Islamic Azad University of ArakTheory of Approximation and Applications2538-221713120190301Domination Number of Nagata Extension Ring19546274ENAbbas ShariatiniaDepartment of Science , Bushehr Branch, Islamic Azad University, Bushehr, IranJournal Article20180227Aََََbstract:Let R is a commutative ring whit Z(R) as the set of zero divisors. The total graph of R, denoted by T ((R)) is the (undirected) graph with all elements of R as vertices, and two distinct vertices are adjacent if their sum is a zero divisor. For a graph G = (V; E), a set S is a dominating set if every vertex in V n S is adjacent to a vertex in S. The domination number is equal |S|where |S| is minimum. For R-module M, an Nagata extension (idealization), denoted by R(+)M is a ring with identity and for two elements (r; m); (s; n) of R(+)M we have (r; m) + (s; n) = (r + s; m + n) and (r; m)(s; n) = (rs; rn + sm). In this paper, we seek to determine the bound for the domination number of total graph T ((R(+)M)).http://msj.iau-arak.ac.ir/article_546274_67e596a92017af7667c727880fa1f3a0.pdfIslamic Azad University of ArakTheory of Approximation and Applications2538-221713120190301Fuzzy Farthest Points and Fuzzy Best Approximation Points in Fuzzy Normed Spaces1125546275ENHamid Mazaheri TehraniFaculty of Mathematics, Yazd University, Yazd, IranS. M Mouavi Shams AbadFaculty of Mathematics, Vali-e-asr University of Rafsenjan, Rafsenjan,
IranM. A DehghanFaculty of Mathematics, Vali-e-asr University of Rafsenjan, Rafsenjan,
IranZ. BizhanzadehFaculty of Mathematics, Yazd University, Yazd, IranJournal Article20180614In this paper we define fuzzy farthest points, fuzzy best approximation points and farthest orthogonality in fuzzy normed spaces and we will find some results. We prove some existence theorems, also we consider fuzzy Hilbert and show every nonempty closed and convex subset of a fuzzy Hilbert space has an unique fuzzy best approximation.<br />It is well know that the conception of fuzzy sets, firstly defined by Zadeh in 1965. Fuzzy set theory provides us with a framework which is wider than that of classical set theory. Various mathematical structures, whose features emphasize the effects of ordered structure, can be developed on the theory. The theory of fuzzy sets has become an area of active research for the last forty years. On the other hand, the notion of fuzzyness has a wide application in many areas of science and engineering, chaos control, nonlinear dynamical systems, etc. In physics, for example, the fuzzy structure of space time is followed by the fat that in strong quantum gravity regime space time points are determined in a fuzzy manner.http://msj.iau-arak.ac.ir/article_546275_8dc9048b57e11dffd6783cca8e2788d3.pdfIslamic Azad University of ArakTheory of Approximation and Applications2538-221713120190301Numerical Solution of the Burgers' Equation Based on Sinc Method2742663606ENGhasem Kazemi GelianDepartment of Mathematics, Shirvan Branch, Islamic Azad University, Shirvan, IranMohammad Ali Fariborzi AraghiDepartment of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.Journal Article20181205Burgers' equation arises in various areas of applied mathematics,<br />such as modeling of dynamics, heat conduction, and acoustic<br />waves Also, this equation has a large variety of applications in<br />the modeling of water in unsaturated soil, dynamics of soil<br />water, models of traffic, turbulence and fluid flow, mixing and<br />turbulent diffusion. <br /><br /><br />Many researchers tried to find analytic and numerical solutions of<br /> this equation by different methods.<br /><br />Sinc method is a powerful numerical tool for finding fast and<br />accurate solution in various areas of problems.<br /><br />In this paper, numerical solution of Burgers' equation<br />is considered by applying Sinc method. For this purpose, we apply<br />Sinc method in cooperative with a classic finite difference<br />formula to Burgers'equation. The purpose of this paper is to extend the application of the<br />sinc method for solving Burgers'equation by considering stability<br />analysis of the method. <br /><br />Numerical examples are provided to verify the validity of proposed methodhttp://msj.iau-arak.ac.ir/article_663606_c22ae49e2b5facb18b4d49e8aaf1c734.pdfIslamic Azad University of ArakTheory of Approximation and Applications2538-221713120190301Measurement of Inefficiency Slacks in Network Data Envelopment Analysis4366663609ENHossein AziziDepartment of Applied Mathematics, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran0000-0002-7359-8790Alireza AmirteimooriDepartment of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, IranSohrab KordrostamiDepartment of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, IranJournal Article20181204The two-stage data envelopment analysis models show the performance of individual