<p>The use of contexts in school mathematics is receiving much attention both nationally and internationally. This as well as the scarcity of research focusing on the topic stimulated me to research the contexts preferred by learners of mathematics. The large-scale project is called the Relevance of School Mathematics Education (ROSME) project. The current study essentially deals with that section of the larger project which investigates the issues and situations that learners in grades eight, nine and ten would prefer to deal with in mathematics. Broadly, this study focuses on the contexts preferred by grade 8, 9 and 10 learners as a domain in which to embed school mathematics.</p>

Thesis (MSc (Mathematics))--University of Stellenbsoch, 2009. / Please refer to full text for abstract

Thesis (MSc (Mathematics))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: In this thesis, a mathematical model describing the interaction between HIV and TB in the presence of TB superinfection is presented. The model takes into account two strains of Mycobacterium tuberculosis (MTB), where one strain is drug-sensitive and the other is resistant to at least one of the first-line anti-tuberculosis drugs. The impact of TB superinfection on the incidence and prevalence of TB in HIV-negative and HIVTB coinfected individuals is evaluated. Various control measures such as condom use, antiretroviral therapy, isoniazid preventive therapy and increased TB detection are studied using this model. Numerical results show that TB superinfection increases the prevalence and incidence of TB and its impact is more in HIV-negative than HIV-TB coinfected individuals. The results also show that TB superinfection promotes strain coexistence and increases the associated HIV mortality. Increased condom use was found to have a high positive impact towards the control of the two epidemics. Antiretroviral therapy decreases the TB notification rate and its impact on HIV prevalence increases with the coverage and efficacy. Isoniazid preventive therapy has a clear effect on the TB prevalence. Finally, increased TB detection was found to have a less impact on the TB incidence in HIV-TB coinfected individuals / AFRIKAANSE OPSOMMING: In hierdie verhandeling word ´n wiskundige model vir die interaksie tussen MIV en TB, in ´n situasie met TB superinfeksie voorgelˆe. Die model neem twee variante van TB in ag. Een van die variante is sensitief vir MTB behandeling, terwyl die ander weerstandig is vir ten minste een van die eerste-linie TB behandenings. Die impak van TB superinfeksie op die insidensie and prevalensie van TB in MIV negatiewe en MIV-TB ko-ge˜ınfekteerde individu word ondersoek. Veskeie beheer maatreels soos kondoom gebruik, anti-retrovirale behandeling (vir MIV) en isonazid voorkomende behandeling en verhoodge TB deteksie (vir TB) word ondersoek. Numeriese resultate wys TB superinfeksie verhoog die prevalense en insidensie van TB en dat dit ´n groter bydrae maak by MIV negatief as by MIV-TB ko-geinfekteerde individu. Die resultate wys veder TB superinfeksie promofeer variant kohabitasie en verhoog MIV verwante mortalitieit. Verhoogde kondoom gebruik is gevind om ´n positiewe bydrae te maak tot die beheer van beide epidemies. Anti-retrovirale terapie verlaag die TB aanmeldings koers en die impak van ART verhoog saam met ´n verhoging in die dekking en effektiwiteit daarvan. Voorkomende behandeling het ´n beduidende impak op TB prevalensie. Ons vind dat TB deteksie ´n beperkte impak maak op TB insidensie by MIV-TB ko-geinfekteerde individu

Microbes usually live in large communities, where they interact with other organisms and species. These interactions include cooperation, when individuals facilitate each others growth and reproduction. Such cooperation has been for instance observed within pathogens in the process of infection. Therefore, given the number and the frequency of infectious diseases, understanding the nature and the dynamics of microbial cooperation may be a crucial step in modern medicine. Microbes often secrete costly enzymes which extracellularly metabolise resources available in the environment. This external metabolism is a form of ’public good cooperation’, in which individuals invest their energy in producing ’public goods’, available to other organisms. To study this phenomenon we deploy mathematical models which are based on biologically relevant assumptions. Our models not only aim to capture the dynamics of studied microbial communities, but also to remove the natural complexity arising in the empirical studies and thus to provide a mechanistic understanding of their results. We first recover and explain the recent empirical finding, about mixed strain infections, showing that an addition of a low virulent strain which does not produce public goods (termed ’cheat’) may counter-intuitively enhance the total population virulence. What drives this result turns out to be an interaction of two different cooperative traits and the presence of spatial structure. Next we study the competition between the strains that do and do not produce public goods. Our results depend on environmental conditions, such as resource concentration and population density, but they are also determined by the degree of spatial structure - the ecological trait which so far has been treated only as a binary variable. Finally, we identify some environmental threats for the external metabolism feeding strategy, and we examine its competitiveness in comparison to ’internal metabolism’, in which the costly enzymes are private.

