A topical issue in financial economics is the development of appropriate stochastic dynamic models for banking items and behavior. The issue here is to fulfil the need to generalize the more traditional discrete-time models of banking activity to a Levy process setting. In this thesis, under the assumption that the loan market is imperfectly competitive, we investigate the evolution of banking items such as bank assets (cash, bonds, shares, Treasuries, reserves, loans and intangible assets), liabilities (demand deposits) and bank capital (bank equity, subordinate debt and loan loss reserves). Here we consider the influence of macroeconomic factors and profitability as well as its indicators return on assets (ROA) and return on equity (ROE). As far as bank assets are concerned, we note that loan pricing models usually reflect the financial funding cost, risk premium to compensate for the risk of default by the borrower, a premium reflecting market power exercised by the bank and the sensitivity of the cost of capital raised to changes in loans extended. On the other hand, loan losses can be associated with an offsetting expense called the loan loss provision (LLP), which is charged against Nett profit. This offset will reduce reported income but has no impact on taxes, although when the assets are finally written off, a tax-deductible expense is created. An important factor influencing loan loss provisioning is regulation and supervision. Measures of capital adequacy are generally calculated using the book values of assets and equity. The provisioning of loans and their associated write-offs will cause a decline in these capital adequacy measures, and may precipitate increased regulation by bank authorities. Greater level of regulation generally entail additional costs for the bank. Currently, this regulation mainly takes the form of the Basel II Capital Accord that has been implemented on the worldwide basis since 2008. It is clear that bank profitability is a major indicator of financial crises for households, companies and financial institutions. An example of this from the 2007-2008 subprime mortgage crisis (SMC) is the U.S. bank, Wachovia Corp., who reported a big loss as from the first quarter of 2007 and eventually was bought by the world's largest bank, Citigroup, on 29 September 2008. A further example from the SMC is that both the failure of the Lehman Brothers investment bank and the acquisition in September 2008 of Merrill Lynch and Bear Stearns by Bank of America and JP Morgan Chase, respectively, were preceded by a decrease in profitability and an increase in the price of loans and loan losses. The subprime mortgage crisis is characterized by contracted liquidity in the global credit markets and banking system. The level of liquidity in the banking sector affects the ability of banks to meet commitments as they become due without incurring substantial losses from liquidating less liquid assets. Liquidity, therefore, provides the defensive cash or near-cash resources to cover banks' liability. An undervaluation of real risk in the subprime market is cascading, rippling and ultimately severely adversely affecting the world economy. The downturn in the U.S. housing market, risky lending and borrowing practices, and excessive individual and corporate debt levels have caused multiple adverse effects tumbled as the US housing market slumped. Banks worldwide are hoarding cash and showing a growing reluctance to lend, driving rates that institutions charge to each other on loans to record highs. Also, global money markets are inoperative, forcing increased injections of cash from central banks. The crisis has passed through various stages, exposing pervasive weaknesses in the global financial system and regulatory framework. The stochastic dynamics of the aforementioned banking items assist in formulating a maximization problem that involves endogenous variables such as profit consumption, the value of the bank's investment in loans and provisions for loan losses as control variants. In particular, we demonstrate that the bank is able to maximize its expected utility of discounted profit consumption over a random time interval, [t,r], and terminal profit at time r. Here the term profit consumption refers to the consumption of the bank's profits by dividend payments on equity and interest and principal payments on subordinate debt. The associated Hamilton-Jacobi-Bellman (HJB) equation has a smooth solution when the optimal controls are computed by means of power, logarithmic and exponential utility functions. This enables us to make a direct comparison between the economic properties of the solutions for different choices of the utility function. In keeping with the main theme of this thesis, we simulate the financial indices ROE and ROA that are two measures of bank profitability. We further discuss optimization with power utility where we show the convergence of the Markov Chain Approximation Method (MCAM) and the impact of varying the model parameters in the form of loan loss severity, P, and loan loss frequency, <f>. We investigate the connections between the banking models and Basel II capital accord as well as the current subprime mortgage crises. As a way of conclusion, we provide remarks about the main issues discussed in the thesis and speculate about future research directions. The contents of this thesis is based on 3 peer-reviewed journal articles (see [105], [106] and [107]) and 1 peer-reviewed conference proceedings paper (see [104]). In addition, the paper [108] is currently being prepared for submission to an accredited journal. / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2009.

