Department of Mathematics
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Graphs of integral distance and their properties
(University of Western Cape, 2021)Understanding the geometries of points in space has been attractive to mathematicians for ages. As a model, twelve years ago, Kurz and Meyer [32] considered point sets in the m-dimensional a ne space Fmq over a nite ... -
Prestasiemotivering by studente aan die Universiteit van Wes-Kaapland.
(University of the Western Cape, 1991)The major objective of this study was to investigate the nature of the relationship between achievement motivation, autonomous and social achievement values, study habits and attitudes, locus of control and socio-economic ... -
The impact of using technology through cooperative learning on learners’ performance on grade 11 circle geometry
(University of the Western Cape, 2019-11)Euclidean geometry was recently re-introduced as a compulsory topic in the Mathematics Curriculum for learners in the Further Education and Training (FET) band in 2012. The diagnostic analysis reports on the National ... -
Model theory of algebraically closed fields and the Ax-Grothendieck Theorem
(University of Western Cape, 2020)We introduce the concept of an algebraically closed field with emphasis of the basic model-theoretic results concerning the theory of algebraically closed fields. One of these nice results about algebraically closed ... -
Measurements of edge uncolourability in cubic graphs
(University of the Western Cape, 2020)The history of the pursuit of uncolourable cubic graphs dates back more than a century. This pursuit has evolved from the slow discovery of individual uncolourable cubic graphs such as the famous Petersen graph and the ... -
Boundedness and pseudocompactness in pointfree topology
(University of Western Cape, 2019)This dissertation is a presentation to generalize boundedness and pseudocompactness in pointfree topology. We rst obtain and introduce a boundedness notion for elements of a frame. This is then further inspiration to ... -
Estimating the cost of deposit insurance for a commercial bank following an optimal investment strategy
(University of Western Cape, 2020)Commercial banks play a dominant role in facilitating the economic growth of a country by acting as an intermediary between the de cit spending unit (borrowers) and the surplus spending unit (lenders). In particular, ... -
The paradox of enrichment in predator-prey systems
(University of Western Cape, 2020)In principle, an enrichment of resources in predator-prey systems show prompts destabilisation of a framework, accordingly, falling trophic communication, a phenomenon known to as the \Paradox of Enrichment" [54]. After ... -
Fractional black-scholes equations and their robust numerical simulations
(University of the Western Cape, 2020)Conventional partial differential equations under the classical Black-Scholes approach have been extensively explored over the past few decades in solving option pricing problems. However, the underlying Efficient Market ... -
Ultrafilters and Compactification
(UWC, 2020)In this thesis, we construct the ultrafilter space of a topological space using ultrafilters as points, study some of its properties and describe a method of generating compactifications through the ultrafilter space. As ... -
Mathematical modeling of TB disease dynamics in a crowded population.
(University of the Western Cape, 2020)Tuberculosis is a bacterial infection which is a major cause of death worldwide. TB is a curable disease, however the bacterium can become resistant to the first line treatment against the disease. This leads to a disease ... -
Efficient Variable Mesh Techniques to solve Interior Layer Problems
(University of Western Cape, 2020)Singularly perturbed problems have been studied extensively over the past few years from different perspectives. The recent research has focussed on the problems whose solutions possess interior layers. These interior ... -
High Accuracy Fitted Operator Methods for Solving Interior Layer Problems
(University of the Western Cape, 2020)Fitted operator finite difference methods (FOFDMs) for singularly perturbed problems have been explored for the last three decades. The construction of these numerical schemes is based on introducing a fitting factor ... -
Robust numerical methods to solve differential equations arising in cancer modeling
(University of the Western Cape, 2020)Cancer is a complex disease that involves a sequence of gene-environment interactions in a progressive process that cannot occur without dysfunction in multiple systems. From a mathematical point of view, the sequence ... -
Fractional Black-Scholes equations and their robust numerical simulations
(University of Western Cape, 2020)Conventional partial differential equations under the classical Black-Scholes approach have been extensively explored over the past few decades in solving option pricing problems. However, the underlying Efficient Market ... -
Design, analysis and simulation of a robust numerical method to solve Zika virus models
(University of the Western Cape, 2019)This thesis deals with the analysis and robust simulation of mathematical models describing Zika virus disease. Some background information about the occurrences of this disease and most recent literature indicating some ... -
Stochastic modeling of an HIV/AIDS epidemic with treatment
(University of the Western Cape, 2019)The HIV/AIDS epidemic continues to be among the most devastating diseases in human history despite the new scientific advances and serious public health interventions. The greatest burden of HIV/AIDS is still in sub-Saharan ... -
Valuation of options for hedging against exchange rate exposure
(University of the Western Cape, 2019)The risk associated with currency exposure is one of the main sources of risk in terms of internationally diversi ed portfolios. Controlling the risk is important for improving the performance of international investments. ... -
Quasi-uniform and syntopogenous structures on categories
(University of the Western Cape, 2019)In a category C with a proper (E; M)-factorization system for morphisms, we further investigate categorical topogenous structures and demonstrate their prominent role played in providing a uni ed approach to the theory ... -
Robust computational methods to simulate slow-fast dynamical systems governed by predator-prey models
(University of the Western Cape, 2019)Numerical approximations of multiscale problems of important applications in ecology are investigated. One of the class of models considered in this work are singularly perturbed (slow-fast) predator-prey systems which ...
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