Abstract: Publication year: 2019Source: American Journal of Computational and Applied Mathematics , Volume 9, Number 5Chinedu Nwaigwe, Azubuike Weli, Oluwole Daniel MakindeWe investigate the heat and mass transfer in a variable-viscosity channel flow simultaneously accounting for viscous dissipation, external pollutant injection and Soret-Dufour effects. By adopting the Boussinesq approximation and assuming a fully developed uni-direction flow, the set of governing equations are presented. We formulate a finite difference scheme which decouples the system and is amenable to parallel computing. Gauss-Seidel solver is adopted for the resulting linear systems. The numerical results show that the thermal and solutal Grashof numbers, the viscosity parameter and the Darcy number all increase the flow velocity, while the magnetic field and the Prandtl number decrease the flow. It is also observed that the concentration and temperature are opposing each other; an increase in one causes a decrease in the other. Hence, we concluded that a strategy to mitigate pollution in the considered fluid system is to increase the fluid’s temperature.

Abstract: Publication year: 2019Source: American Journal of Computational and Applied Mathematics , Volume 9, Number 4Ognyan Ivanov ZhelezovThis article presents a special case of symmetric matrices, matrices of transpositions (Tr matrices) that are created from the elements of given n-dimensional vector X∈Rn, n=2m, m∈N. Has been proposed algorithm for obtaining matrices of transpositions with mutually orthogonal rows (Trs matrices) of dimensions 2, 4, and 8 as Hadamard product of Tr matrix and matrix of Hadamard and has been investigated their application for QR decomposition and n-dimensional rotation matrix generation. Tests and analysis of the algorithm show that obtaining an orthogonal Trs matrix of sizes 4 and 8 that rotates a given vector to the direction of one of the coordinate axes requires less processing time than obtaining a Housholder matrix of the same size.

Abstract: Publication year: 2019Source: American Journal of Computational and Applied Mathematics , Volume 9, Number 4Haruna Issaka, Oluwole Daniel Makinde, David Mwangi TheuriIn this paper we provide a model to describe the dynamics of the species of the ecosystem before and after it has been raided by a bad competing specie. The competing specie invades the native plants for nutrition, carbon dioxide and space. This affects the population of the native species of the ecosystem. We shall consider the effect of this invasion on the dynamics of the native species and the bird population. The essential mathematical features of the present model have been analyzed thoroughly for both local and global stability. We show that the dynamical outcomes of the interactions among the species are much sensitive to the system parameters and initial population densities. Numerical simulations are performed in order to validate the applicability of the model under consideration.

Abstract: Publication year: 2019Source: American Journal of Computational and Applied Mathematics , Volume 9, Number 11Dina Ismail Badawy, Mona Hilmy Youssef Alrayes, Ahmed Yahiya Hegab, Reem SafwatAim of the work: This study aimed to assess the presence of tissue factor and platelet microparticles in cases of acute myocardial infarction in relation to clinical outcome. Patients and methods: This study included 42 patients with acute ST elevation Myocardial infarction. The counting of platelet microparticles carrying CD42b&CD42b (MFI and tissue factor microparticles carrying CD142&CD142 (MFI) was done by flow cytometry. Systemic blood samples of 40 healthy individuals (control) were obtained to assay the studied parameters. A comparison was done between the patients according to their clinical picture and mode of treatment used, and also between patients and control cases. Results: There was high statistical significant elevation of platelet microparticles (count and MFI) and tissue factor microparticles (count and MFI) in patients group in comparison with the control group. There was no statistically significant difference between patients on medical treatment and patients receiving no treatment as regard platelet microparticles and tissue factor microparticles. The study shows highly statistically significant difference between patients without and with primary PCI as regard platelet microparticles and tissue factor microparticles. The study also shows high significant positive correlation between platelet microparticles CD42b (MFI) and tissue factor microparticles CD142 (MFI), and shows non-significant correlation between platelet microparticles CD42b (MFI) and other parameters in control group.