Learners at the public schools of North West Province in the Dr Kenneth Kaunda Education region, within the Matlosana Local municipality’s municipal area of jurisdiction, are exposed to unhygienic health hazard conditions due to insufficient toilet facilities used by a large number of learners and poor health conditions resulting out of it, which might cause and spread health related diseases to the users of these toilet facilities. The primary objective of this research was to investigate the nature and extent of the provisioning and maintenance of toilet facilities in the public schools within the Matlosana Local Municipality’s municipal area. A questionnaire was designed and distributed to obtain information from 57 respondents who comprised of the 3 schools principals who constituted 5% of the research population, 18 educators who constituted 32% and 36 learners who constituted 63%, all totalling 100% of the research sample size, at Are-Fadimeheng; Dominion Reefs and Nkagisang public schools. The findings revealed that the majority, which is 85% of the research population (learners and educators) as users of these facilities are affected and were generally unhappy about the prevailing conditions of the school toilet facilities. This they attribute to lack of proper budgeting as the main cause. The most aggravating factor is the absence of a janitor with plumbing skills to look after the schools’ toilet facilities. Findings highlighted that school learners and educators deserve as their human right to live under acceptable health conditions and clean environment. However it is the responsibility of the Government to expand the existing schools toilet structures which are in line with the National Building regulation ratio of 1:25 of users per toilet as recommended by Department of Water Affairs (DWA), to ensure health for all. The results of this study can assist the government to embark on strategic intervention programmes that can improve conditions of public schools toilet facilities in the North West Province, South Africa to meet the Millenium Development Goals (MDG) target in addressing sanitation backlogs by half in 2015. Conclusions for the study were drawn and recommendations were made for the improvement of conditions in the Public Schools Toilet facilities. / Thesis (M. Development and Management)--North-West University, Potchefstroom Campus, 2011.

A topical issue in financial economics is the development of appropriate stochastic dynamic models for banking items and behavior. The issue here is to fulfil the need to generalize the more traditional discrete-time models of banking activity to a Levy process setting. In this thesis, under the assumption that the loan market is imperfectly competitive, we investigate the evolution of banking items such as bank assets (cash, bonds, shares, Treasuries, reserves, loans and intangible assets), liabilities (demand deposits) and bank capital (bank equity, subordinate debt and loan loss reserves). Here we consider the influence of macroeconomic factors and profitability as well as its indicators return on assets (ROA) and return on equity (ROE). As far as bank assets are concerned, we note that loan pricing models usually reflect the financial funding cost, risk premium to compensate for the risk of default by the borrower, a premium reflecting market power exercised by the bank and the sensitivity of the cost of capital raised to changes in loans extended. On the other hand, loan losses can be associated with an offsetting expense called the loan loss provision (LLP), which is charged against Nett profit. This offset will reduce reported income but has no impact on taxes, although when the assets are finally written off, a tax-deductible expense is created. An important factor influencing loan loss provisioning is regulation and supervision. Measures of capital adequacy are generally calculated using the book values of assets and equity. The provisioning of loans and their associated write-offs will cause a decline in these capital adequacy measures, and may precipitate increased regulation by bank authorities. Greater level of regulation generally entail additional costs for the bank. Currently, this regulation mainly takes the form of the Basel II Capital Accord that has been implemented on the worldwide basis since 2008. It is clear that bank profitability is a major indicator of financial crises for households, companies and financial institutions. An example of this from the 2007-2008 subprime mortgage crisis (SMC) is the U.S. bank, Wachovia Corp., who reported a big loss as from the first quarter of 2007 and eventually was bought by the world's largest bank, Citigroup, on 29 September 2008. A further example from the SMC is that both the failure of the Lehman Brothers investment bank and the acquisition in September 2008 of Merrill Lynch and Bear Stearns by Bank of America and JP Morgan Chase, respectively, were preceded by a decrease in profitability and an increase in the price of loans and loan losses. The subprime mortgage crisis is characterized by contracted liquidity in the global credit markets and banking system. The level of liquidity in the banking sector affects the ability of banks to meet commitments as