Theory of Approximation and ApplicationsTheory of Approximation and Applications
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Feed provided by Theory of Approximation and Applications. Click to visit.Domination Number of Nagata Extension Ring
http://msj.iau-arak.ac.ir/article_546274_116543.html
Aََََbstract: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)).Thu, 28 Feb 2019 20:30:00 +0100Construction of α-cut fuzzy X ̅ control charts based on standard deviation and range using ...
http://msj.iau-arak.ac.ir/article_664501_0.html
Control charts are one of the most important tools in statistical process control that lead to improve quality processes and ensure required quality levels. In traditional control charts, all data should be exactly known, whereas there are many quality characteristics that cannot be expressed in numerical scale, such as characteristics for appearance, softness, and color. Fuzzy sets theory is a powerful mathematical approach to analyze uncertainty, ambiguous and incomplete that can linguistically define data in these situations. Fuzzy control charts have been extended by converting the fuzzy sets associated with linguistic or uncertain values into scalars regarded as representative values. In this paper, we study two different approaches to construct X ̅ control chart, when the observations are fuzzy number. Two methods of defuzzification for calculating the value representing sample means and for determining the control chart limits are presented. In the second approach α-cut control chart for variable are developed using upper control limits and lower control limits. The article also presents a fuzzy decision for in control or out of control of the process, in which membership degrees of in and out of control states of process mean is computed.Wed, 24 Apr 2019 19:30:00 +0100Fuzzy Farthest Points and Fuzzy Best Approximation Points in Fuzzy Normed Spaces
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In 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.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.Thu, 28 Feb 2019 20:30:00 +0100Numerical Solution of the Burgers' Equation Based on Sinc Method
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Burgers' equation arises in various areas of applied mathematics,‎‎such as modeling of dynamics‎, ‎heat conduction‎, ‎and acoustic‎‎waves‎ Also‎, ‎this equation has a large variety of applications in‎‎the modeling of water in unsaturated soil‎, ‎dynamics of soil‎‎water‎, ‎models of traffic‎, ‎turbulence and fluid flow‎, ‎mixing and‎‎turbulent diffusion. Many researchers tried to find analytic and numerical solutions of‎‎ this equation by different methods.Sinc method is a powerful numerical tool for finding fast and‎‎accurate solution in various areas of problems.‎In this paper‎, ‎numerical solution of Burgers' equation‎‎is considered by applying Sinc method‎. ‎For this purpose‎, ‎we apply‎‎Sinc method in cooperative with a classic finite difference‎‎formula to‎ ‎Burgers'equation‎. ‎‎The purpose of this paper is to extend the application of the‎‎sinc method for solving Burgers'equation by considering stability‎‎analysis of the method.‎ Numerical examples are provided to verify the validity of proposed methodThu, 28 Feb 2019 20:30:00 +0100Measurement of Inefficiency Slacks in Network Data Envelopment Analysis
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The 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.‎Thu, 28 Feb 2019 20:30:00 +0100Constacyclic Codes over Group Ring (Zq[v])/G
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Recently, codes over some special ﬁnite rings especially chain rings have been studied. More recently, codes over ﬁnite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over ﬁelds. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum information. The construction of quantum codes via classical codes over 2 F was ﬁrst introduced by Calderbank and Shor [4] and Steane [13] in 1996. This method, known as CSS construction, has received a lot of attention and it has allowed to ﬁnd many good quantum stabilizer codes. Later, construction of quantum codes over larger alphabets from classical linear codes over q F has shown by Ketkar et al. in [10]. One direction of the main research in quantum error correction codes is constructing quantum codes that have large minimum distances [9] for a given size and length. In [14], based on classical quaternary constacyclic linear codes, some parameters for quantum codes are obtained. In [8, 9], respectively based on classical negacyclic and constacyclic linear codes some parameters for quantum MDS codes are presented. In this work, we determine self-dual and self-orthogonal codes arising from constacyclic codes over the group ring(Zq[v]/GThu, 28 Feb 2019 20:30:00 +0100Spectral method for Solving Fuzzy Volterra Integral Equations of Second kind
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This paper, about the solution of fuzzy Volterra integral equation of fuzzy Volterra integral equation of second kind (F-VIE2) using spectral method is discussed. The parametric form of fuzzy driving term is applied for F-VIE2. Then three cases for (F-VIE2) are searched to solve them. This classifications are considered based on the sign of interval. The Gauss-Legendre points and Legendre weights for arithmetics in spectral method are used to solve (F-VIE2). Finally two examples are got to illustrate more.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 bThu, 28 Feb 2019 20:30:00 +0100On Best Proximity Points in metric and Banach spaces
