• Completeness properties in the vector lattice C(X) 

  Afrane-Okese, Kwadwo Nyamedehyee (University of Pretoria, 2024-07-12)

  In this thesis we study certain vector lattice properties of the space $C(X)$ of continuous functions on a given topological space X. We show that C(X) is always relatively uniformly complete, and characterize those X for ...
• Finite element analysis of multi-dimensional and simplified models for beams and plates 

  Du Toit, Rudi (University of Pretoria, 2024-04-26)

  This dissertation is a literature study that investigates the validity of different linear models in application. Validity, in this context, refers to how well simplified lower-dimensional models, such as the Timoshenko ...
• Positive operators and their applications on ordered vector spaces 

  Msibi, Mxolisi (University of Pretoria, 2023)

  A vector space X is called an ordered vector space if for any elements x, y, z ∈ X and α ∈ R+, x ⪯ y implies x + z ≤ y + z and 0 ≤ x implies 0 ≤ αx. If in addition, X is a lattice, that is if for a pair {x, y} the inf{x, ...
• Measures on Boolean Algebras 

  Chamberlain, Tomas (University of Pretoria, 2023)

  This thesis deals with a number of related results on Boolean algebras. First, we prove the Stone Representation Theorem, which shows that every Boolean algebra is isomorphic to an algebra of sets, namely the clopen algebra ...
• Modelling and analysis of plant-virus interaction in the co-infection of plants 

  Matusse, Americo J. (University of Pretoria, 2023)

  Co-infection is a simultaneous multiple parasitic infection within a host, and it is very common in humans and animals. Recently, thanks to molecular tools availability, co-infection has been detected in wild plants and ...
• Analysis of hyperbolic-type partial differential equations for non-fourier type heat conduction models 

  Sieberhagen, Rheinhardt Hendrik (University of Pretoria, 2023)

  Heat transfer modelling is routinely used to model the interaction between a heat source and a material specimen in applications such as additive manufacturing and medical surgery. The Fourier heat conduction model ...
• Application of the finite element method to second order hyperbolic type partial differential equations 

  Tikane, Dipuo Constance (University of Pretoria, 2023)

  In this dissertation various models with variational forms similar to that of the wave equation are considered, i.e. second order hyperbolic type partial differential equations. These models include several linear ...
• Exploring the decay parameter for the exponentially weighted moving average volatility methodology 

  Sibanda, Sharmaine Fanuel Promise (University of Pretoria, 2023)

  Volatility estimation is a crucial task for financial institutions, as it affects various aspects of their operations, such as risk management, capital allocation, investment strategy and derivative valuation. However, the ...
• The theory of Gröbner bases and applications 

  Davies, Andrew Barnard (University of Pretoria, 2023)

  In this dissertation we explore the theory and applications of Gröbner bases, and the algorithms that allow us to compute them.
• Fragmentation-coagulation equation with growth 

  Poka, Wetsi D (University of Pretoria, 2023)

  The theory of fragmentation-coagulation equations began around 1916 with a series of papers by Smoluchowski on pure coagulation and since then continued to incorporate other processes into the model. The intention was to ...
• On groups with few 𝑝′-character degrees 

  Mabena, Lehlogonolo Shaun (University of Pretoria, 2022)

  Seitz’s theorem asserts that a finite group has exactly one non-linear irreducible character of degree greater than one if and only if the group is either an extraspecial 2-group or the group is isomorphic to a one-dimensional ...
• Application of network filtering techniques in finding hidden structures on the Johannesburg Stock Exchange 

  Gopi, Yashin (University of Pretoria, 2023)

  Researchers from the field of econophysics have favoured the idea that financial markets are a complex adaptive system, consisting of entities that behave and interact in a diverse manner, leading to non-linear, emergent ...
• Reaction diffusion modelling of bacteria colonies : microbial quiescence and chemotaxis 

  Dumani, Phindile (University of Pretoria, 2022)

  The physiological structure of microbial communities in natural environments is typically a response to changes in internal and external conditions. External conditions may include the availability or depletion of ...
• A guide to the Rado graph : exploring structural and logical properties of the Rado graph 

  Michau, Michelle (University of Pretoria, 2023)

  The Rado graph, denoted R, is the unique (up to isomorphism) countably infinite random graph. It satisfies the extension property, that is, for two finite sets U and V of vertices of R there is a vertex outside of both U ...
• Analysis of the vibration of flexible structures 

  Blecher, Tatiana Monique (University of Pretoria, 2022)

  Research on vibrations of flexible structures is ongoing in engineering and applied mathematics fields. Flexible structures in practice can be considered as systems of interconnected rod-like components. This dissertation ...
• Applications of direct and inverse limits in analysis 

  Van Amstel, Walt (University of Pretoria, 2022-11-28)

  In this dissertation, we use the categorical notions of direct and inverse limits to solve certain problems in analysis; in particular, in the field of vector lattices. Chapter 1 provides a general overview and motivation ...
• Beyond the tanh method-looking for explicit travelling wave solutions to partial differential equations 

  Maqele, Khanyisani (University of Pretoria, 2022)

  In this work, we focus on a general procedure for finding exact travelling wave solutions for evolution equations with polynomial nonlinearites. Mathematically, looking for travelling wave solutions is asking the question ...
• Invariant solutions of the Black-Scholes equation 

  Mothiba, Makoba Melidah Kholofelo (University of Pretoria, 2022)

  In this study, we discuss derivatives, Lie symmetries and invariant solutions of the Black Scholes equation. We combine the Lie group methods with the Adomian decomposition method to solve the Black and Scholes equation ...
• Semi-order units in vector lattices 

  Chitanga, Painos (University of Pretoria, 2021)

  The space C(X) of real-valued continuous functions on a topological space X is a vector lattice and a locally convex topological vector space, but what is the interaction between these structures? In the case of a compact ...
• The use of personal response systems to renegotiate the didactical contract in tertiary mathematics education 

  Bothma, Karin (University of Pretoria, 2020)

  Challenges experienced by first year students transitioning from secondary to tertiary mathematics education are examined through the lens of the didactical contract or agreement between the lecturer and students that is ...

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