[pt] Neste trabalho apresenta-se o estudo de Previsões de demanda de Energia Elétrica utilizando séries temporais, particularmente a teoria devido a Box & Jenkins. Estuda-se um modelo já existente em uma das cidades proporcionando a hipótese de se estender a validade deste modelo, para cidade de mesmas características onde houver falta de dados. Os dados numéricos utilizados neste estudo são relativos à Centrais Elétricas Fluminense, (CELF). / [en] This paper presents a study of load previsions using chronological series, especially the theory of Box and Jenkins. One model is determined for a city and next a trial is made to extend the vality of this model to other cities with the same characteristics when there is a lack of data. The numerical data use in the work are those of CENTRAIS ELETRICAS FLUMINENSE (CELF).

Radionuclides from natural U-series in sediments from two river catchments in the UK have been studied. The aim was to gain insight into the behaviour of 238U, 234U, 230Th and 226Ra in real natural systems enriched in uranium. A radiochemical method for radium separation followed by alpha spectrometric measurement has been developed. The method allowed use of 225Ra, in equilibrium with the parent 229Th, as a yield determinant, and has been applied in 226Ra concentrations measurements in the selected areas of study.U-series progeny, 238U, 234U, 230Th and 226Ra, in totally dissolved sediments from the valley of the River Noe and the fraction leached by aqua regia, have been measured. Total sediment contents ranged from 9 ± 2 to 184 ± 8 Bq.kg-1 for uranium, 9 ± 3 to 200 ± 13 Bq.kg-1 for thorium and 18 ± 1 to 179 ± 8 Bq.kg-1 for radium. The activity concentrations in the leached fractions, compared with the total, were 46% for uranium, 54% for thorium and 56% for radium, on average. The radionuclides showed extensive disequilibrium and this suggested a complex leaching/accumulation of uranium as well as an impact of organic matter and secondary minerals.Uranium and radium have been geochemically characterised in sediments from near the South Terras abandoned uranium mine, Cornwall. Background activity concentration levels of uranium in sediments ranged from 13 ± 3 to 290 ± 14 Bq.kg-1, with radium from 42 ± 4 to 424 ± 23 Bq.kg-1. Elevated concentrations of uranium and radium were measured in two samples, S3 with 1820 ± 36 Bq.kg-1 for uranium and 940 ± 53 Bq.kg-1 for radium; and S7 with 4350 ± 53 Bq.kg-1 for uranium and 1765 ± 48 Bq.kg-1 for radium. Sequential chemical extraction for the two samples revealed that both uranium and radium were associated with organic and carbonate fractions, with 25 % of the uranium in the resistant phase of S7. 234U/238U activity ratios of the sequential extraction fractions showed different trends in the sediments, and this was linked to the impact of organic matter and/or exchange between water and sediment. Uranium-bearing minerals in association with potassium, calcium, iron, manganese and arsenic have been identified in these sediments.

