Essa dissertação trata de geometria simplética e suas aplicações, apresentando conceitos tais como o gradiente simplético e também o teorema de Darboux. Discutimos a formulação Lagrangeana da mecânica, apresentando as equações de Euler-Lagrange e, usando a geometria simplética, mostramos como estes naturalmente evoluem para o formalismo Hamiltoneano e as equações de Hamilton. Introduzimos também o conceito da métrica de Jacobi e demonstramos o teorema de Noether. Apresentamos o conceito de ações simpléticas e Hamiltoneanas, bem como aplicações momento e comomento. São demonstrados resultados importantes como o teorema de Kirillov-Kostant-Sourieau para órbitas coadjuntas e a redução simplética de Marsden-Weinstein-Meyer. Os resultados centrais apresentados são o teorema de Atiyah-Guillemin-Steinberg de convexidade, o teorema de Schur e Horn para matrizes unitárias e o teorema de Delzant, este último sendo apresentado apenas com uma ideia da prova. / This thesis is about symplectic geometry and its applications, presenting concepts such as the symplectic gradient and also Darboux\'s theorem. We discuss the Lagrangian formulation of mechanics, presenting the Euler-Lagrange equations and, using symplectic geometry, show how those naturally evolve into the Hamiltonian formalism and the Hamilton equations. We instroduce also the concept of the Jacobi metrics and prove Noether\'s theorem. We also introduce the concept of symplectic and Hamiltonian actions as well as moment and comoment maps. We prove important results such as the Kirillov-Kostant-Sourieau theorem for coadjoint orbits and the symplectic reduction of Marsden-Weinstein-Meyer. The central results presented are the convexity theorem of Guillemin-Atiyah-Steinberg, the Schur and Horn theorem for unitary matrices and the Delzant theorem, this last one being presented only with an idea of the proof.

In this dissertation I have argued that the study of stars and gaseous planets has relied too heavily on simplifying assumptions. In particular, I have demonstrated that the assumptions of spherical symmetry, thermal equilibrium, dynamical equilibrium and turbulent anisotropy all hide interesting phenomena which make a true difference to the structure and evolution of these bodies. To begin I developed new theoretical tools for probing these phenomena, starting with a new model of turbulent motion which accounts for many different sources of anisotropy. Building on this I studied rotating convection zones and determined scaling relations for the magnitude of differential rotation. In slowly-rotating systems the differential rotation is characterised by a power law with exponent of order unity, while in rapidly-rotating systems this exponent is strongly suppressed by the rotation. This provides a full characterisation of the magnitude of differential rotation in gaseous convection zones, and is in reasonable agreement with a wide array of simulations and observations. I then focused on the convection zones of rotating massive stars and found them to exhibit significantly anisotropic heat fluxes. This results in significant deviations from spherical symmetry and ultimately in qualitatively enhanced circulation currents in their envelopes. Accordingly, these stars ought to live much longer and have a different surface temperature. This potentially resolves several outstanding questions such as the anomalously slow evolution of stars on the giant branch, the dispersion in the observed properties of giant stars and the difficulty stellar modelling has to form massive binary black holes. In the same vein I examined the convection zones of bloated hot Jupiters and discovered a novel feedback mechanism between non-equilibrium tidal dissipation and the thermal structure of their upper envelopes. This mechanism stabilises shallow radiative zones against the convective instability, which would otherwise take over early on in the planet's formation as it proceeds to thermal equilibrium. Hence tidal dissipation is dramatically enhanced, which serves to inject significant quantities of heat into the upper layers of the planet and causes it to inflate. This mechanism can explain most of the observed population of inflated planets. Finally, I studied material mixing in the outer layers of accreting stars and developed a method for relating the observed surface chemistry to the bulk and accreting chemistries. This enables the direct inference of properties of circumstellar material and accretion rates for a wide variety of systems.

