We present a joint optical/X-ray analysis of the massive galaxy cluster Abell 2744 (z = 0.308). Our strong- and weak-lensing analysis within the central region of the cluster, i.e. at R < 1 Mpc from the brightest cluster galaxy, reveals eight substructures, including the main core. All of these dark matter haloes are detected with a significance of at least 5 sigma and feature masses ranging from 0.5 to 1.4 x 10(14) M-circle dot within R < 150 kpc. Merten et al. and Medezinski et al. substructures are also detected by us. We measure a slightly higher mass for the main core component than reported previously and attribute the discrepancy to the inclusion of our tightly constrained strong-lensing mass model built on Hubble Frontier Fields data. X-ray data obtained by XMM-Newton reveal four remnant cores, one of them a new detection, and three shocks. Unlike Merten et al., we find all cores to have both dark and luminous counterparts. A comparison with clusters of similar mass in the Millennium XXL simulations yields no objects with as many massive substructures as observed in Abell 2744, confirming that Abell 2744 is an extreme system. We stress that these properties still do not constitute a challenge to Lambda cold dark matter, as caveats apply to both the simulation and the observations: for instance, the projected mass measurements from gravitational lensing and the limited resolution of the subhaloes finders. We discuss implications of Abell 2744 for the plausibility of different dark matter candidates and, finally, measure a new upper limit on the self-interaction cross-section of dark matter of sigma(DM) < 1.28 cm(2) g(-1) (68 per cent CL), in good agreement with previous results from Harvey et al.

Cosmological constraints from galaxy clusters rely on accurate measurements of the mass and internal structure of clusters. An important source of systematic uncertainty in cluster mass and structure measurements is the secure selection of background galaxies that are gravitationally lensed by clusters. This issue has been shown to be particular severe for faint blue galaxies. We therefore explore the selection of faint blue background galaxies, by reference to photometric redshift catalogues derived from the Cosmological Evolution Survey (COSMOS) and our own observations of massive galaxy clusters at z similar or equal to 0.2. We show that methods relying on photometric redshifts of galaxies in/behind clusters based on observations through five filters, and on deep 30-band COSMOS photometric redshifts are both inadequate to identify safely faint blue background galaxies with the same 1 per cent contamination level that we have achieved with red galaxies. This is due to the small number of filters used by the former, and absence of massive galaxy clusters at redshifts of interest in the latter. Nevertheless, our least contaminated blue galaxy sample yields stacked weak-lensing results consistent with our previously published results based on red galaxies, and we show that the stacked clustercentric number density profile of these faint blue galaxies is consistent with expectations from consideration of the lens magnification signal of the clusters. Indeed, the observed number density of blue background galaxies changes by similar to 10-30 per cent across the radial range over which other surveys assume it to be flat.

The dark matter paradigm has been a great source of speculation in both the 20th and 21st Centuries. Since its proposed existence in 1933, the mounting evidence has led to this theoretical particle becoming one of the greatest mysteries of modern physics. However, despite its dominant presence in the Universe, little is known about its nature and how it behaves. In this thesis I critically analyse one particular property of dark matter: the self-coupling. The self-interacting dark matter paradigm hypothesises that dark matter is not collisionless as assumed in most cosmological simulations, and in-fact has some probability that it will scatter off itself. Such a self-coupling will resolve many discrepancies that exist between observations and theory, particularly on small, non-linear scales. Moreover, any detection of a self-interaction cross-section will place considerable limitations on the acceptable particle physics models of dark matter and hence has grown to become an important question. In this thesis I develop and implement a method to constrain the self-interaction cross-section of dark matter that exploits continually accreting and merging groups of galaxies as they fall into galaxy clusters. Utilising the ubiquitous nature of accreting substructure, I measure the offsets between dark matter and baryonic gas as they become separated due to their differing interaction properties. Studying this effect over a sample of events, I will be able to make the first ever statistical estimate of the cross-section of dark matter, while averaging over many different unknown merging scenarios. I begin my thesis by deriving an analytical description of sub-halo in-fall, allowing me to constrain dark matter self-interaction models directly from observations. In this study, I find that current archival data should be able to detect a difference in the dynamical behaviour of dark matter and standard model particles at 6σ, and measure the total interaction cross-section σDM/m with 68% confidence limits of ±1 cm2g-1. Having constructed a new method to derive constraints on the cross-section of dark matter I carry out a study into the potential systematics that may affect a measurement. I determine the accuracy of weak gravitational lensing, which is the distortion of light due to intervening mass, as a tool to estimate the positions of substructure in galaxy clusters. I find that the public Lenstool software can measure the position of individual 1:5 x 1013Mʘ peaks with ~ 0:3" systematic bias, as long as they are at least ~ 30" from the cluster centre. Finally, I develop a pipeline that can analyse a sample of inhomogeneous observations from The Hubble Space Telescope and the Chandra X-ray Observatory. By measuring the positions of dark matter, gas and galaxies for 68 individual merging events, from a total of 28 galaxy clusters, I detect a 7:4σ offset between gas and an unobserved dark mass. I make the first ever measurement of cross-section of dark matter from a sample of clusters finding σDM < 0:50cm2/g [95% CL], the best constraints to date. In addition to this I find that the brightest group galaxy in-fact tends to lead the dark matter halo during merging events. Although evidence for the existence of interacting dark matter, I conclude that the astrophysics of the BCG is complicated, and that this apparent directional bias should be considered in all galaxy cluster analyses. Moreover, I show that this technique is easily extendable for future surveys that have larger samples of galaxy clusters, with constraints of σDM < 0:001cm2/g potentially attainable.

