Research Papers/Topics in Mathematics

A categbrial study of initiality in uniform topology

AbstractThis thesis consists of two chapters, of which thefirst presents a categorial study of the concept ofinitiality (also known as projective generation) and thesecond gives applications in the.theory of uniform andquasi-uniform spaces,The' first three sections of chapter 1 expound basicaspects of initiality, such as its relation to categoriallimits and to embeddings, the· latter being defined withrespect to a faithful functor to a bicategory. The notionof a separated object with re...

3-month Bond Option Strategies: An analysis of performance from 1998 to 2010 in the South African market

Abstract Due to the 2008 financial crisis, investors have become more risk averse in investing in equities and have increased their holdings in bonds as they are believed to be less risky. However, South African interest rates have been volatile over the past decade due to changes in the inflation rate. This has caused the returns of bond portfolios to be uncertain since bond prices are inversely related to interest rates. It is thus imperative to manage the interest rate risk inherent...

Mathematical Modelling of Optimal Strategies for Improving Industrial Productive Population in the Presence of Perverse Diseases Pandemic

ABSTRACTIn this theses, we investigate certain key aspects of mathematical modelling to explain theepidemiology of HIV/AIDS, Tuberculosis, Hepatitis B, Tumour,diabetes and stroke at theworkplace and assess the potential benefits of proposed control strategies. The compartmentalepidemiological modelling approach was used in the formulation of the models on HIV/AIDS,tuberculosis (TB), Hepatitis B (HBv), Tumour and Diabetes pandemic. In each of the cases, the dynamicsof the disease was stud...

Toeplitz Projections and Corona with Localization and Toeplitz Algebra on the Bergman Space

We study the operator commuting and essential commutant of analytic Toeplitz operators module the compact operators and Toeplitz operators in several complex variables and on the Bergman space of the until ball. We show the ordered groups and some exact sequences and the commutator ideal of the Toeplitz algebras of spherical isometries and on the Bergman spaces of the unit ball in the unitary space. We give the lower bounds in the matrix, new estimate for the vec...

The formal solution of constrained mechanical system

In this work we discuss the scope of Lagrangian mechanics and constrained systems. We discuss the problem of central force two–bodies and its formal solution. Also we study the rotations and rigid bodies by using Euler’s equations, Lagrangian description and Legender transformations with some examples and applications.

Design Reality Gaps In Open Source Information Systems Development: An Action Research Study Of Education And Healthcare Systems In Tanzania

ABSTRACTThis thesis, Design-Reality Gaps in Open Source Information Systems Development: An Action Research Study of Education and Healthcare Systems in Tanzania, presents a theoretical and empirical informed analysis of Free Open Source Software (FOSS) development in the domain of health and education information systems in Tanzania. Historically, FOSS development has been driven by user-developer communities who are also the users of FOSS applications. The use of Fo...

Transfer Functions and Mathematical Modeling of Dynamic Systems with MATLAB

This study introduces the mechanical elements that are the main components in the dynamic modeling of mechanical systems. It discusses the electrical elements of voltage and current source, resistor, capacitor, inductor, and operational amplifier. We derive mathematical models for electrical systems. The transfer function, enables connecting the input to the output of a dynamic system into the Laplace domain for single-input, single output, multiple-input and multiple...

Twistor Formulation of Some Partial Differential Equations

Twistor theory has been invented by R. Penrose in order to generalize gravity. He introduced a geometrical model for Minkowski space. This geometrical setup has been generalized in solving particle differential equations. In particular zero-rest-mass field equation have been treated this way as a Contour integral of complex twistor function. In our study we consider geometrical interpretations and solutions of conformal field equations. We also studied Twistors i...

On The Characterization Of The Unit Groups Of A Class Of Total Quotient Rings

ABSTRACTLet R be a completely primary nite ring of characteristic pk, where p is a prime and k isa positive integer. Such nite rings have been studied extensively in recent years and thetools necessary for describing completely primary nite rings have been available for sometime. However, their characterization is not exhaustive. Several attempts have been madein the recent past in the characterization of the unit groups of this class of rings though notin general. The characterization of ...

Certain Geometric Aspects Of A Class Of Almostcontact Structures On A Smooth Metric Manifold.

ABSTRACTThe classi cation of Smooth Geometric Manifolds still remains an open problem. Theconcept of almost contact Riemannian manifolds provides neat descriptions and distinctionsbetween classes of odd and even dimensional manifolds and their geometries. Amongthe classes that have been extensively studied in the past are the Hermitian, Symplectic,Khalerian, Complex, Contact and Almost Contact manifolds which have applications inM-Theory and supergravity among other areas. The di erential geo...

Predator-Prey Model With Logistic Growth For Constantand Density-Dependent Delayed Migration

ABSTRACTPredator-prey models describe the interaction between two species, the prey whichserves as a food source to the predator. The migration of the prey for safety reasonsafter a predator attack and the predator in search of food, from a patch to anothermay not be instantaneous. This may be due to barriers such as a swollen river ora busy infrastructure through the natural habitat. Recent predator-prey modelshave either incorporated a logistic growth for the prey population or a time delay...

Mathematical Modelling Of The Impact Of Higher Learning Institutions On Absorption Into Subtance Abuse: Case Study Of Maasai Mara University

ABSTRACT The study is aimed at modelling drug addiction circle to provide a wide picture of the source of the hard drug addiction problem so as to get to know how to solve the menace that is eating up young adults. A schematic review technique is employed where data from a variety of research articles is analyzed and a collection of the findings described. The logistic model is to be used to describe what happens to the university students since they enrolled till they finish their c...

A Characterization Of U-Ideals In Reflexive Banach Spaces

ABSTRACTIn this thesis we show the retlexivity of a Banach space, that is spaces embedded in theirbiduals.The concept is realized for the case that the canonical embedding into its bidualis surjective.We characterize u-ideals in Banach spaces having retlexive properties. Weshow that u-ideal achieves its norm on closed unit ball and for any retlexive Banachspace X; u-ideal is always a closed ideal. We also show that u-deal contained inJacobsonradical is a zero ring.

On The Generators Of Codes Of Ideals Of The Polynomial Ring For Error Control

ABSTRACTShannon introduced error detection and correction codes to address the growing need ofeciency and reliability of code vectors. Ideals in algebraic number system have mainlybeen used to preserve the notion of unique factorization in rings of algebraic integers andto prove Fermat's Last Theorem. Generators of codes of ideals of polynomial rings havenot been fully characterized. Ideals in Noetherian rings are closed in polynomial additionand multiplication. This property has been used t...

Dynamics Of A Fishery Model With Allee Effect In Population Growth

ABSTRACTSustainable exploitation of renewable resources such as marine sh has been a con-cern to both ecologists and economists with threats of species extinction due to over- exploitation a stark reality. Fish exhibits co-operative and social characteristicsamong individuals which increases its survival through predator surveillance andenhanced spawning. Over shing compromises this con - speci c interactions andsocialism. In this study, a mathematical model of a shery with an Allee e ect i...


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