Journal of Mathematical Extension
Volume:5 Issue: 2, Summer 2011

In this paper, we introduce three new types of generalized convex functions, called semi E-pseudoinvex, strictly semi Epseudoinvex and semi E-quasiinvex functions. Then some of their basic properties are studied, We used directional derivative and obtain the new results in this class of functions. As applications of our results, we obtain optimal solutions for multiobjective programming.

We study Bass modules, Bass rings, and related concepts from a model theoretic point of view. We observe that the class of Bass modules (over a fixed ring) is not stable under elementary equivalence. We observe that under which conditions the class of Bass rings are stable under elementary equivalence.

In this paper we prove the convergence of homotopy analysis method (HAM) and present the application of the homotopy analysis method to obtain the exact analytical solution of the Fokker-Planck equation. In the current paper this scheme will be investigated in details and efficiency of the approach will be shown by applying the procedure on several interesting and important examples.

We develop a new empirical Bayes analysis in multiple regression models. In the present work we consider multivariate skewnormal as prior for coefficients of the model in a skew-normal population and give empirical Bayes estimation for parameters of the model. The marginal distribution of response is found to be a closed skew-normal distribution. The empirical Bayes estimator is found in a closed form and the model is applied on a data set.

In this paper, we introduce the following positive-additive functional equation in C-algebras f  x + 4 4 p x3y + 6 p xy + 4 4 p xy3 + y  = f(x) + 4f(x) 34 4 p f(y) + 6 p f(x)f(y) + 4f(y) 3 4 4 p f(x) + f(y). Using the fixed point method, we prove the stability of the positiveadditive functional equation in C-algebras. Moreover, we prove the Hyers-Ulam stability of the above functional equation in C-algebras by the direct method of Hyers-Ulam.

In this paper we prove that if a pair of operators is - hypercyclic for all  > 0, then it is topologically transitive.

Data Envelopment Analysis (DEA) is a technique for measuring the efficiency of a set of Decision Making Units (DMUs) with common data, but in general it is not practical. This paper presents a framework where DEA is used to measure overall profit efficiency with fuzzy data. Specifically, it is shown that as the inputs, outputs and price vectors are fuzzy numbers, the DMUs cannot be easily evaluated. Thus, presenting a new method for computing the efficiency of DMUs with fuzzy data will be benefic. Also, it presents where DEA is used to measure overall profit of efficiency with interval and fuzzy inputs and outputs and an interval will be defined for the efficiency. The proposed method give the best and the worst overall profit efficiency for DMUs. The method is illustrated by solving numerical examples.

In this work, the generalized (G0 G )–expansion method is applied to solve the coupled Boiti-Leon-Pempinelli system (BLP system). Generalized (G0 G )-expansion method was used to construct solitary wave solutions of the nonlinear evolution equations. This method is developed for searching the exact travelling wave solutions of nonlinear partial differential equations. It is shown that the (G0 G )-expansion method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.

In this paper, homotopy analysis method is directly extended to investigate nth order semi-differential equations and to derive their numerical solutions which is introduced by replacing some integer-order space derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for differential equations of integer-order is directly extended to derive explicit and numerical solutions of the fractional differential equations. An optimal value of the convergence control parameter is given through the square residual error. Comparison is made between Homotopy perturbation method, collocation spline method, and the present method.

In this paper, we are giving analytic approximate solutions to nonlinear PDEs using the Homotopy Analysis Method (HAM) and Homotopy Pad´e Method(HPad´eM). The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence regions of solution series. It is illustrated that HPad´eM accelerates the convergence of the related series. The results reveal these methods are remarkably effective.