Philosophiae Doctor - PhD / In a category C with a proper (E; M)-factorization system for morphisms, we further investigate categorical topogenous structures and demonstrate their prominent role played in providing a uni ed approach to the theory of closure, interior and neighbourhood operators. We then introduce and study an abstract notion of C asz ar's syntopogenous structure which provides a convenient setting to investigate a quasi-uniformity on a category. We demonstrate that a quasi-uniformity is a family of categorical closure operators. In particular, it is shown that every idempotent closure operator is a base for a quasi-uniformity. This leads us to prove that for any idempotent closure operator c (interior i) on C there is at least a transitive quasi-uniformity U on C compatible with c (i). Various notions of completeness of objects and precompactness with respect to the quasi-uniformity de ned in a natural way are studied. The great relationship between quasi-uniformities and closure operators in a category inspires the investigation of categorical quasi-uniform structures induced by functors. We introduce the continuity of a C-morphism with respect to two syntopogenous structures (in particular with respect to two quasi-uniformities) and utilize it to investigate the quasiuniformities induced by pointed and copointed endofunctors. Amongst other things, it is shown that every quasi-uniformity on a re ective subcategory of C can be lifted to a coarsest quasi-uniformity on C for which every re ection morphism is continuous. The notion of continuity of functors between categories endowed with xed quasi-uniform structures is also introduced and used to describe the quasi-uniform structures induced by an M- bration and a functor having a right adjoint.

A. Ádám conjectured that for any non-acyclic digraph D, there exists an arc whose reversal reduces the total number of cycles in D. In this thesis we characterize and identify structure common to all digraphs for which Ádám's conjecture holds. We investigate quasi-acyclic digraphs and verify that Ádám's conjecture holds for such digraphs. We develop the notions of arc-cycle transversals and reversal sets to classify and quantify this structure. It is known that Ádám's conjecture does not hold for certain infinite families of digraphs. We provide constructions for such counterexamples to Ádám's conjecture. Finally, we address a conjecture of Reid [Rei84] that Ádám's conjecture is true for tournaments that are 3-arc-connected but not 4-arc-connected.

I examine the effect analysts have on the price response to earnings announcements. To address this question, I exploit an exogenous shock to analyst coverage to show that, following the loss of an analyst, the market reaction to earnings announcements decreases. In cross-sectional analyses, I show that the magnitude of the negative effect is decreasing in information asymmetry and the likelihood that a firm’s earnings are used more for contracting purposes. I further show that the magnitude of the negative effect is increasing in the readability of the financial statements and financial reporting comparability. This study contributes to the literature by providing a deeper understanding of the effect analysts have on the pricing of information contained in earnings announcements. As such, the results of this study should be of interest to regulators, researchers, and investors.

This study compared the effectiveness, in terms of mathematical achievement and mathematics self-efficacy, of online homework to textbook homework over an entire semester for 145 students enrolled in multiple sections of college algebra at a large community college. A quasi-experimental, posttest design was used to analyze the effect on mathematical achievement, as measured by a final exam. A pretest-posttest design was used to analyze the effect on mathematics self-efficacy, as measured by the Mathematics Self-efficacy Scale. The control group completed their homework using the textbook and the treatment group completed similar homework using an online homework system developed by the textbook publisher. All class sections followed a common syllabus, schedule, and homework list and completed a common, departmental final exam. Classroom observations were also used as a way to establish the similarity between groups. The results of the study found that while the treatment group generally scored higher on the final exam, no significant difference existed between the mathematical achievement of the control and treatment groups. Both the control and treatment group did experience significant improvements in their mathematics self-efficacy, but neither group demonstrated more improvement than the other. When students were divided based on incoming math skill level, analysis showed that low-skilled students who used online homework exhibited significantly higher mathematical achievement than low-skilled students who used textbook homework. Exploratory analysis also showed that more students with low incoming skill levels and more repeating students received a passing grade when using online homework than did their higher-skilled, first-time counterparts, although the differences were not significant. Based on this study it appears as if online homework is just as effective as textbook homework in helping students learn college algebra and in improving students' mathematics self-efficacy. Online homework may be even more effective for helping the large population of college algebra students who enroll in the course with inadequate prerequisite math skills. Instructors and researchers should consider the possibility that online homework can successfully help certain populations of students develop understanding better than traditional approaches. This study has implications for mathematics instructors and for online homework system developers.

