School Mathematics, Statistics and Computer Science
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Recent Submissions
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New families of exact solutions for compact stars.
(2018)In this thesis we present new families of exact solutions to the Einstein and Einstein- Maxwell eld equations which are relevant in the description of highly compact stellar objects. We rst impose a linear equation of ... -
Gender classification using facial components.
(2018)Gender classification is very important in facial analysis as it can be used as input into a number of systems such as face recognition. Humans are able to classify gender with great accuracy however passing this ability ... -
Mathematical and numerical analysis of the discrete fragmentation coagulation equation with growth, decay and sedimentation.
(2018)Fragmentation-coagulation equations arise naturally in many branches of engineering and science, the applications stretching from astrophysics, blood clotting, colloidal chemistry and polymer science to molecular beam ... -
A comparative study of metaheuristics for blood assignment problem.
(2018)The Blood Assignment Problem (BAP) is a real world and NP-hard combinatorial optimization problem. The study of BAP is significant due to the continuous demand for blood transfusion during medical emergencies. However, ... -
Semi-tetrad decomposition of spacetime with conformal symmetry.
(2018)In this thesis, we study the kinematical and dynamical properties of a general spacetime that admits a conformal Killing vector. A 1+1+2 decomposition of the spacetime is performed using the fluid 4-velocity and a preferred ... -
First integrals for spherically symmetric shear-free perfect fluid distributions.
(2018)In this dissertation we study spherically symmetric shear-free spacetimes. In particular we analyse the integrability of and find exact solutions to the Emden- Fowler equation yxx = f(x)y2; which is the master equation ... -
Bounds on the extremal eigenvalues of positive definite matrices.
(2018)The minimum and maximum eigenvalues of a positive de nite matrix are crucial to determining the condition number of linear systems. These can be bounded below and above respectively using the Gershgorin circle theorem. ... -
Modelling of artificial intelligence based demand side management techniques for mitigating energy poverty in smart grids.
(2018)This research work proposes an artificial intelligence (AI) based model for smart grid initiatives (for South Africa and by extension sub-Saharan Africa, (SSA)) and further incorporates energy justice principles. Spanning ... -
Evaluation of single and multiple missing data imputation techniques: a comparative application on BMI data.
(2017)Missing data are a common occurrence in various fields of data science and statistics. The research into missing data is one of the most important topics in applied statistics, especially in academic, government and ... -
Solutions of the Volterra integro-differential equation.
(2018)Integro-di erential equations has found extensive applications in the eld of engineering, sciences and mathematical modelling of various physical and biological phenomena. In this thesis we focus on the Volterra type ... -
Star formation as a function of environment in the MeerKAT Galaxy Clusters Legacy Survey.
(2023)Probing the star formation (SF) activity of cluster galaxies paves an important path towards the understanding of cluster evolution. This thesis presents the study of star formation rates (SFR) in clusters using ... -
Study of singularly perturbed models and its applications in ecology and epidemiology.
(2017)In recent years the demand for a more accurate description of real life processes and advances in experimental techniques have resulted in construction of very complex mathematical models, consisting of tens, hundreds, if ... -
Tracing star formation in groups and filaments around a young active galaxy cluster at z ∼ 1.46.
(2022)Abstract available in PDF. -
An assessment of the component-based view for metaheuristic research.
(2023)Several authors have recently pointed to a crisis within the metaheuristic research field, particularly the proliferation of metaphor-inspired metaheuristics. Common problems identified include using non-standard ... -
Policy optimisation and generalisation for reinforcement learning agents in sparse reward navigation environments.
(2021)Sparse reward environments are prevalent in the real world and training reinforcement learning agents in them remains a substantial challenge. Two particularly pertinent problems in these environments are policy optimisation ... -
The evolution of galaxies in Sunyaev-Zel’dovich selected galaxy clusters from ACT DR5.
(2023)Abstract available in PDF. -
Investigation of the South African public TVET colleges’ engineering official mathematics curriculum for entry level artisans.
(2023)One of the main objectives of any mathematics curriculum is to equip students with the necessary thinking skills for real-world problems. As the world evolves every day of our lives, so do the people living in it. ... -
New exact solutions for neutral and charged shear-free relativistic fluids.
(2022)We study shear-free gravitating fluids in general relativity. We first analyse the integrability of the Emden-Fowler equation that governs the behaviour of shear-free neutral perfect fluid distributions. We find a new ... -
Fixed point approach for solving optimization problems in Hilbert, Banach and convex metric spaces.
(2023)In this thesis, we study the fixed point approach for solving optimization problems in real Hilbert, Banach and Hadamard spaces. These optimization problems include the variational inequality problem, split variational ... -
Iterative approximations of certain nonlinear optimization, generalized eqilibrium and fixed point problems in Hilbert and Banach spaces.
(2023)In this thesis, in the framework of Banach spaces, we study several iterative methods for finding the solutions of many important problems in fixed point theory and optimization. Some of these include the equilibrium ...
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