Browsing Doctoral Degrees (Mathematical Sciences) by Title
Now showing items 5170 of 71

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 ... 
Spectral theory in commutatively ordered banach algebras
(Stellenbosch : Stellenbosch University, 201212)ENGLISH ABSTRACT: See full text. 
Spreading waves of invasive species
(Stellenbosch : Stellenbosch University, 201403)ENGLISH ABSTRACT: Invasive species are well known to harm economy as well as ecological assets and impair ecosystems functioning around the world. Timely control and management of new incursions of invasive species ... 
Stochastic visual tracking with active appearance models
(Stellenbosch : University of Stellenbosch, 200912)ENGLISH ABSTRACT: In many applications, an accurate, robust and fast tracker is needed, for example in surveillance, gesture recognition, tracking lips for lipreading and creating an augmented reality by embedding a ... 
Structurefrommotion for enclosed environments
(Stellenbosch : University of Stellenbosch, 200712)A structurefrommotion implementation for enclosed environments is presented. The various aspects covered include a discussion on optimised luminance computations—a technique to compute an optimally weighted luminance ... 
A topological framework for modeling belief revision
(Stellenbosch : University of Stellenbosch, 201012)ENGLISH ABSTRACT: Classical formulations model belief revision as a deterministic process. Under certain circumstances, the process may have more than one outcome, which suggests that belief revision is nondeterministi ... 
Torsion bounds for Drinfeld modules with complex multiplication
(Stellenbosch : Stellenbosch University., 202004)ENGLISH ABSTRACT: The main objective of the present thesis is to prove an analogue for Drinfeld modules of a theorem due to Clark and Pollack. The cardinality of the group of Krational torsion points of an elliptic curve ... 
Two new combinatorial problems involving dominating sets for lottery schemes
(Stellenbosch : University of Stellenbosch, 200412)Suppose a lottery scheme consists of randomly selecting an unordered winning nsubset from a universal set of m numbers, while a player participates in the scheme by purchasing a playing set of any number of unordered ... 
A videobased traffic monitoring system
(Stellenbosch : University of Stellenbosch, 200612)This thesis addresses the problem of bulding a videobased traffic monitoring system. We employ clustering, trackiing and threedimensional reconstruction of moving objects over a long image sequence. We present an ...