This paper seeks to unconventionally maximize the volatility of a portfolio through a quartic optimization based on Markowitz’s modern portfolio theory, which generally seeks to do exactly the opposite. It shows that through this method, a daily leveraged exchange traded fund (ETF) strategy investigated by Posterro can be significantly improved upon in terms of its Sharpe ratio. The original strategy seeks to use a combination of momentum trading and tracking error in leveraged ETFs to trade during the last half an hour of the trading day, but it suffers in a low volatility market. By maximizing the volatility to take better advantage of tracking error and momentum, this problem is addressed by both increasing the mean daily return and significantly decreasing the variance of the strategy’s daily returns. GARCH forecasting is also implemented to assist in the maximization of the daily portfolios’ variances, though this does not prove to make a statistically significant difference in the strategy’s performance.

This thesis investigates the profitability of the Momentum and Contrarian strategies in international equity markets. In particular, I introduce for the first time the use of countries' indices performance to momentum and contrarian portfolio selection. I show that investors can switch back and forth from one country to the other in designing worldwide strategies. The global momentum strategy is consistently profitable between 1969 and 2014. The most successful momentum strategy selects stocks based on their previous performances over 9 months and then holds the portfolio for the next 3 months. This strategy yields 3% per month (42.57% per year). Interestingly, countries' indices' portfolios formed based on prior 48 months; prior losers outperform prior winners by 0.83% per month (10.40% per year) during the subsequent 60 months. The reversal effect is substantially stronger for emerging countries where it yields 1.37% per month (17.70% per year). It remains profitable in the period post-globalization. In addition, I examine for the first time the role of world risks factors in explaining the global momentum and contrarian profits and find that the global momentum strategies obtain significant abnormal returns after adjusting consecutively for world Fama and French risks (0.9% per month or 11.35% per year), and world market states risks (1.31% per month or 16.76% year). Of particular interest, I find a strong relation between world macroeconomic risks factors, notably world industrial production and the momentum return. Second, I find no substantial relation between world risks factors and the contrarian profit. These results suggest that excess return can be earned in the long run by using global investment strategies based on historical prices, challenging the weak form of the Efficient Market Hypothesis. In Chapter 1, I explain the momentum and the contrarian strategies, motivate the importance of what I propose as global momentum and contrarian strategies, and present the results obtained. In chapter 2, I review the Efficient Market Hypothesis' literatures in conformity with the Standard Finance theory. Additionally, I review the Behavioural Finance literatures with a focus on the psychology of investor decision, and the stock market under-reaction and overreaction approach of explaining the momentum and contrarian profitability. In chapter 3, I explain in details the main methodologies used to examine the global momentum and contrarian strategies profitability, and motivate the dataset used. In Chapter 4, I examine the new global momentum strategy profitability internationally. In Chapter 5, I examine the new contrarian strategy profitability internationally. In Chapter 6 I examine the role of global risks factors in explaining the momentum and contrarian profits. Finally, in Chapter 7 I conclude and highlights the limitations of the thesis.

Studying the orbital angular momentum (OAM) of light has become rather fashion- able in the 21st century. Yet, most of major advances in OAM related research have been conducted in the visible regime of light. A significant portion OAM research revolves around using OAM radiation to perform some function that is deemed useful. Examples of this are optical trapping, micro-machine manipulation and the development of advanced communication systems. Photon entanglement measurements also make use of OAM radiation. Interest in probing radiation for naturally generated OAM is far less popular. For example, interest in building OAM sensitive telescopes was sparse at the beginning of this thesis, however the first reported detection of astrophysical OAM was published in 2013. This thesis aims to tackle these two areas of sparse research by developing the components and understanding in order to build OAM sensitive millimetre-wavelength telescopes. Spiral phase plates (SPPs) are the device of choice. The majority of the thesis sets out to test three different SPPs, in order to compare and contrast different methods for their manufacture and design. Electromagnetic theory of OAM and its generation is reviewed first. Then, each SPP is modelled numerically fol- lowed by in-depth modelling of each plate by using the computational electromagnetic package FEKO. Finally, each plate is measured with a three dimensional field scanner developed as part of this thesis. Development of a new modular SPP design concludes this thesis.

