Doctoral Degrees (Mathematical Sciences)
Recent Submissions
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Nevanlinna Theory and Rational Values of Meromorphic Functions
(Stellenbosch : University of Stellenbosch, 2019-04)ENGLISH ABSTRACT: In this thesis, we are concerned with the problem of counting algebraic points of bounded height and degree on graphs of certain transcendental holomorphic and meromorphic functions. Adopting a Nevanlinna ... -
Drinfeld modular forms of higher rank from a lattice-oriented point of view
(Stellenbosch : Stellenbosch University., 2020-04)ENGLISH ABSTRACT: Please refer to full text for abstract -
Torsion bounds for Drinfeld modules with complex multiplication
(Stellenbosch : Stellenbosch University., 2020-04)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 K-rational torsion points of an elliptic curve ... -
Weighted centrality, and a further approach to categorical commutativity
(Stellenbosch : Stellenbosch University, 2019-12)ENGLISH ABSTRACT: We investigate weighted commutators, that is, weighted subobject commutator and weighted normal commutator, as well as commutators in the sense of Huq, Higgins, Ursini and Smith, which are all special ... -
Concrete foundations of the theory of Noetherian forms
(Stellenbosch : Stellenbosch University, 2019-12)ENGLISH ABSTRACT: This thesis concerns certain investigations in abstract algebra that bring together the ideas of the category of algebraic structures and the lattice of substructures. A central notion in such investigation ... -
Contributions to the theory of Beidleman near-vector spaces
(Stellenbosch : Stellenbosch University, 2019-12)ENGLISH SUMMARY: (Please refer to the abstract on the full text for symbols that did not translate well into this abstract). The study of nearfields was started in 1905 by L.E. Dickson. This thesis is a first step toward ... -
An algebraic framework for reasoning about privacy
(Stellenbosch : University of Stellenbosch, 2016-03)ENGLISH ABSTRACT: In this thesis, we study a formal programming language and algebraic tech-niques to analyse computational systems that considers data confidentiality and hidden computations. The reasoning techniques are ... -
Mathematical models of Ebola virus disease with socio-economic dynamics
(Stellenbosch : Stellenbosch University, 2019-04)ENGLISH ABSTRACT : West Africa hosted the deadliest Ebola virus disease epidemic from 2013 to 2016 and one of the common characteristics of the affected countries is their status of being developing countries. Poor ... -
A categorical approach to lattice-like structures
(Stellenbosch : Stellenbosch University, 2018-12)ENGLISH ABSTRACT : This thesis is a first step in a categorical approach to lattice-like structures. Its central notion, that of a majority category, relates to the category of lattices, in a similar way as Mal’tsev ... -
On the inducibility of rooted trees
(Stellenbosch : Stellenbosch University, 2018-12)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 ... -
Analysis of tree spectra
(Stellenbosch : Stellenbosch University, 2018-12)ENGLISH ABSTRACT : We study the set of eigenvalues (spectrum) of the adjacency matrix, Laplacian matrix and the distance matrix of trees. In particular, we focus on the distribution of eigenvalues in the spectra of large ... -
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 ... -
The eco-evolutionary dynamics of complex adaptive food webs
(Stellenbosch : Stellenbosch University., 2017-12)ENGLISH ABSTRACT: Predator-prey interactions are ubiquitous since almost every species on earth participates in at least one predator-prey interaction. As a result, they shape the food web structure, the functioning ... -
Mathematical Modelling of Tumour-Immune Interactions and Cancer Therapy
(Stellenbosch : Stellenbosch University, 2017-12)ENGLISH ABSTRACT : The immune system plays a key role against the development and progression of tumor cells mainly because of its capability of recognizing and destroying cancerous cells. While incredible research efforts ... -
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 ...
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