High-dimensional integrals arise in a variety of areas, including quantum physics, the physics and chemistry of molecules, statistical mechanics and more recently, in financial applications. In order to approximate multidimensional integrals, one may use Monte Carlo methods in which the quadrature points are generated randomly or quasi-Monte Carlo methods, in which points are generated deterministically. One particular class of quasi-Monte Carlo methods for multivariate integration is represented by lattice rules. Lattice rules constructed throughout this thesis allow good approximations to integrals of functions belonging to certain weighted function spaces. These function spaces were proposed as an explanation as to why integrals in many variables appear to be successfully approximated although the standard theory indicates that the number of quadrature points required for reasonable accuracy would be astronomical because of the large number of variables. The purpose of this thesis is to contribute to theoretical results regarding the construction of lattice rules for multiple integration. We consider both lattice rules for integrals over the unit cube and lattice rules suitable for integrals over Euclidean space. The research reported throughout the thesis is devoted to finding the generating vector required to produce lattice rules that have what is termed a low weighted discrepancy . In simple terms, the discrepancy is a measure of the uniformity of the distribution of the quadrature points or in other settings, a worst-case error. One of the assumptions used in these weighted function spaces is that variables are arranged in the decreasing order of their importance and the assignment of weights in this situation results in so-called product weights . In other applications it is rather the importance of group of variables that matters. This situation is modelled by using function spaces in which the weights are general . In the weighted settings mentioned above, the quality of the lattice rules is assessed by the weighted discrepancy mentioned earlier. Under appropriate conditions on the weights, the lattice rules constructed here produce a convergence rate of the error that ranges from O(n−1/2) to the (believed) optimal O(n−1+δ) for any δ gt 0, with the involved constant independent of the dimension.

This research examines active labour market policy, and in particular, training schemes targeted towards unemployed individuals who are the most disadvantaged in the labour market in Aotearoa/New Zealand. The purpose of this research is to first, highlight the main tensions between the current policy frameworks for the design and the practice of such training. The second purpose is to offer explanations for these tensions by highlighting the competitive free-market and rational individualistic assumptions that underpin the current frameworks and, in particular, how these constrain the 'choices' and possibilities for the most disadvantaged unemployed. The study identifies and examines State Active Neoliberalism, as a specific place-time articulation of neoliberalism, adopted by two successive Labour-led governments in New Zealand from 1999-2005. Thirdly, a community development theoretical framework is proposed to underpin recommendations that could support more enabling and empowering policies for the most disadvantaged unemployed and the organisations that seek to assist them. The thesis draws on case studies of major State-funded training schemes for long-term unemployed individuals to illustrate the 'on-the-ground' consequences of the discursive shifts in policy rhetoric. This research combines an in-depth, qualitative field research approach with a critical analysis of policy frameworks and political representations of unemployment, training and labour market issues in documents, publications and communications. The findings of this research are that a competitive quasi-market for training provision and the increased reliance on narrow outcome measurements, position commercial imperatives ahead of assisting the most disadvantaged unemployed. In order to remain viable, training organisations are increasingly faced with the need to sacrifice social motivations for commercial survival. This situation erodes the scope, at the local level, for services that are relevant to the various needs and circumstances of disadvantaged unemployed people. While the overarching policy discourses maintain that training schemes serve the needs of the most disadvantaged unemployed, policy mechanisms and competitive labour market contexts undermine such objectives. Not only are the most disadvantaged unemployed people frequently unable to access services claiming to be for their benefit, they are by definition less likely to succeed in the context of competitive labour markets and individualised society.

