Theory of Approximation and ApplicationsTheory of Approximation and Applications
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Feed provided by Theory of Approximation and Applications. Click to visit.Numerical Solution of fuzzy differential equations of nth-order by Adams-Moulton method
http://msj.iau-arak.ac.ir/article_542644_115211.html
In recent years, Fuzzy differential equations are very useful indifferent sciences such as physics, chemistry, biology and economy. It should be noted, that if the equations that appear to be uncertain, then take help of fuzzy logic at these equations. Considering that most of the time analytic solution of such equations and finding an exact solution has either high complexity or cannot be solved, we applied numerical methods for the solution. The topics of fuzzy differential equations have been rapidly growing in recent years. So far, many methods have been presented to solve the first-order differential equations. Not many studies have been conducted for numerical solution of high-order fuzzy differential equations. In this research, first, the equation by reducing time, we become the first-order equation. Then we have applied Adam-Moulton multi-step methods for the initial approximation of one order differential equations. Finally, we examine the accuracy of method by presenting examples.Fri, 30 Nov 2018 20:30:00 +0100A Preferred Definition of Conditional Rényi Entropy
http://msj.iau-arak.ac.ir/article_541319_115211.html
The Rényi entropy is a generalization of Shannon entropy to a one-parameter family of entropies. Tsallis entropy too is a generalization of Shannon entropy. The measure for Tsallis entropy is non-logarithmic. After the introduction of Shannon entropy , the conditional Shannon entropy was derived and its properties became known. Also, for Tsallis entropy, the conditional entropy was introduced and its properties were shown. But no specific definition has been given for the conditional Rényi entropy. Several authors have used some definitions of the conditional Rényi entropy, to find their properties and relations among them, but there is no general agreement on any specific definition In this paper, we focus on the definitions of the conditional Rényi entropy, and select one of them on the basis of a relation between Rényi and Tsallis entropies, and show that the chain rule holds generally for the case of conditional Rényi entropy. Then, using this definition, we show some of the properties of conditional Rényi entropy. Finally, we show the relations among Rényi, Shannon and Tsallis entropies.Fri, 30 Nov 2018 20:30:00 +0100λ-Symmetry method and the Prelle-Singer method for third-order differential equations
http://msj.iau-arak.ac.ir/article_539140_115211.html
In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry method for third-order differential equations.In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry method for third-order differential equations.In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry method for third-order differential equations.In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry method for third-order differential equations.In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry method for third-order differential equations.Fri, 30 Nov 2018 20:30:00 +0100Application of Chebyshev Polynomials for Solving Abel's Integral Equations of the First and ...
http://msj.iau-arak.ac.ir/article_538502_115211.html
In this paper, a numerical implementation of an expansion method is developed for solving Abel's integral equations of the first and second kind. The solution of such equations may demonstrate a singular behaviour in the neighbourhood of the initial point of the interval ofintegration. The suggested method is based on the use of Taylor series expansion to overcome the singularity which leads to approximating the unknown function and it's derivatives in terms of Chebyshev polynomials of the first kind. The proposed method, transforms the Abel's integral equations of the first and second kind into a system of linear algebraic equations which can be solved by Gaussian elimination algorithm. Finally, some numerical examples are included to clarify the accuracy and applicability of the presented method which indicate that proposed method is computationally very attractive. In thispaper, all numerical computations were carried out on a PC executing some programs written in maple software.Fri, 30 Nov 2018 20:30:00 +0100Higher derivations associated with the Cauchy-Jensen type mapping
http://msj.iau-arak.ac.ir/article_524879_115211.html
Let H be an innite dimensional Hilbert space and K(H) be the set of all compactoperators on H. We will adopt spectral theorem for compact self-adjoint operators, to investigate ofhigher derivation and higher Jordan derivation on K(H) associated with the following Cauchy-Jensentype functional equation
2f((T + S)/2+ R) = f(T ) + f(S) + 2f(R)
for all T, S, R are in K(H).
