Department of Mathematical Sciences

Recent Submissions

  • DSaaS : a cloud service for persistent data structures 

    Le Roux, Pierre Bernard; Kroon, Steve; Bester, Willem (Institute for Systems and Technologies of Information, 2016-04)
    In an attempt to tackle shortcomings of current approaches to collaborating on the development of structured data sets, we present a prototype platform that allows users to share and collaborate on the development of ...

  • 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 ...

  • Modelling of the invasion dynamics of plasmodium falciparum merozoites into red blood cells 

    Meiring, Maynard (Stellenbosch : Stellenbosch University, 2016-03)
    ENGLISH ABSTRACT : BACKGROUND The physiological symptoms of P. falciparum infection are associated with a 48 hour replication cycle whereby parasites (merozoites) invade susceptible red blood cells (RBCs), develop and ...

  • 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 ...

  • On the validity of evolutionary models with site-specific parameters 

    Scheffler, Konrad; Murrell, Ben; Pond, Sergei L. Kosakovsky (PLoS, 2014-04-10)
    Evolutionary models that make use of site-specific parameters have recently been criticized on the grounds that parameter estimates obtained under such models can be unreliable and lack theoretical guarantees of convergence. ...

  • Modelling the transmission of Buruli ulcer in fluctuating environments 

    Assan, Belthasara (Stellenbosch : Stellenbosch University, 2015-12)

  • On commutativity and lie nilpoten y in matrix algebras 

    Sehoana, Mahlare Gerald (Stellenbosch : Stellenbosch University, 2015-12)
    ENGLISH ABSTRACT : In this thesis we first discuss the proof by Mirzakhani [9] of Schur's Theorem which gives the maximum number of linearly independent matrices in a commutative algebra of n×n matrices over a field F. An ...

  • Spectral radii of matrices associated with graphs 

    Dadedzi, Kenneth (Stellenbosch : Stellenbosch University, 2015-12)

  • Calibration and Model Risk in the Pricing of Exotic Options Under Pure-Jump Lévy Dynamics 

    Mboussa Anga, Gael (Stellenbosch : Stellenbosch UniversityStellenbosch University, 2015-12)
    AFRIKAANSE OPSOMMING : Die groeiende belangstelling in kalibrering en modelrisiko is ’n redelik resente ontwikkeling in finansiële wiskunde. Hierdie proefskrif fokusseer op hierdie sake, veral in verband met die prysbepaling ...

  • Analytic methods in combinatorial number theory 

    Baker, Liam Bradwin (Stellenbosch : Stellenbosch University, 2015-12)
    ENGLISH ABSTRACT : Two applications of analytic techniques to combinatorial problems with number-theoretic flavours are shown. The first is an application of the real saddle point method to derive second-order asymptotic ...

  • 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 ...

  • Modelling Drug Abuse and Drug-related Crime: A Systems Approach 

    Coetzee, Lezanie (Stellenbosch : Stellenbosch University, 2015-12)
    ENGLISH ABSTRACT : In this study we look at the syndemic of substance abuse and drug-related crime in the Western Cape province of South Africa. The intent of this study is to provoke critical thinking about the possibilities ...

  • Modelling the role of HIV and its treatment in non-Hodgkin lymphoma growth dynamics 

    Aogo, Rosemary Akinyi (Stellenbosch : Stellenbosch University, 2015-12)

  • Modelling the potential role of control strategies on Ebola virus disease dynamics 

    Njankou, Sylvie Diane Djiomba (Stellenbosch : Stellenbosch University, 2015-12)
    ENGLISH ABSTRACT : The most deadly Ebola disease epidemic ever was still ongoing as of June 2015 in West Africa. It started in Guinea, where the first cases were recorded in March 2014. Control strategies, aiming at ...

  • Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments 

    Gatyeni, Siphokazi Princess (2015-12)
    ENGLISH ABSTRACT : Substance abuse is a major problem globally with immeasurable consequences to the health of users. Rehabilitation is one of the strategies that can help to fight against substance abuse. It is divided ...

