Thesis (MSc)--Stellenbosch University, 2003 / ENGLISH ABSTRACT: A tower of global function fields :F = (FI, F2' ... ) is an infinite tower of separable extensions of algebraic function fields of one variable such that the constituent function fields have the same (finite) field of constants and the genus of these tend to infinity. A study can be made of the asymptotic behaviour of the ratio of the number of places of degree one over the genus of FJWq as i tends to infinity. A tower is called asymptotically good if this limit is a positive number. The well-known Drinfeld- Vladut bound provides a general upper bound for this limit. In practise, asymptotically good towers are rare. While the first examples were non-explicit, we focus on explicit towers of function fields, that is towers where equations recursively defining the extensions Fi+d F; are known. It is known that if the field of constants of the tower has square cardinality, it is possible to attain the Drinfeld- Vladut upper bound for this limit, even in the explicit case. If the field of constants does not have square cardinality, it is unknown how close the limit of the tower can come to this upper bound. In this thesis, we will develop the theory required to construct and analyse the asymptotic behaviour of explicit towers of function fields. Various towers will be exhibited, and general families of explicit formulae for which the splitting behaviour and growth of the genus can be computed in a tower will be discussed. When the necessary theory has been developed, we will focus on the case of towers over fields of non-square cardinality and the open problem of how good the asymptotic behaviour of the tower can be under these circumstances. / AFRIKAANSE OPSOMMING: 'n Toring van globale funksieliggame F = (FI, F2' ... ) is 'n oneindige toring van skeibare uitbreidings van algebraïese funksieliggame van een veranderlike sodat die samestellende funksieliggame dieselfde (eindige) konstante liggaam het en die genus streef na oneindig. 'n Studie kan gemaak word van die asimptotiese gedrag van die verhouding van die aantal plekke van graad een gedeel deur die genus van Fi/F q soos i streef na oneindig. 'n Toring word asimptoties goed genoem as hierdie limiet 'n positiewe getal is. Die bekende Drinfeld- Vladut grens verskaf 'n algemene bogrens vir hierdie limiet. In praktyk is asimptoties goeie torings skaars. Terwyl die eerste voorbeelde nie eksplisiet was nie, fokus ons op eksplisiete torings, dit is torings waar die vergelykings wat rekursief die uitbreidings Fi+d F; bepaal bekend is. Dit is bekend dat as die kardinaliteit van die konstante liggaam van die toring 'n volkome vierkant is, dit moontlik is om die Drinfeld- Vladut bogrens vir die limiet te behaal, selfs in die eksplisiete geval. As die konstante liggaam nie 'n kwadratiese kardinaliteit het nie, is dit onbekend hoe naby die limiet van die toring aan hierdie bogrens kan kom. In hierdie tesis salons die teorie ontwikkel wat benodig word om eksplisiete torings van funksieliggame te konstrueer, en hulle asimptotiese gedrag te analiseer. Verskeie torings sal aangebied word en algemene families van eksplisiete formules waarvoor die splitsingsgedrag en groei van die genus in 'n toring bereken kan word, sal bespreek word. Wanneer die nodige teorie ontwikkel is, salons fokus op die geval van torings oor liggame waarvan die kardinaliteit nie 'n volkome vierkant is nie, en op die oop probleem aangaande hoe goed die asimptotiese gedrag van 'n toring onder hierdie omstandighede kan wees.

International Telemetering Conference Proceedings / October 25-28, 1999 / Riviera Hotel and Convention Center, Las Vegas, Nevada / In this paper, we extended the matched filter bound (MFB) of time-discrete multipath Rayleigh fading channels derived in [1,2] for multiscale wavelet signaling communication.

International Telemetering Conference Proceedings / October 30-November 02, 1995 / Riviera Hotel, Las Vegas, Nevada / The national telemetry ranges are being pushed to provide higher data rate telemetry services by users with increasingly complex test procedure for increasingly complex weapon systems. At the same time they are having trouble obtaining more spectrum in which to provide these higher rates because of the demand for spectrum in SHF range from various mobile/cellular Personal Communications Services (PCS) as well as congress’s desire to auction spectrum and to transfer as much spectrum as possible to commercial uses. In light of these pressures the industry is in need of a modulation standard that will out perform the existing PCM/FM standard. The motivation for the present review and analysis of the performance of various coded/uncoded modulation schemes arises from this issue. Comparison of the performance of these schemes will be utilized in the following work to find a suitable solution to the existing problem.

The aim of this dissertation is to present an algorithm for mixed integer programs which when started with a good heuristic solution can find improved solutions and reduce the error estimate as quickly as possible. This is achieved by using two ideas: a fixed order branch-and-bound method with selective expansion of subproblems and the sieve strategy which uses stronger than optimal bounds. The fixed order branch-and-bound method with selective expansion of subproblems is effective in reducing the error estimate quickly whereas the sieve strategy is effective in reducing the error estimate as well as finding improved solutions quickly. Computational experience is reported.

