Orientador: Rawlilson de Oliveira Araújo / Banca: Jamil Viana Pereira / Banca: Andréa Cristina Prokopczyk Arita / Resumo: Neste trabalho, apresentamos um estudo sobre equações diferenciais ordinárias com o objetivo de compreender alguns modelos matemáticos abordados a nível de ensino médio, como o modelo de crescimento populacional segundo Malthus, Lei do decaimento radioativo, lei de resfriamento de Newton e sistema massa mola ideal. Neste sentido, selecionamos alguns conceitos e resultados matemáticos sobre cálculo diferencial e integral, introduzindo o estudo sobre limite, derivada e, de forma breve, sobre integração. Apresentamos o número de Euler (e) e trabalhamos alguns exercícios envolvendo os modelos citados. Para o desenvolvimento dos assuntos e das atividades propostas, procuramos abordar conceitos em física e utilizamos os softwares GeoGebra e Modellus bem como simuladores disponíveis na internet / Abstract: In this work, we present a study on ordinary differential equations with the objective of understanding some mathematical models addressed at secondary level, such as Malthus' theory of population growth, Law of radioactive decay, Newton's law of cooling and ideal mass spring system. In this sense, we have selected some concepts and mathematical results on differential and integral calculus, introducing the study on limit, derivative, and, briefly, on integration. We present the Euler's number (e) and we work some exercises involving the mentioned models. For the development of the subjects and the proposed activities, we try to approach concepts in physics and we use the software GeoGebra and Modellus as well as simulators available on the internet / Mestre

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In pursuit of knowledge about the performance of agricultural tractors on the market and make the appropriate selection of attachments for each tractor, the research has presented mathematical models as an important tool in the representation of the traction performance of tractors. But that, however, Brazilian researchers found as the main limitation in applying these mathematical models using data characteristic of soil and machinery North American and European. By the need to obtain representative values of soil conditions and Brazilian machinery, the goal was to determine demand models for prediction of traction performance of tractors in operations that require traction force. Sets were used mechanized tractorseeding, disc harrow and chisel plow operating on two soil textures, loamy and silty. Seeking for a graphical representation of demand required traction force, slipage and fuel consumption was held to simulate the different mathematical models by the help of computer program Table Curve 3D v.2.03 (Jandel Scientific) and Table Curve 2Dv.2.03 (Jandel Scientific) capable of providing information for the empirical prediction of these parameters. It was found that the forward speed of the tractor directly influences the demand pull of all sets mechanized, differing from the model proposed by ASAE D497.2 (1995). The speed when interacting with the mass of the disk harrow represents the traction performance parameters using linear models, as well as its interaction with the working depth of the chisel plow by quadratic models with good fit, over 70%. The seeding showed an increase in demand of traction with the linear increase of tractor speed. Predictive theories Cn, Bn and Mn have good correlation with experimental values in soils typical Brazilian, corresponding on average 70% for values measured experimentally. Theory being the most Mn related behavior of energy demand and slipage action. New parameters are needed to estimate the traction force of tillers and planters, as well as the change of coefficients to characterize these machinery. As models for seeding, disc harrow and chisel plow: D = Fi. [1474 + (601.S)]. W.T , D = Fi. [290 + (57.S)]. W.T and D = Fi. [110 + (32.S) + (-2.9. S2)]. W.T, respectively. / Na busca do conhecimento sobre o desempenho de tratores agrícolas disponíveis no mercado e realizar a seleção adequada dos implementos para cada trator, a pesquisa tem apresentado modelos matemáticos como importante ferramenta na representação do desempenho em tração dos tratores. Mas que, no entanto, pesquisadores brasileiros encontram como principal limitação na aplicação destes modelos matemáticos a utilização de dados característicos de solos e máquinas Norte-Americanas e Européias. Pela necessidade de se obterem valores representativos das condições de solo e máquinas brasileiras, o objetivo deste trabalho foi determinar modelos de demanda de tração para predição do desempenho de tratores em operações que demandam força de tração. Foram utilizados os conjuntos mecanizados trator-semadora-adubadora, trator-grade aradora e trator-escarificador operando em duas texturas de solo, média e argilosa. Buscando-se a representação gráfica de demanda requerida de força de tração, patinagem e consumo de combustível realizou-se a simulação dos diferentes modelos matemáticos pelo auxílio do programa computacional Table Curve 3D v.2.03 (Jandel Scientific) e Table Curve 2Dv.2.03 (Jandel Scientific) capaz de oferecer informações para a predição empírica destes parâmetros. Verificou-se que a velocidade de deslocamento do trator influencia diretamente na demanda em tração de todos os conjuntos mecanizados, diferindo do modelo proposto pela ASAE D 497.2 (1995). A velocidade ao interagir com a massa da grade aradora representa os parâmetros de desempenho em tração através de modelos lineares, assim como, a sua interação com a profundidade de trabalho do escarificador por modelos quadráticos, com bom ajuste, acima de 70%. A semeadora apresentou aumento em demanda de tração com o aumento linear da velocidade do trator. As teorias preditivas Cn, Bn e Mn apresentam correlação boa com os valores experimentais sob solos característicos brasileiros, correspondendo em média de 70% ao valores medidos experimentalmente. Sendo a Teoria Mn a mais relacionada ao comportamento de demanda energética e patinagem medidas. Novos parâmetros são necessários para estimativa da força de tração de escarificadores e semeadoras, bem como, a alteração dos coeficientes para caracterizar estes conjuntos mecanizados. Sendo os modelos para semeadora, grade aradora e escarificador: D = Fi.[1474 + (601.S)].W.T; D = Fi.[290 + (57.S)].W.T e D = Fi.[110 + (32.S) + (-2,9.S2)].W.T, respectivamente.