The Intertropical Convergence Zone (ITCZ) is a feature that results from the ocean-atmosphere interactions in the tropics around the world. The ITCZ is characterized by surface wind convergence, tall storm clouds, and it forms a belt of high time-averaged precipitation around the globe. The ITCZ undergoes seasonal migrations between 5°S and 15°N roughly following the subsolar point on Earth with the seasons, with a mean annual position located slightly above the Equator, between 2° and 5°N. This study tested the hypothesis that there was a northward shift in the median position of the ITCZ in the first decade of the 2000’s relative to the 1900’s. This hypothesis has been posed in the literature given a weakening in the intensity of the Trade Winds observed in the southern Caribbean Sea during the first decade of the 2000’s, with concomitant ecological impacts due to weakening in coastal wind-driven upwelling. The hypothesis was tested by analyzing variations in the monthly latitudinal position of the ITCZ over the Atlantic Ocean relative to the median position computed for the period 1987-2011. The position of the ITCZ was derived from satellite-derived ocean surface wind measurements collected from 1987 to 2011. A Mann-Kendall analysis and a Monte Carlo simulation were used to test for trends in the median cross-basin latitudinal position of the ITCZ. The study included an analysis of regional changes across the tropical central Atlantic (50°W to 15°W), the Western Atlantic (50°W to 30°W), and the Eastern Atlantic (30°W to 15°W) within the tropics. The results show a slight southward trend in the median position of the ITCZ over the central Atlantic and also in the Eastern Atlantic in the first decade of the 2000’s relative to the 1990’s. While this trend is barely significant, it is likely simply due to interannual variation in the average annual position of the ITCZ. The data were also examined for the timing and persistence of a double ITCZ in the Atlantic. The double ITCZ over the Atlantic appeared every year in February or March, with the largest separation between the northern and southern branches of the ITCZ observed in June and July. The possible effects of changes in the average latitudinal position of the ITCZ on the upwelling in the Cariaco Basin (southeastern Caribbean Sea off Venezuela) were also examined. Anomalies of the median of the latitudinal position of the ITCZ in the Atlantic were compared with anomalies of in-situ temperature collected during the 1990’s and the first decade of the 2000’s by the CARIACO Ocean Time-Series program and with anomalies of satellite SST (from the Advanced Very High Resolution Radiometer satellite; AVHRR) from 1995 to 2016. Correlation analysis were performed between anomalies of water temperatures at various depths and anomalies of satellite SST with anomalies of the monthly mean ITCZ position with lags up to 3 months for the time series, and also just for the Cariaco basin upwelling months (December-April). For the whole Cariaco time series there were no significant correlations between the anomalies of the ITCZ position and anomalies in subsurface temperatures in the Cariaco Basin. However, during the upwelling period, the central Atlantic and Western Atlantic ITCZ position anomalies were directly correlated with Cariaco Basin temperature anomalies with no-lag (r = 0.20), and the central and Eastern Atlantic ITCZ position anomalies were inversely correlated with Cariaco Basin temperatures (r ~ -0.22 to -0.28) with ITCZ leading Cariaco temperatures by 3 months. However, these correlations were low, indicating that other factors than the position of ITCZ latitudinal position play bigger role on the Cariaco basin upwelling variability. Interannual variability in oceanographic and meteorological characteristics of the Atlantic Ocean are expected as a result of large-scale changes in other regions of the world, including due to changes such as the El Niño Southern Oscillation (ENSO) and the Atlantic Multidecadal Oscillation (AMO). Six oceanic-atmospheric variables are used to monitor ENSO over the tropical Pacific, while the AMO is determined by monitoring SST over the Atlantic. Correlations with lags of up to ± 6 months were conducted with those climate indices and the anomalies of the median monthly latitudinal position of the ITCZ. Significant direct correlations with ENSO (Multivariate ENSO Index) were seen in the Atlantic and Western Atlantic (r = 0.15), with ENSO leading the position of the ITCZ anomalies by 3 months. This implies that within three months after an El Niño event (warm ENSO anomaly in the Pacific) the ITCZ over the mid-Atlantic and Western Atlantic Ocean tends to shift to a more northerly position. The AMO also had a direct influence on the anomalies of the ITCZ position (r = 0.13) in the Central and the Western Atlantic, with the AMO leading ITCZ anomalies by 1 month (i.e. a warming of the North Atlantic led to a northward shift in the ITCZ one month later). Correlations between AMO and the ITCZ anomalies in the Eastern Atlantic were also direct but with no lag. Although significant, these correlations were low. An inverse correlation (~ -0.35) was found between ENSO and anomalies of water temperature of the Cariaco Basin. ENSO lagged ocean temperature anomalies by 3 to 4 months for both the whole Cariaco time series and for the upwelling months of CARIACO data. Correlations with AMO were direct (~ 0.4); for the whole time series AMO led Cariaco temperature anomalies by 3 months, but for the upwelling months AMO lagged Cariaco temperature anomalies by one month.

A lacunary series is a Taylor series with large gaps between its non-zero coefficients. In this thesis we exploit these gaps to obtain results of linear independence of values of lacunary series at integer points. As well, we will study different methods found in Diophantine approximation which we use to study arithmetic properties of values of lacunary series at algebraic points. Among these methods will be Mahler's method and a new approach due to Jean-Paul Bézivin.