Most traditional routing problems assume perfect operability of all arcs and nodes. However, when independent arc failure probabilities exist, a secondary objective must be present to retain some measure of expected functionality. We first briefly consider the reliability-constrained single-path problem, where we look for the lowest cost path that meets a reliability side constraint. This analysis enables us to then examine the reliability-constrained two-path problem, which seeks to establish two minimum-cost paths between a source and destination node wherein at least one path must remain fully operable with some threshold probability. We consider the case in which both paths must be arc-disjoint and the case in which arcs can be shared between the paths. We prove both problems to be NP-hard. We examine strategies for solving the resulting nonlinear integer program, including pruning, coefficient tightening, lifting, and branch-and-bound partitioning schemes. Next, we consider the reliable h-path routing problem, which seeks a minimum-cost set of h ≥ 2 arc-independent paths between a source and destination node, such that the probability that at least one path remains operational is sufficiently large. Our prior arc-based models and algorithms tailored for the case in which h = 2 do not extend well to the general h-path problem. Thus, we propose two alternative integer programming formulations for the h-path problem in which the variables correspond to origin-destination paths. We propose two branch-and-price-and-cut algorithms for solving these new formulations, and provide computational results to demonstrate the efficiency of these algorithms. Finally, we examine the robust design of an evacuation tree, in which evacuation is subject to capacity restrictions on arcs. Given a discrete set of disaster scenarios with varying network populations, arc capacities, transit times, and time-dependent penalty functions, we seek to establish an optimal a priori evacuation tree that minimizes the expected evacuation penalty. The solution strategy is based on Benders decomposition, and we provide effcient methods for obtaining primal and dual sub-problem solutions. We analyze techniques for strengthening the master problem formulation, thus reducing the number of master problem solutions required for the algorithm's convergence.

In some recent papers, the weight based statistical bounds have arguably explained time complexity better than the count based mathematical bounds. This is definitely true for average case where for an arbitrary code it is difficult to identify the pivotal operation or pivotal region in the code for taking the expectation and/or when the probability distribution, over which expectation is taken, becomes unrealistic over the problem domain. In worst case, it can certify whether a mathematical bound is conservative or not. Here we revisit the results on Bubble sort in sequential mode and make an independent study of the same algorithm in parallel mode using statistical bound

Ces dernières années, la phase de roulage au sol des avions a été mise en avant dans l'étude des retards aériens sur les grands aéroports. Cependant, le lien entre cette phase et l'optimisation des séquences d'avions sur les pistes reste encore peu étudié. L'objectif de réaliser des séquences optimales sur les pistes doit pourtant permettre de mieux gérer le trafic au sol, pour respecter les créneaux de décollage imposés tout en réduisant les retards des avions : dans cette thèse, un algorithme de calcul de séquences optimales est mis en place et intégré à la gestion du trafic au sol, modélisée comme un problème de résolution de conflits entre avions. Deux méthodes d'optimisation sont alors comparées : une méthode déterministe (utilisant un algorithme de type branch and bound) et une méthode stochastique (utilisant un algorithme génétique). Chacune des deux méthodes pouvant fonctionner avec et sans considération des séquences optimales sur les pistes. Les simulations effectuées montrent qu'une réduction significative des retards peut être espérée lorsque les séquences sont optimisées et anticipées. La méthode stochastique trouve de meilleures solutions, notamment en ce qui concerne la gestion des arrivées, mais la méthode déterministe reste intéressante, grâce à son temps de calcul bien plus rapide. / In the last few years, many studies concerning air traffic delays have focused on ground traffic management at busy airports. However, the link between the aircraft taxiing stage and runway scheduling optimisation is still rarely considered. Performing optimal aircraft sequences on runways should allow us to enhance the taxiing stage, while applying calculated take-off slots and reducing globally the aircraft mean delay. In this thesis, an algorithm is first defined to compute optimal aircraft schedules on runways. It is then integrated into the ground traffic management process, modeled as a conflict resolution problem between aircraft. A deterministic method (using a branch and bound algorithm) and a stochastic method (using a genetic algorithm) are both used to try and solve this problem. Each of these methods can work with and without the consideration of optimal runway scheduling. The simulations carried out show that the anticipation of the optimal runway schedules can yield a significant delay reduction for airport ground traffic. The stochastic method provides the best solutions, especially for arriving aircraft, while the deterministic method remains a considerable option because of its very fast running time.

An investigation of the ratio of free to bound phenytoin in overdose cases was accomplished by three studies to answer these questions: 1. Will the free to bound ratio change with increasing total phenytoin concentration? 2. Will the free to bound ratio be altered with decreasing total protein concentration? 3. Do these results correlate with overdose cases? The results demonstrated that the ratio of free to bound phenytoin remains constant throughout the therapeutic range as long as a person has a normal total protein concentration. However, the free to bound ratio changes significantly when the total protein decreases by 25 per cent. This substantiates the importance of monitoring free and total phenytoin concentrations in hypoproteinemia.

The independence number of a graph is the maximum number of vertices from the vertex set of the graph such that no two vertices are adjacent. We systematically examine a collection of upper bounds for the independence number to determine graphs for which each upper bound is better than any other upper bound considered. A similar investigation follows for lower bounds. In several instances a graph cannot be found. We also include graphs for which no bound equals $\alpha$ and bounds which do not apply to general graphs.

The paper develops a global vector auto-regressive model with time varying pa- rameters and stochastic volatility to analyse whether international spillovers of US monetary policy have changed over time. The model proposed enables us to assess whether coefficients evolve gradually over time or are better characterized by infrequent, but large, breaks. Our find- ings point towards pronounced changes in the international transmission of US monetary policy throughout the sample period, especially so for the reaction of international output, equity prices and exchange rates against the US dollar. In general, the strength of spillovers has weakened in the aftermath of the global financial crisis. Using simple panel regressions, we link the vari- ation in international responses to measures of trade and financial globalization. We find that a broad trade base and a high degree of financial integration with the world economy tend to cushion risks stemming from a foreign shock such as US tightening of monetary policy, whereas a reduction in trade barriers and/or a liberalization of the capital account increase these risks.