The concept of a computable function is quite a well-studied one, however, it is possible to capture certain important properties of computability categorically. A special type of category used for this purpose is called a Turing category. This thesis starts with a brief overview of Turing categories, followed by a study of additional categorical structure they may contain, based on the types of structure found in the world of computable functions, and how this is reflected in the underlying combinatorial structures.

The formation of atherosclerotic plaques is linked to a change in vascular function, with evidence of endothelial dysfunction and the proliferation of the underlying vascular smooth muscle cells (VSMCs). Prior to plaque development, risk factors are present that are capable of altering vascular function and promoting disease progression. These risk factors include hypercholesterolaemia, obesity and inflammation. The specific mechanisms of these risk factors in the early stages of atherosclerotic disease development have yet to be fully explored and are likely to be closely interwoven. The aim of this thesis was to assess the effects of these atherosclerotic risk factors, with a primary focus on the direct action of hypercholesterolaemia, on vascular function prior to the development of overt atherosclerosis. After acute ex vivo cholesterol depletion and enrichment, a range of contractile and relaxant stimuli were applied to thoracic aortic rings of wildtype C57BL/6 mice. Cholesterol depletion significantly reduced contractility to phenylephrine (p<0.05) and serotonin (p<0.01). Acute cholesterol enrichment had no effect on vascular contractility, however, acetylcholine stimulated endothelial-dependent relaxation was significantly reduced (p<0.05).Feeding with either a standard chow or a high fat ‘western’ diet was undertaken for eight weeks in both ApoE-/- and C57BL/6 mice. The extent of atherosclerotic disease development was measured through en face lipid staining and histological analysis of aortae. Atherosclerosis was present in the aortic root and intercostal branches of chow and high fat fed ApoE-/- mice but not in diet-matched C57BL/6 mice. No atherosclerotic lesions were observed in the thoracic aortae. In addition, to allow the possibility for direct associations to be made between the associated risk factors of hypercholesterolaemia, obesity and inflammation, and vascular function, a phenotypic assessment of these characteristics was conducted. Wire myography was employed to assess the vascular function of thoracic aortic rings from chow and high fat diet fed ApoE-/- mice and their age and diet matched wildtype C57BL/6 controls. It was found that contractility to both phenylephrine and serotonin was significantly increased in chow fed ApoE-/- mice (both p<0.05). Further investigation into the mechanism, using intracellular calcium imaging and the indo-1 dye, concluded that VSMC store-operated calcium entry was not altered. The exact mechanism behind this increase in contractility is therefore still unknown and there was no clear relationship to the atherosclerotic risk factors assessed. In addition to altered contractility, endothelial-dependent relaxation was shown to be significantly enhanced in high fat fed C57BL/6 (p<0.01) and ApoE-/- mice (p<0.001). Enhanced endothelial-dependent relaxations were transient and sensitive to specific inhibition of cyclooxygenase-2 but not nitric oxide synthase. These changes were hypercholesterolaemia-independent but correlated with signs of obesity and inflammation. In summary, this investigation has demonstrated that vascular function was altered in the murine thoracic aorta prior to overt atherosclerotic plaque development. The implications for these observations relate to the possibility of masked early signs of vascular dysfunction and also the induction of compensatory mechanisms which may have amplified effects over a longer time course; possibly promoting the development and advancement of atherosclerotic disease.

