Doctoral Degrees (Pure Mathematics)
Recent Submissions

Combined impulse control and optimal stopping in insurance and interest rate theory.
(2015)In this thesis, we consider the problem of portfolio optimization for an insurance company with transactional costs. Our aim is to examine the interplay between insurance and interest rate. We consider a corporation, such ... 
Approximation methods for solutions of some nonlinear problems in Banach spaces.
(2017)Abstract available in PDF file. 
Spherically symmetric charged EinsteinMaxwell solutions.
(1999)In this thesis we study spherically symmetric spacetimes with a perfect fluid source which incorporates charge. We seek explicit solutions to the Einstein Maxwell system of equations. For nonaccelerating spherically ... 
Lie group analysis of exotic options.
(20140619)Exotic options are derivatives which have features that makes them more complex than vanilla traded products. Thus, finding their fair value is not always an easy task. We look at a particular example of the exotic options ... 
Aspects of distance measures in graphs.
(2011)In this thesis we investigate bounds on distance measures, namely, Steiner diameter and radius, in terms of other graph parameters. The thesis consists of four chapters. In Chapter 1, we define the most significant terms ... 
On convection and flow in porous media with crossdiffusion.
(2012)In this thesis we studied convection and crossdiffusion effects in porous media. Fluid flow in different flow geometries was investigated and the equations for momentum, heat and mass transfer transformed into a system ... 
Measurement and modelling of households' demand and access to basic water in relation to the rapidly increasing household numbers in South Africa.
(2010)Service delivery in postapartheid South Africa has become a topical issue both in the academia and the political arena . The rise of social movements, the xenophobic tensions of May 2008 and protest actions could be ... 
Singularity and symmetry analysis of differential sequences.
(2009)We introduce the notion of differential sequences generated by generators of sequences. We discuss the Riccati sequence in terms of symmetry analysis, singularity analysis and identification of the complete symmetry group ... 
CliffordFischer theory applied to certain groups associated with symplectic, unitary and Thompson groups.
(2012)The character table of a finite group is a very powerful tool to study the groups and to prove many results. Any finite group is either simple or has a normal subgroup and hence will be of extension type. The classification ... 
Algebraic properties of ordinary differential equations.
(1995)In Chapter One the theoretical basis for infinitesimal transformations is presented with particular emphasis on the central theme of this thesis which is the invariance of ordinary differential equations, and their first ... 
Extensions and generalisations of Lie analysis.
(1995)The Lie theory of extended groups applied to differential equations is arguably one of the most successful methods in the solution of differential equations. In fact, the theory unifies a number of previously unrelated ... 
Coherent structures and symmetry properties in nonlinear models used in theoretical physics.
(1994)This thesis is devoted to two aspects of nonlinear PDEs which are fundamental for the understanding of the order and coherence observed in the underlying physical systems. These are symmetry properties and soliton ... 
FischerClifford theory and character tables of group extensions.
(1998)The smallest Fischer sporadic simple group Fi22 is generated by a conjugacy class D of 3510 involutions called 3transpositions such that the product of any noncommuting pair is an element of order 3. In Fi22 there are ... 
Consequences of architecture and resource allocation for growth dynamics of bunchgrass clones.
(2005)In order to understand how bunchgrasses achieve dominance over other plant growth forms and how they achieve dominance over one another in different environments, it is first necessary to develop a detailed understanding ... 
Complete symmetry groups : a connection between some ordinary differential equations and partial differential equations.
(2008)The concept of complete symmetry groups has been known for some time in applications to ordinary differential equations. In this Thesis we apply this concept to partial differential equations. For any 1+1 linear evolution ...