Made available in DSpace on 2014-06-11T19:24:43Z (GMT). No. of bitstreams: 0 Previous issue date: 2001-12Bitstream added on 2014-06-13T20:32:02Z : No. of bitstreams: 1 martins_rm_me_botfca.pdf: 172907 bytes, checksum: bcfa16e4e3781a1de74151d13e2991c2 (MD5) / A matemática e a estatística, como ferramentas de trabalho, são utilizadas para melhor explicar resultados de pesquisas. Na área agronômica, vários trabalhos têm sido desenvolvidos, chegando a diferentes modelos matemáticos. Este trabalho visa verificar a influência da aplicação de vinhaça na produção de cana-de-açúcar através de modelos estatísticos, utilizando dados de artigos publicados, resumidos pelos processos estabelecidos pela meta-análise. Foi possível ajustar o modelo de Mitscherlich e uma regressão de terceiro grau aos dados de produção dos experimentos conduzidos em solo arenoso. Para o solo argiloso foi possível o ajuste de um modelo de terceiro grau. A escolha do modelo que melhor se ajuste a esses resultados é feita através da meta-análise. / The Mathematic and the Statistic, as work tools, they are used for best to explain results of researches. In the agronomic area, several works have been developed, arriving to different mathematical models. This work seeks to verify the influence of the vinasse application in the sugarcane production through statistical models, using data of published articles, summarized by the established processes by the meta-analysis. It was possible to adjust the model of Mitscherlich and a regression of third degree to the data of production of the experiments driven in sandy soil. For the loamy soil it was possible the adjustment of a model of third degree. The choice of the model that better adjusted those results is done through the meta-analysis.

Orientador: Sheila Zambello de Pinho / Resumo: A matemática e a estatística, como ferramentas de trabalho, são utilizadas para melhor explicar resultados de pesquisas. Na área agronômica, vários trabalhos têm sido desenvolvidos, chegando a diferentes modelos matemáticos. Este trabalho visa verificar a influência da aplicação de vinhaça na produção de cana-de-açúcar através de modelos estatísticos, utilizando dados de artigos publicados, resumidos pelos processos estabelecidos pela meta-análise. Foi possível ajustar o modelo de Mitscherlich e uma regressão de terceiro grau aos dados de produção dos experimentos conduzidos em solo arenoso. Para o solo argiloso foi possível o ajuste de um modelo de terceiro grau. A escolha do modelo que melhor se ajuste a esses resultados é feita através da meta-análise. / Abstract: The Mathematic and the Statistic, as work tools, they are used for best to explain results of researches. In the agronomic area, several works have been developed, arriving to different mathematical models. This work seeks to verify the influence of the vinasse application in the sugarcane production through statistical models, using data of published articles, summarized by the established processes by the meta-analysis. It was possible to adjust the model of Mitscherlich and a regression of third degree to the data of production of the experiments driven in sandy soil. For the loamy soil it was possible the adjustment of a model of third degree. The choice of the model that better adjusted those results is done through the meta-analysis. / Mestre

The boundary-layer receptivity resulting from acoustic forcing over a flat plate with a surface irregularity is investigated. The unsteady free-stream disturbances couple with the steady perturbations resulting from the surface irregularity to form a traveling-wave mode. The resonance condition necessary for receptivity requires a forcing at a wave number equal to that of the Tollmien-Schlichting (TS) eigenmode and a frequency equal to that of the free-stream acoustic disturbance. The basic (mean) flow is calculated using an interacting boundary layer (IBL) scheme that accounts for viscous/inviscid interactions. Then, the method of multiple scales is used to find the total amplitude of the generated wave. Results of this study show how the transition process is significantly stimulated. Also, the dependence of the receptivity on the geometry of the roughness element as well as on the amplitude and frequency of the acoustic disturbance is studied. Application of suction is shown to reduce the receptivity resulting from the roughness element. / Master of Science