Au cours des dernières années, la mobilité routière a été marquée par la croissance considérable du trafic des Véhicules à Deux-Roues Motorisés (V2RM), qui demeurant désormais le mode de déplacement le plus dominant et convoité, notamment pour les possibilités qu'il offre d'esquiver les embouteillages de trafic. Cependant, les conducteurs de deux-roues motorisés sont considérés comme les usagers de la route les plus vulnérables. En effet, le risque d'être tué dans un accident est 29 fois plus élevé pour un cyclomoteur que pour un conducteur de voiture de tourisme. Ce problème est d'autant plus important lors du freinage d'urgence ou lors de la prise de virage. Alors que les systèmes de sécurité passifs et actifs (ABS, ESP, ceintures de sécurité, airbags, etc.) développés en faveur des véhicules de tourisme ont amplement contribué à la diminution des risques sur la route, cependant, le retard dans le développement de ces systèmes pour les motos est considérable. Malgré quelques systèmes existants, les conducteurs de motos les utilisent mal ou pas du tout. Ceci est dû à une mauvaise formation et cela ne contribue donc pas à l'amélioration de leur sécurité. Par conséquent, il n'est pas anodin que ce retard, dans le développement des systèmes d'aide à la conduite, résonne avec un retard dans le développement des outils de recherches théoriques. L'objectif principal de la thèse est de concevoir des systèmes d'assistance à la conduite, ARAS (Advanced Rider Assistance Systems), pour les V2RM pouvant alerter ces conducteurs en amont des situations de conduite dangereuses. De nombreux défis sont encore ouverts en ce qui concerne la conception des systèmes ARAS comme l'accessibilité des états dynamiques et paramètres physiques des V2RM ainsi que la synthèse des indicateurs de risques en visitant tous les points d'intérêts. Nous nous intéressons alors à proposer des techniques d'estimation, tout en réduisant le nombre de capteurs et en contournant la problématique de non-mesurabilité de certains variables. Par ailleurs, la synthèse de ces approches répondant à certaines exigences (modélisation, structure simple, précision, instrumentation) constitue un défi supplémentaire. La première partie de thèse est consacrée aux algorithmes d'identification classiques. Ces techniques sont conçues pour estimer les paramètres physiques inconnus des modèles paramétriques des V2RM. La deuxième partie concerne des observateurs basés modèles. Pour cela, un observateur à entrées inconnues (UIO) pour reconstruire la dynamique de la direction en tenant compte de la géométrie de la route, et, un observateur interconnecté (IFO) pour l'estimation de la dynamique longitudinale et latéral, ont été proposées. Ensuite, nous nous sommes penchés sur des méthodes alternatives aux approches d'identification, notamment des techniques d'estimations basées identification capable à la fois d'estimer les états et les paramètres au même temps. À cette occasion, un observateur retardé à entrées inconnues pour les systèmes avec un degré relatif arbitraire (DUIO), et, un observateur de Luenberger adaptative (LAO) pour l'estimation des raideurs pneumatiques ont été développées. Les méthodes proposées nécessitent une combinaison simple de capteurs et prennent en compte des hypothèses réalistes telles que la variation de vitesse longitudinale. Tous ces travaux ont été validés à l'aide de BikeSim et/sur des données expérimentales. En outre, ce manuscrit introduit un algorithme d’auto-calibration pour l’alignement des unités de mesure inertielle (IMU). Une telle méthode d’auto-étalonnage s’applique aux boîtiers télématiques (e-Box) installés sur des véhicules à deux roues, dont les axes des IMU sont souvent mal alignés avec le repère référentielle du véhicule. La dernière partie de cette thèse traite des indicateurs objectifs (comportement sur/sous vireur de la moto et la distance de sortie de la voie de circulation) pour la quantification du risque. / Nowadays, Powered Two-Wheeled Vehicles (PTWV) are an increasingly popular means of transport in daily urban and rural displacements, especially for the possibilities it offers to avoid traffic congestion. However, riders are considered as the most vulnerable road users. In fact, the risk of being killed in an accident is $29$ times higher for a motorcycle than for a driver of a four wheeled vehicle. Therewith, the unstable nature of the PTWV makes them more susceptible to control loss. This problem is even more complex during emergency braking or on cornering maneuvers. As matter of fact, passive and active safety systems (Anti-Lock Braking (ABS), Electronic Stability Control (ESP), seat belts, airbags) developed in favour of passenger vehicles have largely contributed to the reduction of risks on the road. However, the delay in the development of security systems for motorcycles is notable. Moreover, despite some existing systems, motorcycle riders use them badly or they don't use them at all. Therefore, it is not trivial that this delay, in the development of Advanced Rider Assistance Systems (ARAS), coming from a delay in the development of theoretical and research tools. This thesis fits into the context of designing ARAS for PTWV that can alert riders upstream of dangerous driving situations. Our work deals with observation and identification techniques to estimate the PTWV dynamic states and physical parameters. These latter are fundamental for risk quantification in ARAS design and to assess the safety of the PTWV, which are the main focus of our research work. The first part of the thesis concerns classical identification techniques to estimate physical parameters of PTWV. The second part deals with model-based observers implemented to estimate the dynamic states of the PTWV. We proposed an unknown input observer (UIO) for steering and road geometry estimation and an interconnected fuzzy observer (IFO) for both longitudinal and lateral dynamics. An alternative methods for identification algorithms are observer based identifier which provide both parameters identification and states estimation. Therefore, a Luenberger adaptive observer (LAO) to estimate lateral dynamic states and pneumatic stiffness as well as a delayed unknown inputs observer (DUIO) with an arbitrary relative degree, have been developed in this thesis. As matter of fact, all these techniques allow to estimate the vehicle dynamics while reducing the number of sensors and overcoming the problem of non-measurable states and parameters. These proposed methods require a simple combination of sensors and take into account realistic assumption like the longitudinal speed variation. Among others, this manuscript introduces a self calibration algorithm for Inertial Measurement Units (IMUs) alignment. Such a self-calibration method is used for telematic boxes (e-Boxes) installed on two-wheeled vehicles, whose IMUs’ axes are often result not to be aligned with the vehicle reference system. Finally, objective indicators are setting up to quantify riding risks. These functions were studied for ARAS purpose. To highlight the performance of these approaches, we have acquired data from high-fidelity motorcycle simulator and also with data from real motorcycles. To sum up, a comparison tables are drawn up for all the presented approaches. The results of both the numerical simulations and the performed experimentations seem to be quite promising.