The goal of this thesis is to give an exposition of the following recent result of Freeman, Lennard, Odell, Turett and Randrianantoanina. A Banach space has the Schur property if and only if every weakly compact set is contained in the closed convex hull of a weakly null sequence. This result complements an old result of Grothendieck (now called the Grothendieck Compactness Principle) stating that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. We include many of the relevant definitions and preliminary results which are required in the proofs of both of these theorems.

The purpose of this study is to explore the important factors that affect graduate employment such as human capital, social capital and university career services. It focuses on the graduate labour market in the UK and uses mixed methods. While quantitative data derive from a survey, qualitative data come from interviews and secondary sources in a case study. The survey includes 947 university graduates and qualitative data consist of 8 interviews, internal and external reports. The findings show that the level of human capital and social capital affect the way graduates find a job and the use of social capital in job searches varies by ethnicity, age and academic level. However, gender and academic discipline do not affect the use of social capital in the UK graduate labour market. Moreover, the study shows that university career services can play an important role in job searches. Overall, however, direct application and online career services are two most widely used methods to find a job. The originality of the research is twofold. Firstly, it illustrates the relationship between two important components in graduates’ job search processes: human capital and social capital. Secondly, it examines the role of an institution: university career services and displays the importance of institutional approaches in building a bridge between students and employers.

This thesis concentrates on stochastic programming problems based on empirical and theoretical distributions and their relationship. Firstly, it focuses on the case where the empirical distribution is an independent random sample. The basic properties are shown followed by the convergence between the problem based on the empirical distribution and the same problem applied to the theoretical distribution. The thesis continues with an overview of some types of dependence - m-dependence, mixing, and also more general weak dependence. For sequences with some of these types of dependence, properties are shown to be similar to those holding for independent sequences. In the last section, the theory is demonstrated using numerical examples, and dependent and independent sequences, including sequences with different types of dependence, are compared.

Title: Modules with a minimal generating set Author: Michal Hrbek Department: Department of Algebra Supervisor: Mgr. Pavel Růžička, Ph.D., Department of Algebra Abstract: By a minimal generating set of a module we mean a subset which generates the module but any of its proper subsets does not. If the module is not finitely generated, an existence of a minimal generating set is not guaranteed. We say that a module is weakly based if it has a minimal generating set. In the presented thesis, we provide a characterization of weakly based modules over Dedekind domains. As an application of this, we show that the class of weakly based modules is not closed under extensions and the complement of this class is not closed under finite direct sums. Also, we show an example of an abelian group which is weakly based if and only if CH holds. Then we treat rings such that all modules are weakly based. We prove that a Baer regular ring has this property if and only if it is semisimple, and we show that any ℵ0-noetherian commutative semiartinian ring has this property. Final part of the text concerns the problem of Nashier and Nichols - does any generating set of any module over a perfect ring contain a minimal generating set? Keywords: module, minimal generating set, weak basis 1