Thesis (M. Sc. (Chemistry)) --University of Limpopo, 2018 / The dissertation describes the use of 2-benzenesulfonyloxyquinoxaline as a good coupling partner for different amine substrates. The palladium-mediated cross- coupling of aryl electrophiles and amines has become a widely used method of constructing arylamine frameworks. The formation of carbon-nitrogen bonds was accomplished via palladium-catalysed Buchwald-Hartwig amination employing different amine substrates to yield substituted quinoxaline-2-amines compounds in good to moderate yields. Buchwald ligands (Xphos, tButylxphos and BrettPhos), were varied with different amine substrates in an attempt of improving the yields. Compounds 81a N-phenylquinoxalin-2-amine and 82b, N-benzylquinoxalin-2-amine were obtained with the yield over 70 % employing Xphos as the ligand. Significant attention has also been given to the application of cross coupling reaction protocols in substrates bearing electron withdrawing substituents. The presence of deactivating groups on the arylamine such as fluoro, nitro and iodo proved to be a challenge as only few compounds were synthesised in moderate yields. Compound 81b, N-(4-fluorophenyl)quinoxalin-2-amine which has electronegative atom attached, showed significant improvement when employing tButyl-Xphos ligand rather than XPhos since the yield improved from 10 % to 71 %. Furthermore, nucleophilic substitution on Buchwald-Hartwig coupled compounds by treating them with alkyl iodides was successful when using methyl and ethyl electrophiles on the N-H group of 81a 2-quinoxalineamine. The synthesised quinoxaline derivatives comprised 7 novel compounds. The in vitro analysis on anti-tubercular screening against H37RvMA strains of Mycobacterium tuberculosis was conducted on 9 compounds. The results revealed none of the compounds to have promising inhibition percentages against Mycobacterium tuberculosis when compared with rifampicin which was used as a positive control. Screening against malaria with chloroquine as the control also did not yield any active compounds.

It has been twelve years since the last time the yield curve was inverted. Since 2017, the yield curve has been continuing to flatten and has almost entered an inverted state. The last five recessions have been preceded by the inversion of the yield curve. I examine momentum trading strategy’s ability to outperform during an inverted yield curve state. The yield curve can enter the momentum portfolio strategy through the portfolio’s formation and holding period. I document the increased performance of the momentum strategy’s total portfolio return in an inverted state. These results have implications on the timing a momentum trading strategy might be implemented.

Behavioral momentum theory (BMT) provides a theoretical framework for studying the persistence of behavior when challenged. The typical experimental arrangement to study persistence involves reinforcing a behavior according to a multiple schedules design. Unique schedules of reinforcement are programmed to each component. When steady-state responding occurs, the schedules of reinforcement are disrupted by a challenge condition (e.g., extinction, distraction, or prefeeding). The multiple schedules component that maintains the greatest level of responding during disruption is described as being more persistent. Basic research has shown that rate of reinforcement is a reliable predictor of persistence. The multiple schedules component associated with the higher rate of reinforcement persists longer than the multiple schedules component associated with the lower rate of reinforcement during disruption. Applied researchers have recently begun translating BMT to problems of social significance. The success of these initial translations suggests that relations between other dimensions of reinforcement and persistence should be studied. The current two-experiment study investigated the effect of quality of reinforcement on the persistence of task completion. Three participants with a history of engaging in problem behavior to escape from demands participated in Experiment I. After showing the conditions under which participants would and would not allocate away from a work task to engage with a preferred item, a baseline measure of task completion was obtained. Task completion was then reinforced with attention or tangibles within a multiple schedules design. Orange tokens signaled access to tangible reinforcement and yellow tokens signaled access to attention reinforcement. After steady-state responding occurred, preference for attention and tangibles was assessed within a concurrent schedules design. Extinction was then implemented to disrupt task completion within each component of the multiple schedules design. Results showed modest differences in the persistence of task completion with task completion in the multiple schedules component associated with the delivery of the more preferred reinforcer persisting longest. The modest differences in persistence were smaller than what has previously been shown in the literature. Thus, a follow-up experiment was conducted to evaluate the effect of reinforcer potency on the persistence of task completion. Three participants with a history of engaging in problem behavior to escape from demands participated in Experiment II. After identifying relatively more and less preferred stimuli with a multiple stimulus without replacement (MSWO) preference assessment, a unit price analysis was conducted to evaluate the potency of these two items within a concurrent schedules design. Task completion was then reinforced with the more and less potent reinforcers according to a multiple schedules design. After showing steady-state responding, task completion was disrupted by extinction. Results clearly showed greater persistence of task completion under the component associated with the delivery of the more potent reinforcer for two of three participants. Results from both experiments are discussed in terms of their conceptual and applied implications.

