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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 ...
  • 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 ...
  • 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 ...
  • 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 ...
  • A formulation of discrete differential geometry applied to fermionic lattice field theory and its implications for chiral symmetry 

    Watterson, Steven (Trinity College (Dublin, Ireland). School of Mathematics, 2008)
    In this thesis, we develop the Geometric Discretization formulation of Dirac-Kahler fermions. We note that the naive definition of chiral synnnetry is only approximately captured in the formulation. However, we show that ...
  • The radiation bound for a Klein-Gordon field on a static spherical spacetime 

    Collins, Michael Patrick (Trinity College (Dublin, Ireland). School of Mathematics, 2013)
    We establish a well-posed Cauchy problem in Minkowski (R4, η), associated with a radiating Klein-Gordon field ψ(x) = eztψ(xi), in curvature coordinates {xμ = t, p, θ,Φ} on a static spherically symmetric spacetime (M, g). ...
  • CR Singularities in condimension 2 

    Burcea, Valentin Daniel (Trinity College (Dublin, Ireland). School of Mathematics, 2013)
    In this thesis we study the real submanifolds of codimension 2 in a complex manifold near a CR singularity. The thesis has 3 chapters. In Chapter 1 we shall make a small introduction where we will remind some basic notions ...
  • Free Field Representation and Form Factors of the Chiral Gross-Neveu Model 

    Britton, Stephen (Trinity College (Dublin, Ireland). School of Mathematics, 2013)
    The process of using the free field representation to construct form factors of two dimensional integrable models is very promising. In this thesis, this procedure is analysed and adapted for application to the chiral ...
  • Integrable lattice models for strongly correlated electrons 

    Quinn, Eoin (Trinity College (Dublin, Ireland). School of Mathematics, 2013)
    This thesis is dedicated to the study of a new family of integrable lattice models for strongly correlated electrons, namely the Hubbard- Shastry models. The techniques of exactly solvable models, and in particular those ...
  • Static-light-light baryons : a spectroscopic study using distillation 

    Mc Elroy, Finnian (Trinity College (Dublin, Ireland). School of Mathematics, 2013)
    Over the last decade, hadron spectroscopy in lattice QCD has graduated from calculating single rows of the quark propagation matrix to calculating all elements of the quark propagation matrix - the so-called all-to-all ...
  • Spectroscopy and scattering of mesons containing charm quarks from lattice QCD 

    Moir, Graham (Trinity College (Dublin, Ireland). School of Mathematics, 2013)
    We present excited spectra of mesons containing charm-light (D), charm-strange (Ds) and charm-charm (charmoninm) combinations. We perform these spectroscopic calculations on two volumes. 16(3) X 128 and 24(3) x 128, of ...
  • Peturbative study of the Chirally Rotated Schrödinger Functionality in Lattice QCD 

    Mainar, Pol Vilascea (Trinity College (Dublin, Ireland). School of Mathematics, 2014)
    In this thesis we study the renormalisation and O(a) improvement of the Chirally Rotated Schrödinger Functional (xSF) in perturbation theory. The xSF was originally proposed in [1] as a way of rehabiliting the mechanism ...