Doctoral Degrees (Mathematical Sciences)
Recent Submissions
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The definable (p,q)-theorem for dense pairs of certain geometric structures
(Stellenbosch : Stellenbosch University, 2021-12)ENGLISH ABSTRACT: The definable (p, q)-conjecture is a model-theoretic version of a (p, q)- theorem in combinatorics, which was expressed in the form of a question by A. Chernikov and P. Simon in 2015. Researchers have ... -
Complexity and stability of mutualistic local networks and meta-networks
(Stellenbosch : Stellenbosch UniversityStellenbosch : Stellenbosch University, 2021-03)ENGLISH ABSTRACT: Biotic interactions, either in local networks or in meta-networks, are ubiquitous in nature. Species interact with other species of different interaction strengths in the ecosystem. For example, mutualistic ... -
Theoretical study of variable viscosity nanofluids flow in microchannels
(Stellenbosch : Stellenbosch University, 2020-12)ENGLISH ABSTRACT: The study of fluid flow and heat transfer through a microchannel is an important research area due to its wide applications in engineering and industrial processes. Some practical applications include ... -
On contributions to the theory of near-vector spaces and graphs thereof
(Stellenbosch : Stellenbosch University, 2020-12)ENGLISH ABSTRACT: In this thesis, our aim is to add to the existing body of work on near-vector spaces and their representation using graphs. We introduce two new graphs for constructions of nearvector spaces using finite ... -
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: -
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 ...
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