Whilst smaller pitches have become the norm in junior football, they may still be too large for certain ages and levels of skill. To date there has been no research into the relationships between size of the pitch and the technical kicking ability (distance and accuracy) of young players (8 - 14 years of age). The purpose of this investigation was to examine variables that influence actual kicking distance and accuracy and also to measure what differences in play behaviour (passing and dribbling) emerge from self-selected changes in pitch size for different age groups (9 and 10 years of age). Data were collected on 120 (N=120) junior football players: Playing experience (M=2.85 years, SD=2.56), Height (M=1.44 m, SD=1.08), Weight (M=37.8 kg, SD=7.69), Lengths of lower limbs (knee/ankle: M=35.54 cm, SD=4.27; hip/knee: M=35.54 cm, SD=5.25), Step lengths (M=37.66 cm, SD=8.693), Estimated kicking distance (M=31.13 m, SD=16.63). Participants performed a series of three kicks along the ground, using the inside of the foot, and aiming for a target (25 m away). The distance (M=18.04 m; SD=6.56) and accuracy (M=8.32 m; SD=4.38) of each kick were measured. The children (9 and 10 years of age) were then assigned to teams and asked to construct a small-sided game on two different pitch sizes. The first pitch size used was the recommended regulation size. The second pitch size was self-selected by the players. Any changes to the playing dimensions (e.g., width of the pitch) and playing behaviours (e.g., total number of passes, dribbling) were measured and analysed. Kicking distance is best predicted by the player’s height (20.0%, P < 0.000), or a combination of the player’s height and estimated kicking distance (30.0%, P = 0.002). Kicking accuracy can be attributed to the influence of the player’s step lengths (8.1%, P = 0.016) and both their step lengths and estimated kicking distance (15.1%, P = 0.020). Furthermore, our findings demonstrate that the increase in pitch size (18.5% and 25%) resulted in a greater amount of dribbling (63% and 33%) and passing (12%). In general, our results support the idea that young children in New Zealand should be playing on a pitch and at a skill level which matches their football abilities. Grouping young players on a pitch according to their physical (e.g., height) and technical kicking ability (e.g., distance, accuracy) instead of their chronological age, seems to be the key factor to any other set of proposals. The findings of this thesis have important messages that could enhance the effectiveness of coaching, competitive game-play (pitch sizes) and consequently performance at all junior levels of football in New Zealand. Further research should manipulate the number of players per team to see if this factor affects competitive game-play in junior football. Additionally, the mean distances maintained between players in the same team (team-mates) during game play needs to be considered (with regard to the ‘beehive effect’). Further studies should examine different age groups of equivalent skill level and assess their performance in relation to their technical kicking ability on different pitches.

This thesis investigates the major errors and processes affecting the performance of a viable, standalone point positioning technique known as single frequency Precise Point Positioning (PPP). The PPP processing utilises both single frequency code and carrier phase GPS observables. The mathematical model implemented is known as the code and quasi-phase combination. Effective measures to improve the quality of the positioning solutions are assessed and proposed. The a priori observations sigma (or standard deviation) ratio in the sequential least squares adjustment model plays a significant role in determining the accuracy and precision of the estimated solutions, as well as the solutions convergence time. An

Sur les espaces de modules de différentielles abéliennes existe une action naturelle de SL(2,R). Ses orbites, appelées disques de Teichmüller, se projettent dans les espaces de modules de surfaces de Riemann sur des géodésiques complexes. En tirant en arrière la forme dz du tore standard par des revêtements ramifiés au-dessus d'un seul point, on obtient les surfaces à petits carreaux, points entiers des espaces de modules de différentielles abéliennes. Nous étudions en détail les disques de Teichmüller des points entiers de l'espace des modules des différentielles abéliennes en genre deux avec un zéro double: nombre de disques de Teichmüller pour chaque nombre de carreaux, et leur géométrie; propriétés algébriques des stabilisateurs (sous-groupes de SL(2,Z) qui ne sont pas de congruence); comportement asymptotique des constantes de Siegel-Veech (coefficients des taux de croissance quadratiques des géodésiques fermées) lorsque le nombre de carreaux tend vers l'infini.

Cette habilitation est consacrée aux structures algébriques intervenant dans les systèmes uni- et bi-dimensionnels étudiés en physique. Nous y montrons comment ces structures peuvent être utilisées pour obtenir une meilleure compréhension des systèmes physiques qu'elles sous-tendent. Nous y décrivons aussi certains de leurs aspects mathématiques.<br /><br />Quatre parties composent cette présentation. Elles décrivent différents domaines de la physique que j'ai étudiés, et dans lesquels les cadres algébriques peuvent s'appliquer, à savoir:<br /><br />- Les théories conformes à deux dimensions, en particulier les algèbres W. Nous présentons la classification de ces dernières et leur quantification en cohomologie BRS.<br /><br />- Les algèbres W finies et leur application en physique (anyons et leurs généralisations) et en mathématique (représentations des algèbres de Lie).<br /><br />- Les structures d'algèbres de Hopf et leur généralisation dynamique, cadre mathématique utilisé dans la partie suivante.<br /><br />- Les systèmes intégrables, avec deux éclairages différents. D'une part, les chaînes de spins, qui décrivent des modèles unidimensionnels de spins en interaction. Nous parlerons des systèmes périodiques, et des systèmes avec bords. D'autre part, les systèmes intégrables en théorie des champs, avec une attention particulière aux systèmes avec bord ou avec impureté.