The theory of function algebras has been an active field of research over the past two decades and its coming of age has been heralded by the appearance within the last twelve months of three textbooks devoted entirely to them, namely the books by Browder, Leibowitz and Gamelin. One of the attractive features of the theory of function algebras is that it draws on diverse specialities like the theory of Banach algebras, harmonic analysis and the theory of analytic functions of several complex variables. The last mentioned theory has led to some of the most powerful results in the theory of function algebras. Not surprisingly, many of these results, for example Rossi's local maximum modulus principle theorem 2.24, were first proved for finitely generated and then extended to arbitrary function algebras. This observation, together with the fact that there has been no systematic study of finitely generated function algebras, led to the writing of this thesis. We have made use of some of the results of the theory of analytic functions of several complex variables, though we have not specifically used the methods thereof. What we have looked for is ways in which the functions of finitely generated function algebras behave like analytic functions and then tried to see if arbitrarily generated function algebras behave in a similar way.

Generalising the divisibility relation of terms we introduce the lattice of so-called involutive divisions and define the admissibility of such an involutive division for a given set of terms. Based on this theory we present a new approach for building up a general theory of involutive bases of polynomial ideals. In particular, we give algorithms for checking the involutive basis property and for completing an arbitrary basis to an involutive one. It turns out that our theory is more constructive and more exible than the axiomatic approach to general involutive bases due to Gerdt and Blinkov. Finally, we show that an involutive basis contains more structural information about the ideal of leading terms than a Gröbner basis and that it is straight forward to compute the (affine) Hilbert function of an ideal I from an arbitrary involutive basis of I.

During the academic year 1960-1961, the Department of Experimental Surgery, of the University of Cape Town, engaged in a series of experiments concerning the production of profound hypothermia in dogs. Hypothermia was induced by blood-stream cooling, via a heat exchanger incorporated in an extra-corporeal pump-oxygenator system (ef Appendix A). Progress was such that by midyear postoperative survival of experimental animals was assured. At this juncture, it was suggested that, as a member of the Renal-Metabolic Group of the Department of Medicine, I co-operate wit the surgeons, in a study of renal function during profound hypothermia in the dog. This thesis details our progress and results.

