Open Access Original Research Article

IGPR-Continuity and Compactness in Intuitionistic Topological Space

S. Selvanayaki, Gnanambal Ilango

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2015/19568

In this paper, the notion of intuitionistic generalised pre-regular continuity is introduced. Also intuitionistic generalised pre-regular compactness is de ned in intuitionistic topological spaces and several preservation properties are obtained. Moreover, some properties of intuitionistic generalised pre-regular continuity are outlined.

Open Access Original Research Article

Estimation of Stress-Strength Reliability for Exponentiated Inverted Weibull Distribution Based on Lower Record Values

Amal S. Hassan, Hiba Z. Muhammed, Mohammed S. Saad

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/BJMCS/2015/19829

The estimation of stress-strength reliability function based on record values has attracted the attention of authors because of its important role in industrial tests, where in some situations not all observations are considered in the study but only observations which are more extreme than the current observations, which represent record values, are the subject of the study. This paper deals with the estimation of R = P [Y < X ] , when X and  are two  independently exponentiated inverted Weibull distributed random variables based on lower record values. Non-Bayesian estimator using maximum likelihood method and Bayesian estimators using squared error and LINEX loss functions are derived. The exact confidence interval of the reliability is also derived. For illustrative purposes, analysis of a simulated data set has been performed to compare the different estimators and to investigate the coverage probabilities of confidence intervals.

Open Access Original Research Article

Open Access Original Research Article

Galerkin RBF for Integro-Differential Equations

Jafar Biazar, Mohammad Ali Asadi

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2015/19265

Two methods based on the Galerkin method with Radial basis Functions (RBF) as bases are applied to solve integro-differential equations (IDEs). In the rst approach, direct Galerkin RBF method, the unknown function of the IDE is approximated by RBFs and then the derivatives of it are replaced by the derivatives of RBFs. In the second one, indirect Galerkin RBF method, the derivative of the unknown function is approximated by RBFs and then lower order derivatives and unknown function itself are computed by integrating of RBFs. Therefore the Galerkin method is applied to compute these coecients. Double integrals that appeared in the process, can be reduced to single integrals by using a formula of iterated integrals. In complicated cases, single integrals approximated by Legendre-Gauss-Lobatto quadrature. Illustrative examples are included to demonstrate the validity and applicability of the presented techniques. A comparison of applying these methods shows the eciency and high accuracy of the indirect Galerkin RBF method rather than direct Galerkin RBF method.

Open Access Original Research Article

Open Access Original Research Article

Approximate Solutions for a Couple of Reaction-diffusion Equations with Self-diffusion

Shaker M. Rasheed, Majeed A. Yousif, Bewar A. Mahmood

Journal of Advances in Mathematics and Computer Science, Page 1-11
DOI: 10.9734/BJMCS/2015/19573

In this paper, a competition model of a reaction diffusion system with self-diffusion has been studied using homotopy perturbation method, variational iteration method and Finite element method FEM (COMSOL package). The traveling wave solutions for this system are found and compared numerically.It was shown that the competition will lead at the end of the winning of one species. The effect of self diffusion is shown in the dispersing of traveling wave solution. Also, it was shown that the solution of finite element method and homotopy perturbation method are convergent to each other compared to the variation iteration method.

Open Access Original Research Article

A Performance Evaluation of OpenCL and Intel Cilk Plus on a Graphic Rendering Problem

Y. J. Gambo, S. B. Junaidu, S. E. Abdullahi, C. I. Saidu

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2015/19422

Parallel programming is fast evolving into a central core of high performance computing. Several computing hardware vendors now embed several processors into computers to increase speed and performance thus the need to maximize and utilize computing resources for maximum performance. Rendering of graphics has also been a challenge in terms of speed that architects and graphic experts have found it difficult to render graphics in a timely manner at minimal cost. In this paper, a comparative study was carried out on two recent and powerful multiprocessor parallel programming languages OpenCL and Intel Cilk Plus which were used to separately program an embarrassingly parallel graphic rendering algorithm, raytracing. The programs were ran and profiled on three different computers with varying specifications on windows using Microsoft Visual Studio 2012 as IDE. The result showed that OpenCL was consistent after first run without restart than Intel Cilk Plus and as raytracing depth increased the performance gap between OpenCL and Intel Cilk Plus also increased with OpenCL showing the better performance.