Asian Research Journal of Mathematics 2019-11-17T07:07:17+00:00 Asian Research Journal of Mathematics Open Journal Systems <p style="text-align: justify;"><strong>Asian Research Journal of Mathematics (ISSN: 2456-477X)</strong> aims to publish high-quality papers (<a href="/index.php/ARJOM/general-guideline-for-authors">Click here for Types of paper</a>) in all areas of ‘Mathematics and Computer Science’. By not excluding papers on the basis of novelty, this journal facilitates the research and wishes to publish papers as long as they are technically correct and scientifically motivated. The journal also encourages the submission of useful reports of negative results. This is a quality controlled, OPEN peer-reviewed, open access INTERNATIONAL journal.</p> On some Ternary Linear Codes and Designs obtained from the Projective Special Linear Goup PSL3(4) 2019-11-17T07:07:17+00:00 Yvonne W. Kariuki Ojiema M. Onyango Okombo M. Immaculate <p>Let (G, ∗) be a group and X any set, an action of a group G on X, denoted as G×X → X, (g, x) 7→ g.x, assigns to each element in G a transformation of X that is compatible with the group structure of G. If G has a subgroup H then there is a transitive group action of G on the set (G/H) of the right co-sets of H by right multiplication. A representation of a group G on a vector space V carries the dimension of the vector space. Now, given a field F and a finite group G, there is a bijective correspondence between the representations of G on the finitedimensional F-vector spaces and finitely generated FG-modules. We use the FG -modules to construct linear ternary codes and combinatorial designs from the permutation representations of the group L<sub>3</sub>(4). We investigate the properties and parameters of these codes and designs.</p> <p>We further obtain the lattice structures of the sub-modules and compare these ternary codes with the binary codes constructed from the same group.</p> 2019-11-05T00:00:00+00:00 ##submission.copyrightStatement## Hyperbolic Jacobsthal Numbers 2019-11-17T07:07:17+00:00 Can Murat Dikmen <p>In this paper, we introduce the Hyperbolic Jacobsthal numbers and we present recurrence relations, Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we investgate Lorentzian inner product for the hyperbolic Jacobsthal vectors.</p> 2019-11-05T00:00:00+00:00 ##submission.copyrightStatement## An Approximate Solution for a Nonlinear Duffing – Harmonic Oscillator 2019-11-17T07:07:17+00:00 Van Hieu – Dang <p>The equivalent linearization method introduced by Caughey is a powerful tool for analyzing random oscillations. The method is also easy to apply for deterministic oscillations. However, with strong nonlinear systems, the error of this method is usually quite large and even not acceptable. In conjunction with a weighted averaging, the equivalent linearization method has shown more accuracy than the classical one in which the conventional averaging value is used. Combining advantages of the classical equivalent linearization method and accuracy of the weighted averaging, the proposed method has shown that it is a useful tool for analyzing nonlinear oscillations including strong nonlinear systems. In this paper, the proposed method is applied to analyze a nonlinear Duffing – harmonic oscillator. The present results are compared with the results obtained by using other analytical methods, exact results and numerical results.</p> 2019-11-05T00:00:00+00:00 ##submission.copyrightStatement## A Study on Properties and Applications of a Lomax Gompertz-Makeham Distribution 2019-11-17T07:07:16+00:00 Innocent Boyle Eraikhuemen Terna Godfrey Ieren Tajan Mashingil Mabur Mohammed Sa’ad Samson Kuje Adana’a Felix Chama <p>The article presents an extension of the Gompertz-Makeham distribution using the Lomax generator of probability distributions. This generalization of the Gompertz-Makeham distribution provides a more skewed and flexible compound model called Lomax Gompertz-Makeham distribution. The paper derives and discusses some Mathematical and Statistical properties of the new distribution. The unknown parameters of the new model are estimated via the method of maximum likelihood estimation. In conclusion, the new distribution is applied to two real life datasets together with two other related models to check its flexibility or performance and the results indicate that the proposed extension is more flexible compared to the other two distributions considered in the paper based on the two datasets used.</p> 2019-11-06T00:00:00+00:00 ##submission.copyrightStatement## Analysis of Two Finite Dierence Schemes for a Channel Flow Problem 2019-11-17T07:07:16+00:00 Chinedu Nwaigwe Azubuike Weli <p><strong>Aims/ Objectives:</strong> To investigate the influence of a model parameter on the convergence of two finite difference schemes designed for a convection-diffusion-reaction equation governing the pressure-driven flow of a Newtonian fluid in a rectangular channel.<br><strong>Methodology</strong>: By assuming a uni-directional and incompressible channel flow with an exponentially time-varying suction velocity, we formulate a variable-coefficient convectiondiffusion- reaction problem. In the spirit of the method of manufactured solutions, we first obtain a benchmark analytic solution via perturbation technique. This leads to a modified problem which is exactly satisfied by the benchmark solution. Then, we formulate central and backward difference schemes for the modified problem. Consistency and convergence results are obtained in detail. We show, theoretically, that the central scheme is convergent only for values of a model parameter up to an upper bound, while the backward scheme remains convergent for all values of the parameter. An estimate of this upper bound, as a function of the mesh size, is derived. We then conducted numerical experiments to verify the theoretical results.<br><strong>Results:</strong> Numerical results showed that no numerical oscillations were observed for values of the model parameter less than the theoretically derived bound.<br><strong>Conclusion:</strong> We therefore conclude that the theoretical bound is a safe value to guarantee non-oscillatory solutions of the central scheme.</p> 2019-11-08T00:00:00+00:00 ##submission.copyrightStatement## A New and Simple Condensation Method of Computing Determinants of Large Matrices and Solving Large Linear Systems 2019-11-17T07:07:16+00:00 Okoh Ufuoma <p>The chief object of this work present a new and simple condensation method of finding determinants of large matrices and solving large linear systems.</p> 2019-11-11T00:00:00+00:00 ##submission.copyrightStatement## Overview of Optimality of New Direct Optimal Methods for the Transportation Problems 2019-11-17T07:07:15+00:00 Sanaullah Jamali Muhammad Mujtaba Shaikh Abdul Sattar Soomro <p>In this paper, we investigate the claimed optimality of a new method – Revised Distribution (RDI) Method – for finding optimal solution of balanced and unbalanced transportation models directly and compare the RDI method with other such methods. A large set of problems have been tested by RDI and other methods, and the results were compared with the Modified distribution (MODI) method – an optimal method. We found that the mostly the results of RDI are not optimal. For reference to prove our observations, we have added three example transportation problems here in this work and compared their results with MODI method to show that the RDI method like the direct exponential approach (DEA) method is not optimal method; but it is just an initial basic feasible solution (IBFS) for transportation problems.</p> 2019-11-13T00:00:00+00:00 ##submission.copyrightStatement##