Browsing Doctoral Degrees (Mathematical Sciences) by Title
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Neighbourhood operators on Categories
(Stellenbosch : Stellenbosch University, 201303)ENGLISH ABSTRACT: While the notions of open and closed subsets in a topological space are dual to each other, they take on another meaning when points and complements are no longer available. Closure operators have ... 
Offline signature verification
(Stellenbosch : University of Stellenbosch, 200503)A great deal of work has been done in the area of offline signature verification over the past two decades. Offline systems are of interest in scenarios where only hard copies of signatures are available, especially ... 
On the analysis of refinable functions with respect to mask factorisation, regularity and corresponding subdivision convergence
(Stellenbosch : University of Stellenbosch, 200712)We study refinable functions where the dilation factor is not always assumed to be 2. In our investigation, the role of convolutions and refinable step functions is emphasized as a framework for understanding various ... 
On the coefficients of Drinfeld modular forms of higher rank
(Stellenbosch : Stellenbosch University, 201404)ENGLISH ABSTRACT: Rank 2 Drinfeld modular forms have been studied for more than 30 years, and while it is known that a higher rank theory could be possible, higher rank Drinfeld modular forms have only recently been de ... 
On the computation of freely generated modular lattices
(Stellenbosch : Stellenbosch University, 200812)Please refer to full text for abstract. 
On the constant reductions of valued function fields and their automorphism groups
(Stellenbosch : Stellenbosch University, 20151120)ENGLISH ABSTRACT : The aim of the project is to investigate properties of the automorphism group of a function field in one variable over an algebraically closed field in relation to its reductions with respect to special ... 
On the inducibility of rooted trees
(Stellenbosch : Stellenbosch University, 201812)ENGLISH ABSTRACT : The density of appearances of a fixed tree in a larger tree is examined for rooted trees without vertices of outdegree 1 (also known as topological trees). Given a topological tree S with k leaves and ... 
On the LatimerMacDuffee theorem for polynomials over finite fields
(Stellenbosch : University of Stellenbosch, 201103)ENGLISH ABSTRACT: Latimer & MacDuffee showed in 1933 that there is a onetoone correspondence between equivalence classes of matrices with a given minimum polynomial and equivalence classes of ideals of a certain ring. ... 
On the maximum degree chromatic number of a graph
(Stellenbosch : Stellenbosch University, 200712)ENGLISH ABSTRACT: Determining the (classical) chromatic number of a graph (i.e. finding the smallest number of colours with which the vertices of a graph may be coloured so that no two adjacent vertices receive the same ... 
On the numerical evaluation of finitepart integrals involving an algebraic singularity
(Stellenbosch : Stellenbosch University, 197508)ENGLISH ABSTRACT: Some problems of applied mathematics, for instance in the fields of aerodynamics or electron optics, involve certain singular integrals which do not exist classically. The problems can, however, be ... 
On towers of function fields over finite fields
(Stellenbosch : University of Stellenbosch, 200703)Explicit towers of algebraic function fields over finite fields are studied by considering their ramification behaviour and complete splitting. While the majority of towers in the literature are recursively defined by a ... 
Oriented 123TQFTs via StringNets and StateSums
(Stellenbosch : Stellenbosch University, 201803)ENGLISH ABSTRACT :In a series of papers Bartlett, Douglas, SchommerPries, and Vicary discovered a finite generatorsandrelations presentation of the oriented bordism bicategory. This simplifies the task of finding ... 
Polynomial containment in refinement spaces and wavelets based on local projection operators
(Stellenbosch : Stellenbosch University, 200703)ENGLISH ABSTRACT: See full text for abstract 
Properties of graph polynomials and related parameters
(Stellenbosch : Stellenbosch University, 201712)ENGLISH ABSTRACT : In this thesis, we investigate various problems related to graph polynomials. We first define twovariable polynomials for rooted trees and specific posets, which are motivated by the Tutte polynomial. ... 
Random walk hitting times in random trees
(Stellenbosch : Stellenbosch University, 201712)ENGLISH ABSTRACT : The hitting time Hxy, between two vertices x and y of a graph, is the average time that the standard simple random walk takes to get from x to y. We start by giving a recursive formula for higher moments ... 
Rank matrix cascade algorithm, hermite interpolation
(Stellenbosch : University of Stellenbosch, 200712)ENGLISH ABSTRACT: (Math symbols have changed) Wavelet and subdivision techniques have developed, over the last two decades, into powerful mathematical tools, for example in signal analysis and geometric modelling. Both ... 
Refinable functions with prescribed values at the integers
(Stellenbosch : Stellenbosch University, 201203)ENGLISH ABSTRACT: See full text 
Refinable vector splines and multiwavelets with shortest matrix filters
(Stellenbosch : Stellenbosch University, 201803)ENGLISH ABSTRACT : A widely used class of basis functions in signal analysis is obtained from the dilation and integer shifts of a given (compactly supported) wavelet ψ : R → R, by means of which a (scalar) signal can ... 
Sensitivity analysis of multilayer neural networks
(Stellenbosch : Stellenbosch University, 199912)ENGLISH ABSTRACT: The application of artificial neural networks to solve classification and function approximation problems is no longer an art. Using a neural network does not simply imply the presentation of a data set ... 
Solving embedding problems with bounded ramification
(Stellenbosch : Stellenbosch University, 201612)ENGLISH ABSTRACT : Given a Galois extension K/K0 of number fields, a finite group G, and an epimorphism α: G→ Gal(K/K0) with solvable kernel, our goal is to embed K into a Galois extension N of K0 with Galois group ...