov algebras. Moreover, we introduce the concept of c-perfect pair of Filippov algebras and obtain some relations between c-isoclinic and c-perfect pairs of Filippov algebras. https://gadm.du.ac.ir/article_286_42f0d51f4c69f09a196c573e7e73b69e.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417120221101Dominated Coloring of Certain Graphs899928710.22128/gadm.2022.624.1081ENFatemehChoopaniDepartment of Mathematics, Ferdowsi University of Mashhad, Mashhad, IranAbbasJafarzadehDepartment of
Mathematics, Quchan University of Technology, Quchan, IranDoost AliMojdehDepartment of Mathematics, University of Mazandaran, Babolsar, IranJournal Article20221014A proper coloring of a graph <em>G</em> is called a dominated coloring whenever each color class is dominated by at least one vertex. The minimum number of colors among all dominated colorings of <em>G</em> is called its dominated chromatic number, denoted by <em>χ<sub>dom</sub>(G)</em>. We define a parameter related to dominated coloring, namely dominated chromatic covering. For a minimum dominated coloring of <em>G</em>, a set of vertices <em>S</em> is called a dominated chromatic covering if each color class is dominated by a vertex of <em>S</em>. The minimum cardinality of a dominated chromatic covering of <em>G</em> is called its dominated chromatic covering number, denoted by <em>θ<sub>χdom</sub>(G)</em> . It is clear that <em>θ<sub>χdom</sub>(G)</em> ≤ <em>χ<sub>dom</sub>(G)</em>. In this paper, we obtain the dominated chromatic number and <em>θ<sub>χdom</sub>(G)</em> when <em>G</em> is middle and total graph of paths and cycles.https://gadm.du.ac.ir/article_287_6ee28d4d597d24bb863fc400911de72a.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417120221101Conformity of Fractional Volterra Integro-Differential Equation Solution with an Integral Equation of Fractional Order10110828810.22128/gadm.2022.587.1077ENLeilaTorkzadehDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran.0000-0002-2504-4048SomayyehDadsetadiDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran.Journal Article20220820For the feasibility of using analytical and numerical studies and findings on fractional integral equations for integro-differential of the fractional order, in this work, the equivalence of a fractional Volterra integro-differential equation of the Hammerstein type with a fractional integral equation is investigated in the Banach space. For this purpose, we use the mutual properties of the fractional order derivative and integral on each other.https://gadm.du.ac.ir/article_288_ec051a1b021c92ce61a1beb32d972061.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417120221101Nonsplit Domination Vertex Critical Graph10911528910.22128/gadm.2022.517.1070ENGirishV RajashekharaiahPES UniversityUsha PMurthySiddaganga Institute of technologyJournal Article20220316A dominating set <em>D</em> of a graph <em>G = (V, E)</em> is a nonsplit dominating set if the induced graph<em> ⟨V − D⟩</em> is connected. The nonsplit domination number <em>γ<sub>ns</sub>(G)</em> is the minimum cardinality of a nonsplit domination set. The purpose of this paper is to initiate the investigation of those graphs which are critical in the following sense: A graph <em>G</em> is called vertex domination critical if <em>γ(G − v) < γ(G) </em>for every vertex <em>v</em> in <em>G</em>. A graph <em>G</em> is called vertex nonsplit critical if <em>γ<sub>ns</sub>(G −v) < γ<sub>ns</sub>(G)</em> for every vertex <em>v</em> in <em>G</em>. Initially we test whether some particular classes of graph are <em>γ<sub>ns</sub></em>-critical or not and then we have shown that there is no existence of 2-<em>γ<sub>ns</sub></em>-critical graph. Then 3-<em>γ<sub>ns</sub></em>-critical graphs are characterized.https://gadm.du.ac.ir/article_289_b1e711a3a5abd833621ff522e424ce93.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417120221101Infinitely Many Solutions for Discrete Fourth-Order Boundary Value Problem with Four Parameters11712929010.22128/gadm.2022.557.1075ENMohammadAbolghasemiDepartment of Mathematics, Faculty of Sciences, Razi
University, 67149 Kermanshah, IranShahinMoradiDepartment of Mathematics, Faculty of Sciences, Razi
University, 67149 Kermanshah, IranJournal Article20220608The aim of this paper is to study the existence of infinitely many solutions for discrete fourth-order boundary value problem with four parameters involving oscillatory behaviors of nonlinearity at infinity. The approach is based on variational methods. In addition, one example is presented to illustrate the feasibility and effectiveness of the main result.https://gadm.du.ac.ir/article_290_d69d8a36fb90432d8776e8aa156a1dfb.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417120221101Optimization in Internet Networks Using Data Envelopment Analysis Model with Undesirable Outputs13114328410.22128/gadm.2021.371.1030ENElhamAlipour ChavariDepartment of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranMohsenRostamy-MalkhalifehDepartment of Mathematics, Science and Research Branch, IAU,
Hesarak, poonakFarhadHosseinzadeh LotfiDepartment of mathematics, Science and Research Branch, Islamic Azad University, , Tehran, IranJournal Article20200912The purpose of this paper is to use the decision making techniques of Data Envelopment Analysis (DEA) in order to evaluate the existing Internet networks to select the most desirable networks.To achieve this goal, we first begin by simulating a specific Internet network called Differentiated Service (DS) network that provides the quality of service to the user through the mechanism of Call Admission Control (CAC). We then evaluate and rank the networks by proposing a novel DEA model in the literature of undesirable outputs. Finally, by using the results of DEA model, we select the optimal Internet network.https://gadm.du.ac.ir/article_284_5601b3895eb79c7bbeb7ba77dd885564.pdf