Philosophiae Doctor - PhD / This study attempts to understand how distance education practices influence the learning of calculus. Understanding student learning in a distance education environment is an important factor to consider in improving the learning experiences of those students who for one reason or the other opt not to study in conventional institutions of higher education. On one hand, understanding student learning may illuminate the influences that the learning environment has on student learning and on the other hand, it may inform on how learning experiences can be improved. The aim of this study is to acquire a deeper understanding of the diverse manner in which distance students learn calculus. Specific focus is also placed on how the distance education context of the Zimbabwe Open University (ZOU) influences student learning. The study describes a group of students' experiences of learning calculus in the ZOU distance education environment. The study also describes the students' learning styles and relates these to their mathematical understanding of certain calculus concepts. The specific content topics of "limit of function" and "derivative of function" are used to view achievement and performance, thereby indicating the distance students' mathematical understanding. The information processing learning theory is used as the theoretical framework for this study. The constructs of learning styles and mathematical understanding are used to illuminate the student's learning processes. The study used the Felder-Silverman learning styles model and Hiebert and Carpenter's notion of mathematical understanding to expound these constructs. The distance education environment of the B.Sc. Mathematics and Statistics (BSMS) programme at the ZOU provided the context of the study and an interpretive case study approach was adopted. A group of students registered in a first year first semester calculus course were studied. Data were collected from students based in four ZOU regional centres; namely Harare, Mashonaland Central, Mashonaland West, and Masvingo. These regional centres were conveniently selected for the study on the basis of proximity and accessibility. A total sample of twenty six students was involved and data for the in-depth part of the study emanated from five students who were purposively selected to participate in interviews. The interviewees were selected on the basis of their performance in a written calculus test. Data for this study were collected through use of learning journals, learning styles preference questionnaires, calculus tests and interviews. The data on students' learning experiences were predominantly qualitative in nature though supported by some quantitative data. The data on learning styles and mathematical understanding were also qualitatively analysed and presented case by case for the five interviewees. The study established that in a distance education system, the type of learning environment has the potential to influence students' learning, both positively and negatively, of which the main contributing factor is the learning support system. The study found that the learning support system provided by the institution and distance educators can have an impact on student learning. With reference to the calculus course in the BSMS programme, the study identified specific aspects where the environment facilitated or deterred learning. The study also revealed that students have varied learning style preferences, and that the learning environment has the potential to impact on students' learning styles. Since learning styles occupy a central place when it comes to improving distance learning materials, the study further explored the relationship between the constructs of learning styles and mathematical understanding. The study revealed that students' learning styles can influence the students' mathematical understanding. Improving students' learning in a distance education environment rests mainly on improving the learning materials and the support systems. A carefully designed and well supported instructional distance learning package can facilitate learning. Implications of the findings point towards the improvement of the distance teaching processes through the improvement of learning materials and the learning support systems for the BSMS distance education programme.

The aim of diploma thesis named “QRS detection using wavelet transform” is to simplify and accelerate the work of doctors. This can be achieved by using application for QRS detection, which can use one of four proposed algorithms. Application shows basic informations about inserted electrocardiogram. Part of this program is a graphical window with displayed record and with coloured marks on detected QRS complexes. By another algorythm are marks color-coded due to accurancy percentil of every detected complex. This program is designed for a several hours record from Holter ECG monitoring.

Afin de mieux cerner les enjeux de la transition entre le secondaire et le postsecondaire, nous proposons un examen du passage de la notion de fonction à celle de dérivée. À la lumière de plusieurs travaux mettant en évidence des difficultés inhérentes à ce passage, et nous basant sur les recherches de Carlson et ses collègues (Carlson, 2002; Carlson, Jacobs, Coe, Larsen et Hsu, 2002; Carlson, Larsen et Jacobs, 2001; Oehrtman, Carlson et Thompson, 2008) sur le raisonnement covariationnel, nous présentons une analyse de la dynamique du développement de ce raisonnement chez des petits groupes d’élèves de la fin du secondaire et du début du collégial dans quatre situations-problèmes différentes. L’analyse des raisonnements de ces groupes d’élèves nous a permis, d’une part, de raffiner la grille proposée par Carlson en mettant en évidence, non seulement des unités de processus de modélisation (ou unités de raisonnement) mises en action par ces élèves lors des activités proposées, mais aussi leurs rôles au sein de la dynamique du raisonnement. D’autre part, cette analyse révèle l’influence de certaines caractéristiques des situations sur les interactions non linéaires entre ces unités. / To better understand the transitional challenges between high-school and post-secondary education, we propose a study of the passage from the notion of function to the notion of derivative. Based on numerous studies on the difficulties related to this passage and, more specifically, on the work of Carlson and colleague’s (Carlson, 2002; Carlson, Jacobs, Coe, Larsen & Hsu, 2002; Carlson, Larsen & Jacobs, 2001; Oehrtman, Carlson & Thompson, 2008) on covariational reasoning, we present an analysis of the dynamics of the development of covariational reasoning. By submitting four different problem-situations to small groups of students ending secondary school and beginning college (15-18 years old), we were able to examine that development. On one hand, the analysis of the reasoning of those students allowed us to refine the grid proposed by Carlson, bringing out, not only the reasoning units used by those students during the proposed activities, but also their role in the dynamic of the reasoning. On the other hand, this analysis reveals the influence of certain characteristics of the situations on the non-linear interactions between those units.

