Damghan University Global Analysis and Discrete Mathematics 2476-5341 7 2 2022 09 01 On Invariant Graph Of Γ-Near-Ring 145 150 296 10.22128/gadm.2022.582.1076 EN Elaheh Khamseh Department of mathematics, Islamic Azad university, Shahr-e-Qods Branch, Tehran, Iran. Journal Article 2022 07 21 Let <em>U</em> be an invariant subset of finite <em>Γ</em>-near-ring M. There are many papers that consider the graph respect to the near-ring and the interplay between algebraic structures and graphs are studied. Indeed, it is worthwhile to relate algebraic properties of near-ring to the combinatorics properties of assigned graphs. In this paper the graph with respect to an invariant subset <em>U</em> of <em>Γ</em>-near-ring <em>M</em>, denoted by <em>Γ <sup>α</sup> <sub>U</sub> (M)</em> is introduced and the basic properties of it is investigated. Also the relation between the commutativity of <em>M</em> and properties of this graph is presented. https://gadm.du.ac.ir/article_296_89bbaf346995e5fcbd1776f928f16e01.pdf
Damghan University Global Analysis and Discrete Mathematics 2476-5341 7 2 2022 09 01 Numerical Integration of Symmetric Multivariate Function 151 159 300 10.22128/gadm.2022.480.1058 EN Mohammad Gholami Baladezaei Department of Applied Mathematics, Faculty of Sciences, Islamic Azad University, Damghan Branch, Damghan, Iran 0000-0001-9290-7766 Morteza Gachpazan Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran Journal Article 2021 11 22 In this paper, we introduce a method for finding the integral of symmetric multivariate function. We compute the number of nodes which the method use them, and also by using the Gauss-Legendre integrating, we obtain the approximate value the generalized symmetric function. Theoretical consideration has been discussed and some examples were presented to show the ability of the method for approximate value of integral of the symmetric functions. In this numerical integration approach, for a symmetric function that has the same calculations at a number of different node points, only calculations are performed for a node and the result is multiplied by the number of repetitions of similar cases. In addition to modulating errors due to rounding and expanded error during calculations, much less memory is used than the numerical integration method. Also in this approach, the time of numerical integration is reduced and the numerical results confirm this. https://gadm.du.ac.ir/article_300_354844167cb3ed966fae0795ef6aa55b.pdf
Damghan University Global Analysis and Discrete Mathematics 2476-5341 7 2 2022 09 01 On Schur Multiplier of a Pair of Lie Algebras 161 169 325 10.22128/gadm.2022.531.1072 EN Homayoon Arabyani Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran. Journal Article 2022 05 03 Nilpotent Lie algebras have played an important role in mathematics in the classification theory of<br />Lie algebras. Let (<em>N, L</em>) be a pair of finite dimensional Lie algebras. Let <em>K</em> be an ideal of <em>L</em> such<br />that <em>L = N </em>⊕<em> K </em>and N be a filiform ideal of <em>L</em>. Also, let dim <em>N = n</em> and dim <em>K = m</em>. Then<br /><em>s′(N, L) = 1/2(n − 1)(n − 2) + 1 + (n − 1)m </em>−<em> dim M(N, L).</em> In this paper, we characterize the pair<br />(<em>N, L</em>) for <em>s′(N; L)</em> = 0, 1, 2,..., 15. https://gadm.du.ac.ir/article_325_43d79850781837cd5a4fa08e99fe230b.pdf
Damghan University Global Analysis and Discrete Mathematics 2476-5341 7 2 2022 09 01 On Clique Mantel's Theorem 171 178 326 10.22128/gadm.2022.630.1084 EN Hossein Teimoori Faal Department of Mathematics and Computer Science, Allameh Tabataba’i University, Tehran, Iran Journal Article 2022 11 30 A complete subgraph of any simple graph <em>G</em> on <em>k</em> vertices is called a <em>k-clique</em> of <em>G</em>. In this paper, we first introduce the concept of the value of a <em>k-clique (k>1)</em> as an extension of the idea of the degree of a given vertex. Then, we obtain <br />the generalized version of handshaking lemma which we call it clique handshaking lemma. The well-known classical result of Mantel states that the maximum number of edges in the class of triangle-free graphs with <em>n</em> vertices is equal to n<sup>2</sup>/4. Our main goal here is to find an extension of the above result for the class of <em>K<sub>ω+1</sub></em>-free graphs, using the ideas of the value of cliques and the clique handshaking lemma. https://gadm.du.ac.ir/article_326_7bc8a3ae1e7f8e50e11f41b038cce1c4.pdf