Orientador: Reginaldo Palazzo Junior / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-18T16:51:18Z (GMT). No. of bitstreams: 1 Leskow_LucilaHelenaAllan_D.pdf: 2583405 bytes, checksum: 3161d9deabaa60a8965a9e3d20ff36aa (MD5) Previous issue date: 2011 / Resumo: Neste trabalho apresentamos como contribuição um novo conjunto de tesselações do plano hiperbólico construídas a partir de uma tesselação bem conhecida, a tesselação de Farey. Nestas tesselações a região de Dirichlet é formada por polígonos hiperbólicos de n lados, com n > 3. Explorando as características dessas tesselações, apresentamos alguns tipos possíveis de aplicações. Inicialmente, estudando a relação existente entre a teoria das frações contínuas e a tesselação de Farey, propomos um novo método de codificação de geodésicas. A inovação deste método está no fato de ser possível realizar a codificação de uma geodésica pertencente a PSL(2,Z) em qualquer uma das tesselações ou seja, para qualquer valor de n com n > 3. Neste método mostramos como é possível associar as sequências cortantes de uma geodésica em cada tesselação à decomposição em frações contínuas do ponto atrator desta. Ainda explorando as características dessas novas tesselações, propomos dois tipos de aplicação em teoria de codificação de fontes discretas. Desenvolvendo dois novos códigos para compactação de fontes (um código de árvore e um código de bloco), estes dois métodos podem ser vistos como a generalização dos métodos de Elias e Tunstall para o caso hiperbólico / Abstract: In this work we present as contribution a new set of tessellations of the hyperbolic plane, built from a well known tessellation, the Farey tessellation. In this set of tessellations the Dirichlet region is made of hyperbolic polygons with n sides where n > 3. While studying these tessellations and theirs properties, we found some possible applications. In the first one, while exploring the relationship between the continued fractions theory and the Farey tessellation we propose a new method for coding geodesics. Using this method, it is possible to obtain a relationship between the cutting sequence of a geodesic belonging to PSL(2,Z) in each tessellation and the continued fraction decomposition of its attractor point. Exploring the characteristics of these tessellations we also propose two types of applications regarding the discrete memoryless source coding theory, a fixed-to-variable code and a variable length-to-fixed code. These methods can be seen as a generalized version of the Elias and Tunstall methods for the hyperbolic case / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica

Orientador: Wagner Caradori do Amaral, Ricardo José Gabrielli Barreto Campello / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-18T18:57:59Z (GMT). No. of bitstreams: 1 Braga_MarcioFeliciano_M.pdf: 1946648 bytes, checksum: 782ab3e1f3a89e6527c7b9c090b00ac0 (MD5) Previous issue date: 2011 / Resumo: Enfoca-se a modelagem de sistemas não-lineares usando modelos de Volterra com bases de funções ortonormais (Orthonormal Basis Functions - OBF) distintas para cada direção do kernel. Os modelos de Volterra constituem uma classe de modelos polinomiais não-recursivos, modelos sem realimentação da saída. Tais modelos são parametrizados por funções multidimensionais, chamadas kernels de Volterra, e representam uma generalização do bem conhecido modelo de resposta ao impulso (FIR) para a descrição de sistemas não-lineares. Como os modelos de Volterra não possuem realimentação do sinal de saída, um número elevado de parâmetros é necessário para representar os kernels de Volterra, especialmente quando o comportamento não-linear do sistema depende fortemente do sinal de saída. No entanto, é possível contornar esta desvantagem por descrever cada kernel por meio de uma expansão em bases de funções ortonormais (OBF). Resultando num modelo que, em geral, possui um número menor de termos para representar o sistema. O modelo resultante, conhecido como modelo OBF-Volterra, pode ser truncado em um número menor de termos se as funções da base forem projetadas adequadamente. O problema reside na questão de como selecionar os polos livres que completamente parametrizam estas funções de forma a reduzir o número de termos a serem utilizados em cada base. Uma abordagem já utilizada envolve a otimização numérica das bases de funções ortonormais usadas para a aproximação de sistemas dinâmicos. Esta estratégia é baseada no cálculo de expressões analíticas para os gradientes da saída dos filtros ortonormais com relação aos polos da base. Estes gradientes fornecem direções de busca exatas para otimizar uma dada base