# Research Papers/Topics in Mathematics

##### Open Channel Flow Over a Permeable River Bed

ABSTRACT We have modelled an open channel flow through a porous media (River). In the model, we considered water as an incompressible fluid; the flow as steady and uniform; the system is assumed to be isothermal and the flow, also a laminar flow. We have solved the resulting equation using analytical method. By some mathematical operations, the momentum partial differential equation (PDE) was reduced to ordinary differential equation (ODE) and the resulting equations are solved analytically u...

69 PAGES (10385 WORDS)
##### Portfolio Selection and Optimal Financial Investment in Nigerian Economy

TABLE OF CONTENT Title Page - - - - - - - - - i Approval Page- - - - - - - - - ii Certification - - - - - - - - - iii Dedication - - - - - - - - - iv Acknowledgement - - - - - - - - v Table of Content - - - - - - - - vi Abstract - - - - - - - - - vii Chapter One : Introduction - - - - - - 1 1.1 Background of the Study - - - - - - - 1 1.2 Aims and Objective of the Study - - - - - - 5 1.3 Limitations - - - - - - - - 6 1.4 Scope of the study - - - - - - - 6 1.5 The Study- - - - - - - - - 6 1.6 D...

81 PAGES (18916 WORDS)
##### Bifurcation and Stability of Steady Solutions of Evolution Equations

ABSTRACT We considered the evolutional problems in two-dimensional autonomous system. We showed that the bifurcating steady solutions are obtained from the points of intersection of the two conic sections and we used the implicit function theorem to justify their existence, and also we applied the Lyapunov theorem to establish their stability. CONTENTS Title Page i Certification ii Dedication iii Acknowledgement iv Contents v Abstract vi Chapter One INTRODUCTION 1 Chapter Two LITERATURE REVIE...

65 PAGES (9090 WORDS)
##### Travelling Waves Solutions for the Transesterification Reaction Kinetics of Biodiesel Production Using Tanh Method.

ABSTRACT A mathematical model consisting of a set of two coupled non-linear reaction diffusion equations has been developed. The model is based on the chemical kinetics of transesterification for biodiesel production using irreversible and non-catalytic conditions. Employing the hyperbolic tangent approach, an exact analytical solution for the travelling-waves of a finite series form was found. The wave number and the speed of the wave were determined. Furthermore,physical interpretations wer...

43 PAGES (6418 WORDS)
##### Generalized Mathematical Modeling of Aqueous Humour Flow in the Anterior Chamber and Through a Mesh Channel in the Human Eye

ABSTRACT In this work, we propose mathematical models for the processes that take place in the human eye and how they contribute to the development of pathological states. We considered and studied two related dynamics processes that take place in the eye. Firstly, a generalized mathematical model of aqueous humour flow driven by temperature gradient in the anterior chamber is presented. This predicts the flow behavior when the ambient temperature is higher than the core body temperature. The...

137 PAGES (28969 WORDS)
##### Weak and Strong Convergence of an Iterative Algorithm for Lipschitz Pseudo-Contractive Maps in Hilbert Spaces

ABSTRACT Let H be a real Hilbert space and K a nonempty, closed convex subset of H.Let T : K → K be Lipschitz pseudo-contractive map with a nonempty fixed points set. We introduce a modified Ishikawa iterative algorithm for Lipschitz pseudo-contractive maps and prove that our new iterative algorithm converges strongly to a fixed point of T in real Hilbert space. Contents Certification ii Dedication iii Acknowledgement iv Abstract viii 1 Introduction 1 1.1 General Introduction . . . . . . . ...

65 PAGES (15657 WORDS)
##### Mathematical Model on Glucose, Insulin and Β-Cells Mass Dynamics in Type 2 Diabetes

ABSTRACT A mathematical model, describing glucose, insulin and β-cells mass dynamics of a type 2 diabetic patient was developed in the form of a system of ordinary differential equation, considering insulin resistance, the body inability to overcome the resistance and the fact that glucose production from food intake is not constant. Numerical solution of the model using RungeKutta code in MATLAB, graphically shows rise in blood glucose concentration and further decline over time in glucose ...