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Notice that best proximity point results have been studied to find necessaryconditions such that the minimization problemminx∈A∪Bd(x,Tx)has at least one solution, where T is a cyclic mapping defined on A∪B.A point p ∈ A∪B is a best proximity point for T if and only if thatis a solution of the minimization problem (2.1). Let (A,B) be a nonemptypair in a normed linear space X and S,T : A∪B → A∪B be two cyclicmappings. Let (A,B) be a nonempty pair in a normed linear space X andS,T : A∪B → A∪B be two cyclic mappings. A point p ∈ A∪B is called acommon best proximity point for the cyclic pair (T,S) provided that∥p − Tp∥ = d(A,B) = ∥p − Sp∥In this paper, we survey the existence, uniqueness and convergence of a com-mon best proximity point for a cyclic weak ST − ϕ-contraction map, whichis equivalent to study of a solution for a nonlinear programming problem inthe setting of uniformly convex Banach spaces. We will provide examples toillustrate our results.Wed, 07 Aug 2019 19:30:00 +0100The Iterative Method for Solving Non-Linear Equations
http://msj.iau-arak.ac.ir/article_664208_116543.html
In 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.Thu, 28 Feb 2019 20:30:00 +0100Sequential Optimality Conditions and Variational Inequalities
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In recent years, sequential optimality conditions are frequently used for convergence of iterative methods to solve nonlinear constrained optimization problems. The sequential optimality conditions do not require any of the constraint qualications. In this paper, We present the necessary sequential complementary approximate Karush Kuhn Tucker (CAKKT) condition for a point to be a solution of a nonlinear optimization problem. The nonlinear optimization problem is associated with the variational inequality problem. We also extend the complementary approximate Karush Kuhn Tucker condition from scalar optimization problem to multiobjective optimization problem and associated with the vector variational inequality problem. Further, we prove that with some extra conditions of convexity and affinity, complementary approximate Karush Kuhn Tucker conditions are sufficient for the variational inequality problem and vector variational inequality problem. Finally, we verify our results via illustrative examples. An example shows that a point which is a solution of variational inequality problem is also a CAKKT point.Wed, 07 Aug 2019 19:30:00 +0100A Second-Order Accurate Numerical Approximation for Two-Sided Fractional Boundary Value ...
http://msj.iau-arak.ac.ir/article_664232_116543.html
Fractional order partial differential equations are generalization of classical partialdifferential equations. Increasingly, these models are used in applications such as fluid flow, financeand 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}nwaldformula is unconditionally stable. Some numerical examples are presented and compared with the exact analytical solutionfor its order of convergence.Fractional order partial differential equations are generalization of classical partialdifferential equations. Increasingly, these models are used in applications such as fluid flow, financeand 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}nwaldformula is unconditionally stable. Some numerical examples are presented and compared with the exact analytical solutionfor its order of convergence.Thu, 28 Feb 2019 20:30:00 +0100Application of semi-analytic method to compute the moments for solution of logistic model
http://msj.iau-arak.ac.ir/article_666926_0.html
The population growth, is increase in the number of individuals in population and it depends on some random environment eﬀects. There are several diﬀerent mathematical models for population growth. These models are suitable tool to predict future population growth. One of these models is logistic model. In this paper, by using Feynman-Kac formula, the Adomian decomposition method is applied to compute the moments for the solution of logistic stochastic diﬀerential equation.Wed, 07 Aug 2019 19:30:00 +0100On fuzzy wave equation based on generalized Hukuhara differentiability
http://msj.iau-arak.ac.ir/article_666927_0.html
In this paper, analytical fuzzy solutions for a fuzzy one-dimensional homogeneous and non-homogeneous wave equation are investigated and the new fuzzy solutions for these equations based on the type of generalized Hukuhara differentiability are presented. The existence and the uniqueness of the solutions, and the stability of the Cauchy problems are shown. In this scheme, a fuzzy wave equation can be solved without converting it to two crisp equations. Different types ofexamples are employed to show the effectiveness and efficiency of the approach.Wed, 07 Aug 2019 19:30:00 +0100Some coupled fixed point theorems in $G$-metric spaces
http://msj.iau-arak.ac.ir/article_669884_0.html
In this paper, we establish some coupled fixed point theorems for the weakly increasing mappings $f$ and $g$ with respect to partial ordering relation in the framework of generalized metric spaces and illustrated the usability of result with the help of an example.Thu, 26 Dec 2019 20:30:00 +0100Nonlinear Viscosity Algorithm with Perturbation for Nonexpansive Multi-Valued Mappings
http://msj.iau-arak.ac.ir/article_670251_0.html
In this paper, based on viscosity technique with perturbation, we introduce a new non-linear viscosity algorithm for finding a element of the set of fixed points of nonexpansivemulti-valued mappings in a Hilbert space. We derive a strong convergence theorem for thisnew algorithm under appropriate assumptions. Moreover, in support of our results, somenumerical examples (using Matlab software) are also presented.Wed, 01 Jan 2020 20:30:00 +0100An approximate method for solving fractional system differential equations
http://msj.iau-arak.ac.ir/article_671125_0.html