In this thesis we cover the dynamics of the macro magnetic transformations (spin avalanches) in crystals of molecular nanomagnets, also known as magnetic deflagration and detonation. Taking a single-molecule Hamiltonian, we calculate the dependence of Zeeman energy and the activation energy as a function of an external magnetic field at different angles relative to the easy axis of the crystal. Using quantum mechanical calculations, we show that the energy levels of the molecule exhibit complex behavior in presence of a transverse component of the magnetic field. For an arbitrarily aligned magnetic field, the energy levels do not arrange in a simple "double-well" manner. We extend existing theoretical models by generalizing the Zeeman energy for a wide range of magnetic fields and its different orientations. We obtain a new type of front instability in magnetization-switching media. Due to the dipole-dipole interaction between the molecules magnetic instability results to the front banding and change in the front propagation velocity. The magnetic instability has a universal physical nature similar to the Darrieus-Landau instability. The instability growth rate and the cutoff length are calculated for the spin avalanches in the crystals of nanomagnets. Finally, we investigate the internal structure of the magnetic detonation front. We calculate the continuous shock profile using the transport processes of the crystal such as thermal conduction and volume viscosity. Such an approach can be applied to any weak shock wave in solids. Zero volume viscosity leads to an isothermal jump, i.e., the temperature changes continuously while the pressure and the density experience discontinuity. The analysis has shown that the volume viscosity plays a major role in the formation of the detonation front.

As the community land trust (CLT) movement in the United States approaches its 50th anniversary, CLT members, practitioners and researchers are exploring and pushing the boundaries of the model. CLTs offer an alternative model of land use tenure that permanently removes properties from the speculative market for the ongoing common good of the community. Most frequently associated with the provision of affordable housing in strong real estate markets, several CLTs across the country are now expanding into the commercial realm. This thesis compares the incipient commercial development efforts underway in St. Paul, Minnesota and New Orleans, Louisiana in order to better understand the potential role of CLTs in helping communities preserve and create commercial assets under a wide range of market forces.

[pt] Referências fracas e finalizadores constituem uma alternativa elegante para se obter controle sobre a interação entre a aplicação e o coletor de lixo. No entanto, em alguns contextos, finalizadores são desnecessários, pois é possível estender o mecanismo de referências fracas a fim de dar suporte a finalização. Neste trabalho, realizamos um estudo detalhado sobre os usos desses mecanismos e mostramos como é possível substituir finalizadores por referências fracas propondo uma implementação baseada em referências fraca para cada uso de finalizadores. Baseado nesse estudo, desenvolvemos um mecanismo de finalização via referências fracas para a linguagem Lua. Motivados por nossa proposta de uma maior exploração do mecanismo de referências, desenvolvemos um algoritmo para um importante problema relacionado a ciclos em tabelas fracas, uma estrutura criada a partir de referências fracas. A existência de referências cíclicas entre chaves e valores impede que os elementos que compõem o ciclo sejam coletados, mesmo que eles não sejam mais utilizados pelo programa. Isso acaba dificultando o uso de tabelas fracas em determinadas aplicações. A linguagem Haskell resolveu esse problema através de uma adaptação do mecanismo de ephemerons ao seu coletor de lixo. Partindo desse fato, modificamos a implementação do coletor de lixo de Lua para que este oferecesse suporte ao mecanismo de ephemerons. Dessa forma, pudemos eliminar o problema de ciclos em tabelas fracas nessa linguagem. / [en] Weak References and finalizers constitute an elegant alternative to obtain control over the interaction between the application and the garbage collector. However, in some contexts, finalizers are not necessary because it`s possible to extend the weak reference mechanism in order to give support to finalization. In this work, we present a survey of the most common uses of these mechanisms. We also show how weak references can replace finalizers proposing a weak reference based implementation for each finalizer use. Based on this survey, we developed a finalization mechanism based on weak references for the Lua programming language. Motivated by our proposal of a better exploration of the weak reference mechanism, we developed a solution for an important problem related to cycles on weak tables, an structure created using weak references. Cyclic references between keys and values prevents the elements inside the cycle from being collected, even if they are no more reachable. This ends up bringing difficulties to the use of weak tables in certain kinds of applications. The Haskell programming language solved this problem implementing an adaptation of a mechanism called ephemerons. Based on this fact, we modified the Lua garbage collector in order to offer support to ephemerons. As a result, we were able to solve the problem of cycles on weak tables in Lua.