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  • Fourier analysis, multiresolution analysis and dilation equations 

    Malone, David (Trinity College (Dublin, Ireland). School of Mathematics, 1998)
    This thesis has essentially two parts. The first two chapters are an introduction to the related areas of Fourier analysis, multiresolution analysis and wavelets. Dilation equations arise in the context of multi resolution ...
  • Logarithmic asymptotics in Queueing Theory and Risk Theory 

    Duffy, Ken (Trinity College (Dublin, Ireland). School of Mathematics, 2000)
    This thesis addresses four distinct, but related, problems. All four involve large deviation theory. The first problem is to relate the logarithmic asymptotics of the single server queue length distribution to the long ...
  • Aspects of Chern-Simons theory 

    Prodanov, Emil Mihaylov (Trinity College (Dublin, Ireland). School of Mathematics, 2000)
    This thesis is based on 4 papers resulting from my work during my stay in the School of Mathematics, Trinity College Dublin. Each of them forms an individual part of the thesis. The relation between these parts is ...
  • Solutions to dilation equations 

    Malone, David (Trinity College (Dublin, Ireland). School of Mathematics, 2001)
    This thesis aims to explore part of the wonderful world of dilation equations. Dilation equations have a convoluted history, having reared their heads in various mathematical fields. One of the early appearances was in the ...
  • Random sampling and large deviations 

    McGurk, Brian (Trinity College (Dublin, Ireland). School of Mathematics, 2001)
    In this thesis, we are concerned with the effect of randomly sampling a stochastic process. We consider two stochastic processes: the underlying process, {Xt}tεT and the observation process {Tn}nεN, a strictly increasing ...
  • Elements of an operator calculus 

    Hughes, Arthur (Trinity College (Dublin, Ireland). School of Mathematics, 2001)
    The operational calculus developed by the Irish School of the Vienna Development Method (VDM) has a life of its own independent of its applications. This thesis is interested in the operational calculus that arose from the ...
  • Black holes and string theory : selected topics 

    Kennedy, Conall (Trinity College (Dublin, Ireland). School of Mathematics, 2001)
    This thesis is divided into three parts. In Part I the concept of holography in the context of the Maldacena conjecture and the three-dimensional black hole of Banados, Teitelboim and Zanelli (BTZ) is studied. In particular, ...
  • Extending geometric discretisation 

    Sen, Samik (Trinity College (Dublin, Ireland). School of Mathematics, 2002)
    Geometric discretisation (GD) [1] is a novel approach capable of capturing topological properties, based on a correspondence between discrete objects and operations on a triangulation with continuum ones on a manifold. We ...
  • Quality improvement using Alexander moves 

    Golden, Darach (Trinity College (Dublin, Ireland). School of Mathematics, 2003)
    The objects under consideration in this work are simplicial meshes. We are interested in the geometric shape of the constituent simplices. This interest is justified by the impact of simplicial shape on the error bounds ...
  • Multidimensional second order generalised stochastic processes on locally compact Abelian groups 

    Keville, Bernard (Trinity College (Dublin, Ireland). School of Mathematics, 2004)
    This thesis is concerned with the harmonic analysis of multidimensional generalised stochastic processes on locally compact Abelian groups. A multidimensional generalised stochastic process is a continuous linear operator ...
  • Large scale parallel network simulation 

    Lawless, Eoin (Trinity College (Dublin, Ireland). School of Mathematics, 2004)
    Simulation is one of the primary tools used in studying computer networks. However the difficulties of simulating a network grow with its size. With the hardware resources currently available it is not feasible to simulate ...
  • Discrete exterior calculus with applications to flows and spinors 

    De Beaucé, Vivien (Trinity College (Dublin, Ireland). School of Mathematics, 2005)
  • Robust layer-resolving methods for various Prandtl problems 

    Butler, John (Trinity College (Dublin, Ireland). School of Mathematics, 2005)
    In this thesis we deal with four Prandtl boundary layer problems for incompressible laminar flow. When the Reynolds and Prandtl numbers are large the solution of each problem has parabolic boundary layers. For each problem ...
  • Comparing the excitations of the periodic flux tube with effective string models. 

    Maresca, Francesca (Trinity College (Dublin, Ireland). School of Mathematics, 2005)
    The spectrum of a periodic flux tube in pure SU(3) Yang-Mills theory is evaluated non-perturbatively through computations on the lattice in the region from intermediate to long distances (1.5 < L < 4 fm ). For these flux ...
  • Methods for calculating option prices with early-exercise features 

    Cooney, Michael (Trinity College (Dublin, Ireland). School of Mathematics, 2006)
    In this dissertation we deal with two distinct methods for pricing financial options with early-exercise features. First we use finite difference methods to calculate the prices, examining in particular two new schemes ...
  • Novel methods for heavy-quark physics from lattice QCD 

    Foley, Justin (Trinity College (Dublin, Ireland). School of Mathematics, 2006)
    The application of 3+1 anisotropic lattices to numerical simulations of hadrons containing heavy quarks is investigated. It is expected that using a fine temporal lattice spacing will suppress large mass-dependent errors ...
  • Anisotropic discretisations and practical all-to-all propagators for lattice QCD 

    Ó Cais, Ailein (Trinity College (Dublin, Ireland). School of Mathematics, 2006)
    In this thesis, we concern ourselves primarily with improving the accuracy of the determination of correlation functions in lattice QCD. We detail two avenues of improvement and implement them both, separately and in ...
  • Simulated annealing of Skyrme model configurations 

    Magee, Shane (Trinity College (Dublin, Ireland). School of Mathematics, 2006)
    The Skyrme model is a topological field theory that has been shown to be a good low energy approximation to QCD. A particular quantum theoretical treatment of the model reduces the quantization to a finite-dimensional ...
  • Aspects of the mathematical theory of water waves 

    Henry, David (Trinity College (Dublin, Ireland). School of Mathematics, 2007)
    In this thesis we study various aspects of the mathematical theory of water waves. In Chapter 2 some qualitative results for two recently-derived nonlinear models for shallow water waves are presented. In the first part ...
  • A theoretical study of spin filtering and its application to polarizing antiprotons 

    O'Brien, Domhnaill (Trinity College (Dublin, Ireland). School of Mathematics, 2008)
    There has been much recent research into possible methods of polarizing an antiproton beam, the most promising being spin filtering, the theoretical understanding of which is currently incomplete. The method of polarization ...