ortonormal. As direções de busca, por sua vez, podem ser usadas como parte de um procedimento de otimização para obter o mínimo de uma função de custo que leva em consideração o erro de estimação da saída do sistema. Esta abordagem considerou apenas os modelos lineares e não-lineares cujas direções dos kernels foram todas parametrizadas por um mesmo conjunto de polos. Neste trabalho, estes resultados foram estendidos de forma a permitir o uso de uma base independente para cada direção dos kernels. Isto permite reduzir ainda mais o erro de truncamento quando as dinâmicas dominantes do kernel ao longo das múltiplas direções são diferentes entre si. As expressões dos gradientes relativas à base de Kautz e à base GOBF são obtidas recursivamente o que permite uma redução no tempo de processamento. Esta metodologia utiliza somente dados de entrada-saída medidos do sistema a ser modelado, isto é, não exige nenhuma informação prévia sobre os kernels de Volterra. Exemplos de simulação ilustram a aplicação dessas abordagens para a modelagem de sistemas não-lineares. Por último, apresentam-se resultados referentes à identificação robusta de modelos não-lineares sob a hipótese de erro desconhecido mas limitado, cujo objetivo é definir os limites superior e inferior dos parâmetros de modelos (intervalos de pertinência paramétrica). É analisado o caso em que se tem informação somente sobre a incerteza na saída do sistema, fornecendo-se o cálculo dos limitantes das incertezas para modelos OBF-Volterra. Estuda-se também os processos que possuem incerteza estruturada, i.e., os parâmetros do modelo, ou os kernels de Volterra, são definidos por meio de intervalos de pertinência e a ordem do modelo é conhecida. Apresenta-se uma solução exata para este problema, eliminando restrições impostas por metodologias anteriores / Abstract: It focuses in the modeling of nonlinear systems using Volterra models with distinct orthonormal basis functions (OBF) to each kernel direction. The Volterra models are a class of nonrecursive polynomial models, models without output feedback. Such models are parameterized by multidimensional functions, called Volterra kernels, they represent a generalization of the well-known impulse response model and are used to describe nonlinear systems. As the Volterra models do not have output feedback, it is required a large number of parameters to represent the Volterra kernels, especially when the nonlinear behavior strongly depends of the output signal. However, such drawback can be overwhelmed by describing each kernel by un expansion in orthonormal basis functions (OBF). Resulting in a model that, in general, requires fewer parameters to represent the system. The resulting model, so-called OBF-Volterra, can be truncated into fewer terms if the basis functions are properly designed. The underlying problem is how to select de free-design poles that fully parameterize these functions in order to reduce the number of terms to be used in each bases. An approach, already used, involves the numeric optimization of orthonormal bases of function used for approximation of dynamic systems. This strategy is based on the computation of analytical expressions for the gradient of the orthonormal filters output with respect to the basis poles. Such gradient provides exact search directions for optimizing the poles of a given orthonormal basis. The search direction can, in turn, be used as part of an optimization procedure to locate the minimum of a cost-function that takes into consideration the estimation error of the system output. Although, that approach took in count only the linear models and nonlinear models which kernels directions were parameterized by a single set of poles. In this work, these results are extended in such a way to allows a use of an independent basis to each kernel direction. It can reduce even more the truncation error when dominant dynamics of the kernel are different along its directions. The gradient expressions to Kautz and GOBF bases are obtained in a recursive way which allows reducing the time processing. This methodology relies solely on input-output data measured from the system to be modeled, i.e., no previous information about the Volterra kernels is required. Simulation examples illustrate the application of this approach to the modeling of nonlinear systems. At last, it is presented some results about robust identification of nonlinear models under the hypothesis of unknown but bounded error, whose aim is to define the upper and lower bounds of the model parameters (parameter uncertainty interval). It is analyzed the case where the information available is about the uncertainty in the system output signal, providing the calculation for the uncertainty intervals to OBF-Volterra models. The process having structured uncertainty, i.e., the models parameters, or the Volterra kernels, are defined by intervals and the model order is known, is also studied. An exact solution to this problem is developed, eliminating restrictions imposed by previous approach / Mestrado / Automação / Mestre em Engenharia Elétrica

