Theory of Approximation and Applications
Volume:7 Issue: 1, Winter and Spring 2011

Let R be a commutative noetherian ring. We study the behavior of injective and at dimension of R-modules under the functors HomR(-,-) and -×R-.

We shall generalize the concept of z = (1-􀀀t)+ty to n times which contains to verify some their properties and inequalities in CAT(0) spaces. In the sequel with introducing of -nonexpansive mappings, we obtain some xed points and approximate fi xed points theorems.

This paper presented methods to determine the aerodynamic forces that act on an aircraft wing during flight. These methods are initially proposed for a simplified two degree-of-freedoms airfoil model and then are extensively applied for a multi-degree-of-freedom airfoil system. Different airspeed conditions are considered in establishing such methods. The accuracy of the presented methods is verified by comparing the estimated aerodynamic forces with the actual values. A good agreement is achieved through the comparisons and it is verified that the present methods can be used to correctly identify the aerodynamic forces acting on the aircraft wing models.

In this paper we introduce a generalization of Meir-Keeler contraction for random mapping T: Ω×C → C, where C be a nonempty subset of a Banach space X and (Ω,Σ) be a measurable space with  being a sigma-algebra of sub- sets of. Also, we apply such type of random fixed point results to prove the existence and unicity of a solution for an special random integral equation.

In this paper, an application of homotopy perturbation method is applied to nding the solutions of the seven-order Sawada-Kotera (sSK) and a Lax's seven-order KdV (LsKdV) equations. Then obtain the exact solitary-wave so- lutions and numerical solutions of the sSK and LsKdV equations for the initial conditions. The numerical solutions are compared with the known analytical solutions. Their remarkable accuracy are nally demonstrated for the both seven-order equations.

In a recent paper in this journal, Yang et al. [Feng Yang, Dexiang Wu, Liang Liang, Gongbing Bi & Desheng Dash Wu (2009), supply chain DEA:production possibility set and performance evaluation model] defined two types of supply chain production possibility set which were proved to be equivalent to each other. They also proposed a new model for evaluating supply chains. There are, however, some shortcomings in their paper. In the current paper, we correct the model, the theorems, and their proofs.

Suppose K is a nonempty closed convex subset of a complete CAT(0) space X with the nearest point projection P from X onto K. Let T: K → X be a nonself mapping, satisfying condition (C) with F(T): ={x ε K: Tx = x}≠Φ. Suppose fxng is generated iteratively by x1ε K, xn+1 = P((1- αn)xn+αnTP[(1- αn)xn+β nTxn]),n≥1, where {αn}and {βn} are real sequences in[ε,1-ε] for some  ε in (0,1). Then {xn} is Δ-
􀀀convergence to some point x* in F(T). This work extends a result of Laowang and Panyanak [5] to the case of generalized nonexpansive nonself mappings.

In this paper, we use a combination of Legendre and Block-Pulse functions on the interval [0; 1] to solve the nonlinear integral equation of the second kind. The nonlinear part of the integral equation is approximated by Hybrid Legen- dre Block-Pulse functions, and the nonlinear integral equation is reduced to a system of nonlinear equations. We give some numerical examples. To show applicability of the proposed method.

Let R = L n2N0 Rn be a Noetherian homogeneous graded ring with local base ring (R0;m0) of dimension d. Let R+ = Ln2N Rn denote the irrelevant ideal of R and let M and N be two nitely generated graded R-modules. Let t = tR+(M;N) be the rst integer i such that Hi R+(M;N) is not minimax. We prove that if i  t, then the set AssR0 (Hi R+(M;N)n) is asymptotically stable for n! 1 and Hj m0 (Hi R+(M;N)) is Artinian for 0  j  1. More- over, let s = sR+(M;N) be the largest integer i such that HR+(M;N) is not minimax. For each i  s, we prove that R0 m0 R0Hi R+(M;N) is Artinian and that Hj m0 (Hi R+(M;N)) is Artinian for d 1  j  d. Finally we show that Hd 2 m0 (Hs R+(M;N)) is Artinian if and only if Hd m0 (Hs1 R+ (M;N)) is Artinian.