they become due without incurring substantial losses from liquidating less liquid assets. Liquidity, therefore, provides the defensive cash or near-cash resources to cover banks' liability. An undervaluation of real risk in the subprime market is cascading, rippling and ultimately severely adversely affecting the world economy. The downturn in the U.S. housing market, risky lending and borrowing practices, and excessive individual and corporate debt levels have caused multiple adverse effects tumbled as the US housing market slumped. Banks worldwide are hoarding cash and showing a growing reluctance to lend, driving rates that institutions charge to each other on loans to record highs. Also, global money markets are inoperative, forcing increased injections of cash from central banks. The crisis has passed through various stages, exposing pervasive weaknesses in the global financial system and regulatory framework. The stochastic dynamics of the aforementioned banking items assist in formulating a maximization problem that involves endogenous variables such as profit consumption, the value of the bank's investment in loans and provisions for loan losses as control variants. In particular, we demonstrate that the bank is able to maximize its expected utility of discounted profit consumption over a random time interval, [t,r], and terminal profit at time r. Here the term profit consumption refers to the consumption of the bank's profits by dividend payments on equity and interest and principal payments on subordinate debt. The associated Hamilton-Jacobi-Bellman (HJB) equation has a smooth solution when the optimal controls are computed by means of power, logarithmic and exponential utility functions. This enables us to make a direct comparison between the economic properties of the solutions for different choices of the utility function. In keeping with the main theme of this thesis, we simulate the financial indices ROE and ROA that are two measures of bank profitability. We further discuss optimization with power utility where we show the convergence of the Markov Chain Approximation Method (MCAM) and the impact of varying the model parameters in the form of loan loss severity, P, and loan loss frequency, <f>. We investigate the connections between the banking models and Basel II capital accord as well as the current subprime mortgage crises. As a way of conclusion, we provide remarks about the main issues discussed in the thesis and speculate about future research directions. The contents of this thesis is based on 3 peer-reviewed journal articles (see [105], [106] and [107]) and 1 peer-reviewed conference proceedings paper (see [104]). In addition, the paper [108] is currently being prepared for submission to an accredited journal. / Thesis (Ph.D. (Applied Mathematics))--North-West University, Potchefstroom Campus, 2009.

Learners at the public schools of North West Province in the Dr Kenneth Kaunda Education region, within the Matlosana Local municipality’s municipal area of jurisdiction, are exposed to unhygienic health hazard conditions due to insufficient toilet facilities used by a large number of learners and poor health conditions resulting out of it, which might cause and spread health related diseases to the users of these toilet facilities. The primary objective of this research was to investigate the nature and extent of the provisioning and maintenance of toilet facilities in the public schools within the Matlosana Local Municipality’s municipal area. A questionnaire was designed and distributed to obtain information from 57 respondents who comprised of the 3 schools principals who constituted 5% of the research population, 18 educators who constituted 32% and 36 learners who constituted 63%, all totalling 100% of the research sample size, at Are-Fadimeheng; Dominion Reefs and Nkagisang public schools. The findings revealed that the majority, which is 85% of the research population (learners and educators) as users of these facilities are affected and were generally unhappy about the prevailing conditions of the school toilet facilities. This they attribute to lack of proper budgeting as the main cause. The most aggravating factor is the absence of a janitor with plumbing skills to look after the schools’ toilet facilities. Findings highlighted that school learners and educators deserve as their human right to live under acceptable health conditions and clean environment. However it is the responsibility of the Government to expand the existing schools toilet structures which are in line with the National Building regulation ratio of 1:25 of users per toilet as recommended by Department of Water Affairs (DWA), to ensure health for all. The results of this study can assist the government to embark on strategic intervention programmes that can improve conditions of public schools toilet facilities in the North West Province, South Africa to meet the Millenium Development Goals (MDG) target in addressing sanitation backlogs by half in 2015. Conclusions for the study were drawn and recommendations were made for the improvement of conditions in the Public Schools Toilet facilities. / Thesis (M. Development and Management)--North-West University, Potchefstroom Campus, 2011.