66 PAGES (13965 WORDS)
##### Boundary Value Problems for Quasilinear Second Order Differential Equations

Abstract This project is concerned with the review of some boundary value problems for nonlinear ordinary differential equations using topological and variational methods. A more classical boundary value problems for ordinary differential equations (like the boundary value problems on a ball, initial value problems, problems on annular domains and positone problems) which represent the main interest of a wide number of researchers in the world is studied. Contents Certification ii Dedication ...

50 PAGES (12116 WORDS)
##### Mathematical Modeling and Control of a No - Isothermal Continuous Stirred Tank Reactor, Cstr

ABSTRACT Mathematical Models describing the variations in the volume of the system, concentration of reactant (s) yet to react, temperature of the system, and the temperature of the cooling jacket over time in a non-isothermal CSTR that handles a simple, irreversible, first order or second order exothermic reaction in liquid phase were formulated. This work is with a particular reference to the synthesis of propylene from cyclopropane and that of cumene (isopropyl benzene) from benzene and pr...

136 PAGES (37067 WORDS)
##### Mathematical Model on a Three Way Catalytic Converter: A Comparative Study of Gas Phase Concentration and Temperature.

ABSTRACT We comparatively studied gas phase concentration and gas temperature of three way catalytic converter models. We considered channel level models and provided concise solutions for them. Solutions to the models were graphically represented and we found that gas phase temperature increases with time and gas phase concentration of gaseous species attain light-off at temperature above 600K. TABLEOFCONTENTS Title page………………………………………………………………...

46 PAGES (6828 WORDS)
##### Stationary Analysis of the M/M/1 Queuing System with Two Customer Subgroups

Abstract A single server Markovian queuing system called the M/M/1 queuing system with two distinct customer types namely; the constraint customer type and the un-constraint customer type is studied. This model is that of a production system with heterogeneous customer structures devoid of a single customer in the intersection category group wise. Initially, relevant literature covering methodologies, analysis and results derived for single server production systems are reviewed and a gap ide...

51 PAGES (10255 WORDS)
##### Combinatorial Properties of the Alternating & Dihedral Groups and Homomorphic Images of Fibonacci Groups

Abstract Let Xn = { } 1,2,…,n be a finite n -element set and let Sn An and Dn , be the Symmetric, Alternating and Dihedral groups of Xn , respectively. In this thesis we obtained and discussed formulae for the number of even and odd permutations (of an n − element set) having exactly k fixed points in the alternating group and the generating functions for the fixed points. Further, we give two different proofs of the number of even and odd permutations (of an n − element set) having ex...

55 PAGES (11826 WORDS)
##### Feasibility Of Using Geogebra In The Teaching And Learning Of Geometry Concepts In Secondary Schools In Kajiado County, Kenya

ABSTRACT GeoGebra is a free computer application software that provides an algebra view, geometry view, spreadsheet view and an input bar. This study looked at if and how this resource can be used to enhance the teaching of Geometry in secondary schools in Kajiado County in Kenya. The objectives of this study were to assess the applicability of GeoGebra in the teaching of mathematics in secondary schools in Kenya. The relationship in performance of students taught with the help of this innov...

197 PAGES (32258 WORDS)
##### Simulating Natural Turbulent Convection Fluid Flow In An Enclosure Using The Two-Equation Turbulent Models

ABSTRACT This study assesses the performance of three numerical turbulence models; k -e , k -w and k -w - SST in predicting heat transfer due to natural convection inside an air filled cavity. The heat transfer due to natural convection inside a rectangular closed cavity should be modeled to include the effect of turbulence for Rayleigh number greater than or equal to 9 10 .The non-linear terms i j u u and qi u in the averaged momentum and energy equations respectively were modeled using...

135 PAGES (28050 WORDS)
##### Integrating Information Communication And Technology In Mathematics Education At Secondary Level, A Case Of Nairobi County, Kenya

ABSTRACT The purpose of this study was to explore the various challenges and opportunities influencing integration of ICT in teaching and learning Mathematics in secondary schools in Nairobi County. The study sought to: Determine the levels of ICT integration in teaching and learning Mathematics; identify the challenges and opportunities of ICT use in teaching and learning Mathematics; and identify best pedagogical practices used in teaching Mathematics using ICT. The study adopted Rogers’s...

97 PAGES (18885 WORDS)

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