MATHEMATICAL SCIENCES
Year:2011 | Volume:5 | Issue:1|Papers Count:8

In this paper, we have used Chebyshev polynomials to solve linear and nonlinear Volterra-Fredholm integral equations, numerically. First we introduce these polynomials, then we use them to change the Volterra-Fredholm integral equation to a linear or nonlinear system. Finally, the numerical examples illustrate the effi ciency of this method.

Let R=Ån³0 Rn be a graded Noetherian ring with local base ring R0 and let R+=Ån³1 Rn. Let M and N be finitely generated graded R-modules. In this paper, we prove some results on the asymptotic behaviour of the n-th graded components HiR+ (M; N)n of HiR+ (M; N) for n®-¥. We also study the tameness and asymptotical stability of the homogeneous components of HiR+ (M; N) for some i; s with a specified property.

In the current paper, we deal with generalized notion of amenability which is called approximate cyclic amenability. We introduce this concept and we show by means of an example, its distinction with its classic analogs. Moreover we show the relationship between approximate trace extension property and approximate cyclic amenability. This answers partially, question 9.1 of [3] for approximate cyclic amenability.

In this paper, analytic solutions of the modified Burgers-Korteweg-de Vries equation (mBKdVE) and the Newell -Whitehead equation are obtained by the Ho-motopy analysis method (HAM) and the Homotopy Pade method (HPadeM). The obtained approximation by using HAM contains an auxiliary parameter which is a way to control and adjust the convergence region and rate of the solution series.The approximation solution by [m; m] HPadeM is often independent of auxiliary parameter`h and this technique accelerate the convergence of the related series.

In this paper, the modification of He's variational iteration method (MVIM) is developed to solve fractional ordinary differential equations and fractional partial differential equations. It is used the free choice of initial approximation to propose the reliable modification of He's variational iteration method. Some of the fractional differential equations are examined to illustrate the effectiveness and convenience of the method.The results show that the proposed method has accelerated convergence.

In this paper we study the structure of Clifford Algebras Clp,q associated with a non degenerate symmetric bilinear form of signature (p, q), where p, q are positive integer. Also we present a description of these algebras as matrix algebras, and then we will discuss the periodicity of these algebras completely. As a consequence, We create the related algebra matrix tables for these algebras, when 0£p£8 and 8£q£13. We also present an isomorphism between Cl0q,p and Cl0p,q.

In this paper, the variational iteration and the homotopy perturbation methods are adopted to obtain the solution of the one-dimensional wave equation. The solutions procedure reveal that the applied methods are very efficient. In addition, the result obtained is the same as the D' Alembert's formula for the wave equation.

For every integer n³1 and every odd prime p, an efficient presentation is given for the wreath product Zp Zpn which, is of nilpotency class (p-1) n+1. Moreover, the Fibonacci length is proved to be 8x3n when p=3, and in general, k (p)xpn, where k (p) is the period of Fibonacci length modulo p (the Wall number of p).