Fri, 30 Nov 2018 20:30:00 +0100Viscosity Approximation Methods for W-mappings in Hilbert space
http://msj.iau-arak.ac.ir/article_515033_0.html
We suggest a explicit viscosity iterative algorithm for nding a common el-ement of the set of common fixed points for W-mappings which solves somevariational inequality. Also, we prove a strong convergence theorem with somecontrol conditions. Finally, examples and numerical results are also given.Sun, 20 Sep 2015 19:30:00 +0100Some L^p inequalities concerning the rate of growth of polynomials
http://msj.iau-arak.ac.ir/article_515063_0.html
In this paper we establish some Lp inequalities for polynomials withrestricted zeros. Our results constitute multifarious generalizationswhich besides yielding several interesting results as corollaries alsolead to some striking conclusions giving extensions and renements ofsome known polynomial inequalities.Sun, 20 Sep 2015 19:30:00 +0100A second-order accurate numerical approximation for two-sided fractional boundary value ...
http://msj.iau-arak.ac.ir/article_523169_0.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, 16 Jun 2016 19:30:00 +0100Bifurcation problem for biharmonic asymptotically linear elliptic equation
http://msj.iau-arak.ac.ir/article_523794_0.html
In this paper, weinvestigate the existence of positive solutions for the elliptic equation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navierboundary conditions. Here $lambda>0$ is a parameter, $c(x)$ is positive continuous function defined on $Omega$ and $f$ is a $C^{1}$ function, defined on $[0,+infty)$, positive, nondecreasing, convex andasymptotically linear that is ${lim_{t rightarrow infty}}frac{f(t)}{t}=a0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution but for $lambda> lambda^{ast}$, the problem has no solution even in the week sense.For $lambda = lambda^{ast}$, the problem has a solution said extremal provided that $ lim_{trightarrowinfty}f(t)-at=lMon, 11 Jul 2016 19:30:00 +0100یک قضیه وجود و یکتایی جدید برای جواب های معادلات ...
http://msj.iau-arak.ac.ir/article_526453_0.html
Most of phenomena and events in the real world occur unexpectedly among which are the changes in economic and political systems, collapse of governments, conflicts between tribes, wars, terrorist attacks. Thus, it is not possible to anticipate or estimate, the price of stocks, valuable papers, monetary units and precious metals accurately. Therefore, the only way find out how this factor can affect the growth or drop in the value of companies is focusing on the price of stocks. Investigation on effects of the factors along with uncertainty theory can help better understanding and more exact modeling of these phenomena. Most of phenomena and events in the real world occur unexpectedly among which are the changes in economic and political systems, collapse of governments, conflicts between tribes, wars, terrorist attacks. Thus, it is not possible to anticipate or estimate, the price of stocks, valuable papers, monetary units and precious metals accurately. Therefore, the only way find out how this factor can affect the growth or drop in the value of companies is focusing on the price of stocks. Investigation on effects of the factors along with uncertainty theory can help better understanding and more exact modeling of these phenomena.Sat, 26 Nov 2016 20:30:00 +0100A Chance – Constrained DEA model with random input and output data: Considering maintenance ...
http://msj.iau-arak.ac.ir/article_528446_0.html
Data Envelopment Analysis (DEA) is a nonparametric method based on mathematical programming for evaluating the efficiency firms or Decision Making Unit (DMU) using deterministic inputs and outputs. In real-world situations, the observed values of the input and output data are sometimes inexact, incomplete or vague. These kinds of uncertainty data can be represented as stochastic data. The stochastic data in DEA can be explained by random variables. Several methods have been associated with the random data in DEA. In this paper, we use an input oriented chance-constrained DEA model with random inputs and outputs. A super-efficiency model with chance constraints is used for ranking. However, for convenience in calculations a non-linear deterministic equivalent model is obtained to solve the models. The non-linear model is converted into a model with quadratic constraints to solve the non-linear deterministic model. Finally, data related to twenty-eight maintenance groups of Iranian Aluminum Company (IRALCO) is used to demonstrate the applicability of the used Models in this paper.Tue, 07 Feb 2017 20:30:00 +0100New Generalized Interval Valued Intuitionistic Fuzzy Numbers
http://msj.iau-arak.ac.ir/article_528447_0.html
مفهوم عدد فازی شهودی فاصله مقدار در مدلسازی مسائل واقعی زندگی توام با عدم دقت و عدم اطمینان بسیار مفید است و آنها در بسیاری از زمینه های مختلف علوم استفاده شده است. هدف این مقاله بررسی مفهوم عدد فازی شهودی فاصله مقدار تعمیم یافته بر اساس مجموعه ای فازی شهودی تعمیم یافته مربوط به بالوئی جامخانه(2015) می باشد که تعمیم عدد فازی شهودی فاصله مقدار است. مجموعه ای فازی شهودی تعمیم یافته ترکیب مجموعه های فازی شهودی و مجموعه ای فازی فاصله مقدار بوده که توابع عضویت و عدم عضویت آنها بجای عدد بصورت فاصله هستند. بعد از معرفی اعداد فازی شهودی فاصله مقدار تعمیم یافته عملکرهای حسابی و الفا برش های آن را بررسی سپس مقدار و ابهام درجه عضویت ، مقدار و ابهام عدم عضویت و شاخص مقدار و شاخص ابهام در عدد فازی شهودی فاصله مقدار تعمیم یافته تعریف می شوند. نهایتا روش رتبه بندی اعداد فازی شهودی فاصله مقدار تعمیم یافته بر اساس شاخص مقدار و شاخص ابهام ارائه می شود.Tue, 07 Feb 2017 20:30:00 +0100رویکردی نوین برای حل معادلات انتگرال دیفرانسیل ...