Les marchés futures de matières premières existent depuis des siècles. Néanmoins, depuis le début du 21e siècle, le développement en parallèle de la financiarisation et de marchés futures sur une matière première non-stockable (l’électricité) a bouleversé leur fonctionnement.Les trois essais de cette thèse étudient théoriquement et empiriquement les marchés futures de matières premières dans différentes conditions de fonctionnement.Le premier essai est une étude empirique qui montre l’existence de l’effet Samuelson sur les marchés futures d’électricité. Ce faisant, il montre que le stockage n’est pas une condition nécessaire à l’existence d’un tel effet.Le second essai est un modèle qui montre comment le comportement dynamique des prix d’une matière première stockable sur un marché futures segmenté du reste de l’économie est impacté par ses caractéristiques physiques, et notamment par le coût de stockage.Enfin, le troisième essai est un modèle qui montre que la financiarisation modifie la fonction de partage des risques des marchés futures de matières premières, et ce, quelle que soit la maturité concernée. / Commodity futures markets have a long history. However, since the beginning of the 21st century, both the financialization process and the development of futures markets on a non-storable commodity (the electricity) have shake up their functioning.The three essays of this thesis study theoretically and empirically commodity futures markets in different situations of functioning.The first essay is an empirical study that shows that the Samuelson effect exists on electricity derivative markets. As a consequence, it shows that storage is not a necessary condition for such an effect.The second essay is a model that shows how the dynamic behavior of storable commodity prices on a segmented futures market is affected by its physical characteristics, and more precisely by the cost of storage.Further, the third essay is a model that shows that financialization changes the risk sharing function of commodity futures markets, whatever the concerned maturity.

Orientador: Marcelo Carvalho Minhoto Teixeira / Resumo: Esta tese propõe projetos de controle H_infinito e controle H_infinito chaveado para uma classe de sistemas lineares com incertezas invariantes no tempo, nos quais apenas a derivada do vetor de estado é considerada para realimentação. Neste cenário, as estratégias propostas utilizam dinâmicas auxiliares, cujas variáveis de estado estão disponíveis para realimentação, para controlar a planta original. São propostas estruturas e procedimentos de projeto por meio de desigualdades matriciais lineares. A primeira estrutura de controle apresentada, considera a saturação do atuador e um integrador para definir a estratégia de controle, e se as condições propostas são factíveis, assegura que o ponto de equilíbrio do sistema de malha fechada seja localmente assintoticamente estável, para todas as condições iniciais em uma região elipsoidal, contida em uma determinada região definida para a nova dinâmica. Na segunda estrutura, é proposta uma técnica sem o uso de integradores para definir as estratégias para o controle chaveado e controle H_infinito chaveado, para plantas com e sem saturação da entrada de controle. Na terceira estrutura, considera-se um caso mais geral porém com o uso de integradores para definir as estratégias para o controle chaveado e controle H_infinito chaveado, para plantas sem saturação da entrada de controle. Embora todos os projetos propostos considerem a dinâmica auxiliar, são asseguradas as propriedades de estabilidade, taxa de decaimento e custo garantido pa... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This thesis proposes H_infinite switched control designs for a class of linear systems with time invariant uncertainties, where only the derivative of the state vector is considered for feedback. In this scenario, the proposed strategies use auxiliary dynamics, whose state variables is accessible for feedback, to control the original plant. The proposed structures and design procedures are based on LinearMatrix Inequalities (LMIs). The first structure considers the actuator saturation and an integrator to define the control strategy, and if the proposed conditions are feasible, it assures that the equilibrium point of the closed-loop system is locally asymptotically stable, for all initial conditions in an ellipsoidal region, which is within a given region defined for this new dynamic. In the second structure, we adopted a technique without the use of integrators to define the strategies for the switched control and H_infinite switched control, for plants with and without control input saturation. In the third structure, we study a more general case, however, with the use of integrators to define the strategies for the switched control and H_infinite switched control, for plants without control input saturation. Although all proposed designs consider the auxiliary dynamics, it is assured the stability, decay rate proprieties, and H_infinite guaranteed cost for the original plant. Simulation examples and practical implementation illustrate the effectiveness of the proposed app... (Complete abstract click electronic access below) / Doutor

