Department of Mathematical Sciences
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The seesaw effect of winter temperature change on the recruitment of cotton bollworms Helicoverpa armigera through mismatched phenology
(John Wiley & Sons Ltd., 2015)Knowing how climate change affects the population dynamics of insect pests is critical for the future of integrated pest management. Rising winter temperatures from global warming can drive increases in outbreaks of some ...
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An optimal proportion of mixing broad-leaved forest for enhancing the effective productivity of moso bamboo
(John Wiley & Sons Ltd., 2015-03-17)Moso bamboos (Phyllostachys edulis) are important forestry plants in southern China, with substantial roles to play in regional economic and ecological systems. Mixing broad-leaved forests and moso bamboos is a common ...
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Ultraproducts and Los’s Theorem: A Category-Theoretic Analysis
(Stellenbosch : Stellenbosch University, 2017-03)ENGLISH ABSTRACT : Ultraproducts are an important construction in model theory, especially as applied to algebra. Given some family of structures of a certain type, an ultraproduct of this family is a single structure ...
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Imaginaries in dense pairs of real-closed fields
(Stellenbosch : Stellenbosch University, 2017-03)ENGLISH ABSTRACT : Imaginaries are definable equivalence classes, which play an important role in model theory. In this thesis, we are interested in imaginaries of dense pairs of real-closed fields. More precisely, we ...
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Immune biomarker reference range estimation for healthy paediatric patients in South Africa
(Stellenbosch : Stellenbosch University, 2017-03)ENGLISH ABSTRACT : Understanding and quantifying human peripheral blood T-lymphocyte immunophenotypes is necessary for the diagnosis and treatment of immune and haematological disorders. This is only possible if comparison ...
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Thermodynamics analysis of variable viscosity hydromagnetic Couette flow in a rotating system with Hall effects
(MDPI, 2015-11-20)In this paper, we employed both first and second laws of thermodynamics to analyze the flow and thermal decomposition in a variable viscosity Couette flow of a conducting fluid in a rotating system under the combined ...
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Whole body modelling of glucose metabolism in malaria patients
(Stellenbosch : Stellenbosch University, 2017-03)
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The double Heston model via filtering methods
(Stellenbosch : Stellenbosch University, 2016-12)ENGLISH ABSTRACT : Stochastic volatility models are well-known for their ability to generate a volatility smile for financial securities. The development of the stochastic volatility models followed shortly after the ...
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An integrated framework modelling susceptibility to tuberculosis in homogeneous and admixed populations
(Stellenbosch : Stellenbosch University, 2016-12)ENGLISH ABSTRACT : In spite of the wide variety of anti-tuberculosis drugs, tuberculosis (TB), caused by mycobacterium tuberculosis (MTB), is the second leading infectious disease after Human Immunode ciency Virus (HIV) ...
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Elliptic curve cryptography
(Stellenbosch : Stellenbosch University, 2016-12)ENGLISH ABSTRACT : In this thesis we present a selection of Diffie-Hellman cryptosystems, which were classically formulated using the multiplicative group of a finite field, but which may be generalised to use other group ...
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A mathematical model for onchocerciasis and its treatment with ivermectin
(Stellenbosch : Stellenbosch University, 2016-12)ENGLISH ABSTRACT : Onchocerciasis is a human disease that is caused by the filirial worm Onchocerca volvulus. It occurs close to oxygen rich flowing streams and rivers in the inter-tropical zones. The disease is a serious ...
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Geometry of Complex Polynomials: On Sendov's Conjecture
(Stellenbosch : Stellenbosch University, 2016-12)ENGLISH ABSTRACT : Sendov’s conjecture states that if all the zeroes of a complex polynomial P(z) of degree at least two lie in the unit disk, then within a unit distance of each zero lies a critical point of P(z). In a ...
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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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Computational and theoretical analysis of human diseases associated with infectious pathogens
(Hindawi, 2015)Mathematical models and computer simulations are useful experimental tools for building and testing theories, assessing quantitative conjectures, answering specific questions, determining sensitivities to changes in parameter ...
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DSaaS : a cloud service for persistent data structures
(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 ...
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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 ...
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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 ...
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Modelling of the invasion dynamics of plasmodium falciparum merozoites into red blood cells
(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 ...
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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 ...
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On the validity of evolutionary models with site-specific parameters
(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. ...
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Modelling the transmission of Buruli ulcer in fluctuating environments
(Stellenbosch : Stellenbosch University, 2015-12)
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On commutativity and lie nilpoten y in matrix algebras
(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 ...
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Spectral radii of matrices associated with graphs
(Stellenbosch : Stellenbosch University, 2015-12)
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Calibration and Model Risk in the Pricing of Exotic Options Under Pure-Jump Lévy Dynamics
(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 ...
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Analytic methods in combinatorial number theory
(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 ...
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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 ...
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Modelling Drug Abuse and Drug-related Crime: A Systems Approach
(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 ...
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Modelling the role of HIV and its treatment in non-Hodgkin lymphoma growth dynamics
(Stellenbosch : Stellenbosch University, 2015-12)
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Modelling the potential role of control strategies on Ebola virus disease dynamics
(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 ...
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Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments
(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 ...
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