L'objectif de cette thèse est de développer des méthodes d'optimisation et de contrôle optimal pour l'amélioration du rendement des cultures en utilisant le modèle de croissance de plantes GreenLab. Les méthodes proposées doivent se placer dans le contexte suivant: (1) la recherche d'amélioration du rendement se fait par des simulations basées sur le modèle structure-fonction GreenLab et (2) les méthodes utilisées sont des algorithmes d'optimisation heuristiques et des techniques de contrôle optimal. L'application de ces méthodes à plusieurs espèces de plantes, allant des plantes agronomiques aux arbres, et avec des différents objectifs a permis d'identifier certaines caractéristiques associées à des plantes ayant un bon rendement. En particulier, les résultats d'optimisation ont révélé la dynamique des relations source-puits au sein de la plante durant sa croissance. Ces résultats peuvent être considérés comme des références pour guider la sélection génétique pour l'amélioration variétale, et également pour l'amélioration des itinéraires culturaux. La perspective à long terme de cette thèse est l'intégration de ses résultats dans des outils d'aide à la décision pour l'agriculture. Pour atteindre les objectifs de cette thèse, nous avons analysé successivement les effets de facteurs endogènes et exogènes (environnementaux) sur la croissance de la plante et sur son rendement. Plus précisément, l'effet des facteurs endogènes a été étudié à conditions environnementales fixées, puis des méthodes de contrôle optimal ont été appliquées sur les variables environnementales, pour un génotype de plante fixé. En conséquence, les problèmes traités dans cette thèse relèvent à la fois de la théorie de l'optimisation et du contrôle optimal. Les principales contributions de cette thèse incluent les points suivants : Des problèmes d'optimisation simple objectif, d'optimisation multi-objectif et d'optimisation sous contrainte ont été formulés et résolus, dans le but de trouver les paramètres endogènes associés à la plante ayant le plus haut rendement, ce qui correspond à la définition d'un idéotype, pour une plante d'espèce donnée. Pour la plupart des problèmes d'optimisation présentés, la méthode la plus appropriée est celle d'un algorithme basé sur une population. Plusieurs algorithmes de ce type ont été comparés et celui ayant les meilleures performances est un algorithme heuristique nommé Particle Swarm Optimization (PSO). Du contrôle optimal a été appliqué pour définir la stratégie d'élagage optimale (application aux feuilles de thé). Come GreenLab peut être formulé comme un système dynamique discret et que la fonction objectif est analytique, une méthode basée sur le gradient, basée sur une approche variationnelle et sur la théorie de Lagrange, a été utilisée. La solution trouvée à été comparée à celle obtenue par la méthode PSO afin de valider cette dernière. Un modèle de dynamique de population d'insectes a été développé à des échelles spatiales et temporelles compatibles avec le modèle GreenLab, afin d'étudier l'interaction plante-insectes. Plus précisément, un écosystème tritrophique a été modélisé, incluant les interactions entre les plantes, les insectes ravageurs et des prédateurs des ravageurs, appelés insectes auxiliaires. un modèle des interaction. L'originalité de ce travail est la rétro-action entre la dynamique de population des insectes et la croissance de la plante, ainsi que la prise en compte de la répartition spatiale des insectes sur chacun des organes de la plantes. Une analyse de sensibilité basée sur la méthode de Morris a été appliquée pour identifier les paramètres les plus ou moins influents sur les sorties d'intérêt. Cela a permis de calculer des stratégies optimales pour l'application des techniques d'éradication des ravageurs. Les paramètres de GreenLab ont été estimés sur environ 400 jeux de données correspondant à 44 génotypes de tomates, à l'aide d'un algorithme des moindres carrés non linéaires généralisés. Considérant l'ensemble des valeurs estimées comme l'espace des paramètres possibles, nous avons calculé les valeurs optimisant le rendement en fruits des tomates. Nous avons analysé les corrélations entre les paramètres estimés ou optimaux et le rendement à l'aide de méthodes statistiques, ce qui a permis d'identifier les plus importants paramètres responsables des différences observées parmi les rendements des différentes plantes. Ainsi, à partir de ces résultat d'optimisation et d'analyse des corrélation, les différences phénotypiques entre différents génotypes ont pu être expliquées d'un point de vue physiologique. / The objective of the thesis is to improve plant yield through optimization and optimal control based on the GreenLab plant growth model. Therefore, the thesis proposed a methodology for investigation of plant yield improvement，whose characteristics are that (1) investigations are all based on the functional-structural plant growth model GreenLab and (2) heuristic optimization algorithm and optimal control techniques are applied to the plant growth model in order to improve plant yield. By applying optimization techniques on different species of plants (crops or trees) and for different kinds of optimization problems, common characteristics that a plant with high yield should possess were obtained. The optimal results in the thesis revealed the source-sink dynamics during the plant growth. The optimization results can be considered as references to guide breeding for ideotype and to improve cultivation modes. The optimization application of GreenLab could thus be possibly used to the agricultural decision support system.To achieve the aims of the thesis, the thesis investigated the effects of endogenous factors and exogenous environmental factors of plant growth on plant yield separately. First, given environmental conditions, the thesis investigated endogenous factors, and then the thesis did optimal control on exogenous environmental factors given plant genotype. Therefore, the problems investigated in the thesis consist of general optimization problems and optimal control problems.The main contributions of the thesis include following issues: According to the species of plants, single optimization problems, multi-objective optimization problems and optimization problems with constraints with respect to plant endogenous factors were formulated and investigated, in order to find the ideotype of plants with high plant yield. A population based algorithm is more suitable for the optimization problems in this thesis. Due to its better performance compared with other heuristic optimization algorithms, all optimization problems were solved by a population-based, heuristic optimization algorithm, namely Particle Swarm Optimization (PSO). Optimal control on the pruning strategy was formulated and investigated in the thesis. As GreenLab can be considered as discrete dynamic system and the objective function of the optimal control problem is analytical, the gradient based method, which is based on the variational approach and Lagrange theory, was used to solve the optimal control problem. Moreover, the optimal solutions were compared with the ones found by PSO, in order to validate the PSO method. The insect population dynamics was modeled mathematically, which was compatible with the plant model GreenLab in terms of spatial and temporal scales, to study the effect of biotic factors on plant growth. The interaction among plants, pests and auxiliaries was implemented, and the ecosystem model, which involves the three tri-trophic components, was thus developed in the thesis. The tri-trophic ecosystem model can simulate the insect population dynamics and the plant growth with consideration of the interaction of insects. Moreover, the tri-trophic ecosystem model considered the partition of individuals in the insect population among plant organs, which is not taken into account in the previous works. A global sensitivity analysis method Morris method was used to analyze the most important parameters and the least influential parameters to model outputs of interest. Through optimization on pest management techniques, the optimal strategies of the application of the pest management techniques were obtained. Estimation of GreenLab parameters with about 400 sets of observation data of 44 tomato genotypes was done in the thesis, by using a generalized non-linear least square algorithm. Taking the estimated parameter values as parameter space, the GreenLab model parameters were optimized, in order to maximize the fruit yield. Through the analysis of the correlation of estimated and optimal parameters with the fruit yield by statistical analysis methods, the most important parameters that result in the difference of fruit yield were found. According to the correlation and optimization results, the phenotypic differences among genotypes were explained from the physiological point of view.