Orientadores: Jansle Vieira Rocha, Rubens Augusto Camargo Lamparelli / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Agricola / Made available in DSpace on 2018-08-14T11:30:01Z (GMT). No. of bitstreams: 1 Fernandes_JefersonLobato_M.pdf: 2074887 bytes, checksum: af58e53746d7d186e6f1331527b3c3e8 (MD5) Previous issue date: 2009 / Resumo: O atual sistema de previsão de safras para a cultura da cana-de-açúcar utilizado no Brasil depende, em boa parte, de informações subjetivas, baseadas no conhecimento de técnicos do setor e informações da cadeia produtiva. Apesar da experiência dos técnicos envolvidos, este sistema está sujeito a questionamentos sobre a qualidade dos números apresentados e abre margem a ações especulativas por parte de agentes externos. O monitoramento da cultura de cana-de-açúcar por meio de séries multitemporais de índices NDVI do sensor SPOT Vegetation, associado a dados meteorológicos provenientes do modelo do ECMWF, viabiliza o acompanhamento do desenvolvimento da cultura e sua correlação com a produtividade, diminuindo assim a subjetividade das estimativas. Este trabalho avaliou o potencial de uso de imagens decendiais do sensor SPOT Vegetation para a identificação de áreas canavieiras do estado de São Paulo e a capacidade de inferir sobre os dados de produtividade oficiais registrados em municípios e safras previamente selecionados, baseando-se em dados provenientes dos perfis temporais do NDVI - SPOT Vegetation e de variáveis meteorológicas do modelo do ECMWF. Foram selecionados 20 municípios do estado de São Paulo e sete safras compreendidas entre o período de 1999 e 2006. A identificação das áreas canavieiras foi realizada por meio do perfil temporal do NDVI de cada pixel, onde foram selecionados os pixels que ao longo da safra apresentaram comportamento característico da cultura. Para a determinação da produtividade média da safra por meio de dados espectrais e meteorológicos, foram extraídos valores dos perfis temporais do NDVI e das variáveis meteorológicas temperatura mínima, temperatura média, temperatura máxima, precipitação e radiação global, onde, utilizando-se técnicas de mineração de dados, separou-se a produtividade média da safra em 3 classes, baixo-média, média e média-alta. Os resultados de identificação de áreas canavieiras no estado de São Paulo foram avaliados em escala estadual e municipal. Para a escala estadual, o método proposto apresentou resultados satisfatórios. Os índices de determinação (R²), obtidos através da correlação entre a área colhida de cana-de-açúcar oficial e a estimada, por município e safra, considerando os 637 municípios do Estado, variaram entre 0,771 e 0,829. Para a escala municipal não foi possível determinar com exatidão a área de cana-de-açúcar colhida de cada município devido à baixa resolução espacial das imagens. Para o método de classificação da produtividade média municipal proposto, houve maior correlação com os dados os dados espectrais que com os dados meteorológicos. Valores extraídos do perfil temporal do NDVI entre os meses de dezembro e janeiro permitiram classificar a tendência do resultado de produtividade alcançado no final da safra. Os resultados foram mais efetivos para os casos onde a produtividade foi classificada como sendo média ou acima da média, com acertos de 86,5 e 66,7% respectivamente. Existe potencial no uso de imagens de NDVI do SPOT Vegetation para a identificação de áreas canavieiras em escala estadual e para a classificação da produtividade média municipal da safra. / Abstract: The current crop yield forecasting system for sugar cane used in Brazil is dependent on subjective information which are based on personal knowledge of technicians and information from the industry. Despite the experience of technicians, this system is vulnerable once it allows questioning about the quality of the figures presented, what could lead to speculation by market agents. Sugar cane monitoring through multitemporal series of the NDVI data from SPOT Vegetation, associated with meteorological data from the ECMWF model, provides information about the plant development and its correlation with yield, contributing to the decrease in the subjectivity of the