processes and thus, provide more information for decision-making compared with conventional one-stage models. This article presents a set of additive models (optimistic and pessimistic) to measure inefficiency slacks in which observations are shown with crisp numbers. In the concept of pessimistic efficiency, DMU with balanced input and output data can be scored as efficient. Since pessimistic efficiency represents the minimum efficiency that is guaranteed in any unfavorable conditions, the assessment based on this efficiency is in compliance with our natural meaning, especially in risk-averse situations. Therefore, pessimistic efficiency solely can play a useful role in the DMU ranking. However, it is not a good idea to ignore optimistic efficiency. Hence, it is an inevitable necessity to integrate different performance sizes in order to achieve an overall performance assessment for each DMU. An example of resin manufacturer companies in Iran is presented to explain how to calculate the system and process inefficiency slacks.http://msj.iau-arak.ac.ir/article_663609_8c37d86aa7729eb56dbff77427dbfd8b.pdfIslamic Azad University of ArakTheory of Approximation and Applications2538-221713120190301Spectral method for Solving Fuzzy Volterra Integral Equations of Second kind6781663608ENLaleh HooshangianDepartment of Mathematics, Dezful Branch, Islamic Azad University, Dezful, IranJournal Article20181129This paper, about the solution of fuzzy Volterra integral equation of fuzzy Volterra integral equation<br /> <br />of second kind (F-VIE2) using spectral method is discussed. The parametric form of fuzzy driving term<br /> <br />is applied for F-VIE2. Then three cases for (F-VIE2) are searched to solve them. This classifications are<br /> <br />considered based on the sign of interval. The Gauss-Legendre points and Legendre weights for arithmetics<br /> <br />in spectral method are used to solve (F-VIE2). Finally two examples are got to illustrate more.<br /><br />b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bhttp://msj.iau-arak.ac.ir/article_663608_ffde5bc6acff2191b57be90f5a6e9749.pdfIslamic Azad University of ArakTheory of Approximation and Applications2538-221713120190301The Iterative Method for Solving Non-Linear Equations8393664208ENParvaneh MansouriDepartment of Computer Science, Arak Brancg, Islamic Azad Univeristy, Arak, Iran branch0000-0002-6027-2193Journal Article20190408In this paper, we have combined the ideas of the False Position (FP) and Artificial Bee Colony (ABC) algorithms to find a fast and novel method for solving nonlinear equations. Additionally, to illustrate the efficiency of the proposed method, several benchmark functions are solved and compared with other methods such as ABC, PSO and GA.http://msj.iau-arak.ac.ir/article_664208_3b0254e2b5ac72aa20e38cf49f2b542f.pdfIslamic Azad University of ArakTheory of Approximation and Applications2538-221713120190301A Second-Order Accurate Numerical Approximation for Two-Sided Fractional Boundary Value Advection-Diffusion Problem119135664232ENElyas ShivanianDepartment of Mathematics, Imam Khomeini International
University, Qazvin, 34149-16818, IranHamid Reza KhodabandehloDepartment of Mathematics, Imam Khomeini International
University, Qazvin, 34149-16818, Iran0000-0002-9890-2218Journal Article20160124Fractional order partial differential equations are generalization of classical partial<br />differential equations. Increasingly, these models are used in applications such as fluid flow, finance<br />and others. In this paper we examine some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain. An approach based on the classical Crank-Nicolson method combined with spatial extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Stability, consistency, and convergence of the method are examined. It is shown that the fractional Crank-Nicolson method based on the shifted Gr"{u}nwald<br />formula is unconditionally stable. Some numerical examples are presented and compared with the exact analytical solution<br />for its order of convergence.<br /><br /><br />Fractional order partial differential equations are generalization of classical partial<br />differential equations. Increasingly, these models are used in applications such as fluid flow, finance<br />and others. In this paper we examine some practical numerical methods to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain. An approach based on the classical Crank-Nicolson method combined with spatial extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Stability, consistency, and convergence of the method are examined. It is shown that the fractional Crank-Nicolson method based on the shifted Gr"{u}nwald<br />formula is unconditionally stable. Some numerical examples are presented and compared with the exact analytical solution<br />for its order of convergence.