Doctoral Degrees (Mathematical Sciences)
Recent Submissions
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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 ... -
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 ... -
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 ... -
The eco-evolutionary dynamics of mutualistic networks: from pattern of emergence to stability
(Stellenbosch : Stellenbosch University, 2016-03)ENGLISH ABSTRACT: Mutualistic interactions, such as the interactions between flowering plants and their pollinators are ubiquitous in nature. A community in which members are involved in multiple mutualistic interactions ... -
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
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