Browsing Pure & Applied Mathematics (Theses and Dissertations) by Date of Publication
Now showing items 120 of 26

Fourier analysis, multiresolution analysis and dilation equations
(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
(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 ... 
Elements of an operator calculus
(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 ... 
Random sampling and large deviations
(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 ... 
Discrete exterior calculus with applications to flows and spinors
(Trinity College (Dublin, Ireland). School of Mathematics, 2005) 
The radiation bound for a KleinGordon field on a static spherical spacetime
(Trinity College (Dublin, Ireland). School of Mathematics, 2013)We establish a wellposed Cauchy problem in Minkowski (R4, η), associated with a radiating KleinGordon 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
(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 GrossNeveu Model
(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
(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 ... 
Staticlightlight baryons : a spectroscopic study using distillation
(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 socalled alltoall ... 
Spectroscopy and scattering of mesons containing charm quarks from lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2013)We present excited spectra of mesons containing charmlight (D), charmstrange (Ds) and charmcharm (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
(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 ... 
CFTs on Riemann surfaces of genus g ≥ 1
(Trinity College (Dublin, Ireland). School of Mathematics, 2014)The purpose of this thesis is to argue that Npoint functions of holomorphic fields in rational conformal field theories can be calculated by methods from algebraic geometry. We establish explicit formulae for the 2point ... 
Interferometry and nonequilibrium noise in the fractional quantum Hall effect
(Trinity College (Dublin, Ireland). School of Mathematics, 2014)We study theoretical aspects of fractional quantum Hall devices based on tunnelling point contacts. The fractional quantum Hall effect is the prime example of a (2 + 1) dimensional system with nontrivial topological order. ... 
Cₒ(X)structure in C*algebras, multiplier algebras and tensor products
(Trinity College (Dublin, Ireland). School of Mathematics, 2015)We begin in Chapter 2 with an introduction to the various notions of a bundle of C*algebras that have appeared throughout the literature, and clarify the definitions of upper and lowersemicontinuous C*bundles not ... 
Spectral functions from lattice QCD at finite temperature
(Trinity College (Dublin, Ireland). School of Mathematics, 2015)An investigation of the bottonionium spectrum above and below the QCD deconfinement crossover temperature, Tc, was performed using a nonrelativistic treatment of the heavy quark on anisotropic lattices with Nf = 2 + 1 ... 
Spike train analysis
(Trinity College (Dublin, Ireland). School of Mathematics, 2015)This thesis focuses on the study of spike trains, the information carrying signals conveyed by neurons in the nervous system. Spiking data from songbirds from [Narayan et al., 2006] was used prominently in this thesis. ... 
A dynamical study of the chirally rotated Schrödinger functional in lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2015)In this work, we present first results from dynamical simulations of the chirally rotated Schrödinger functional (SF) in lattice QCD. More specifically, we discuss the determination of renormalization constants of ... 
The Ads/CFT spectrum via Integrabilitybased algorithms
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2017)The spectral problem of the AdS/CFT correspondence is believed to be integrable in the planar limit. The Quantum Spectral Curve captures the underlying mathematical structure in a relatively simple RiemannHilbert problem. ... 
Pionpion scattering amplitudes and timelike pion form factor from Nf=2+1 Lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2017)We study isovector pionpion scattering and extract the electromagnetic pion form factor in the timelike region from Nf = 2 + 1 Lattice QCD ensembles at a single lattice spacing and two pion masses mπ = 200MeV and mπ = ...