http://msj.iau-arak.ac.ir/article_528448_0.html
در این مقاله ، به بررسی حل معالات انتگرال - دیفرانسیل فردهلم ، با روش هستۀ بازتولید اشاره شده است . در روش جدید ، فرایند متعامد سازی از روش اصلی حذف شده است . در بحث مقاله ، این روش جدید مبتنی بر روش هستۀ بازتولید به صورت مفصل معرفی شده است، هم چنین الگوریتم روش ، به همراه آنالیز آن ، همگرایی آن ، با بیان قضایا ی و لم های مربوطه وهم چنین اثبات آنها ، به طور کامل آمده است . در پایان با ارایه ی چندین مثال گوناگون از معادلات انتگرال - دیفرانسیل فردهلم و حل عددی آنها با دو روش ، نتایج عددی روش اخیر مبتنی بر حذف فرایند متعامد سازی گرام اشمیت با روش هستۀ بازتولید اصلی مقایسه شده است . نتایج عددی نشان دهنده کارایی و برتری این روش تغییر یافته برروش اصلی می باشند.در این روش دقت و سرعت عملیاتی افزایش داشته اند.Tue, 07 Feb 2017 20:30:00 +0100On co-Farthest Points in Normed Linear Spaces
http://msj.iau-arak.ac.ir/article_529128_115211.html
In this paper, we consider the concepts co-farthest points innormed linear spaces. At first, we define farthest points, farthest orthogonalityin normed linear spaces. Then we define co-farthest points, co-remotal sets,co-uniquely sets and co-farthest maps. We shall prove some theorems aboutco-farthest points, co-remotal sets. We obtain a necessary and coecient conditionsabout co-farthest points and dual space. Also, we show that everyco-remotal set is co-uniquely set.Fri, 30 Nov 2018 20:30:00 +0100Analysis of Convergence of Solution of General Fuzzy Integral Equation with Nonlinear Fuzzy Kernels
http://msj.iau-arak.ac.ir/article_529129_0.html
Fuzzy integral equations have a major role in the mathematics and applications.In this paper, general fuzzy integral equations with nonlinear fuzzykernels are introduced. The existence and uniqueness of their solutions are approved and an upper bound for them are determined.Finally an algorithm is drawn to show theorems better.ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا اSun, 26 Mar 2017 19:30:00 +0100Analytic solution of fuzzy second order equation under H-derivation
http://msj.iau-arak.ac.ir/article_529130_0.html
In this paper, the solution of linear second order equations with fuzzy initial values are investigated. The analytic general solutions of them using a ﬁrst solution is founded. The parametric form of fuzzy numbers to solve the second order equations is applied. The solutions are searched in four cases. Finally the example is got to illustrate more.Keywords: Second order equation, Fuzzy initial values, H-derivations, General solution./ / / / / / / / / / / / / / / / / / / / / / / / / / ^ ^ ^ ^ ^ ^ / ^ ^ ^ ^ ^^ ^ ^ ^ ^/ / / / / / / / / / / / / / / // / / / / / / / / // // / / / / / / / / / / / / // / / / / / / /Sun, 26 Mar 2017 19:30:00 +0100کاهش مرتبه و مو-قانون بقاء برای معادله غیر شبه طیفی ...
http://msj.iau-arak.ac.ir/article_531095_0.html
هدف از این مقاله، محاسبه کاهش مرتبه معادله غیر شیه طیفی KdV با ضرایب متغیر با استفاده از روش مو-تقارن است. همچنین بدست آوردن مو-قانون بقاء معادله غیر شیه طیفی KdV با ضرایب متغیر با استفاده از روش مسئله تغیراتی است.The nvcKdV is important as this equation often model realisticsituations in certain case. However, literature on the nvcKdV israther limited compared to the constant coefficient counterparts.Due to the physical applications and mathematical properties ofthe nvcKdV, we have been motivated to obtain -symmetry and-conservation law, etc.Many researchers studied of the KdV type equation and the nvcKdVfor obtaining solutions, stabilization of global solutions, numericalsolution, Lie symmetry analysis using different methods. But, tothe best of our knowledge, the nvcKdV is not investigated via the-symmetry method to order reduction and the variational problemmethod to -conservation law. In this article, we calculate an orderreduction of the nvcKdV using the -symmetry method. Moreoverwe calculate -conservation law of the nvcKdV using the variationalproblem method.2Wed, 31 May 2017 19:30:00 +0100رویکردی جدید از روش هسته باز تولید برای حل معادلات ...
