Doctoral Degrees (Mathematical Sciences)
Recent Submissions
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Refinable vector splines and multi-wavelets with shortest matrix filters
(Stellenbosch : Stellenbosch University, 2018-03)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 ... -
Oriented 123-TQFTs via String-Nets and State-Sums
(Stellenbosch : Stellenbosch University, 2018-03)ENGLISH ABSTRACT :In a series of papers Bartlett, Douglas, Schommer-Pries, and Vicary discovered a finite generators-and-relations presentation of the oriented bordism bicategory. This simplifies the task of finding ... -
Centrality in random trees
(Stellenbosch : Stellenbosch University, 2017-12)ENGLISH ABSTRACT : We consider two notions of centrality—namely, the betweenness centrality of a node and whether or not it is a centroid—in families of simply generated and increasing trees. Both of these concepts are ... -
Properties of graph polynomials and related parameters
(Stellenbosch : Stellenbosch University, 2017-12)ENGLISH ABSTRACT : In this thesis, we investigate various problems related to graph polynomials. We first define two-variable polynomials for rooted trees and specific posets, which are motivated by the Tutte polynomial. ... -
Random walk hitting times in random trees
(Stellenbosch : Stellenbosch University, 2017-12)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 ... -
Generalised sequences and compactness notions in point-free topology
(Stellenbosch : Stellenbosch University, 2017-12)ENGLISH ABSTRACT : While sequences and naturally associated notions like convergence and clustering have received extensive attention in classical topology, the same cannot be said for the point-free setting. The aim of ... -
Solving embedding problems with bounded ramification
(Stellenbosch : Stellenbosch University, 2016-12)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 ... -
Binary closure operators
(Stellenbosch : Stellenbosch University, 2016-03)ENGLISH ABSTRACT : In this thesis we provide a new foundation to categorical closure operators, using more elementary binary closure operators on posets. The original goal of the thesis was to study a categorical closure ... -
Fredholm theory in ordered Banach algebras
(Stellenbosch : Stellenbosch University, 2016-03)ENGLISH ABSTRACT : Since its inception, Fredholm theory has become an important aspect of spectral theory. Among the spectra arising within Fredholm theory is the Weyl spectrum which has been intensively studied by several ... -
Contributions to the analysis of approximate counting
(Stellenbosch : Stellenbosch University, 2016-03)ENGLISH ABSTRACT : Approximate Counting is a classical technique with very challenging questions re- lated to its performance analysis. It is also somewhat similar to parameters around Digital Search trees. Surprising ... -
Modeling the impact of early HIV treatment on the HIV epidemic in South Africa
(Stellenbosch : Stellenbosch University, 2016-03)ENGLISH SUMMARY: Amajor international randomized clinical trial fromStrategic Timing of AntiRetroviral Treatment (START) has found that HIV-infected individuals have a considerably lower risk of developing AIDS if they ... -
On the constant reductions of valued function fields and their automorphism groups
(Stellenbosch : Stellenbosch University, 2015-11-20)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 ... -
Combinatorics of oriented trees and tree-like structures
(Stellenbosch : Stellenbosch University, 2015-03)ENGLISH ABSTRACT : In this thesis, a number of combinatorial objects are enumerated. Du and Yin as well as Shin and Zeng (by a different approach) proved an elegant formula for the number of labelled trees with respect ... -
Modelling water-borne infections : the impact of hygiene, metapopulation movements and the biological control of cholera
(Stellenbosch : Stellenbosch University, 2014-12)ENGLISH ABSTRACT: Water-borne infections have been a menace in many countries around the globe, claiming millions of lives. Cholera in particular has spread to all continents and now on its seventh epidemic. Although ... -
Arithmetic of carlitz polynomials
(Stellenbosch : Stellenbosch University, 2014-12)ENGLISH ABSTRACT: See pdf for abstract -
Spreading waves of invasive species
(Stellenbosch : Stellenbosch University, 2014-03)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 ... -
On the coefficients of Drinfeld modular forms of higher rank
(Stellenbosch : Stellenbosch University, 2014-04)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 ... -
Mathematical modelling of the effectiveness of two training interventions on infectious diseases in Uganda
(Stellenbosch : Stellenbosch University, 2013-12)ENGLISH ABSTRACT: Nurses, midwives and clinical officers referred to as Mid-level Practioners (MLPs) play an important role in the health care system especially in rural Africa. With particular reference to rural Uganda, ... -
Neighbourhood operators on Categories
(Stellenbosch : Stellenbosch University, 2013-03)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 ... -
Modelling of non-Newtonian fluid flow through and over porous media with the inclusion of boundary effects
(Stellenbosch : Stellenbosch University, 2013-03)ENGLISH ABSTRACT: Different generalized Newtonian fluids (where the normal stresses were neglected) were considered in this study. Analytical expressions were derived for time independent, fully developed velocity profiles ...
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