Portfolio optimization involves the optimal assignment of limited capital to different available financial assets to achieve a reasonable trade-off between profit and risk objectives. Markowitz’s mean variance (MV) model is widely regarded as the foundation of modern portfolio t…
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In this thesis we study the neutron transport (Boltzmann transport equation) which is used to model the movement of neutrons inside a nuclear reactor. More specifically we consider the mono-energetic, time independent neutron transport equation. The neutron transport equation ha…
A Josephson junction is formed by sandwiching a non-superconducting material between two superconductors. If the phase difference across the superconductors is zero, the junction is called a conventional junction, otherwise it is unconventional junction. Unconventional Josephson…
This thesis starts from the following observation; if v;w are solutions of y" + Py = 0 where P is entire, and v and w are both 0 at z0 ε C, then W(v,w) = vw' - v'w ≡ 0 and v,w are linearly dependent. It is then natural to ask what happens if v;w solve different equations, but ha…
To each pair of characters (χ,ψ) on a Fuchsian group of the first kind we associate a space of functions generalizing the space of second--order cusp forms. We determine the dimensions of these spaces and construct explicit bases. We separate two cases according to the weight. T…
When fluid droplets coalesce, the flow is initially controlled by a balance between surface tension and viscosity. For low viscosity fluids such as water, the viscous lengthscale is quickly reached, yielding a new balance between surface tension and inertia. Numerical and asympt…
Drying is an old traditional method of removing liquid from inside material, suchas wood, food, paper, ceramics, building materials, textiles, granular products, pharmaceutical and electronic devices. The kinetics of this liquid removal depends on the material properties of the …
Ca2+ is an important messenger which mediates several physiological functions, including muscle contraction, fertilisation, heart regulation and gene transcription. One major way its cytosolic level is raised is via a G-protein coupled receptor (GPCR)- mediated release from intr…
In this thesis, exact and semiclassical approaches are derived for predicting wave energy distributions in coupled cavities with variable material properties. These approaches are attractive because they can be extended to more complex built-up systems. For the exact treatment, …
We investigate the canonical BRST–quantisation and refined algebraic quantisation within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling constraints with nonconstant functions on the configuration space. The quantum …
UNIFORM algebras have been extensively investigated because of their importance in the theory of uniform approximation and as examples of complex Banach algebras. An interesting question is whether analogous algebras exist when a complete valued field other than the complex numb…
The Nikolaevskiy equation is considered as a simple model exhibiting spatiotemporal chaos due to the coupling of finite-wavelength patterns to a long-wavelength mode (Goldstone mode). It was originally proposed as a model for seismic waves and is also considered as a model for v…
This thesis deals with a detailed linear analysis for a two-component reaction-diffusion system with constant diffusion coefficients. A comprehensive linear stability analysis results in three types of instabilities: (1) stationary periodic instability, (2) oscillatory uniform a…
In this thesis, we present Kohn variational calculations of scattering and annihilation parameters for very low energy interactions of positrons with molecular hydrogen. Our analysis includes the first application of the Kohn method for this system in which the interelectronic p…
This thesis examines various aspects of time series and their applications. In the rst part, we study numerical and asymptotic properties of Box-Pierce family of portmanteau tests. We compare size and power properties of time series model diagnostic tests using their asymptotic …
This thesis considers the statistical analysis of diffusion tensor imaging (DTI). DTI is an advanced magnetic resonance imaging (MRI) method that provides a unique insight into biological microstructure \textit{in vivo} by directionally describing the water molecular diffusion. …
Distributive laws in Computer Science are rules governing the transformation of one programming structure into another. In programming, they are programs satisfying certain formal conditions. Their importance has been to date documented in several isolated cases by diverse forma…
A bearing chamber may be modelled as a horizontal cylinder, stationary or rotating about its axis, with a film of fluid coating the inside of the cylinder wall. The impact of droplets from a two-phase flow in the core of the chamber drives the motion of the oil film. In this the…
Some real-world applications involve situations where different physical phenomena acting on very different time scales occur simultaneously. The partial differential equations (PDEs) governing such situations are categorized as "stiff" PDEs. Stiffness is a challenging property …