Submitted by MARCIA ROVADOSCHI (marciar@unifra.br) on 2018-08-16T12:53:12Z No. of bitstreams: 2 Dissertacao_RafaeliOlequesPires.pdf: 1220663 bytes, checksum: 54cb1e137bd526bbde3fe44c848329e7 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2018-08-16T12:53:12Z (GMT). No. of bitstreams: 2 Dissertacao_RafaeliOlequesPires.pdf: 1220663 bytes, checksum: 54cb1e137bd526bbde3fe44c848329e7 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2011-03-29 / From the 60s, a debate about a new and promising world-wide technologies started, and it was called nanotechnology. Together with the global growth, many fields of research had started to use in their studies, for example, in the pharmaceutical area. Among these innovations, we can include the discovery of new composites, biodegradable products and the development of carries in nanoscale. Among the most used nanocarries there are nanosphere and nanocapsules, showing controlled release compared to conventional drug delivery systems. The release process was studied by some authors that described this process using mathematical equations, one for each use. However, actually, there is no mathematical equation that represents the behavior of the nanocarries, emphasizing the factors relevant at nanoscale. Then, the present study analyzed a specific carrier - nanocapsule - to develop a mathematical equation that represents the behavior of the drug release from polymeric nanocapsules. For the construction of the mathematical model, we used mathematical modeling as methodology. We proved there isn’t change in particle size during the release process, when used poly ( -caprolactone). After that, we noticed that the parameters that interfere in the release process were drug solubility in the oil core of nanocapsule and the encapsulation efficiency. Based in these two parameters, the mathematical model was constructed and then validated, showing to be an good model to describe the drug release profiles from nanocapsules. / A partir da década de 60, iniciou-se o debate sobre uma das mais novas e promissoras tecnologias mundiais, a nanotecnologia. Juntamente com o crescimento mundial, vários campos de pesquisa começaram a utilizá-la em seus estudos, como por exemplo, as inovações na área farmacêutica. Entre estas inovações destacam-se a descoberta de novos compostos, produtos biodegradáveis e o desenvolvimento de carreadores em escala nanométrica: os nanocarreadores. Estes, os mais utilizados são as nanoesferas e nanocápulas, por apresentarem uma liberação sustentada e controlada de fármaco comparada a formulações convencionais. À medida que os anos foram passando, o processo de liberação de fármaco foi sendo explicado e representado por equações matemáticas distintas, cada uma com suas aplicações e peculiaridades. Mas, atualmente, não existe nenhuma equação matemática que represente o comportamento dos nanocarreadores, dando ênfase aos fatores relevantes na nanoescala. Assim, o presente trabalho analisou um carreador específico – nanocápsula – para modelar uma equação matemática que represente o comportamento da liberação de fármacos a partir do mesmo. Para a construção do modelo matemático, foi utilizada a modelagem matemática como metodologia. Foi comprovado que não ocorre modificação no tamanho de partícula durante o processo de liberação, quando utilizado o polímero poli( -caprolactona). Depois disso, percebeu-se que o parâmetro que influencia no processo de liberação é a solubilidade do fármaco no núcleo oleoso da nanocápsula e a taxa de associação às naopartículas. Baseado nestas duas variáveis, foi construído o modelo matemático, que quando validado, mostrou-se ser um excelente modelo para descrever os perfis de liberação de fármacos através das nanocápsulas.

