Damghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901On Invariant Graph Of Γ-Near-Ring14515029610.22128/gadm.2022.582.1076ENElahehKhamsehDepartment of mathematics, Islamic Azad university, Shahr-e-Qods Branch, Tehran, Iran.Journal Article20220721Let <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.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901Numerical Integration of Symmetric Multivariate Function15115930010.22128/gadm.2022.480.1058ENMohammadGholami BaladezaeiDepartment of Applied Mathematics, Faculty of Sciences, Islamic Azad University, Damghan
Branch, Damghan, Iran0000-0001-9290-7766MortezaGachpazanDepartment of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, IranJournal Article20211122In 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.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901On Schur Multiplier of a Pair of Lie Algebras16116932510.22128/gadm.2022.531.1072ENHomayoonArabyaniDepartment of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran.Journal Article20220503Nilpotent 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.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901On Clique Mantel's Theorem17117832610.22128/gadm.2022.630.1084ENHosseinTeimoori FaalDepartment of Mathematics and Computer Science, Allameh Tabataba’i University, Tehran,
IranJournal Article20221130A 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.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901A Solution for Sparse PDE-Constrained Optimization by the Partition of Unity and RBFs17919232710.22128/gadm.2022.649.1089ENMajidDarehmirakiDepartment of Mathematics, Behbahan Khatam Alanbia University of Technology, Khouzestan, Iran.ArezouRezazadehDepartment of mathematics, University of Qom, Qom, Iran.Journal Article20230130In 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.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901Isoclinisms in n-Hom-Lie Algebras19320832810.22128/gadm.2022.629.1083ENMinaSadeghlooMathematical Institute, Golestan University, Gorgan, Iran.MahboubehAlizadehMathematical Institute, Golestan University, Gorgan, Iran.Journal Article20221108In 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.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901Some Results on Isologism of Pairs of Groups20921732910.22128/gadm.2022.623.1080ENHomayoonArabyaniDepartment of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran.Journal Article20221013Let 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.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901Computing the spectrum of L^t(G) for a regular graph21922733010.22128/gadm.2022.641.1088ENSaeedMohammadian SemnaniDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences,
Semnan University, Semnan, Iran.Journal Article20230107If <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.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901A Study on the Existence and Uniqueness of Uncertain Fractional Differential Equations with Monotone Condition22924133110.22128/gadm.2022.632.1085ENMohammadGholamianDepartment of Mathematics, West Tehran Branch, Islamic Azad University, Tehran, Iran.SamiraSiah MansouriUniversity of applied science and technology, central of peechkar, Pakdasht, Iran.HedayatFattahiDepartment of Mathematics, Marivan Branch, Islamic Azad University, Marivan, Iran.MasoumehSangianUniversity of applied science and technology, central of peechkar, Varamin, Iran.Journal Article20221213The 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.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901The Fastest Three-Step with Memory Method by Four Self-Accelerating Parameters24326334310.22128/gadm.2022.682.1092ENValiTorkashvandDepartment of Mathematics Farhangian University Tehran, IranManochehrKazemiDepartment of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran.0000-0001-8392-6690Journal Article20230519In 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.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901Performance Evaluation in the Presence of Heterogeneous Indicators in Data Envelopment Analysis: A Case Study on Top Investment Companies of Tehran Stock Exchange26527134410.22128/gadm.2022.668.1091ENMahnazAhadzadeh NaminDepartment of mathematics, Islamic Azad University, Shahr-e-Qods Branch, Tehran, Iran.ElahehKhamsehDepartment of mathematics, Islamic Azad university, Shahr-e-Qods Branch, Tehran, Iran.Journal Article20230319Evaluating the performance of organizations can provide managers with useful information about the status of the organization compared to other organizations so that managers can take a step towards the growth and excellence of the organization. Obviously, the number of indicators and their amount affect the performance evaluation of organizations. So, by collecting the exact values of the indicators, an accurate and accurate performance evaluation will be provided to managers of organizations. In this article, we intend to evaluate the companies investing in the stock exchange. Since in the table of indices related to these companies published by the Iran Stock Exchange Organization there are indices whose values have been lost for any reason (not available - heterogeneous index), it is necessary to use envelopment analysis models. We used data (DEA) in the presence of heterogeneous indicators. We have used the model of Cook et al.'s (2013) article to evaluate companies. For the conceptual use of research, we have described and implemented their method step by step. Lastly, we have analyzed the results.https://gadm.du.ac.ir/article_344_411c7b63029a1ebe241ce72b2f554634.pdfDamghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901Fuzzy Linear Regression Method for Analyzing Profits and Stock Returns in Selected Industries in Tehran Stock Exchange27328334510.22128/gadm.2022.662.1090ENMohammadGholami BaladezaeiDepartment of Mathematics, Damghan Branch, Islamic Azad University, Damghan, Iran0000-0001-9290-7766ElaheSarfiDepartment of Mathematics, Damghan Branch, Islamic Azad University, Damghan, Iran.MonireHosein AllianiDepartment Of Accounting, Damghan Branch, Islamic Azad University, Damghan, IranJournal Article20230306In recent years, use of fuzzy linear regression has expanded significantly in economics, accounting and financial mathematics. In this type of regression, for data analysis, there is no need to meet the prerequisites that are required in normal linear regression. In addition, it is necessary to solve a linear programming problem to find coefficients of this type of regression. Since in examining the status of stability and the cash and accrual components of companies’ profits, the calculation of accruals is based on forecasts and estimates and is measured by less reliability, so implied greater stability of profit due to its cash component. Among the cases that have an accrual basis, the non-objectivity of the amount, especially the cash amount of the earnings, is very important for the future profitability. In this study, focusing on profit cash components and the stability, the profitability of the company and its efficiency compared to the accrual basis are investigated using fuzzy linear regression. In the issue of technical analysis and to check profits sustainability, a sample of four selected industries, vehicle manufacturing, pharmaceuticals, basic metals, and ceramic tiles during the years 2011-2016, has been selected in the Tehran Stock Exchange market. In this study, sign constraints are added to the set of constraints in the main linear programming problem so obtained solutions can be interpreted and justified. The results confirmed the hypothesis “cash components of profit have more stability of profit than accrual components”, but the hypothesis “more stability of profit due to cash components of profit has a greater impact on the amount of cash and the rights Stockholders” and also the hypothesis” the profit expectations implicit in the stock price fully reflect the stability of the profit related to the cash components of the profit”, were not confirmed.https://gadm.du.ac.ir/article_345_63259c3d394c5be1e1ae4a39afe1eac6.pdf