Abstract: Publication year: 2019Source: American Journal of Computational and Applied Mathematics , Volume 9, Number 4Janeth J. Ngana, Livingstone S. Luboobi, Okelo J. AbonyoVery few ecological studies have modeled Population Dynamics of the Serengeti Ecosystem. This paper seeks to analyze and forecast the trends of the Population Dynamics of the migratory ungulates of the Serengeti Ecosystem, under normal conditions. To get the Population Dynamics, we formulated a model of the four Ordinary Differential Equations for: Vegetation biomass, Herbivores, Lions and Cheetahs. For analysis we used the Least Mean Square method to simulate the model. We found that as the Vegetation biomass increases, the Herbivores population also increases and as a result the population of the Lions increases and the small Cheetah population decreases and goes to extinct due to competition with the Lions.

Abstract: Publication year: 2019Source: American Journal of Computational and Applied Mathematics , Volume 9, Number 3Janeth J. Ngana, Livingstone S. Luboobi, Okelo J. AbonyoVery few ecological studies have modeled Population Dynamics of the Serengeti Ecosystem under variable weather conditions. This paper seeks to analyze and forecast the trends of the Population Dynamics of the migratory ungulates of the Serengeti Ecosystem, under consistent monthly rainfalls and under varying rainfalls, when there is Climate Change. To get the Population Dynamics, we formulated a model of five Ordinary Differential Equations for: Vegetation biomass, Herbivores, Lions, Cheetahs and Crocodiles. For analysis of the model data, we used the Least Mean Square method. We found that in general, as the Vegetation volume grows logistically yearly, the Herbivores population decreases and as a result the populations of the Lions, the Cheetahs and the Crocodiles also decrease.

Abstract: Publication year: 2019Source: American Journal of Computational and Applied Mathematics , Volume 9, Number 3Iwundu M. P., Otaru O. A. P.Hat-Matrix aided composite designs, comparable with Standard Response Surface Methodology (RSM) designs and Computer-Generated designs for Seconds-Order models are presented alongside their optimality and efficiency properties. The construction of the new designs depends on the principles of the loss function of Akhtar and Prescott, which are represented by the diagonal elements of the “Hat” matrix. Through the Hat-matrix, design points that enhance efficiency of second-order designs are selected. Unlike computer-generated designs which may not be unique for a specific model and which may present some less efficient designs, the Hat-Matrix (H-M) aided designs are unique and require at least two categories of discrete design runs formed from the complete factorial design runs, only on the basis of the diagonal elements of the hat matrix that promote maximizing determinant of the information matrix thereby minimizing the loss function.

Abstract: Publication year: 2019Source: American Journal of Computational and Applied Mathematics , Volume 9, Number 3R. ThukralThe aim of this paper is to present further improvement of the Simpson-type methods for finding zeros of a nonlinear equation. The new Simpson-type methods are shown to converge of the same order four and five, but with better precision of the zeros. In terms of computational cost, the new iterative methods require four evaluations of functions per iteration and therefore the new methods have an efficiency index better than the classical Simpson method. It is proved that the new methods have a convergence of order four and five. We examine the effectiveness of the new Simpson-type methods by approximating the simple root of a given nonlinear equation. Numerical comparisons are included to demonstrate exceptional convergence speed of the proposed methods and thus verifies the theoretical results.

Abstract: Publication year: 2019Source: American Journal of Computational and Applied Mathematics , Volume 9, Number 3L. A. UkpeborThis paper proposes a four-point block method for the numerical solution of second order ordinary differential equations. In the construction of the method, interpolation and collocation techniques were involved, while Legendre Polynomial served as both the interpolation and collocation equations. The proposed scheme was analyzed and it was found to be A-stable, consistent and convergent.Numerical examples of ordinary differential equations were solved using the proposed method to test its performance. The results obtained compared favourably with other methods considered.

Abstract: Publication year: 2019Source: American Journal of Computational and Applied Mathematics , Volume 9, Number 2Bosson-Amedenu Senyefia, Vivian Nimoh, Osei-Asibey EuniceMultivariate analysis was applied to hospital data in this study. The underlying assumptions of MANOVA were verified with the data and were satisfied. The results from the post hoc test showed a positive and significant mean difference between children below the age of five years and patients between the ages of 5 and 19 years (MD=3.333, P