An (e,2e) electron scattering spectrometer has been constructed and used for the first time to investigate the spectral momentum density of the valence bands of a solid target. This technique provides fundamental information about the electronic structure of both crystalline and amorphous solids. The three fundamental quantities, the band structure, electron density of states, and electron momentum distribution can be simultaneously derived from the measured (e,2e) cross section. A review of single electron and (e,2e) scattering theory is given with an emphasis on scattering from solids. The effects of multiple scattering are discussed and a method of deconvoluting those effects from the measured (e,2e) cross section is developed. There is a detailed description of the spectrometer design and operation with particular attention given to the electron optics and voltage distribution. The algorithms and software for computer aided data acquisition and analysis are also outlined, as is error analysis. The techniques employed in the preparation and characterization of extremely thin film samples of a-C and single crystal graphite are described An analysis of the data taken for a-C samples is complementary experiments and theory for graphite, diamond, and a-C which are given in a review of the literature. The existence of a definite dispersion relation ε(q) in amorphous carbon is demonstrated. The a-C band structure appears to be more similar to that of graphite than to that of diamond, however it differs significantly from both in some respects. The measured spectral momentum density seems compatible with a model of a-C based on small, randomly-oriented islands of quasi-2D graphite-like continuous random network structures. However, no definitive interpretations can be made until higher resolution experiments are performed on both a-C and single crystal graphite.

The basic behavioral process of operant conditioning contributes to problem behaviors in psychological disorders. Escape from aversive situations in depression, the rewarding effects of drugs in substance abuse, and the receipt of caregiver attention for disruptive behavior in intellectual or developmental disabilities are just a few examples of operant reinforcement contingencies that perpetuate undesirable behavior. Behavioral treatment strategies often introduce alternative sources of reinforcement for a desirable alternative behavior. Although treatments can be effective, alternative reinforcement removal can trigger relapse of the problem behavior, called resurgence. Persistence in alternative reinforcement treatments and resurgence can be understood from the prospective of behavioral momentum theory, which predicts greater operant persistence and resurgence when there is a greater history of reinforcement associated with the context in which an operant response occurs. Shahan and Sweeney incorporated resurgence into the framework of behavioral momentum theory, and the proposed model makes explicit qualitative and quantitative predictions that are tested in this dissertation. Chapter 1 provides the background and significance of resurgence of operant behavior, and gives an introduction to behavioral momentum theory and the quantitative model of resurgence. Chapter 2 reports two recently published experiments that show increased time with alternative reinforcement treatment reduces subsequent resurgence in an animal model with pigeon subjects. The study presented in Chapter 3 examined how persistence and resurgence may be affected when alternative reinforcement is delivered in a novel context. This experiment, which used rat subjects, integrated and compared the animal model of resurgence with another operant relapse phenomenon, renewal, in which context change alone is known to induce relapse of a previously reduced response. Chapter 4 describes a study with college undergraduates as participants that tested the feasibility of a brief, three-alternative, forced-choice procedure as a human operant model of resurgence. Despite procedural manipulations of the length of training and probability of reward for choice of the target stimulus, resurgence was never consistently observed. Chapter 5 provides an integrative discussion of these research topics.