MATHEMATICAL SCIENCES
Year:2012 | Volume:6 | Issue:-|Papers Count:8

Purpose: This paper investigates a different method to evaluate different real improper integrals and also to obtain the solutions of various types of Cauchy-type singular integral equations of the first kind.Methods: Methods using the analysis of functions of real variables only are reviewed and utilized for the above purpose. These methods clearly demonstrate that details of complex function theory which are normally employed in handling such integral equations for their solutions can be avoided altogether. Also, some approximate methods of solution of such integral equations are developed.Results: The solutions of real singular integral equations over different intervals such as (-1, 1); (a, b); (0, a) U (b, c); (-1, k) U (k, 1); (-¥, b); (a, +¥); (-¥, +¥); infinite intervals with a gap are obtained by using the proposed methods.Conclusion: The proposed methods are new and each has its own structure.

Purpose: This paper investigates an analytical solution to a physical model called (2+1)-dimensional Zoomeron equation.Methods: The solutions of Zoomeron are obtained using direct methods such as the extended tanh, the exponential function and the sechp-tanhp function methods.Results: Several soliton solutions are obtained using the proposed methods.Conclusions: The obtained solutions are new, and each has its own structure.

Purpose: Although there is a declining trend in the global burden of leprosy, there are 15 countries in Asia and Africa which account for 94% of the global total of the new-case detection rate. Here, we assess the impact of different intervention strategies aimed at leprosy eradication through targeting non-symptomatic and symptomatic individuals.Methods: We develop a mathematical model of leprosy transmission and treatment amongst symptomatic and non-symptomatic, in order to investigate the effects of leprosy relapse cases, case finding of non-symptomatic individuals and compliance to therapy of individuals administered with treatment. Comparison theory has been qualitatively used to analyze the global stability of the disease-free equilibrium. With the aid of centre manifold theory, the local stability of the endemic equilibrium has been investigated. Population-level effects of increased case findings and high treatment rate (guaranteed by compliance and completion of therapy via educational campaigns) are evaluated through numerical simulations and presented in support of the analytical results.Results: Comprehensive and qualitative mathematical analysis of the model reveals that, the disease-free equilibrium is globally, asymptotically stable whenever the reproductive number is less than unity. Further, we have established that the model has a locally, asymptotically stable endemic equilibrium when the reproductive number is greater, but close to unity. Numerical simulation suggests that case finding of non-symptomatic leprosy carriers, greater that 40% is necessary for reducing leprosy prevalence and maybe useful on attaining leprosy eradication.Conclusions: At its best, the study suggests that high level of case finding targeting non-symptomatic and symptomatic individuals, together with high level of compliance by individuals on treatment, may have a substantial effect on controlling leprosy relapses and possible may assist on attaining leprosy eradication.

Purpose: In this paper, we shall present an algorithm for solving more general singular second-order multi-point boundary value problems.Methods: The algorithm is based on the quasilinearization technique and the reproducing kernel method for linear multi-point boundary value problems.Results: Three numerical examples are given to demonstrate the efficiency of the present method.Conclusions: Obtained results show that the present method is quite efficient.

Purpose: The purpose of this paper is to research the solution of the perturbed coupled Korteweg-de Vries (KdV) equations.Methods: The results are obtained through researching a system of corresponding partial differential equations which approximates the perturbed coupled KdV equations and the symmetry method.Results: The symmetry structure and the corresponding general approximate symmetry reduction are derived. Then, using the symmetry reduction, the infinite series solutions are obtained.Conclusions: The approximate symmetry reduction approach can be used to search for similar results of other perturbed nonlinear differential equations with small parameters.

Purpose: The purpose of this paper is to develop a set of identities for Euler type sums of products of harmonic numbers and reciprocal binomial coefficients.Method: We use analytical methods to obtain our results.Results: We obtain identities for variant Euler sums of the type ¥Sn=1H2n/n (n+k)k, and its finite counterpart, which generalize some results obtained by other authors.Conclusions: Identities are successfully achieved for the sums under investigation. Some published results have been successfully generalized.

Purpose: The purpose of this paper is to study a common fixed point theorem for two maps in partial metric spaces.Methods: To prove Cauchy sequence, we used Ψ-f contractive method and obtain common fixed points.Results: We obtained a common fixed point result and illustrated with one example.Conclusions: It is concluded from the present study that one can generalize some results from metric spaces to partial metric spaces.

Purpose: Our aim in this paper is to study generalized composition operators on a- Bloch and QK, ω (p, q) spaces.Methods: By the help of generalized composition operators, we act between several classes of weighted function spaces. Some important results obtained by using modified Nevanlinna counting function.Results: The boundedness and compactness of the generalized composition operator Cg f acting between two different Mobius invariant spaces QK1 (p, q) and QK2 (p, q) are studied.Conclusions: Our results in this paper extend, generalize and improve a lot of previous results.