On propose quatre familles de méthodes itératives pour le raffinement d'éléments propres approches d'un opérateur compact dans un espace de Banach complexe. Ces méthodes sont de type Newton et le calcul de l'inverse de la dérivée de l'opérateur non linéaire dont on calcule un zéro est fait à l'aide de techniques fondées sur le principe de correction du résidu. Selon la précision de ce calcul, on peut atteindre une convergence quadratique, superlinéaire ou linéaire. On pressente des applications aux opérateurs intégraux à noyau continu ou faiblement singulier. Les discrétisations considérées sont les approximations de Galerkin, projection et Sloan avec ou sans quadrature - et les approximations de Fredholm et Nystroem. On donne des exemples numériques

Call number: LD2668 .T4 1964 C15 / Master of Science

The South African government’s integrated resource plan for electricity IRP2010 states that the country plans to have an additional 9.6 GW of nuclear power on the national electricity grid by 2030. In support of this, the NRF-funded SARChI Research Chair in Nuclear Engineering within the School of Mechanical and Nuclear Engineering at the North-West University recently initiated research studies focused on Light Water Reactor (LWR) systems. These studies inter alia involve coupled neutronic and thermal hydraulic analyses of selected LWR systems. This study focuses on the steady state neutronic analysis of the European Pressurised Reactor (EPR) using Monte-Carlo N-Particle (MCNP5). The neutronic model will in due course be coupled to a thermal hydraulic model forming part of a broader study of the system. The Monte Carlo neutron transport code MCNP5 has been widely used since the 1950s for analysis of existing and future reactor systems due to its ability to simulate complex fuel assemblies without making any significant approximations. The primary aim of the study was to develop an input model for a representative fresh fuel assembly of the US EPR reactor core from which the fluxes and fission power of the reactor can be obtained. There after a 3D model of full EPR core developed by the school of mechanical and nuclear engineering based on findings of this work is also tested. The results are compared to those in the US EPR Final Safety Analysis Report. Agreement in major core operational parameters including the keff eigenvalue, axial and radial power profiles and control rod worth are evaluated, from which consistency of the model and results will be confirmed. Further convergence of the model within a reasonable time is assessed. / MSc (Engineering Sciences in Nuclear Engineering), North-West University, Potchefstroom Campus, 2014

The South African government’s integrated resource plan for electricity IRP2010 states that the country plans to have an additional 9.6 GW of nuclear power on the national electricity grid by 2030. In support of this, the NRF-funded SARChI Research Chair in Nuclear Engineering within the School of Mechanical and Nuclear Engineering at the North-West University recently initiated research studies focused on Light Water Reactor (LWR) systems. These studies inter alia involve coupled neutronic and thermal hydraulic analyses of selected LWR systems. This study focuses on the steady state neutronic analysis of the European Pressurised Reactor (EPR) using Monte-Carlo N-Particle (MCNP5). The neutronic model will in due course be coupled to a thermal hydraulic model forming part of a broader study of the system. The Monte Carlo neutron transport code MCNP5 has been widely used since the 1950s for analysis of existing and future reactor systems due to its ability to simulate complex fuel assemblies without making any significant approximations. The primary aim of the study was to develop an input model for a representative fresh fuel assembly of the US EPR reactor core from which the fluxes and fission power of the reactor can be obtained. There after a 3D model of full EPR core developed by the school of mechanical and nuclear engineering based on findings of this work is also tested. The results are compared to those in the US EPR Final Safety Analysis Report. Agreement in major core operational parameters including the keff eigenvalue, axial and radial power profiles and control rod worth are evaluated, from which consistency of the model and results will be confirmed. Further convergence of the model within a reasonable time is assessed. / MSc (Engineering Sciences in Nuclear Engineering), North-West University, Potchefstroom Campus, 2014

Master of Science / Department of Agricultural Economics / Michael R. Langemeier / This thesis will determine if economies of size are present in production agriculture or the farming sector and if convergence or divergence is occurring. Change in the farming sector was analyzed using five-year moving averages from 1973 to 2007. Six key variables were analyzed; value of farm production, total acres, economic total expense ratio, operating profit margin ratio, asset turnover ratio, and percent of livestock income. Data from the Kansas Farm Management Association were used in this study. To be included in the study, a farm had to have five years of continuous, usable data for a five-year period between 1973 and 2007. Moving five-year averages were calculated for the farms that met this qualification. Data were sorted by value of farm production and broken down by quartiles and deciles. Trend regressions were used to calculate growth rates of the key variables and the difference between the top and bottom quartiles of the variables. Results suggested that acreage per farm is increasing, farms are doing better at covering their total economic costs, profit margin per farm has decreased, farms are utilizing their assets better, and the percent of livestock income per farm has decreased. When regressing the difference between the top and bottom quartiles to determine growth rates, it was evident that the gaps between the top and bottom quartiles of five of the six variables have widened. The differences in the percent of livestock income between farm quartiles and deciles were not significant. Convergence analysis confirmed the results of the trend regressions and suggested that divergence is evident in the Kansas farming sector. Graphical representation supports the findings of this thesis.