L'objet de cette thèse est l'étude du processus métastatique par la confrontation de données in vivo chez la souris avec des modèles mathématiques. Plus précisément, des données longitudinales sur la masse métastatique totale combinées à des données IRM fournissant des informations sur le nombre et la taille des macrométastases ont été confrontées à un modèle décrivant l'évolution de la distribution en tailles des métastases par une équation aux dérivées partielles de populations structurées. La théorie sous-jacente au modèle, décrivant le processus métastatique par des métastases initiées par quelques cellules et croissant indépendamment les unes des autres, s'est révélée incapable de décrire les distributions de tailles métastatiques observées à l'IRM, suggérant la présence de phénomènes non pris en compte dans la théorie \standard" du développement métastatique. Ces résultats nous ont conduit à proposer des hypothèses expliquant les différences de distributions métastatiques entre le modèle et les données. Ces hypothèses ont été étudiées expérimentalement par nos collaborateurs biologistes mais également in silico à l'aide de modèles d'équations aux dérivées partielles décrivant la croissance de plusieurs métastases pouvant interagir spatialement. Les résultats obtenus à l'aide de notre approche de modélisation suggèrent des interactions jouant un rôle important dans la dynamique métastatique, comme l'agrégation de germes métastatiques ou l'attraction de cellules métastatiques par des foyers métastatiques déja existants. Une partie de cette thèse est également dédiée à l'analyse mathématique et numérique du nouveau modèle spatial introduit pour l'étude quantitative précédemment évoquée. Ce modèle mécanique décrit notamment l'effet de la pression sur la prolifération des cellules tumorales. Des résultats de convergence de la méthode numérique utilisée sont présentés, ainsi qu'une confrontation du modèle à des données de croissance de métastases pulmonaires. Enfin, une partie traitant des interactions métastases-microenvironnement est également présentée. Des études récentes ont en effet montré que certaines cellules progénitrices de la lignée hématopoïétique ou encore certaines cellules immunitaires pourraient jouer un r^ole important dans le développement métastatique. Au cours de cette thèse, ce phénomène appelé niche prémétastatique a été étudié dans la littérature biologique puis modélisé mathématiquement afin de mieux comprendre le rôle de cette niche dans la dynamique métastatique. / In this thesis, a quantitative study of the metastatic process in the mouse has been performed thanks to mathematical modeling. Precisely, longitudinal data of the total metastatic burden and MRI data on the macrometastatic size distribution are confronted to a mathematical model describing the metastatic process by the independent growths of metastatic foci starting from one or few cells. This \standard" theory, able to describe the dynamics of the total metastatic burden, is on the other hand unable to describe the observed metastatic size distributions. Indeed, this model predicts many small metastases, whereas the observed metastases are much larger and fewer. In order to explain these differences, we proposed two hypotheses that were not taken into account in the initial theory. In the first one, metastases that are growing in close vicinity could merge, resulting in one larger metastasis. In the second one, metastatic foci could attract arriving circulating tumor cells, resulting also in fewer foci but much larger ones. These hypotheses have been tested experimentally by our biologists collaborators, and in silico thanks to a spatial model of tumor growth. The results of this study show that the previously suggested phenomena could have a substantial impact on the number and the sizes of the metastatic foci during metastatic development. Another part of this thesis is devoted to the numerical and mathematical analysis of the previous spatial model. This model takes into account the effect of the pressure on the proliferation of tumor cells. Numerical convergence of the numerical method that has been used and data assimilation on imaging data of pulmonary metastases are presented. Finally, a last part deals with the interactions between metastasis and its supportive stroma. Recent studies shed light on the implication of hematopoietic progenitors in the formation of a permissive soil in the future metastatic site, a phenomenon so-called premetastatic niche. In this thesis, a mathematical model describing the premetastatic and metastatic dynamics is proposed to study quantitative aspects of this phenomenon.

