American Journal of Applied Mathematics and Statistics

In this paper, we solve a class of boundary value problems of the composite first Weber system. In the process of solving the problem, first of all, we introduce functions of guide solution. Secondly, we constructive similar kernel functions. Finally, solutions with a form of continued fraction product to boundary value problem of the composite first Weber system are obtained by assembling coefficients of the non-homogeneous left boundary condition, functions of guide solution, coefficients of two connection conditions and similar kernel functions. Then a new method is obtained for solving the composite boundary value problem-Similar Constructing Method (shortened as SCM). This method is not only simple and effective for solving the complicated boundary value problem of differential system, but also is a kind of innovative idea.

American Journal of Applied Mathematics and Statistics. 2013, 1(4), 76-82. DOI: 10.12691/ajams-1-4-5
Pub. Date: October 02, 2013

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On the Homotopy Analysis Method for an Seir Tuberculosis Model

by M.O. Ibrahim and S.A. Egbetade

Original Research

In this paper, we provide a very accurate, non-perturbative, semi-analytical solution to a system of nonlinear first-order differential equations modeling the transmission of tuberculosis (TB) in a homogeneous population. Our analysis is based on Homotopy Analysis Method (HAM). Maple 15 software is used to carry out the computations. Our results show the validity and potential of HAM for computing the solution of nonlinear equations.

American Journal of Applied Mathematics and Statistics. 2013, 1(4), 71-75. DOI: 10.12691/ajams-1-4-4
Pub. Date: September 28, 2013

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The Improved (G^’/G)-Expansion Method to the (3+1)-Dimensional Kadomstev-Petviashvili Equation

by Hasibun Naher and Farah Aini Abdullah

Review Article

In this article, the improved (G^’/G)-expansion method has been implemented to generate travelling wave solutions, where G(ξ) satisfies the second order linear ordinary differential equation. To show the advantages of the method, the (3+1)-dimensional Kadomstev-Petviashvili (KP) equation has been investigated. Higher-dimensional nonlinear partial differential equations have many potential applications in mathematical physics and engineering sciences. Some of our solutions are in good agreement with already published results for a special case and others are new. The solutions in this work may express a variety of new features of waves. Furthermore, these solutions can be valuable in the theoretical and numerical studies of the considered equation. Also, in order to understand the behaviour of solutions, the graphical representations of some obtained solutions have been presented.

American Journal of Applied Mathematics and Statistics. 2013, 1(4), 64-70. DOI: 10.12691/ajams-1-4-3
Pub. Date: September 24, 2013

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Stochastic DEA with a Perfect Object and Its Application to Analysis of Environmental Efficiency

by Alexander Y. Vaninsky

Original Research

The paper introduces stochastic DEA with a Perfect Object (SDEA PO). The Perfect Object (PO) is a virtual Decision Making Unit (DMU) that has the smallest inputs and greatest outputs. Including the PO in a collection of actual objects yields an explicit formula of the efficiency index. Given the distributions of DEA inputs and outputs, this formula allows us to derive the probability distribution of the efficiency score, to find its mathematical expectation, and to deliver common (group–related) and partial (object-related) efficiency components. We apply this approach to a prospective analysis of environmental efficiency of the major national and regional economies.

American Journal of Applied Mathematics and Statistics. 2013, 1(4), 57-63. DOI: 10.12691/ajams-1-4-2
Pub. Date: July 11, 2013

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On A Class of New Type Generalized Difference Sequences Related to the P-Normed l^p Space Defined By Orlicz Functions

by AYHAN ESİ

Original Research

The idea of difference sequence spaces were defined by Kizmaz [6] and generalized by Et and Colak [5]. Later Esi et al. [4] introduced the notion of the new difference operator

for fixed n,m∈N. In this article we introduce new type generalized difference sequence space

using by the Orlicz function. We give various properties and inclusion relations on this new type difference sequence space.

American Journal of Applied Mathematics and Statistics. 2013, 1(4), 52-56. DOI: 10.12691/ajams-1-4-1
Pub. Date: June 27, 2013

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