The characteristics of the left ventricle of the human heart considered as a pump have been extensively analysed. Using a new approach relying heavily on the Tensor Calculus, a theoretical model describing the mechanical and dynamical operation of the left ventricle has been developed. This has considerably greater versatility than previously proposed models. In particular the physiological shape, both under normal as well as many abnormal situations, is realistically simulated. Further, the mechanical behaviour of the ventricular wall is synthesised from anatomical data concerning the cardiac muscle fibre structure of the wall. Its mechanical and dynamical properties are then, as in the physiological situation, dependent on those of the muscle fibre. These fibre properties have also been fully investigated and a simple new model for cardiac muscle dynamics, incorporating active state, proposed. This description of the ventricular behaviour in terms of muscle properties represents the first logically structured link between cardiac muscle fibre characteristics and ventricular performance.

Motivated by a study of social spider behavior, we discuss the distribution of the distances from all the events in a spatial point pattern to a point of reference that has a known location at a given moment of time. The distribution depends on both the shape of the region and the location of the point of reference. The empirical CDF is used to describe the distribution of the distances and compare it to the CDF derived under complete spatial randomness. Empirical distributions are then compared through time focusing on the case in which the point of reference changes with time.

Let f be a real valued function with the domain dom(f) in some vector space X and let C be the collection of convex subsets of X. The following two questions are investigated; 1. Do there exist maximal convex restrictions g of f with dom(g) 2 C? 2. If f is convex with dom(f) 2 C, do there exist maximal convex extension g of f with dom(g) 2 C? We will show that the answer to both questions is positive under a certain condition on C. We also show that the extreme points of the epigraph of a real continuous strictly convex function are dense in the graph of such a function, and the set of such extreme points of an epigraph may be equal to the graph. Moreover we show that a set of extreme points of an epigraph may be equal to a graph of such a convex function under certain conditions. We also discuss conditions under which an epigraph of a real convex function on a Banach space X may, and may not, have extreme points, denting points and/or strongly exposed points. One of the interesting results in this discussion is that boundary points, extreme points, denting points and the graphs in an closed epigraph of a strictly convex function coincide. Moreover, we show that there is relationship between the extremal structure of an epigraph of a convex function and a point in a domain on which such a function attains its minimum.

Transition metal Dichalcogenide MoS2in the monolayer and few-layer form have generated intense interest in the fundamental and applied research community due to its surprisingly strong light-matter interactions, strong excitonic effect, and unique elec-tronic and chemical activity at the edges. In this thesis work, I have conducted a series of synergistic experimental and computational investigations focused on understanding the fundamental optical properties of few-layer MoS2(experiment with supporting computational calculations) and its potential application into the electrochemical reduction of CO2(computational)In the first part of the thesis, I show that sulfur vacancies affect the optical properties of few-layer thin films deposited using magnetron sputtering. In particular, I show that sulfur vacancies can obscure the well-defined A/B excitons in MoS2. Next, while contributing with the process of developing high-quality MoS2films, I designed an approach to accurately determine the optical constants by combining transmission spectroscopy with spectroscopic ellipsometry. The method, which we call Transmission-assisted spectroscopic ellipsometry (TASE), is demonstrated on high-quality MoS2films deposited on transparent and absorbing substrates. Next, Transmission spectroscopy combined with the Kramers-Kronig consistent optical model was employed to determine the complex dielectric function of few-layer MoS2in the broadband energy range of 0.7-6.5 eV. Optical transitions leading to peaks in the dielectric functions are assigned to the band structure. In particular, a new peak is observed and assigned at 4.5 eV in few-layer MoS2. Finally, I have examined the effectiveness of doped MoS2on the catalytic activity for CO reduction using density functional theory method. The structural calculation shows that doping Mo edge site of MoS2with transition metals that have higher work function than Mo atom results a lowering in the CO adsorption energy which suppresses the dissociation reaction and enhances the hydrogenation reaction. The Bader charge analysis shows that the dopant atom does not contribute to CO adsorption directly but it reduces the charge density at the edge atom that is indicated from the Density of states.