Charitable food assistance programs such as food banks, food pantries, soup kitchens and community meals are the main food resource available to Canadians who are experiencing food insecurity. A survey was conducted with 48 agencies that operate food assistance programs in Greater Victoria, 30 of which were providing meals. In comparison to groceries or hampers, meals made up the majority of food relief available in the region. An exploration of the characteristics, resources and resource-related challenges of charitable meal programs provided insight as to how the food relief system operates, who is being served and the limitations facing agencies responding to food needs at the community-level. A comparison of meal provisioning in a selection of meal programs in 2011 to a similar survey conducted in 2008 found meal provisioning increased two-fold over this three year time span, all while agencies relied more on food donations and nearly half underwent major changes to their services mainly due to constrained resources. This study afforded the opportunity to discuss responsiveness of this system to food insecurity in Greater Victoria. / Graduate

Capacity pooling in production systems, in the form of production capacity or inventory pooling, has been extensively studied in the literature. While production capacity pooling has been proven to be beneficial, the impact of inventory pooling has been less significant. These results cannot be easily extended to repairable systems due to fundamental differences between repairable and production systems. For one thing, in repairable systems, the demand rate is a function of the number of operational machines, whereas it is exogenous and constant in production systems. In this Thesis, to serve different fleets of machines possibly at different locations, we study whether repair shop pooling is more cost effective than having dedicated on-site repair shops for each fleet. In the first model, we consider transportation delays and related costs, which have been traditionally ignored in the literature. We include on-site spare-part inventories that operate according to a continuous-review base-stock policy. Our numerical findings indicate that when transportation costs are reasonable, repair shop pooling is a better alternative. Next, we model a pooled repair shop that fixes failed components from different k-out-of-n:G systems. We permit a shared spare parts inventory serving all systems and/or reserved spare parts inventories for each system; we call this a hybrid model. The destination for a repaired component can be chosen either on a first-come-first-served basis or by following a static priority rule. Our findings show that both hybrid policies are more cost effective than having separate repair shops and inventories for each system. We propose implementing the multilevel rationing (MR) policy in systems with shared inventory. The MR policy prioritizes classes, and stops serving a class from inventory if the inventory level is below the inventory threshold identified for that class. When there is no inventory, the repaired component is sent to the highest priority class among those with down machines. To approximate the cost of the MR policy, we study an M/G/1//N queueing system serving multiple classes of customers with an unreliable server. Our numerical findings indicate that the MR policy performs as well as the epsilon-optimal policy and outperforms the hybrid policies.

Capacity pooling in production systems, in the form of production capacity or inventory pooling, has been extensively studied in the literature. While production capacity pooling has been proven to be beneficial, the impact of inventory pooling has been less significant. These results cannot be easily extended to repairable systems due to fundamental differences between repairable and production systems. For one thing, in repairable systems, the demand rate is a function of the number of operational machines, whereas it is exogenous and constant in production systems. In this Thesis, to serve different fleets of machines possibly at different locations, we study whether repair shop pooling is more cost effective than having dedicated on-site repair shops for each fleet. In the first model, we consider transportation delays and related costs, which have been traditionally ignored in the literature. We include on-site spare-part inventories that operate according to a continuous-review base-stock policy. Our numerical findings indicate that when transportation costs are reasonable, repair shop pooling is a better alternative. Next, we model a pooled repair shop that fixes failed components from different k-out-of-n:G systems. We permit a shared spare parts inventory serving all systems and/or reserved spare parts inventories for each system; we call this a hybrid model. The destination for a repaired component can be chosen either on a first-come-first-served basis or by following a static priority rule. Our findings show that both hybrid policies are more cost effective than having separate repair shops and inventories for each system. We propose implementing the multilevel rationing (MR) policy in systems with shared inventory. The MR policy prioritizes classes, and stops serving a class from inventory if the inventory level is below the inventory threshold identified for that class. When there is no inventory, the repaired component is sent to the highest priority class among those with down machines. To approximate the cost of the MR policy, we study an M/G/1//N queueing system serving multiple classes of customers with an unreliable server. Our numerical findings indicate that the MR policy performs as well as the epsilon-optimal policy and outperforms the hybrid policies.

