Browsing Pure Mathematics by Issue Date
Now showing items 120 of 31

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) ... 
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 ... 
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 ... 
Parameters related to fractional domination in graphs.
(1995)The use of characteristic functions to represent wellknown sets in graph theory such as dominating, irredundant, independent, covering and packing sets  leads naturally to fractional versions of these sets and corresponding ... 
The paradigms of mechanics : a symmetry based approach.
(1996)An overview of the historical developments of the paradigms of classical mechanics, the free particle, oscillator and the Kepler problem, is given ito (in terms of) their conserved quantities. Next, the orbits of the three ... 
Noether's theorem and first integrals of ordinary differential equations.
(1997)The Lie theory of extended groups is a practical tool in the analysis of differential equations, particularly in the construction of solutions. A formalism of the Lie theory is given and contrasted with Noether's theorem ... 
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 ... 
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 ... 
On the theory and examples of group extensions.
(1999)The work described in this dissertation was largely motivated by the aim of producing a survey on the theory of group extensions. From the broad scope of the theory of group extensions we single out two aspects to discuss, ... 
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, ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ... 
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 ...