Master of Arts / Department of Economics / Yang M. Chang / This paper empirically examines whether there is a tendency for trade-induced price convergence - in other words if price differences among city pairs separated by a border decline with increased levels of trade. The paper examines the prices of goods in cities across Brazil and Paraguay after the implementation of MERCOSUR. Evidence of a border effect - the failure of the law of one price - between Brazil and Paraguay is found. However, the data show that since the beginning of MERCOSUR, price dispersion between Brazil and Paraguay is less for those goods that are traded more between these partners.

Le milieu du livre québécois assiste, depuis les années 1980, à une concentration progressive de son secteur. Intégré au domaine des médias et des communications, il est un acteur et un spectateur de premier plan des phénomènes de concentration et de convergence qui touchent la majorité des industries contemporaines. Un des cas emblématiques de cette situation demeure la société Quebecor qui, entre autres, par le biais de sa filiale Quebecor Media, possède 17 maisons d'édition, en plus d'une entreprise de diffusion et de distribution. Comme partout ailleurs sur le globe, la concentration - et la convergence qu'elle permet - suscite la crainte et la critique de plusieurs intervenants du livre. Malgré les appréhensions du milieu, force est de constater que trop peu d'études empiriques ont été entreprises pour corroborer ou valider les idées reçues sur le sujet. Dans l'optique de combler cette lacune et s'appuyant sur une analyse historique et quantitative, ce mémoire s'intéresse aux enjeux provoqués par les phénomènes de concentration et de convergence dans le domaine de l'édition au Québec. Plus précisément, il tente d'analyser l'émergence et l'évolution de ces phénomènes ainsi que d'en décrire les effets sur la production éditoriale, en partant du cas des Éditions Libre Expression, aujourd'hui filiale du groupe Librex, lui-même partie intégrante de Quebecor Media. Cette étude propose ainsi, en premier lieu, de remettre en perspective l'évolution du milieu du livre québécois, du début du XXe siècle à nos jours, tout en illustrant le contexte de fondation de Libre Expression. Elle expose, en deuxième lieu, l'historique de la maison d'édition, de sa fondation à son intégration au groupe Quebecor, et analyse les différents choix commerciaux de l'entreprise. Enfin, la recherche examine la production de la maison et tente de discerner son évolution ainsi que de déterminer les principaux effets engendrés par le rachat de Libre Expression par Quebecor.

Le présent mémoire porte sur deux problématiques distinctes qui s'inscrivent toutefois chacune dans le domaine de l'analyse des dépenses sociales des provinces canadiennes. La première, d'une approche essentiellement descriptive et comparée, cherche à vérifier si le Québec se distingue du rest of Canada (ROC) dans ses dépenses sociales pour la période allant de 1961 à 2008, alors que la seconde, de type plus explicatif, vise à évaluer l'influence de l'idéologie des partis politiques au pouvoir sur l'évolution des dépenses sociales provinciales pour la même période. Les résultats du chapitre consacré à la première problématique laissent tout d'abord croire que le Québec se démarque du ROC à partir du milieu des années 1970 jusqu'à la fin de la période observée par des dépenses en proportion de son PIB plus importantes dans la majorité des secteurs sociaux. Or, malgré cette claire distinction québécoise, la plupart des domaines de dépenses de la province francophone semblent tout de même suivre des tendances sensiblement similaires à celles du reste du Canada pour l'ensemble de la période, ce qui témoigne alors d'une appartenance du Québec à un certain pattern pancanadien d'évolution des dépenses sociales. Les résultats du chapitre portant sur la seconde problématique paraissent quant à eux confirmer l'existence d'un cycle partisan provincial global aux effets toutefois limités, l'alternance gauche/droite au pouvoir ayant vraisemblablement un impact modeste sur l'évolution des dépenses sociales provinciales en général. La modestie de ce cycle partisan"pancanadien" semble par ailleurs attribuable à l'existence de divergences majeures entre les provinces par rapport à ce cycle, le facteur idéologique ayant un effet considérable sur l'évolution des dépenses sociales de six d'entre elles mais étant pratiquement nul sur l'évolution des dépenses des quatre autres provinces.