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No description available.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Computational molecular evolution is a field that attempts to characterize how genetic sequences evolve over phylogenetic trees – the branching processes that describe the patterns of genetic inheritance in living organisms. It has a long history of developing progressively more sophisticated stochastic models of evolution. Through a probabilist’s lens, this can be seen as a search for more appropriate ways to parameterize discrete state continuous time Markov chains to better encode biological reality, matching the historical processes that created empirical data sets, and creating useful tools that allow biologists to test specific hypotheses about the evolution of the organisms or the genes that interest them. This dissertation is an attempt to fill some of the gaps that persist in the literature, solving what we see as existing open problems. The overarching theme of this work is how to better model variation in the action of natural selection at multiple levels: across genes, between sites, and over time. Through four published journal articles and a fifth in preparation, we present amino acid and codon models that improve upon existing approaches, providing better descriptions of the process of natural selection and better tools to detect adaptive evolution. / AFRIKAANSE OPSOMMING: Komputasionele molekulêre evolusie is ’n navorsingsarea wat poog om die evolusie van genetiese sekwensies oor filogenetiese bome – die vertakkende prosesse wat die patrone van genetiese oorerwing in lewende organismes beskryf – te karakteriseer. Dit het ’n lang geskiedenis waartydens al hoe meer gesofistikeerde waarskynlikheidsmodelle van evolusie ontwikkel is. Deur die lens van waarskynlikheidsleer kan hierdie proses gesien word as ’n soektog na meer gepasde metodes om diskrete-toestand kontinuë-tyd Markov kettings te parametriseer ten einde biologiese realiteit beter te enkodeer – op so ’n manier dat die historiese prosesse wat tot die vorming van biologiese sekwensies gelei het nageboots word, en dat nuttige metodes geskep word wat bioloë toelaat om spesifieke hipotesisse met betrekking tot die evolusie van belanghebbende organismes of gene te toets. Hierdie proefskrif is ’n poging om sommige van die gapings wat in die literatuur bestaan in te vul en bestaande oop probleme op te los. Die oorkoepelende tema is verbeterde modellering van variasie in die werking van natuurlike seleksie op verskeie vlakke: variasie van geen tot geen, variasie tussen posisies in gene en variasie oor tyd. Deur middel van vier gepubliseerde joernaalartikels en ’n vyfde artikel in voorbereiding, bied ons aminosuur- en kodon-modelle aan wat verbeter op bestaande benaderings – hierdie modelle verskaf beter beskrywings van die proses van natuurlike seleksie sowel as beter metodes om gevalle van aanpassing in evolusie te vind.

This thesis aims to contribute towards a better understanding of the optimal coordination of monetary and fiscal policy in complex economic environments. We analyze the characteristics of optimal dynamics in an economy in which neither prices nor wages adjust instantaneously and lump-sum taxes are unavailable as a source of government finance. We then propose that monetary and fiscal policy should be coordinated to satisfy a pair of simple `specific targeting rules', a rule for inflation and a rule for the growth of real wages. We show that such simple rule-based conduct of policy can do remarkably well in replicating the dynamics of the economy under optimal policy following a given shock. We study optimal policy coordination in the context of an economy where a constant proportion of agents lacks access to the asset market. We find that the optimal economy moves along an analogue of a conventional inflation-output variance frontier in response to a government spending shock, as the population share of non-Ricardian agents rises. The optimal output response rises, while inflation volatility subsides. There is little evidence that increased government spending would crowd in private consumption in the optimal economy. We investigate the optimal properties and wider implications of a macroeconomic policy framework aimed at meeting an unconditional debt target. We show that the best stationary policy in terms of an unconditional welfare measure is characterized by highly persistent debt dynamics, less history-dependence in the conduct of policy, less reliance on debt finance and more short-term volatility following a government spending shock compared with the non-stationary `timelessly optimal' plan.

The underlying causes of variability in the electrical activity of hearts from individuals of the same species are not well understood. Understanding this variability is important to enable prediction of the response of individual hearts to diseases and therapies. Current experimental and computational methods for investigating the behaviour of the heart do not incorporate biological variation between individuals. In experimental studies, experimental results are averaged together to control errors and determine the average behaviour of the studied organism. In computational studies, averaged experimental data is usually used to develop models, and these models therefore represent a 'typical' organism, with all information on variability within the species having been lost. In this thesis we develop a methodology for modelling variability between individuals of the same species in cardiac cellular electrophysiology, motivated by the inability of traditional computational modelling approaches to capture experimental variability. A first study is conducted using traditional modelling approaches to investigate potentially pro-arrhythmic abnormalities in rabbit Purkinje fibres. A comparison with experimental recordings highlights their wide variability and the inability of existing computer modelling approaches to capture it. This leads to the development of a novel methodology that integrates the variability observed in experimental data with computational modelling and simulation, by building experimentally-calibrated populations of computational models, that collectively span the variability seen in experimental data. We apply this methodology to construct a population of rabbit Purkinje cell models. We show that our population of models can quantitatively predict the range of responses, not just the average response, to application of the potassium channel blocking drug dofetilide. This demonstrates an important potential application of our methodology, for predicting pro-arrhythmic drug effects in safety pharmacology. We then analyse a data set of experimental recordings from human ventricular tissue preparations, and use this data to develop a population of human ventricular cell models. We apply this population to study how variability between individuals alters the susceptibility of cardiac cells to developing drug-induced repolarisation abnormalities. These abnormalities can increase the chance of fatal arrhythmias, but the mechanisms that determine individual susceptibility are not well-understood.