In this work we develop and analyze algorithms motivated by the parameter estimation problem corresponding to a multilayer aquifer/interbed groundwater flow model. The parameter estimation problem is formulated as an optimization problem, then addressed with algorithms based on adjoint equations, quasi-Newton schemes, and multilevel optimization. In addition to the parameter estimation problem, we consider properties of the parameter to solution map. This includes invertibility (known as identifiability) and differentiability properties of the map. For differentiability, we expand existing results on Fréchet sensitivity analysis to convection diffusion equations and groundwater flow equations. This is achieved by proving that the Fréchet  derivative of the solution operator is Hilbert-Schmidt, under smoothness assumptions for the parameter space. In addition, we approximate this operator by time dependent matrices, where their singular values and singular vectors converge to their infinite dimension peers. This decomposition proves to be very useful as it provides vital information as to which perturbations in the distributed parameters lead to the most significant changes in the solutions, as well as applications to uncertainty quantification. Numerical results complement our theoretical findings. / Ph. D.

In this work we present a new tool for the convergence analysis of numerical optimization methods. It is based on the concepts of the Clarke derivative and set-valued mappings. Our goal is to apply this tool to minimization problems with non-smooth and noisy objective functions. After deriving a necessary condition for minimizers of such functions, we examine two unconstrained optimization routines. First, we prove new convergence theorems for Implicit Filtering and General Pattern Search. Then we show how these results can be used in practice, by executing some numerical computations. / Master of Science

No / Despite promising early data, the natural product dolastatin 10 has not been successful as a single agent in phase II clinical trials. Herein the mechanism of action and efficacy of a synthetic analogue, auristatin PYE, was investigated in 2 human colon adenocarcinoma models, DLD-1 and COLO 205. In vivo efficacy was assessed in subcutaneous xenografts following intravenous administration. Mechanistic studies investigated effects of auristatin PYE on microtubule disruption using immunocytochemistry, whilst cell cycle effects were studied using flow cytometry. Possible effects on tumour functional blood vasculature were assessed in tumour-bearing mice. Auristatin PYE was less potent in vitro than dolastatin 10, but was significantly more effective (p<0.01) in vivo against both tumours. Significant effects on tumour blood vasculature were seen, with optimal shutdown at 6-h post-treatment. Extensive necrosis became more evident over time after treatment. Auristatin PYE caused severe disruption of normal microtubule structure at concentrations and times comparable with the IC50 data, and also instigated a G2/M cell cycle block. Auristatin PYE was more effective in the DLD-1 and COLO 205 models than dolastatin 10, with anti-tumour effects mediated through vascular shutdown. These data suggest that auristatin PYE has good potential as an anti-cancer agent.

Corn production is scattered geographically over various continents, but most of it is grown in the United States. As such, the world price of corn futures contracts is largely dominated by North American corn prices as traded on the Chicago Board of Trade. In recent years, this market has been characterised by an increase in price volatility and magnitude of price movement as a result of decreasing stock levels. The development and implementation of an effective and successful derivative price risk management strategy based on the Chicago Board of Trade corn futures contract will therefore be of inestimable value to market stakeholders worldwide. The research focused on the efficient market hypothesis and the possibility of contesting this phenomenon through an application of a derivative price risk management methodology. The methodology is based on a combination of an analysis of market trends and technical oscillators with the objective of generating returns superior to that of a market benchmark. The study found that market participants are currently unable to exploit price movement in a manner which results in returns that contest the notion of efficient markets. The methodology proposed, however, does allow the user to consistently achieve returns superior to that of a predetermined market benchmark. The benchmark price for the purposes of this study was the average price offered by the market over the contract lifetime, and such, the efficient market hypothesis was successfully contested. / Business Management / D. Com. (Business Management)

Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2006. / An overview of modern and historical interest rate model theory is given with the specific aim of derivative pricing. A variety of stochastic interest rate models are discussed within a South African market context. The various models are compared with respect to characteristics such as mean reversion, positivity of interest rates, the volatility structures they can represent, the yield curve shapes they can represent and weather analytical bond and derivative prices can be found. The distribution of the interest rates implied by some of these models is also found under various measures. The calibration of these models also receives attention with respect to instruments available in the South African market. Problems associated with the calibration of the modern models are also discussed.

In this dissertation, we use the Natural transform decomposition method to obtain approximate analytical solution of fractional differential equations. This technique is a combination of decomposition methods and natural transform method. We use the Adomian decomposition, the homotopy perturbation and the Daftardar-Jafari methods as our decomposition methods. The fractional derivatives are considered in the Caputo and Caputo- Fabrizio sense. / Mathematical Sciences / M. Sc. (Applied Mathematics)

