Pure & Applied Mathematics (Theses and Dissertations): Recent submissions
Now showing items 21-40 of 71
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Ranges of bimodule projections and conditional expectations
(Trinity College (Dublin, Ireland). School of Mathematics, 2011)The algebraic theory of comer subrings introduced by Lam (as an abstraction of the properties of Peirce corners eRe of a ring R associated with an idempotent e E R) are investigated here in the context of Banach and ... -
Decay widths from Euclidean quantum field theory a scalar model and applications to QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2009)Lüscher provided a method by which the Euclidean correlation function, used in lattice field theories, can be used to evaluate the scattering phase shift, side-stepping the Maiani-Testa Theorem. This result is explored in ... -
A non-perturbative study of the renormalisation of action parameters in anisotropic lattice QCD with applications to finite temperature QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2009)The advantages of using anisotropic lattices, instead of the more usual isotropic lattices, in QCD simulations are well estabhshed. Anisotropic lattices can be used to increase signal resolution and allow computational ... -
Resonances and lattice field theory
(Trinity College (Dublin, Ireland). School of Mathematics, 2012)In this thesis, we look at the extraction of resonance parameters in lattice field theory. In particular we detail two major methods of dealing with resonances and consider them in a perturbative and nonpertnrbative ... -
Methods of ascent and descent in multivariable spectral theory
(Trinity College (Dublin, Ireland). School of Mathematics, 2009)In this dissertation the theory of ascent and descent for a linear operator acting on a vector space is extended to arbitrary sets of operators and applied to the study of joint spectra for finite commuting systems of bounded ... -
Efficient coding of sensory stimuli
(Trinity College (Dublin, Ireland). School of Mathematics, 2011)An important goal of mathematical neuroscience is to understand the coding principles governing the behaviour of sensory systems under stimulation. Here, we investigate the theory of efficient coding in nenral sensory ... -
A geometrical approach to spike train noise
(Trinity College (Dublin, Ireland). School of Mathematics, 2012)Mathematically, spike trains are elusive processes. They encode information, although how this information is contained in a spike train is still not clear. Same-stimulus spike trains display structural similarities, yet ... -
Sigma models of the AdS/CFT correspondence
(Trinity College (Dublin, Ireland). School of Mathematics, 2011)The thesis is dedieated to the investigation of the properties of particular two-dimensional quantum field theories, i.e. sigma-models with target space of the form AdS5 x S5γ and AdS4 x CP3. The main results of the thesis ... -
The associative filtration of the dendriform operad
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)The associative filtration of the dendriform operad Norah Mohammed Alghamdi A dendriform algebra is a vector space V with two binary operations denoted < and > that satisfy the following three algebraic properties for all ... -
Extending geometric discretisation
(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 ... -
Aspects of Chern-Simons theory
(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 ... -
Comparing the excitations of the periodic flux tube with effective string models.
(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 ... -
Large scale parallel network simulation
(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 ... -
Multidimensional second order generalised stochastic processes on locally compact Abelian groups
(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 ... -
Black holes and string theory : selected topics
(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, ... -
Quality improvement using Alexander moves
(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 ... -
Logarithmic asymptotics in Queueing Theory and Risk Theory
(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 ... -
On the Symanzik improvement of gradient flow observables
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)The gradient flow provides a new class of renormalised observables which can be measured with high precision in lattice simulations. This is relevant for many interesting applications. However, such applications are made ... -
A formulation of discrete differential geometry applied to fermionic lattice field theory and its implications for chiral symmetry
(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 ... -
A theoretical study of spin filtering and its application to polarizing antiprotons
(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 ...
