Browsing Applied Mathematics by Title
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On new and improved seminumerical techniques for solving nonlinear fluid flow problems.
(2012)Most real world phenomena is modeled by ordinary and/or partial differential equations. Most of these equations are highly nonlinear and exact solutions are not always possible. Exact solutions always give a good account ... 
On singularly perturbed problems and exchange of stabilities.
(2015)Singular perturbation theory has been used for about a century to describe models displaying different timescales, that arise in applied sciences; particularly, models displaying two timescales, namely slow time and fast ... 
On Stephani universes.
(1992)In this dissertation we study conformal symmetries in the Stephani universe which is a generalisation of the RobertsonWalker models. The kinematics and dynamics of the Stephani universe are discussed. The conformal ... 
On the integrity of domination in graphs.
(1993)This thesis deals with an investigation of the integrity of domination in a.graph, i.e., the extent to which domination properties of a graph are preserved if the graph is altered by the deletion of vertices or edges or ... 
On the physical viability of horizonfree collapse.
(20150904)The socalled Cosmic Censorship Conjecture has drawn widespread attention amongst astrophysicists and particle physicists. In particular, the endstate of gravitational collapse of a bounded matter distribution is a ... 
Optimisation of the population Monte Carlo algorithm : application to cosmology.
(20150904)In this thesis we study the Population Monte Carlo (PMC) algorithm and utilise simulations to improve the efficiency of the algorithm by optimising the algorithm parameters. We then ap ply these optimisation results to ... 
Partial exchangeability and related topics.
(1991)Partial exchangeability is the fundamental building block in the subjective approach to the probability of multitype sequences which replaces the independence concept of the objective theory. The aim of this thesis is ... 
Relativistic radiating stars with generalised atmospheres.
(2010)In this dissertation we construct radiating models for dense compact stars in relativistic astrophysics. We first utilise the standard Santos (1985) junction condition to model Euclidean stars. By making use of the ... 
Relativistic spherical stars.
(1993)In this thesis we study spherically symmetric spacetimes which are static with a perfect fluid source. The Einstein field equations, in a number of equivalent forms, are derived in detail. The physical properties of a ... 
Relativistic thermodynamics of radiating stars.
(2016)In this research, on the topic of relativistic thermodynamics of radiating stars, the following three case studies are investigated: Gravitational collapse in spacially isotropic coordinates { The nature of a ... 
Shearfree models for relativistic fluids with heat flow and pressure isotropy.
(2014)We model the interior dynamics of a relativistic radiating fuid in a nonstatic spher ically symmetric spacetime. The matter distribution takes the form of an imperfect fuid with a nonvanishing radially directed heat ... 
Solution generating algorithms in general relativity.
(2011)We conduct a comprehensive investigative review of solution generating algorithms for the Einstein field equations governing the gravitational behaviour of an isolated neutral static spherical distribution of perfect ... 
Some Mal'cev conditions for varieties of algebras.
(1991)This dissertation deals with the classification of varieties according to their Mal'cev properties. In general the so called Mal'cevtype theorems illustrate an interplay between first order properties of a given class ... 
Southern African Large Telescope observations of SunyaevZel'dovich effect selected clusters from the Atacama Cosmology Telescope.
(2014)We present Southern African Large Telescope (SALT) followup observations of seven massive clusters detected by the Atacama Cosmology Telescope (ACT) using the SunyaevZel’dovich effect (SZE). We conducted multiobject ... 
Spatial modelling of fire dynamics in Savanna ecosystems.
(1999)Fire is used in the management of ecosystems worldwide because it is a relatively inexpensive means of manipulating thousands of hectares of vegetation. Deciding how, where and when to apply fire depends primarily on the ... 
The theory of option valuation.
(1992)Although options have been traded for many centuries, it has remained a relatively thinly traded financial instrument. Paradoxically, the theory of option pricing has been studied extensively. This is due to the fact ... 
Thermal evolution of radiation spheres undergoing dissipative gravitational collapse.
(20150904)In this study we investigate the physics of a relativistic radiating star undergoing dissipative collapse in the form of a radial heat flux. Our treatment clearly demonstrates how the presence of shear affects the collapse ... 
Transport on network structures.
(20140512)This thesis is dedicated to the study of flows on a network. In the first part of the work, we describe notation and give the necessary results from graph theory and operator theory that will be used in the rest of ... 
Using epidemiological mathematical models to understand the transmission dynamics of bovine tuberculosis in buffalo and cattle populations.
(2015)In South Africa, buffalo are the maintenance hosts of Mycobacterium bovis (M. bovis), a pathogen that causes bovine tuberculosis in wildlife and domesticated animals. To understand the transmission dynamics of M. bovis, ... 
Using spectral methods on HIV infection with TAT and SSU72 activation.
(2016)HIV dynamics within the host are complex especially when a reservoir of latently infected CD4+ T cells are present. The failure of the immune system and antiviral therapy to suppress the virus has been suggested to be ...