Mečislovas Mariūnas

This paper presents methods for determining resonant and parametric excitation frequencies in a nonlinear two-degree-of-freedom dynamic system. It is clarified that in order to determine the resonant frequencies in the system, it must be divided into two subsystems. The results show that in nonlinear dynamic system there are nine groups of resonant frequencies, which are defined by energy, force, stiffness connection peculiarities, as well as the total stiffness of the system. The results also demonstrate that the system for determining the parametric frequencies must not be divided into subsystems. It is clarified that the system generated a very wide spectrum of parametric excitation frequencies, and when they coincide with the resonant frequency, the level of system vibrations increases significantly. It has been found that vibrations at high amplitude resonant frequency also become generators of parametric vibrations in a nonlinear dynamic system. By setting the parameters of the system (stiffness, mass, damping, etc.), we determine its resonant frequencies; however, the magnitude of the parametric vibration frequency and their number of a dynamic system depend on the level of nonlinearity of the system. Thus, the frequency of parametric vibration is independent of their amplitude. The certainty of the analytical methods presented in the paper was verified by numerical calculations.

]]>KW Bunonyo, E. Amos

This research is focused on investigating the blood flow through a sine-shaped atherosclerotic aorta with a source wall temperature and magnetic field. In the study we formulate models for the problem, scaled the governing models to be dimensionless, and reduced the coupled system to ordinary differential equations using perturbation method with an oscillation. The resulting ODEs are solved directly for velocity and temperature profiles with some pertinent parameters obtained. Mathematica codes were developed to simulate each of the functions to investigate the influence of the pertinent parameters such as radiation parameter, Hartmann number, womersley number, the treatment parameter, the wall temperature and the height of stenosis on the blood flow through an aorta that has lost its elasticity assuming the radius of the aorta as Conclusively, we noticed that the blood velocity increases for the increase in Darcy number and treatment parameter but reversed for the increase of wall temperature, Hartmann number, womersley number, height of stenosis and oscillatory frequency parameter. The temperature profile decreases with the increase of radiation parameter, oscillatory parameter, height of stenosis and womersley number, while it increases with the increase of wall temperature and treatment parameters. Finally, the flow rate, shear stress and rate of heat transfers are also increased and decreased with the increase of radiation parameter, treatment parameter, womersley number, Hartmann number, height of stenosis and the oscillatory parameter, and this work is recommended for clinicians and other scientists/mathematicians alike who are interested in investigating blood flow through the circulation system.

]]>R. Thukral

This paper presents new three-point Secant-type methods for finding simple root of nonlinear equations. It is proved that the new methods have the convergence order of 1.84 or 1.80 requiring only one function evaluations per full iteration. Some of the three-point Secant-type iterative methods are shown to have the same order of convergence as the Tiruneh et al. method, the Muller method and the Traub methods. Numerical comparisons are made to demonstrate exceptional convergence speed of the proposed methods. It is observed that the new three-point Secant-type iterative methods are very competitive with the similar robust methods.

]]>Mečislovas Mariūnas

**Abstract** This paper presents methods for determining resonant and parametric excitation frequencies in a nonlinear single-degree-of-freedom dynamic system. The results show that in nonlinear dynamic system there are four groups of resonant frequencies, which are defined by energy, force, stiffness connection peculiarities, as well as the total stiffness of the system. The results also demonstrate that the system generates a very wide spectrum of parametric excitation frequencies, such that when they coincide with the resonant frequency the level of system vibrations increases significantly. By setting the parameters of the system (stiffness, mass, damping, etc.), we determine its resonant frequencies, however the frequency and number of parametric vibrations of a dynamic system depend on the level of nonlinearity of the system. Thus, the frequency of parametric vibration is independent of their amplitude. The certainty of the analytical methods presented in the article was verified by numerical calculations**.**

S. Saravi, M. Saravi

This paper introduces a survey of mathematical models to tumor growth modelling using Ordinary Differential Equations (ODEs) on cancer research. Since the tumor grows voraciously, the scientists and mathematicians have tried to have a better understanding how it grows. Usually, study of such treatments on the models of tumor growth lead to one or more ODEs which gives some ideas on relation between such equations and tumor growth of cancer cells, in particular breast and ovarian cancer cells. In this survey, we introduce some ODEs to provide mathematical models in tumor growth. We emphasis that this paper is useful for the researchers in the field of cancer, hence some objective and new contribution may not clear for the reader. Main goal of this paper is to familiarize reader to applications of ODEs on epidemiology.

]]>Chinedu Nwaigwe, Azubuike Weli, Oluwole Daniel Makinde

We 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.

]]>Ognyan Ivanov Zhelezov

This 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∈R^{n}, n=2^{m}, 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.

Haruna Issaka, Oluwole Daniel Makinde, David Mwangi Theuri

In 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.

]]>Dina Ismail Badawy, Mona Hilmy Youssef Alrayes, Ahmed Yahiya Hegab, Reem Safwat

Aim 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.

]]>Janeth J. Ngana, Livingstone S. Luboobi, Okelo J. Abonyo

Very 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.

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