Journal of Mathematical Extension
Volume:6 Issue: 4, Autumn 2012

Two new topologies are defined on C(X). These topologies makeC(X) to be a zero-dimensional (completely regular) Hausdorff space.C(X) endowed by these topologies is denoted by Co(X) andCo−1 (X). The relations between X, Co(X) and Co−1 (X) are studied and closedness of z-ideals and maximal ideals are investigated in Co(X)and Co−1 (X).

Let (R,m) be a Noetherian local ring. Two notions of filter regular sequence and generalized local cohomology module with respectto a pair of ideals are introduced, and their properties are studied. Somevanishing and non-vanishing theorems are given for this generalized versionof generalized local cohomology module.

In this paper we suggest a procedure for testing reversibilityof time series. Our approach is based on a necessary and sufficientcondition for time reversibility of linear models. An attractive featureof the procedure is that in converse with other approaches it doesn’trequire important assumptions, especially existence of moments of orderhigher than two. Our simulation confirms the procedure and some empirical examples are given.

In this paper, modification of Steffensen’s method with eight-order convergence is presented. We propose a family of optimalthree-step methods with eight-order convergence for solving the simpleroots of nonlinear equations by using the weight function and interpolationmethods. Per iteration this method requires four evaluations of thefunction which implies that the efficiency index of the developed methodsis 1.682. Some numerical examples illustrate that the algorithm ismore efficient and performs better than other methods.

In this paper, we introduce the notion of generalized pseudolinearityfor nondifferentiable and nonconvex but locally Lipschitzfunctions defined on a Banach space. We present some characterizationsof generalized pseudolinear functions. The characterizations ofthe solution set of a convex and nondifferentiable but generalized pseudolinearprogram are obtained. The results of this paper extend variousresults for pseudolinear functions, pseudoinvex functions and pseudolinearfunctions, and also for pseudoinvex programs, pseudolinear programsand pseudolinear programs.

Let R be a ring with derivation d, such that (d(xy))n =(d(x))n(d(y))n for all x, y 2 R and n > 1 a fixed integer. In this paper,we show that ifR is prime, then d = 0 or R is commutative. If R is semiprime, thend maps R into its center. Moreover in semiprime case letA = O(R) be the orthogonal completion of R and B = B(C ) be the Boolian ring ofC, where C is the extended centroid of R . Then there exists an idempotente 2 B such that eA is a commutative ring and dinduces a zero derivation on (1− e)A .

In this article we investigate the two-term Abel’s integralequations. We will do this in two different ways and show that such equation is reducible to an integro −differential equation of Volterra type.