A partir des années 1970, la remise en cause du système monétaire des parités fixes entraine l'apparition de risques nouveaux sur les marchés, et conduit les opérateurs financiers à rechercher de nouvelles techniques pour en maitriser les effets : les premiers instruments financiers dérivés naissent de cette volonté. Pour autant, au moment de reconnaitre juridiquement ces instruments, le législateur quant à lui ne prévoit aucune qualification ni définition précises et adopte la technique peu concluante de l'énumération. Ce qui laisse présager que les dérivés ne peuvent fonder une notion juridique unitaire mais constituent simplement l'addition de modèles financiers hétérogènes. Dès lors, la recherche de la nature juridique du dérivé se doit de démontrer sa spécificité en tant qu'instrument de transfert du risque financier à part entière et le caractériser par rapport aux autres familles de contrats nommés. En outre, si le dérivé opère un transfert de risque, il s'avère lui-même générateur d'un risque spécifique, à la fois pour les parties qui le concluent et pour les tiers en relation avec ces dernières: par ses attributs intrinsèques, il est donc fondamentalement porteur de risque pour le système financier dans son ensemble. La nécessité de reconnaitre ce risque et de le contrôler étroitement se pose alors en objectif impérieux. / From 1970s, the questioning of the monetary system of the fixed parities causes the appearance of new risks on markets, and leads financial players to look for new techniques to master the effects: the first derivative financial instruments arise from this will. However, at the time of recognizing legally these instruments, the legislator as for him plans no precise qualification and no definition and adopts the little decisive technique of the enumeration. What leads to predict that derivatives cannot base a unitarian legal notion but constitute simply the addition of heterogeneous financial models. From then on, the research for the legal nature of derivative owes demonstrate its specificity as instrument of transfer of the full financial risk and to characterize it with regard to the other families of named contracts. Besides, if the derivative operates a transfer of risk, it turns out itself generator of a specific risk, at the same time for the parties which conclude it and for thirds in connection with the latter: by its intrinsic attributes, it is fundamentally carrying risk to the whole financial system. The necessity of recognizing this risk and of controlling it closely settles then in compelling objective.

This thesis deals with the introduction of function of two variables and differential calculus of this function. This work should serve as a textbook for students of elementary school's teacher. Each chapter contains a summary of basic concepts and explanations of relationships, then solved model exercises of the topic and finally the exercises, which should solve the student himself. Thesis have transmit to students basic knowledges of differential calculus of functions of two variables, including practical knowledges.

This thesis includes solving the basic examples of differential calculus (especially two and three variables). The work covers examples of the solutions of the domain, the first and second partial derivatives, determining the functions of local extremes (both explicitly and implicitly given) and find the equation of the tangent plane to a point in the graphs of functions. The examples are sorted by difficulty.

Actuellement, le traitement des pathologies infectieuses chez les bovins et les animaux de compagnie est menacé par l’accroissement de l’antibiorésistance et des bactéries multirésistantes. Il est donc primordial pour les entreprises pharmaceutiques vétérinaires de développer de nouvelles gammes d’agents antibactériens spécifiques au domaine animale. Dans ce contexte, il a été montré que certains polyaminostérols naturels tels que la squalamine possèdent un fort potentiel antimicrobien. Ainsi, l’objectif de ce travail de thèse est de répondre à la problématique présentée par la société Virbac dans le traitement des mammites (bovins) et des otites/pyodermites (chien) par le développement d’une nouvelle classe de dérivés polyaminostéroïdiens synthétiques à large spectre antimicrobien. Pour cela, nous avons constitué une chimiothèque de composés originaux préparés à partir de différents acides biliaires selon des voies de synthèse inédites. Ces composés ont été évalués in vitro pour leur cytotoxicité et leurs activités antibactériennes contre diverses bactéries à Gram positif et à Gram négatif et nous avons pu établir la preuve de concept in vitro de leur potentiel thérapeutique en tant qu’agents antibactériens ou adjuvants d’antibiotiques. De plus, nous avons montré que l’un de ces nouveaux dérivés, la claramine A1, agit sur l’intégrité physique des membranes bactériennes et sur les performances d'efflux des pompes AcrAB-TolC. Ainsi, il apparaît finalement que ces dérivés polyaminostéroïdiens au mode d’action non conventionnel pourraient constituer une nouvelle classe d’agents antibactériens pour un usage en tant que substituts d’antibiotiques en médecine vétérinaire. / Currently, the treatment of infectious pathologies in cattle and pets is threatened by the growing antimicrobial resistance and the development of multidrug-resistant bacteria. Thus it is necessary for the veterinary pharmaceutical firms to develop new lines of antibacterial agents. In this context, some natural polyaminosterols such as squalamine have gained interest due to their potent antimicrobial activities. Thus the aim of this PhD work is to provide an answer in the treatment of mastitis (cattle) and otitis/pyoderma (dog) by the development of a new class of synthetic polyaminosterols with a broad spectrum of antibacterial activity. In this purpose, a chemical library of original compounds has been prepared starting from various bile acids by using unprecedented synthesis procedures. These compounds were evaluated for their in vitro cytotoxicity on CHO cells as well as their antibacterial activities against Gram-positive and Gram-negative bacteria and we have establish the in vitro proof of concept of the therapeutic potential of this family of molecules as antibacterial agent or antibiotic adjuvant. Additional investigations were then conducted on one of these novel derivatives namely claramine A1 to deepen knowledge of its mechanism of action and showed that claramine A1 acts on the physical integrity of bacterial membranes and the efflux performance of AcrAB-TolC pumps. Based on the results of claramine A1, it finally appears that these new polyaminosterol derivatives possessing a non-classical mode of action pertain to a new class of antibacterial agents and could constitute a substitute for traditional antibiotics in veterinary medicine.