http://msj.iau-arak.ac.ir/article_534599_0.html
آنچه در این مقاله به آن پرداخته شده است ، تکنیک و رویکردی نوین از روش هسته بازتولید در فضای هیلبرت برای حل معالات انتگرال - دیفرانسیل ولترا است که به طور کامل این روش جدید معرفی شده است . در روش هسته بازتولید برای ایجاد پایه های متعامد برای فضای هیلبرت حل مساله از روش متعامد سازی گرام - اشمیت استفاده می شد . اما در این مقاله روشی جدید با حذف فرایند متعامد سازی گرام - اشمیت در روش هسته باز تولید کلاسیک و جایگزینی آن با حل دستگاه خطی این روش ارایه شده است . در بخش هایی مفصل از مفاله پیاده سازی ، تحلیل و آنالیز روش اخیر به همراه همگرایی آن به طور کامل همراه با قضایای مربوط پرداخته شده است . در پایان کارایی و صحت این روش با مثال هایی عددی متعدد ارایه شده است که مقایسه روش اخیر با روش کلاسیک در جداول مربوط کارایی روش را تایید می کنند .Fri, 27 Oct 2017 20:30:00 +0100Study on the new graph constructed by a commutative ring
http://msj.iau-arak.ac.ir/article_537969_0.html
Let R be a commutative ring and G(R) be a graph with vertices as proper andnon-trivial ideals of R. Two distinct vertices I and J are said to be adjacentif and only if I + J = R. In this paper we study a graph constructed froma subgraph G(R)Δ(R) of G(R) which consists of all ideals I of R such thatI ⋬ J(R), where J(R) denotes the Jacobson radical of R. In this paper westudy about the relation between the number of maximal ideal of R and thenumber of partite of graph G(R)n△(R). Also we study on the structure of ringR by some properties of vertices of subgraph G(R)△(R). In another section,it is shown that under some conditions on the G(R), the ring R is Noetherianor Artinian. Finally we characterize clean rings and then study on diameterof this constructed graph.Sun, 28 Jan 2018 20:30:00 +0100Generalization of Dodgson's "Virtual Center" Method; an Efficient Method for ...
http://msj.iau-arak.ac.ir/article_539139_115211.html
Charles Dodgson (1866) introduced a method to calculate matrices determinant, in asimple way. The method was highly attractive, however, if the sub-matrix or the mainmatrix determination is divided by zero, it would not provide the correct answer. Thispaper explains the Dodgson method's structure and provides a solution for the problemof "dividing by zero" called "virtual center".Fri, 30 Nov 2018 20:30:00 +0100The Most Efficient Unit in Data Envelopment Analysis Using Genetic Algorithm
http://msj.iau-arak.ac.ir/article_544735_0.html
Data Envelopment Analysis (DEA) is a useful and practical to evaluate the performance based on multiple inputs and multiple outputs.Data Envelopment Analysis can determine efficient and non-efficient decision-making units (DMUs) through performance calculations. The most efficient unit is the DMU that is ranked among the most efficient units. However, there is no need to rank all units in order to obtain the most efficient decision-making unit.The most efficient unit in data envelopment analysis (ٍَِDEA) using genetic algorithm can be applied to most organizations and companies.In this paper, the efficient unit hyperplane is selected with the help of the genetic algorithm of all the efficient units, which is the total distance between all the units on the other side of this hyperplane is the maximum amount possible with this hyperplane.I hope that this article will be of interest to Dear readers.Keywords: Data Envelopment Analysis (DEA), Genetic Algorithm, Hyperplane, Efficient Unit.Sun, 25 Nov 2018 20:30:00 +0100Spectral Cheme for Solving Fuzzy Volterra Integral Equations of First Kind
http://msj.iau-arak.ac.ir/article_545173_115211.html
This paper discusses about the solution of fuzzy Volterra integral equation of first-kind (F-VIE1) using spectral method. The parametric form of fuzzy driving term is applied for F-VIE1, then three classifications for (F-VIE1) are searched to solve them. These classifications are considered based on the interval sign of the kernel. The Gauss-Legendre points and Legendre weights for arithmetics in spectral method are used to solve (F-VIE1). Finally, two examples are got to illustrate more. However, accuracy and efficiency are shown in tables. Fri, 30 Nov 2018 20:30:00 +0100