This thesis presents an analysis of the dynamic process of economic growth, national welfare and the HIV/AIDS epidemic. An assessment of the methodological designs of applied growth research is undertaken in order to polarise the limitations associated with cross-sectional growth regressions. The cross-country cross- sectional methodology that has been the dominant feature of empirical growth analysis may suffer from an endogeneity and omitted variable bias. A panel data approach is adopted in order to address the econometric issues associated with cross-sectional study designs. To highlight the discrepancies between theory and empirics, a rudimentary description of the Solow model is offered. Extensions of the Solow paradigm are also discussed and form the basis of the theoretical foundations of the research. The relationship between health and economic growth within the existing literature has considered the consequences of poor population health in determining national income levels. Disease-specific effects have been included in growth regressions to capture the output losses associated with the widespread reduction in human capabilities. This thesis contributes to the existing literature by testing the empirical relationship between economic growth and the HIV/AIDS epidemic for a broad cross-section of countries. Previous empirical studies have not presented a unified account of the epidemic's effects in determining cross- country productivity differentials. The way in which the epidemic might impede economic prosperity is considered by drawing upon the existing literature. The strengths and limitations of previous study estimates are considered in relation to the study design. A more robust empirical estimator for growth regressions is proposed in the form of a system Generalised Method of Moments estimator. The research extends on previous study estimates by considering the epidemic's effect across the conditional quantiles of the growth distribution. A central prediction of the neoclassical growth paradigm relates to the convergence hypothesis in which poorer economies are considered to achieve faster growth rates. By drawing upon the distributional changes in national income over time for the entire cross-section of countries, this thesis will assess the potential barriers that may violate the theoretical predictions of the convergence hypothesis. An empirical assessment of the role of convergence clubs, mortality and poverty traps will be presented through an analysis of the changes in health and income inequality over time. The distributional shifts that have occurred over the period under analysis consider the consequences of growth as a measure of national welfare.

It is frequently the case that deterministic optimization models could be made more practical by explicitly incorporating uncertainty. The resulting stochastic optimization problems are in general more difficult to solve than their deterministic counterparts, because the objective function cannot be evaluated exactly and/or because there is no explicit relation between the objective function and the corresponding decision variables. This thesis develops random search algorithms for solving optimization problems with continuous decision variables when the objective function values can be estimated with some noise via simulation. Our algorithms will maintain a set of sampled solutions, and use simulation results at these solutions to guide the search for better solutions. In the first part of the thesis, we propose an Adaptive Search with Resampling and Discarding (ASRD) approach for solving continuous stochastic optimization problems. Our ASRD approach is a framework for designing provably convergent algorithms that are adaptive both in seeking new solutions and in keeping or discarding already sampled solutions. The framework is an improvement over the Adaptive Search with Resampling (ASR) method of Andradottir and Prudius in that it spends less effort on inferior solutions (the ASR method does not discard already sampled solutions). We present conditions under which the ASRD method is convergent almost surely and carry out numerical studies aimed at comparing the algorithms. Moreover, we show that whether it is beneficial to resample or not depends on the problem, and analyze when resampling is desirable. Our numerical results show that the ASRD approach makes substantial improvements on ASR, especially for difficult problems with large numbers of local optima. In traditional simulation optimization problems, noise is only involved in the objective functions. However, many real world problems involve stochastic constraints. Such problems are more difficult to solve because of the added uncertainty about feasibility. The second part of the thesis presents an Adaptive Search with Discarding and Penalization (ASDP) method for solving continuous simulation optimization problems involving stochastic constraints. Rather than addressing feasibility separately, ASDP utilizes the penalty function method from deterministic optimization to convert the original problem into a series of simulation optimization problems without stochastic constraints. We present conditions under which the ASDP algorithm converges almost surely from inside the feasible region, and under which it converges to the optimal solution but without feasibility guarantee. We also conduct numerical studies aimed at assessing the efficiency and tradeoff under the two different convergence modes. Finally, in the third part of the thesis, we propose a random search method named Gaussian Search with Resampling and Discarding (GSRD) for solving simulation optimization problems with continuous decision spaces. The method combines the ASRD framework with a sampling distribution based on a Gaussian process that not only utilizes the current best estimate of the optimal solution but also learns from past sampled solutions and their objective function observations. We prove that our GSRD algorithm converges almost surely, and carry out numerical studies aimed at studying the effects of utilizing the Gaussian sampling strategy. Our numerical results show that the GSRD framework performs well when the underlying objective function is multi-modal. However, it takes much longer to sample solutions, especially in higher dimensions.