IIn this research work, we have shown that it is possible to use fuzzy transform method (FTM) for the estimate solution of fractional system differential equations (FSDEs). In numerical methods, in order to estimate a function on a particular interval, only a restricted number of points are employed. However, what makes the F-transform preferable to other methods is that it makes use of all points in this interval. A number of clear and specific examples have been enumerated for the purpose of illustrating the simplicity and efficiency of the suggested method.Tue, 04 Feb 2020 20:30:00 +0100Quasi-orthogonal expansions for functions in BMO
http://msj.iau-arak.ac.ir/article_671468_0.html
For {φ_n(x)}, x ε [0,1] an orthonormalsystem of uniformly bounded functions, ||φ_n||_{∞}≤ MSun, 23 Feb 2020 20:30:00 +0100Fixed point of generalized contractive maps on S^{JS}- metric spaces with two metrics
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In this paper we prove existence of fixed point theorems for Z-contractive map, Geraghty type contractive map and interpolative Hardy-Rogers type contractive mapping in the setting of S^{JS}- metric spaces with two metrics. Examples are constructed to high light the significance of newly obtained results.Tue, 25 Feb 2020 20:30:00 +0100Neutrosophic-Cubic Analaytic Hierarchy Process with Applications
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In this paper we extend fuzzy analytic hierarchy process into neutrosophic cubic environment. The neutrosophic cubic analytic hierarchy process can be used to manage more complex problems when the decision makers has a number of uncertainty, assigning preferences values to the considered object. We also define the concept of triangular neutrosophic cubic numbers and their operations laws. The advantages of the proposed methodology and the application of neutrosophic cubic analytic hierarchy process in decision making are shown by testing the numerical example in practical life.Tue, 25 Feb 2020 20:30:00 +0100SIMULATION FUNCTIONS AND INTERPOLATIVE CONTRACTIONS
http://msj.iau-arak.ac.ir/article_672067_0.html
In this manuscript, we consider the interpolative contractions mappings via simulation func-tions in the setting of complete metric space. We also express an illustrative example to show the validity of our presented results.Wed, 25 Mar 2020 19:30:00 +0100REMOTAL CENTERS AND CHEBYSHEV CENITERS IN NORMED SPACES
http://msj.iau-arak.ac.ir/article_672425_0.html
In this paper, we consider Nearest points" and Farthestpoints" in normed linear spaces. For normed space (X; ∥:∥), the set W subset X,we dene Pg; Fg;Rg where g 2 W. We obtion results about on Pg; Fg;Rg. Wend new results on Chebyshev centers in normed spaces. In nally we deneremotal center in normed spaces.Thu, 16 Apr 2020 19:30:00 +0100A new method for solving two-dimensional fuzzy Fredholm integral equations of the second kind
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In this work, we introduce a novel method for solving two-dimensional fuzzy Fredholm integral equationsof the second kind (2D-FFIE-2). We use new representation of parametric form of fuzzy numbers and converta two-dimensional fuzzy Fredholm integral equation to system of two-dimensional Fredholm integral equationsof the second kind in crisp case. We can use Adomian decomposition method for nding the approximationsolution of the each equation, hence obtain an approximation for fuzzy solution of 2D-FFIE-2. We prove theconvergence of the method and nally apply the method to some examplesMon, 04 May 2020 19:30:00 +0100Using finite difference method for solving linear two-point fuzzy boundary value problems based ...
http://msj.iau-arak.ac.ir/article_673612_0.html
In this paper an efficient Algorithm based on Zadeh's extension principle has been investigated to approximate fuzzy solution of two-point fuzzy boundary value problems, with fuzzy boundary values. We use finite difference method in term of the upper bound and lower bound of $r$- level of fuzzy boundary values. The proposed approach gives a linear system with crisp tridiagonal coefficients matrix. This linear system determines $r$-level of fuzzy solution at mesh points. By combining of this solutions, we obtain fuzzy solution of main problem at mesh points, approximately. Its applicabilityis illustrated by someexamplesTue, 16 Jun 2020 19:30:00 +0100An extension of stochastic differential models by using the Grunwald-Letnikov fractional derivative
http://msj.iau-arak.ac.ir/article_673613_0.html
Stochastic differential equations (SDEs) have been applied by engineers and economists because it can express the behavior of stochastic processes in compact expressions. In this paper, by using Grunwald-Letnikov fractional derivative, the stochastic differential model is improved. Two numerical examples are presented to show efficiency of the proposed model. A numerical optimization approach based on least square approximation is applied to determine the order of the fractional derivative. Numerical examples show that the proposed model works better than the SDE to model stochastic processes with memory.Tue, 16 Jun 2020 19:30:00 +0100A new reproducing kernel method for solving Volterra integro-dierential equations
http://msj.iau-arak.ac.ir/article_674821_0.html
This paper is concerned with a technique for solving Volterra integro-dierential equationsin the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernelmethod, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series. An iterative method is given toobtain the approximate solution. The convergence analysis is established theoretically. Theapplicability of the iterative method is demonstrated by testing some various examples.Fri, 14 Aug 2020 19:30:00 +0100