Journal of Mathematical Extension
Volume:7 Issue: 3, Summer 2013

Let C(X) be the ring of real continuous functions on aTychonoff space X and T(X) be the set of all torsion elements of C(X).We prove that if X and Y are two zero dimensional compact spaces,then X ' Y if and only if the rings generated by T(X) and T(Y ) areisomorphic.

The concept of essential submodules is a well known concept.In this paper we try to replace an arbitrary submodule of M,say T, instead of 0 in the definition of essential submodules. By this,essential submodules are precisely {0}-essential submodules. For a submoduleK of right R-module M, we have K ess M if and only if(K : m) is annr(m)-essential right ideal of R, for each m 2 M \ {0}.Among other things, this generalization of essential submodules gives anecessary and sufficient condition for MT being finitely co-generated.

A numerical technique based on hybrid of radial basisfunctions including Guassians (GAs) and Multiquadrics (MQs) is proposedto obtain the solution of nonlinear Fredholm integral equations.Zeros of the shifted Legendre polynomials are used as the collocationpoints. The integral involved in the formulation of the problems are approximatedbased on Legendre-Gauss-Lobatto integration rule. Somenumerical examples illustrate the accuracy and validity of the proposedmethod.

In this paper we will give sufficient conditions for the powers of the multipliction operator Mz to be reflexive on formal Laurent sequence spaces.

In this paper, solving fuzzy ordinary differential equationsof the n th order by Runge-Kutta method have been done, and the convergenceof the proposed method is proved. This method is illustratedby some numerical examples.

According to fuzzy arithmetic, general dual fuzzy linearsystem (GDFLS) cannot be replaced by a fuzzy linear system (FLS). Inthis paper, we use new notation of fuzzy numbers and convert a GDFLSto two linear systems in crisp case, then we discuss complexity of theproposed method. Conditions for the existence of a unique fuzzy solutionto n × n GDFLS are derived.

Since various problems in science and engineering fieldscan be modeled by nonlinear Volterra-Fredholm integral equations, themain focus of this study is to present an effective numerical method forsolving them. This method is based on the hybrid functions of Legendrepolynomials and block-pulse functions. By using this approach, anonlinear Volterra-Fredholm integral equation reduces to a nonlinearsystem of mere algebraic equations. The convergence analysis and associatedtheorems are also considered. Test problems are provided toillustrate its accuracy and computational efficiency.

We consider the dualistic partial metric spaces on a set X,and we give necessary conditions for existence of fixed point and \epsilon−fixed point for some maps.