Many next-generation e-science applications require fast and reliable transfer of large volumes of data, now frequently termed as ``big data", with guaranteed performance, which is typically enabled by the bandwidth reservation service in high-performance networks (HPNs). Users normally specify the properties and requirements of their data transfers in the bandwidth reservation requests (BRRs), and want to make bandwidth reservations on the HPNs to satisfy the requirements of their data transfers. The challenges of the bandwidth reservation arise from the requirements desired by both the users and the bandwidth reservation service providers of the HPNs. We focus on two important bandwidth reservation problems formulated from the combinations of the requirements from both users and the bandwidth reservation service providers of the HPNs: (i) Problem of scheduling all BRRs in one batch while achieving their best average data transfer earliest completion time and shortest duration, and (ii) Problem of scheduling two generic types of BRRs concerning data transfer reliability with different objectives and constraints in unreliable HPNs that are subject to node and link failures. We prove the two subproblems of the first problem are NP-complete problems, and fast and efficient heuristic algorithms are proposed. While the two subproblems of the second problem can be optimally solved in polynomial time. The corresponding optimal algorithms and proofs are given. We conduct extensive simulations to compare the performance of the proposed heuristic and optimal algorithms with naive scheduling algorithms and the algorithms currently used in production network in various performance metrics. The performance superiority of the proposed heuristic and optimal algorithms is verified.

L’IMS (IP Multimedia Subsystem) constitue l’architecture clé de contrôle pour les réseaux de nouvelle génération (NGN : Next Generation Network). IMS offre aux opérateurs réseaux la possibilité d'étendre leurs services, en intégrant la voix et des communications multimédia et de les livrer dans de nouveaux environnements avec de nouveaux objectifs. Sa sécurité totale mais à moindre coût est donc primordiale, principalement l’authentification. En IMS l’authentification est divisée en deux phases, une au niveau du domaine PS (Packet-Switch) avec le protocole 3GPP-AKA, et l’autre au niveau IMS en utilisant le protocole IMS-AKA. Dans notre première contribution, nous proposons un nouveau protocole d’authentification plus sécurisé que celui utilisé en IMS (IMS-AKA) et plus performant en termes d’utilisation de la bande passante et de temps de traitement. Notre méthode d’analyse repose sur la quantification de la signalisation induite par l’authentification IMS. La quantification est effectuée à l’aide d’expérimentations réelles. Sur la base des résultats obtenues, nous pouvons confirmer que notre protocole (1) peut économiser au moins 21,5% du trafic SIP/Cx par rapport à l’IMS-AKA, (2) permet de réduire la consommation de la bande passante de 27% par rapport à l’IMS-AKA, (3) résiste aux attaques atteignant la confidentialité et l’intégrité des données lors d’un enregistrement IMS (validé par AVISPA). Dans notre seconde contribution, nous avons présenté un nouveau modèle, nommé virtual walled-garden, de fourniture de services centré sur l'utilisateur en IMS. Ce modèle de fourniture de service permet d'offrir plus de liberté d'utiliser les services de tout fournisseur de contenu en fonction des besoins et préférences des utilisateurs. De cette manière les trois parties (utilisateur, fournisseurs de services et opérateur IMS) sont satisfaites. Les utilisateurs auront accès à un plus large éventail de services soutenus par l'IMS, les fournisseurs de services peuvent mettre en œuvre un large éventail de services IMS/SIP sans aucun investissement sur la mise en œuvre d'un réseau de cœur IMS ou de sa maintenance. Quant aux opérateurs cette façon de faire constitue une nouvelle forme de partenariat d'affaires avec les fournisseurs de services. Le modèle virtual walled-garden se base sur une fédération d'identité multi niveaux pour prendre en considération plusieurs niveaux de sécurité selon la criticité des applications sollicitées. / The IMS (IP Multimedia Subsystem) architecture is the key control for next generation networks (NGN). IMS gives network operators the opportunity to extend their services, including voice and multimedia communications and deliver them in new environments with new goals. Its security is paramount, especially authentication. In IMS, authentication is divided into two phases a PS (Packet-Switch) domain-level with the 3GPP-AKA protocol, and a second at IMS level using the IMS-AKA protocol. In our first contribution, we propose a new IMS authentication mechanism that improves the IMS-AKA in terms of security and more efficient in the use of bandwidth and processing time. Based on the results obtained, we can confirm that our protocol can save at least 21.5% of SIP/Cx traffic compared to the IMS-AKA and resists to attack reaching the confidentiality and integrity of data in an IMS registration (validated by AVISPA). In our second contribution, we propose a new Service provisioning model: Virtual Walled-Garden. This new model allows the user accessing all the applications, even the external ones transparently, simulating a walled-garden environment. This model will create a trust link between IMS domain and external services, and will reduce the burden of both end users and SPs through a Single Sign-On (SSO) feature, using identity federation. We also introduce the notion of security level to classify the SPs in a Multi-level model.