This thesis critically examines the statutory unfair prejudice remedy provided for in section 163 of the Companies Act 71 of 2008 (‘the Act’). Section 163 is evaluated against its equivalents in England, Australia and Canada. Section 163 is considered against its predecessors to determine whether problems associated with the formulation and application of its predecessors have now been eradicated. It is argued that although it is important to ensure that company legislation is able to provide protection of an international standard to shareholders to be able to attract capital investment in a competitive market, one has to be cautious of slavishly following legislative trends in foreign jurisdictions. The South African legislature indiscriminately incorporated only parts of the Canadian unfair prejudice remedy in section 163. This approach also resulted, amongst others, in the introduction of foreign concepts. The legislature further failed to take cognisance of the unique historical developments relating to the unfair prejudice remedy in South Africa. This has led to the reintroduction of problems experienced with previous formulations of the statutory unfair prejudice remedy in South Africa and left certain problems relating to the interpretation and application of the statutory unfair prejudice remedy unresolved. Consideration is also given to the interrelationship between section 163 and some of the statutory remedies in the Act. Section 163 is also assessed in the context of the Constitution of the Republic of South Africa, 1996. In conclusion, recommendations for possible legislative amendments are made and an interpretational framework for the interpretation and application of the statutory unfair prejudice remedy in section 163 is provided. / Mercantile Law / LL. D. (Mercantile Law)

L'objectif de ce travail fut le développement de nouvelles méthodes pour aborder certainsproblèmes inverses en élasticité, en tirant parti de la présence d'un petit paramètre dans ces problèmespour construire des approximation asymptotiques d'ordre élevé.La première partie est consacrée à l'identification de la taille et la position d'une inhomogénéité$BTrue$ enfouie dans un domaine élastique tridimensionnel. Nous nous concentrons sur l'étude defonctions-co^uts $Jbb(Br)$ quantifiant l'écart entre $BTrue$ et une hétérogénéité ``test'' $Br$. Unetelle fonction-co^ut peut en effet être minimisée par rapport à tout ou partie des caractéristiques del'inclusion ``test'' $Br$ (position, taille, propriétés mécaniques ...) pour établir la meilleurecorrespondance possible entre $Br$ et $BTrue$. A cet effet, nous produisons un développement asymptotique de $Jbb$en la taille $incsize$ de $Br$, qui en constitue une approximation polynomiale plus aisée à minimiser. Cedéveloppement, établi jusqu'à l'ordre $O(incsize^6)$, est justifié par une estimation du résidu. Uneméthode d'identification adaptée est ensuite présentée et illustrée par des exemples numériques portant surdes obstacles de formes simples dans l'espace libre $Rbb^3$.L'objet de la seconde partie est de caractériser une inclusion microstructurée de longueur $ltot$, modéliséeen une dimension, composée de couches de deux matériaux alternés périodiquement, en supposant que les plusbasses de ses fréquences propres de transmission (TEs) sont connues. Ces fréquences sont les valeurs propres d'unproblème dit de transmission intérieur (ITP). Afin de disposer d'un modèle propiceà l'inversion, tout en prenant en compte les effets de la microstructure, nous nous reposons sur des approximationsde l'ITP exact obtenues par homogénéisation. A partir du modèle homogénéisé d'ordre 0, nous établissonstout d'abord une méthode simple pour déterminer les paramètres macroscopiques ($ltot$ et contrastes matériaux)d'une telle inclusion. Pour avoir accès à la période de la microstructure, nous nous intéressons ensuite àdes modèles homogénéisés d'ordre élevé, pour lesquels nous soulignons le besoin de conditions aux limitesadaptées. / The purpose of this work was to develop new methods to address inverse problems in elasticity,taking advantage of the presence of a small parameter in the considered problems by means of higher-order asymptoticexpansions.The first part is dedicated to the localization and size identification of a buried inhomogeneity $BTrue$ in a 3Delastic domain. In this goal, we focused on the study of functionals $Jbb(Br)$ quantifying the misfit between $BTrue$and a trial homogeneity $Br$. Such functionals are to be minimized w.r.t. some or all the characteristics of the trialinclusion $Br$ (location, size, mechanical properties ...) to find the best agreement with $BTrue$. To this end, weproduced an expansion of $Jbb$ with respect to the size $incsize$ of $Br$, providing a polynomial approximationeasier to minimize. This expansion, established up to $O(incsize^6)$ in a volume integral equations framework, isjustified by an estimate of the residual. A suited identification procedure is then given and supported by numericalillustrations for simple obstacles in full-space $Rbb^3$.The main purpose of this second part is to characterize a microstructured two-phases layered1D inclusion of length $ltot$, supposing we already know its low-frequency transmission eigenvalues (TEs). Thoseare computed as the eigenvalues of the so-called interior transmission problem (ITP). To provide a convenient invertiblemodel, while accounting for the microstructure effects, we then relied on homogenized approximations of the exact ITPfor the periodic inclusion. Focusing on the leading-order homogenized ITP, we first provide a straightforward method torecover the macroscopic parameters ($ltot$ and material contrast) of such inclusion. To access to the period of themicrostructure, higher-order homogenization is finally addressed, with emphasis on the need for suitable boundaryconditions.

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We consider reduced Hsieh-Clough-Tocher basis functions with respect to a splitting into subtriangles at the barycenter of the original triangular element. This article gives a proof that the second derivatives of those functions, which in general may jump at the subtriangle boundaries, do not jump at the barycenter.:1 Introduction 2 Shape functions 3 Transformation of second derivatives 4 Second derivatives at the barycenter