Browsing Pure Mathematics by Title
Now showing items 120 of 33

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 ... 
Analysis of mixed convection in an air filled square cavity.
(2010)A steady state twodimensional mixed convection problem in an air filled square unit cavity has been numerically investigated. Two different cases of heating are investigated and compared. In the first case, the bottom ... 
Approximation methods for solutions of some nonlinear problems in Banach spaces.
(2017)Abstract available in PDF file. 
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 ... 

Centre manifold theory with an application in population modelling.
(2009)There are basically two types of variables in population modelling, global and local variables. The former describes the behavior of the entire population while the latter describes the behavior of individuals within this ... 
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 ... 
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 ... 
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 ... 
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 ... 
Continuous symmetries of difference equations.
(20130604)We consider the study of symmetry analysis of difference equations. The original work done by Lie about a century ago is known to be one of the best methods of solving differential equations. Lie's theory of difference ... 
Ermakov systems : a group theoretic approach.
(1993)The physical world is, for the most part, modelled using second order ordinary differential equations. The timedependent simple harmonic oscillator and the ErmakovPinney equation (which together form an Ermakov system) ... 
Evolutionary dynamics of coexisting species.
(2000)Ever since MaynardSmith and Price first introduced the concept of an evolutionary stable strategy (ESS) in 1973, there has been a growing amount of work in and around this field. Many new concepts have been introduced, ... 
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 ... 
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 ... 
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 ... 
Lie symmetries of junction conditions for radiating stars.
(20131031)We consider shearfree radiating spherical stars in general relativity. In particular we study the junction condition relating the pressure to the heat flux at the boundary of the star. This is a nonlinear equation in ... 
Mathematical modeling of R5 and X4 HIV : from within host dynamics to the epidemiology of HIV infection.
Most existing models have considered the immunological processes occurring within the host and the epidemiological processes occurring at population level as decoupled systems. We present a new model using continuous ... 
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 ...