Doctoral Degrees (Mathematical Sciences)


Recent Submissions

  • Refinable vector splines and multi-wavelets with shortest matrix filters 

    Ranirina, Dinna (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 

    Goosen, Gerrit (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 

    Durant, Kevin (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 

    Misanantenaina, Valisoa Razanajatovo (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 

    Oosthuizen, Joubert (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 

    Masuret, Jacques (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 

    Ramiharimanana, Nantsoina Cynthia (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 

    Abdalla, Abdurahman Masoud (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 

    Benjamin, Ronalda Abigail Marsha (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 

    Prodinger, Helmut (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 

    Bekele, Bewketu Teshale (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 

    Razafindramahatsiaro, Tovondrainy Christalin (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 

    Okoth, Isaac Owino (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 

    Njagarah, Hatson John Boscoh (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 

    Bamunoba, Alex Samuel (Stellenbosch : Stellenbosch University, 2014-12)
    ENGLISH ABSTRACT: See pdf for abstract

  • Spreading waves of invasive species 

    Ramanantoanina, Andriamihaja (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 

    Basson, Dirk Johannes (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 

    Ssebuliba, Doreen (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 

    Razafindrakoto, Ando Desire (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 

    Cloete, Maret (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 ...

  • Modelling the control of tsetse and African trypanosomiasis through application of insecticides on cattle in Southeastern Uganda 

    Kajunguri, Damian (Stellenbosch : Stellenbosch University, 2013-03)
    ENGLISH ABSTRACT: In Uganda, cattle are an important reservoir of Trypanosoma brucei rhodesiense, a parasite that causes human African trypanosomiasis or sleeping sickness. We developed mathematical models to examine the ...

  • An analogue of the Andre-Oort conjecture for products of Drinfeld modular surfaces 

    Karumbidza, Archie (Stellenbosch : Stellenbosch University, 2013-03)
    ENGLISH ABSTRACT: This thesis deals with a function eld analog of the André-Oort conjecture. The (classical) André-Oort conjecture concerns the distribution of special points on Shimura varieties. In our case we consider ...

  • Mathematical modelling on interaction between malaria parasites and the host immune system 

    Marijani, Theresia (Stellenbosch : Stellenbosch University, 2012-12)
    Please refer to full text for abstract.

  • Spectral theory in commutatively ordered banach algebras 

    Muzundu, Kelvin (Stellenbosch : Stellenbosch University, 2012-12)
    ENGLISH ABSTRACT: See full text.

  • Improved models of biological sequence evolution 

    Murrel, Benjamin (Stellenbosch : Stellenbosch University, 2012-12)
    ENGLISH ABSTRACT: Computational molecular evolution is a field that attempts to characterize how genetic sequences evolve over phylogenetic trees – the branching processes that describe the patterns of genetic inheritance ...

  • Comparative analysis of predictive equations for transfer processes in different porous structures 

    Woudberg, Sonia (Stellenbosch : Stellenbosch University, 2012-12)
    ENGLISH ABSTRACT: Research on transfer processes in various types of porous media has become important for the optimization of high technology engineering devices and processes. In this study the micro-structural parameters ...

  • Dreieckverbande : lineare und quadratische darstellungstheorie 

    Wild, Marcel Wolfgang (University of Zurich, 1987-05)
    ABSTRACT: A linear representation of a modular lattice L is a homomorphism from L into the lattice Sub(V) of all subspaces of a vector space V. The representation theory of lattices was initiated by the Darmstadt school ...

  • Integration of multifunctions with respect to a multimeasure 

    Brink, Harry Edward (Stellenbosch : Stellenbosch University, 1999-12)
    ENGLISH SUMMARY: The main objective of this thesis is to define and investigate the properties of the integral of a multifunction F (where F is from a point set T into a Banach space X) with respect to a multimeasure M ...

  • On the numerical evaluation of finite-part integrals involving an algebraic singularity 

    Kutt, H. R. (Helmut Richard) (Stellenbosch : Stellenbosch University, 1975-08)
    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 ...

  • Aspects of the pre- and post-selection classification performance of discriminant analysis and logistic regression 

    Louw, Nelmarie (Stellenbosch : Stellenbosch University, 1997-12)
    ENGLISH ABSTRACT: Discriminani analysis and logistic regression are techniques that can be used to classify entities of unknown origin into one of a number of groups. However, the underlying models and assumptions for ...

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