Radial basis functions are well known for their applications in scattered data approximation and interpolation. They can also be applied in collocation methods to solve partial differential equations. We develop and analyse a mesh-free discretization method for Darcy's problem. …
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In 2004 an inner city primary school, Hawksridge, found itself in the 99th percentile in mathematics and second to bottom nationally. Confronted with a plethora of local authority and National Strategy intensive programmes, which the school did not have the capacity to execute o…
The adhesive interactions between cells and surfaces play a key role in many vital physiological processes, such as the innate immune response or wound healing, but also in targeted drug delivery and active control on the adhesion of viruses. Adhesion is often mediated by specif…
An element \(\char{cmti10}{0x78}\) of a Lie algebra \(\char{cmmi10}{0x4c}\) over the field \(\char{cmmi10}{0x46}\) is extremal if [\(\char{cmti10}{0x78}\), [\(\char{cmti10}{0x78}\), \(\char{cmmi10}{0x4c}\)]] \(\subseteq\)\(\char{cmmi10}{0x46}\)\(\char{cmti10}{0x78}\). One can de…
Let \(\char{cmmi10}{0x54}\) : \(\char{cmmi10}{0x58}\) → \(\char{cmmi10}{0x58}\) be a function from a countably infinite set \(\char{cmmi10}{0x58}\) to itself. We consider the following problem: can we put a structure on \(\char{cmmi10}{0x58}\) with respect to which \(\char{cmmi1…
In this work, we look at the dynamics of four different spaces, the interval, the unit circle, subshifts of finite type and compact countable sets. We put our emphasis on chaotic dynamical system and exhibit sufficient conditions for the system on the interval, the unit circle a…
The interaction between hosts and parasites in bird populations has been studied extensively. I use game theoretic methods to model this interaction. This has been done previously but has not been studied taking into account the detailed sequential nature of this game. I introdu…
Let Ω ⊂ Rn be a bounded Lipschitz domain and consider the energy functional F[u, Ω] := ∫ Ω F(∇u(x)) dx, over the space Ap(Ω) := {u ∈ W 1,p(Ω, Rn): u|∂Ω = x, det ∇u> 0 a.e. in Ω}, where the integrand F : Mn×n → R is quasiconvex, sufficiently regular and satisfies a p-coercivity a…
The aim of the thesis is to classify certain geometric structures, called arcs, in a particular setting, namely the projective plane of order seventeen. The main computing tool is the mathematical programming language GAP. First, subsets of the line PG(1; 17) are classiffied. Th…
Functions in finite dimensional spaces are, in general, not smooth enough to be differentiable in the classical sense and “recovered” versions of their first and second derivatives must be sought for certain applications. In this work we make use of recovered derivatives for app…
In this thesis we investigate a model for biological pattern formation during growth development. The pattern formation phenomenon is described by a reaction-diffusion system on a time-dependent domain. We prove the global existence of solutions to reaction-diffusion systems on …
This thesis aims to introduce and analyse a primal-dual active set strategy for solving Allen-Cahn variational inequalities. We consider the standard Allen-Cahn equation with non-local constraints and a vector-valued Allen-Cahn equation with and without non-local constraints. Ex…
The objective of this thesis is to carry out a survival analysis for patients with breast cancer. Using data from the Nanakaly and Hewa hospitals in the cities of Erbil and Suleimaniah, respectively, cases where there is hidden censoring on survival time were investigated. The a…
This study has investigated the relationship between elderly poverty and their labour force participation based on the Egyptian Household Observatory Survey - Round 7 dataset (IDSC, 2010). I have considered two methodological problems that plague many existent researches, endoge…
This dissertation has investigated the use of multigrid methods in certain classes of optimization problems, with emphasis on structural, namely topology optimization. We have investigated the solution bound constrained optimization problems arising in discretization by the fini…
In this thesis we study ergodicity and metastability of solutions to the stochastic quantisation equation of the P2Euclidean Quantum Field theory. The main difficulty arises from the fact that solutions of this equation can be interpreted only in a renormalised sense and classic…
This thesis addresses the use of probabilistic predictive modelling and machine learning for quantifying uncertainties. Predictive modelling makes inferences of a process from observations obtained using computational modelling, simulation, or experimentation. This is often achi…
This research is mainly concerned with numerical optimisation techniques applied to general non-linear econometric simultaneous equations systems. The method of estimation used is maximum likelihood. An estimation program which applies gradient-type procedures, specifically the …
First chapter of my thesis reviews recent developments in the theory and practice of volatility measurement. We review the basic theoretical framework and describe the main approaches to volatility measurement in continuous time. In this literature the central parameter of inter…