forecasts. This study evaluated the potential use of decadal images of the SPOT Vegetation sensor to identify sugar cane areas in São Paulo state and the feasibility to estimate the official productivity registered in municipalities and crops previously selected by the use of NDVI - SPOT Vegetation and ECMWF meteorological data. For this study 20 municipalities of São Paulo state and seven cropping seasons were selected between 1999 and 2006. To identify sugar cane areas the temporal profile of each pixel was analysed during the cropping season, selecting pixels that presented a characteristic temporal NDVI profile of sugar cane. To determine the average yield using spectral and meteorological data, values of the temporal profiles of NDVI and minimum, mean and maximum temperature, precipitation and global radiation were extracted. Through data mining techniques, the average yield was classified in three classes: low-mean, mean and mean-high. Results for the identification of sugar cane areas in São Paulo state were evaluated at regional and local scale. For the regional scale the proposed method showed good results. The R² for the correlation between official and estimated sugar cane planted area, considering the 637 municipalities of the state, varied between 0,771 and 0,829. For the local scale, it was not possible to determine the sugar cane area due to the low spatial resolution of the images. For the classification of the average crop yield, by proposed method, spectral data was more relevant than meteorological data. Some values extracted from the temporal profile of NDVI between December and January permitted to classify the yield tendency. Best results were found when the yield was classified as mean or mean-high, with 86,5 and 66,7 percent correctively classified, respectively. The results showed that there is potential for the use of NDVI - SPOT Vegetation images to identify sugar cane areas at regional scale and to classify the average crop yield. / Mestrado / Planejamento e Desenvolvimento Rural Sustentável / Mestre em Engenharia Agrícola

Orientador: Luiz Fernando Milanez / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-27T23:42:49Z (GMT). No. of bitstreams: 1 Dalmas_Sergio_D.pdf: 5052580 bytes, checksum: 18c083502953c8bf9d4aa3a089a26162 (MD5) Previous issue date: 2015 / Resumo: Excluídos problemas simples de condução de calor nos quais a temperatura depende apenas do tempo ou apenas de uma coordenada de posição, os demais levam a equações diferenciais parciais, as quais tem soluções em termos de séries obtidas de vários métodos como a separação de variáveis, a superposição, a função de Green, a técnica da transformada integral, a transformada de Laplace e o teorema de Duhamel. Estas soluções dependem de autovalores que são obtidos das raízes de equações transcendentais que na maioria dos casos não podem ser expressas em forma fechada, mas podem ser obtidas de tabelas, expressões aproximadas, e expressões iterativas. O objetivo desse estudo é encontrar novas expressões para estas raízes, que sejam mais simples ou que tenham mais exatidão do que as já existentes. As três equações transcendentais que são consideradas aqui são as mais frequentemente utilizadas entre as que não tem solução fechada, e surgem quando as condições de contorno são convectivas. Uma nova família de funções iterativas é obtida, a qual inclui várias funções clássicas e, em particular, toda a família de métodos de Householder. Um novo método obtido é o que tem convergência mais rápida para as presentes equações. Apesar das tabelas de raízes apresentarem valores com vários dígitos significativos, problemas reais dificilmente levam a um valor da variável independente que pode ser diretamente encontrado, tornando-se necessário o uso de interpolação. Então, a exatidão de raízes obtidas por estas tabelas é limitada pela exatidão da interpolação, a qual pode ser comparada com a das expressões aproximadas. As expressões existentes são analisadas utilizando propriedades das raízes. Uma expressão aproximada desenvolvida para a primeira raiz das três equações é baseada no método do ponto fixo, outra é obtida da aplicação do conceito de MiniMax para se reajustar expressões de outros autores, e uma final tem forma algébrica. O conceito de MiniMax não é obtido através de algum método que possa ser considerado elementar, e dois novos métodos são desenvolvidos para aplicá-lo. Modernos sistemas algébricos computacionais são utilizados para gerar novas expressões aproximadas para a primeira raiz, mas encontrou-se que elas podem ser melhoradas através de métodos analíticos. Expansão em frações contínuas e novamente