Aspects of Minimality in Abelian Groups

This thesis investigates those abelian groups which are minimal with respect to certain quasi-orders defined on Abk, the category of abelian groups of a given infinite cardinality k. Six such quasi-orders are defined and groups which are minimal with respect to these quasi-orders are called either quasi-minimal, with the associated concepts of purely and directly quasi-minimal groups, or simple minimal with the corresponding associated groups. A complete characterisation is derived for the quasi-minimal groups and, assuming GCH, for the purely quasi-minimal groups. Moreover, it is shown that the direct quasi-minimality of a group may be undecidable in ZFC. In the minimal case, consideration of torsion groups can be reduced to that of p-groups, and a criterion for the minimality of a p-group is found in terms of its Ulm invariants. The minimality of various classes of torsion free groups is determined. In particular, a characterisation in terms of their critical typesets is found for all finite rank and for large classes of infinite rank completely decomposable groups. Sever equivalent conditions are given for the minimality of general separable groups. The minimality of mixed groups is also investigate, particularly those of torsion-free rank 1

An Cuardach ar Infreastruchtur Pobail - Bhainistithe Athleimneach in Eirinn

This presentation explores the search for resilient community infrastructure provision. Chun Straitéis Chomhtháite a fhorbairt d’Éireann, teastaíonn: Smaoineamh Nuálach, Teicneolaíochtaí Inbhuanaithe agus Athléimneach, Leasú ar churaclam oideachais, Gníomhaíocht Rialtais agus Phobail Comhordaithe, •Tuiscint do bháisteach agus fuíolluisce mar acmhainní luachmhara

Calculation of the K→πl+l- rare kaon decay amplitude using lattice quantum chromodynamics

The K→πl+l- decay is a flavor changing neutral current process which is forbidden at tree level in the Standard Model and instead occurs as a second-order electroweak process. This suppression causes the decay to be sensitive to potential New Physics, however the decay channels are dominated by long-distance contributions which require non-perturbative methods of investigation. The details of a lattice calculation on a 483x96 zMöbius domain wall fermion action, with near-physical pion and kaon masses, Mπ ∼ 140 MeV and MK ∼ 500 MeV respectively, will be presented in this thesis. The challenges that occur when evaluating four-point correlation functions which include two effective operators, that are required to study second-order electroweak processes, will be discussed. These challenges include extracting unphysical intermediate states that grow exponentially in the Euclidean-space correlators, the ultra-violet divergence that occurs when the operators approach each other and the extrapolation to the physical charm quark mass needed to deal with this divergence. A comparison of different methods of creating quark propagators, the All-to-All method and using Coulomb gauge-fixed wall sources, will also be presented, showing that the All-to-All method is not suited for a study of this type of decay. The form factor V(z) for the K→πl+l- decay, where z = q2/MK2 and q is difference in the 4-momenta of the kaon and pion, is found to be V(z) = -0.8(5.9) for z = 0.0151(5). The large error on this result, that leads to our calculation of V(z) being consistent with zero, stems from a statistical decorrelational between the single-propagator traces of physical light- and charm-quarks. This statistical decorrelational will be presented along with a discussion on how it may be tackled in the future

Isospin-breaking corrections to light leptonic decays in lattice QCD+QED at the physical point

We report on the physical-point RBC/UKQCD calculation of the leading isospin-breaking corrections to light-meson leptonic decays. This is highly relevant for future precision tests in the flavour physics sector, in particular the first-row unitarity of the Cabibbo-Kobayashi-Maskawa matrix containing the elements $V_{us}$ and $V_{ud}$. The simulations were performed using Domain-Wall fermions for $2+1$ flavours, and with isospin-breaking effects included perturbatively in the path integral through order $\alpha$ and $(m_u - m_d)/\Lambda _{\mathrm{QCD}}$. We use QED$_{\mathrm{L}}$ for the inclusion of electromagnetism, and discuss here the non-locality of this prescription which has significant impact on the infinite-volume extrapolation.Comment: Proceedings for The 39th International Symposium on Lattice Field Theory, 8th-13th August, 2022, Rheinische Friedrich-Wilhelms-Universit\"at Bonn, Bonn, German

Joint multi-field T1 quantification for fast field-cycling MRI

Acknowledgment This article is based upon work from COST Action CA15209, supported by COST (European Cooperation in Science and Technology). Oliver Maier is a Recipient of a DOC Fellowship (24966) of the Austrian Academy of Sciences at the Institute of Medical Engineering at TU Graz. The authors would like to acknowledge the NVIDIA Corporation Hardware grant support.Peer reviewedPublisher PD

Myth or Memory? Recollections of Penal Times in Irish Folklore

Stories of priests being hunted down and murdered at Mass Rocks by priest catchers and soldiers during the Penal era in Ireland persist to the present day. Using Ó Ciosáin’s (2004) tripartite taxonomy of memory this paper explores the reasons why these images continue to dominate and reflect persecuted nature of Catholicism

Use of contrast agents with fast field-cycling magnetic resonance imaging

Fast Field-Cycling (FFC) MRI allows the magnetic field to be switched during an imaging scan. FFC-MRI can be used to exploit a characteristic of contrast agents, i.e. the variation of its spin-lattice relaxation time (T1) or rate (R1= 1/T1) with magnetic field in order to increase contrast. Contrast agents play an essential role in MRI, allowing improved diagnosis and delineation of diseased tissue. However, the R1, and hence the effectiveness of contrast agents, varies significantly with magnetic field. Thus, Fast Field-Cycling (FFC) MRI can be used to take advantage of this variation to improve image contrast, allowing more sensitive detection of the agent. In this project new contrast agents, developed by a collaborating group (Invento S.r.l., Italy) were investigated for use with FFC-MRI. R1 dispersion curves of samples containing a range of contrast agents were first obtained using both a commercial relaxometer and a home-built whole-body FFC-MRI system, and the accuracy of the home-built FFC-MRI system was verified. The magnetisation behaviour of these samples during field-cycling pulse sequences was modelled in order to predict the pulse sequence parameters necessary for maximum T1 contrast. Images were obtained, using a number of novel imaging techniques developed on the home-built whole-body FFC-MRI system, and also, using standard T1 weighted imaging on a 3 T Philips clinical MRI scanner. A new FFC-MRI imaging method, ΔR1 mapping was employed to show an increase in contrast using a novel Mn2+ based liposomal contrast agent compared with T1 weighted images at 5 mT, 59 mT and 3 T. The low concentrations of Mn2+ based liposomal contrast agents used with ΔR1 mapping indicate suitability for molecular imagingEThOS - Electronic Theses Online ServiceGBUnited Kingdo