Damghan University Global Analysis and Discrete Mathematics 2476-5341 7 2 2022 09 01 ‎A Solution for Sparse PDE-Constrained Optimization by the Partition of Unity and RBFs 179 192 327 10.22128/gadm.2022.649.1089 EN Majid Darehmiraki Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Khouzestan, Iran. Arezou Rezazadeh Department of mathematics, University of Qom, Qom, Iran. Journal Article 2023 01 30 ‎In this paper‎, ‎we propose a radial basis function partition of unity (RBF-PU) method to solve sparce optimal control problem governed by the elliptic equation‎.‏ The objective function, in addition to the usual quadratic expressions, also includes an ‎L<sub>1</sub>-norm‎‎‎ of the control function to compute its spatio sparsity. ‎Meshless methods based on RBF approximation are widely used for solving PDE problems but PDE-constrained optimization problems have been barely solved by RBF methods‎. RBF methods have the benefits of being versatile in terms of geometry, simple to use in higher dimensions, and also having the ability to give spectral convergence. ‎In spite of these advantages‎, ‎when globally RBF collocation methods are used‎, ‎the interpolation matrix becomes dens and computational costs grow with increasing size of data set‎. ‎Thus‎, ‎for overcome on these problemes RBF-PU method will be proposed‎. ‎RBF‎ -‎PU methods reduce the computational effort‎. ‎The aim of this paper is to solve the first-order optimality conditions related to original problem‎.‎‎‎ https://gadm.du.ac.ir/article_327_576cefc998684120f5bdc64841517942.pdf
Damghan University Global Analysis and Discrete Mathematics 2476-5341 7 2 2022 09 01 Isoclinisms in n-Hom-Lie Algebras 193 208 328 10.22128/gadm.2022.629.1083 EN Mina Sadeghloo Mathematical Institute, Golestan University, Gorgan, Iran. Mahboubeh Alizadeh Mathematical Institute, Golestan University, Gorgan, Iran. Journal Article 2022 11 08 In the present article, we define the concept of isoclinism for n-Hom-Lie algebras and investigate some of its properties. Also, we introduce the factor sets on n-Hom-Lie algebras. As a result, it is shown that the equivalency between isoclinism and isomorphism of two finite- dimensional n-Hom-Lie algebras just depends on whether one of them be regular. https://gadm.du.ac.ir/article_328_8f8a793a72c8182f807dd4daf8c91bd7.pdf
Damghan University Global Analysis and Discrete Mathematics 2476-5341 7 2 2022 09 01 Some Results on Isologism of Pairs of Groups 209 217 329 10.22128/gadm.2022.623.1080 EN Homayoon Arabyani Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran. Journal Article 2022 10 13 Let ν be a variety of groups defined by a set <em>V</em> of laws. Then the verbal subgroup and the marginal subgroup of a group <em>G</em> associated with the variety are denoted by <em>V (G)</em> and <em>V<sup>∗</sup>(G)</em>, respectively. Let (<em>N, G</em>) be a pair of groups in which <em>N</em> is a normal subgroup of <em>G</em>. In the paper, we study the lower and upper ν-marginal series of the pair (<em>N, G</em>) and prove some properties of isologism of pairs of groups. https://gadm.du.ac.ir/article_329_27df04ce1260e9d6c2cab718de068f44.pdf
Damghan University Global Analysis and Discrete Mathematics 2476-5341 7 2 2022 09 01 Computing the spectrum of L^t(G) for a regular graph 219 227 330 10.22128/gadm.2022.641.1088 EN Saeed Mohammadian Semnani Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran. Journal Article 2023 01 07 If <em>L(G)</em> is the line graph of <em>G</em>, it is difficult to get the adjacency matrix of L<sup>t</sup>(G)=L(L(L ... L(G))); t≥3 and also its spectrum. In this paper, we present a formula to compute the spectrum of <em>L<sup>t</sup>(G)</em>, for each positive integer <em>t</em>, where <em>G</em> is a regular graph. https://gadm.du.ac.ir/article_330_53c988d0f4857574cb5cb0d472c99568.pdf
Damghan University Global Analysis and Discrete Mathematics 2476-5341 7 2 2022 09 01 A Study on the Existence and Uniqueness of Uncertain Fractional Differential Equations with Monotone Condition 229 241 331 10.22128/gadm.2022.632.1085 EN Mohammad Gholamian Department of Mathematics, West Tehran Branch, Islamic Azad University, Tehran, Iran. Samira Siah Mansouri University of applied science and technology, central of peechkar, Pakdasht, Iran. Hedayat Fattahi Department of Mathematics, Marivan Branch, Islamic Azad University, Marivan, Iran. Masoumeh Sangian University of applied science and technology, central of peechkar, Varamin, Iran. Journal Article 2022 12 13 The aim of this paper is to investigate the existence and uniqueness of solutions to uncertain fractional differential equations proposed by Canonical Liu’s process. To this end, we provide and prove a novel existence and uniqueness theorem for uncertain fractional differential equations under Local Lipschitz and monotone conditions is provided and proved. This result helps us to consider and analyze solutions to a wide range of nonlinear uncertain fractional differential equations driven by Canonical’s process to be considered and analyzed. https://gadm.du.ac.ir/article_331_0fee37ee4a402e9c08f1bf6366c7b6d6.pdf
Damghan University Global Analysis and Discrete Mathematics 2476-5341 7 2 2022 09 01 The Fastest Three-Step with Memory Method by Four Self-Accelerating Parameters 243 263 343 10.22128/gadm.2022.682.1092 EN Vali Torkashvand Department of Mathematics Farhangian University Tehran, Iran Manochehr Kazemi Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran. 0000-0001-8392-6690 Journal Article 2023 05 19 In this paper,a new family of eighth-order iterative methods for solving simple roots of nonlinear equations is developed.Each member of the proposed family requires four functional evaluations in each iteration that it is optimal according to the sense of Kung-Traub’s conjecture.They have four self-accelerating parameters that are calculated using the adaptive method.The R-order of convergence has increased from 8 to 16 (maximum improvement). https://gadm.du.ac.ir/article_343_0256ebc80217959b409c9c29b472e7ca.pdf