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Browsing by Supervisor "Anguelov, Roumen"
Now showing items 1-15 of 15
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(University of Pretoria, 2019)In mathematical epidemiology, the threshold theory introduced by W.O. Kermack and A.G. McKendrick (1927) can be expressed in terms of the basic reproduction number R0. This is defined as the average number of secondary ...
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(University of Pretoria, 2020)Order properties are normally derived from maximum principles associated with an operator, say $P$, in classical formulation. This result is often formulated as a comparison theorem for solutions of linear elliptic PDEs ...
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(University of Pretoria, 2013-05-17)The LULU operators Ln and Un operate on neighbourhoods of size n. The Discrete Pulse Transform (DPT) of images is obtained via recursive peeling of so-called local maximum and minimum sets with the LULU operators as n ...
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(University of Pretoria, 2015)The Allee e ect is characterized by a positive relationship between population density or size and the per capita population growth rate in small populations. There are several mechanisms responsible for the Allee e ects. ...
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(University of Pretoria, 2009-06-02)In this thesis, we establish a general and type independent theory for the existence and regularity of generalized solutions of large classes of systems of nonlinear partial differential equations (PDEs). In this regard, ...
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Hausdorff continuous viscosity solutions of Hamilton-Jacobi equations and their numerical analysis (University of Pretoria, 2007)The theory of viscosity solutions was developed for certain types of nonlinear first-order and second-order partial differential equations. It has been particularly useful in describing the solutions of partial differential ...
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(University of Pretoria, 2010-08-17)The LULU operators, Ln and Un, are smoothers, that is they smooth data received as a signal. They are nonlinear and this nonlinearity makes them more robust but also more complicated to study since the projection theorem ...
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(University of Pretoria, 2016)In Mathematical Epidemiology disease free states are commonly represented as equilibria of dynamical systems which model the respective epidemiological processes. However, in cases when the equilibrium is zero and is related ...
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(University of Pretoria, 2018)Despite the increase in agricultural crop yield over the last century, the world's food supply is in grave danger, as an estimated 16% of global yield is lost to various pathogens annually. As a result, mathematical ...
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(University of Pretoria, 2007-05-15)We study the order convergence of sequences on a vector lattice. It is shown that this mode of convergence is induced by a convergence structure. One such a convergence structure is defined and its properties are studied. ...
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(University of Pretoria, 2016)The Brusselator model is widely used to illustrate and study basic features of models of chemical reactions involving trimolecular steps. We provide the necessary mathematical theory related to Reaction-Diffusion systems ...
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(University of Pretoria, 2020)General aggregation diffusion equations have been used in a variety of different settings, including the modelling of chemotaxis and the biological aggregation of insects and herding of animals. We consider a non-local ...
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(University of Pretoria, 2011)It is well known that a classical solution of the initial value problem for a scalar conservation law may fail to exist on the whole domain of definition of the problem. For this reason, suitable generalized solutions of ...
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(University of Pretoria, 2016)This thesis provides a mathematical framework for the development of efficient control strategies that satisfy the charters of Integrated Pest Management (IPM) which aims to maintain pest population at a low impact level. ...
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(University of Pretoria, 2018)The long term properties, like coexistence and extinction, are usually determined by the demographics of the competing species or other competitive advantages. In this dissertation we consider the effect of conspecific ...
Now showing items 1-15 of 15