Magister Educationis - MEd / The use of contexts in school mathematics is receiving much attention both nationally and internationally. This as well as the scarcity of research focusing on the topic stimulated me to research the contexts preferred by learners of mathematics. The large-scale project is called the Relevance of School Mathematics Education (ROSME) project. The current study essentially deals with that section of the larger project which investigates the issues and situations that learners in grades eight, nine and ten would prefer to deal with in mathematics. Broadly, this study focuses on the contexts preferred by grade 8, 9 and 10 learners as a domain in which to embed school mathematics. / South Africa

Nowadays, minimization of the negative environmental impact of manufacturing processes is considered one of the most challenging problems in various industrial fields. Research communities and environmental legislators are continuously working to address these problems by placing significant efforts in devising new strategies to increase environmental sustainability. One of these problems is the lack of a comprehensive framework that can simultaneously improve economic aspects and lessen the impact on the environment. The need for a mathematical model that can assist firms in reaching suitable investment decisions has become of paramount importance. In this context, this study aims at optimizing the environmental and economic sustainability of batch production systems (i.e. a series of workstations where products are manufactured in batches). To this end, a profit maximization model was created by incorporating constraints such as budget, demand, greenhouse gas emissions and hazardous wastes within the manufacturing stage of product life cycle. Moreover, the model provides detailed guidelines on required improvements in a specific manufacturing system and calculates the investment associated with such implementations. This new approach was tested by using two different software packages and results were probed and discussed in different scenarios to investigate its validity. Sensitivity analysis and simulation results proved the consistency of the proposed mathematical model. In particular, in order to further assess the validity of the model, a pharmaceutical plant was selected as a case study, which also permitted discussion on additional aspects of the problem.

Renewable energy integration is increasing – alongside it, the main limiting factors of such sources of energy have to be considered. Each source of energy comes with its unique sets of challenges, namely the way that the generation curves behave. These patterns should be considered, if photovoltaics can contribute at a larger rate to the grid. The current non-renewable sources provide a high response rate and great control over voltage/frequency – key parameters of the grid. Proper utilization of renewable energies is key to sustainable systems of the future.The work considers the possibility of regulating the energy flow through the usage of electric vehicles (EV). The thesis proposes a model within which particle swarm optimization is used to derive EV charging rates, which contribute to the overall performance of a controlled household system. Three control strategies are considered – individual, bottom-up and top-down control. The methodologies are introduced and compared in the study.Top-down control proves to be the most stable and most efficient at reducing energy mismatch when compared to other control strategies. It should however be underlined that any control strategy proposed in the study leads to a greater utilization of renewable energy and can greatly benefit any system with EVs and PV energy present.