The production of energy alternative can provide economic development and employment opportunities, especially in agricultural areas. The work seeks as main objectives the rising and the statistical treatment of the data of winds of the State of Sergipe. As specific objectives still seek the simulation of the annual energy generated starting from an aerogenerating for rural use, and the simulation of the amount of water capable of being pumped through a low cost bomb and potency.The values of the meteorological variables were obtained in stations automatic meteorological and you stipulate distributed in the State. These elements served as base for rising of the medium speeds of wind, the schedules of better use of the system aeolian. The statistical treatment for determination of the behavior of the winds in the researched municipal districts was beacon in the calculation of averages, variances, distribution of frequencies and of the function of distribution of probability Rayleigh, case peculiar of the distribution Weibull, thoroughly diffused in studies of potential aeolian. These analyses allowed to extract all the information starting from the obtained gross data of the stations and they were simulate in the software Statistica 7.0. The period of the day in that were registered to largest medium speeds it is the period of the afternoon understood between 12:00 hours and 18:00 hours for all the researched municipal districts, being this period chosen for the simulations in software. As the use and simulations of the system aeolian to assist the needs of agricultural electric feeding were used as model for the tests a turbine aeolian with potency of 400 W, simulated in the Software EOLOSOFT of NUTEMA-PUCRS and all the municipal districts presented conditions of wind speed capable to supply the essential provisioning, mainly in what it tells respect the provisioning of water for consumption and irrigation. It was not white of this work the study of economic viability of the system aeolian in relation to the cost of the turbine and accessories of the system for maker. / A produção de energia alternativa pode prover desenvolvimento econômico e oportunidades de emprego, especialmente em áreas Rurais. O trabalho visa como objetivos principais o levantamento e o tratamento estatístico dos dados de ventos do Estado de Sergipe. Como objetivos específicos visa ainda a simulação da energia anual gerada a partir de um aerogerador para uso rural, e a simulação da quantidade de água capaz de ser bombeada através de uma bomba de baixo custo e potência. Os valores das variáveis meteorológicas foram obtidos em estações agrometeorológicas automáticas e convencionais distribuídas no Estado. Estes elementos serviram de base para levantamento das velocidades médias de vento, os horários de melhor aproveitamento do sistema eólico. O tratamento estatístico para determinação do comportamento dos ventos nos municípios pesquisados balizou-se no cálculo de médias, variâncias, distribuição de freqüências e da função de distribuição de probabilidade Rayleigh, caso particular da distribuição Weibull, amplamente difundida em estudos de potencial eólico. Estas análises permitiram extrair todas as informações a partir dos dados brutos obtidos das estações e foram simuladas no software Statistica 7.0. O período do dia em que foram registradas a maiores velocidades médias é o período da tarde compreendido entre 12:00 horas e 18:00 horas para todos os municípios pesquisados, sendo este período escolhido para as simulações em software. Quanto a utilização e simulações do sistema eólico para atender as necessidades de alimentação elétrica rural foi utilizado como modelo para os testes uma turbina eólica com potência de 400 W, simulada no Software EOLOSOFT do NUTEMA-PUCRS e todos os municípios apresentaram condições de velocidade de vento capaz de fornecer o abastecimento essencial, principalmente no que diz respeito a abastecimento de água para consumo e irrigação. Não foi alvo deste trabalho o estudo de viabilidade econômica do sistema eólico em relação ao custo da turbina e acessórios do sistema por fabricante.