Research Papers/Topics in Mathematics

Convergence in Norm of Modified Krasnoselskii-Mann Iteration for Fixed Points of Asymptotically Demi Contractive Mappings

Abstract  This project report deals with the class of asymptotically demicontractive mappings in Hilbert spaces. We noted some historical aspects concerning the concept of asymptotically demicontractivity and studied a regularized variant of the Krasnoselskii-Mann iteration scheme, which ensured the strong convergence of the generated sequence towards the least norm element of the set of fixed points of asymptotically demicontractive mapping. Contents Certification ii Dedication iii Acknow...

Solving Linear Systems

The object of this paper is to  solve linear systems.

Mathematical Model on Human Population Dynamics Using Delay Differential Equation

ABSTRACT Simple population growth models involving birth rate, death rate, migration, and carrying capacity of the environment were considered. Furthermore, the particular case where there is discrete delay according to the sex involved in the population growth were treated. The equilibrium and stability analysis of each of the cases were considered also. The stability analysis shows that the discrete delays in the population growth lead to instability in the growth. TABLE OF CONTENTS CERTIFI...

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...

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...

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...

Fractional Mechanical Oscillator

TABLE OF CONTENTS Title Page i Certificate of Approval ii Dedication iii Acknowledgment iv Abstract v Table of contents vi 1. FRACTIONAL ORDER CALCULUS 2. FUNCTIONS OF FRACTIONAL CALCULUS 2.1 The Gamma function 3 2.2 The Beta Function 5 2.3 The Mittag-Leffler Function 5 2.4 Laplace Transform 7 2.5 The Convolution Theorem 9 2.6 Riemann-Liouville Fractional integral 10 2.7 Riemann-Liouville Fractional derivative 13 2.8 The Caputo’s Fractional Derivative 14 2.9 Laplace Transform of Fractional ...

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...

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...

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 . . . . . . . ...

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 ...

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 ...

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...

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………………………………………………………………...

Pagano's theorem (short proof of generalized cauchy residue theorem)

shortly we can derive the Cauchy's residue theorem (its general form) just by direct integration of a Taylor series placing an open curve onto a specific domain, in order to satisfy holomorphic properties


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