  • Unlocking patterns of nature - the marriage of mathematics and ecology 

    Hui, Cang (Stellenbosch : Stellenbosch University, 2015-03)
    Professor Cang Hui was born in the ancient capital of China, Xi’an, where the Terracotta Warriors were unearthed. In 1994, he went to Xi’an Jiaotong University, a C9 League, and obtained his BSc in applied mathematics ...

  • On the effciency of code-based steganography 

    Ralaivaosaona, Tanjona Fiononana (Stellenbosch : Stellenbosch University, 2015-03)
    ENGLISH ABSTRACT: Steganography is the art of hiding information inside a data host called the cover. The amount of distortion caused by that embedding can influence the security of the steganographic system. By secrecy ...

  • Quantitative Risk Management and Pricing for Equity Based Insurance Guarantees 

    Leboho, Nakedi Wilson (Stellenbosch : Stellenbosch University, 2015-03)
    ENGLISH ABSTRACT : Equity-based insurance guarantees also known as unit-linked annuities are annuities with embedded exotic, long-term and path-dependent options which can be categorised into variable and equity indexed ...

  • Building Interest Rate Curves and SABR Model Calibration 

    Mbongo Nkounga, Jeffrey Ted Johnattan (Stellenbosch : Stellenbosch University, 2015-03)
    ENGLISH ABSTRACT : In this thesis, we first review the traditional pre-credit crunch approach that considers a single curve to consistently price all instruments. We review the theoretical pricing framework and introduce ...

  • The Levy-LIBOR model with default risk 

    Walljee, Raabia (Stellenbosch : Stellenbosch University, 2015-03)
    ENGLISH ABSTRACT : In recent years, the use of Lévy processes as a modelling tool has come to be viewed more favourably than the use of the classical Brownian motion setup. The reason for this is that these processes provide ...

  • 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 ...

  • Heath–Jarrow–Morton models with jumps 

    Alfeus, Mesias (Stellenbosch : Stellenbosch University, 2015-03)
    ENGLISH ABSTRACT : The standard-Heath–Jarrow–Morton (HJM) framework is well-known for its application to pricing and hedging interest rate derivatives. This study implemented the extended HJM framework introduced by ...

  • Bifibrational duality in non-abelian algebra and the theory of databases 

    Weighill, Thomas (Stellenbosch : Stellenbosch University, 2014-12)
    ENGLISH ABSTRACT: In this thesis we develop a self-dual categorical approach to some topics in non-abelian algebra, which is based on replacing the framework of a category with that of a category equipped with a functor ...

  • A no-arbitrage macro finance approach to the term structure of interest rates 

    Thafeni, Phumza (Stellenbosch : Stellenbosch University, 2015-03)
    ENGLISH ABSTRACT: This work analysis the main macro-finance models of the term structure of interest rates that determines the joint dynamics of the term structure and the macroeconomic fundamentals under no-arbitrage ...

  • Analysing ranking algorithms and publication trends on scholarly citation networks 

    Dunaiski, Marcel Paul (Stellenbosch : Stellenbosch University, 2014-12)
    ENGLISH ABSTRACT: Citation analysis is an important tool in the academic community. It can aid universities, funding bodies, and individual researchers to evaluate scientific work and direct resources appropriately. With ...

  • Modelling the dynamics of alcohol and methamphetamine co-abuse in the Western Cape Province of South Africa 

    Orwa, Titus Okello (Stellenbosch : Stellenbosch University, 2014-12)
    ENGLISH ABSTRACT: Clinical results have indicated that abuse of multiple drugs/substances has devastating health and social consequences. The combined abuse of alcohol and the highly addictive methamphetamine has worsened ...

  • The risk parity approach to asset allocation 

    Galane, Lesiba Charles (Stellenbosch : Stellenbosch University, 2014-12)
    ENGLISH ABSTRACT: We consider the problem of portfolio's asset allocation characterised by risk and return. Prior to the 2007-2008 financial crisis, this important problem was tackled using mainly the Markowitz mean-variance ...

  • 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 ...

  • Virtual world accessibility: a multitool approach 

    Kruger, Rynhardt Pieter (Stellenbosch : Stellenbosch University, 2014-12)
    ENGLISH ABSTRACT: Computer-based virtual worlds are increasingly used for activities which previously required physical environments. However, in its mainstream form, such a virtual world provides output on a graphical ...

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