a aproximação de Padé são utilizadas para se obter expressões de grande exatidão. Expressões que levam a bons resultados para a primeira raiz são generalizadas para que elas sirvam para as demais raízes. Finalmente, uma comparação é feita considerando todas expressões aproximadas, indicando quais são consideradas as melhores / Abstract: Apart from simple problems of heat conduction in which the temperature depends only on the time or just on a position coordinate, the others lead to partial differential equations, which have solutions in terms of series obtained from various methods such as separation variables, superposition, the Green's function, the technique of integral transform, the Laplace transform and Duhamel's theorem. These solutions depend on eigenvalues, which are obtained from the roots of transcendental equations that in most cases cannot be expressed in closed form, but they can be obtained from tables, approximate expressions and iterative expressions. The objective of this study is to find new expressions for these roots, which are simpler or have more accuracy than the existing ones. The three transcendental equations that are considered here are the most frequently used among those that have not closed solution, and appear when the boundary conditions are convective. A new family of iterative functions is proposed, which includes several classical functions and, in particular, the entire family of Householder methods. A new method is obtained which has faster convergence to the present equations. Although the tables of roots present values with various significant digits, real problems hardly lead to a value of the independent variable that can be directly found, making it necessary to use interpolation. Then, the accuracy of the roots obtained from these tables is limited by the accuracy of the interpolation, which can be compared with the approximate expressions. Existing expressions are analyzed using the root properties. An approximate expression developed for the first root of the three equations is based on the fixed point method, another is obtained from the application of the concept of MiniMax to readjust expressions of others authors, and the last one has an algebraic form. The MiniMax concept is not obtained through any method that can be considered elementary, and two new methods are developed to apply it. Modern computer algebra systems are used to generate new approximate expressions for the first root, but it is found that they can be improved by analytical methods. Expansion in continuous fractions is adopted and the Padé approximation to obtain expressions of greater accuracy. Expressions leading to good results for the first root are generalized so that they serve for the other roots. Finally, a comparison is made considering all approximate expressions, indicating what are considered the best / Doutorado / Termica e Fluidos / Doutor em Engenharia Mecânica

In this thesis the author presents a history of non-convergent series which, in the past, played an important role in mathematics. Euler's formula, Stirling's series and Poincare's theory are examined to show the development of asymptotic series, a subdivision of divergent series.

Les études de pharmacoépidémiologie consistent à étudier l’effet de médicaments en vie réelle, et sont menées de plus en plus souvent sur bases de données médico-administratives. Ce sont principalement des études observationnelles, et sont donc soumises à des biais liés à des facteurs de confusion. Ces facteurs ne sont pas toujours recueillis dans les bases de données médico-administratives qui sont implémentées à d’autres fins que la recherche. Des plans expérimentaux self-controlled designs (où le patient est son propre témoin, et dont les principaux sont le case-crossover et le self-controlled case-series) permettent d’étudier l’effet transitoire d'expositions brèves sur des évènements à début brutal. Ils sont soumis à certaines conditions d’application. Ils ont la particularité de réaliser des comparaisons sur différentes périodes plutôt que sur différents groupes de patients, permettant ainsi de prendre en compte des facteurs de confusion, y compris non mesurés, et qui ne varient pas entre les périodes observées. Ces méthodes ont montré leur utilité pour pallier l’absence de randomisation, et leur utilisation est recommandée quand leurs conditions d’application sont remplies. Nous avons étudié la fréquence d’utilisation des self-controlled designs en pharmacoépidémiologie sur bases de données, les opportunités manquées d’utilisation et leur usage approprié au regard de leurs conditions d’application, ainsi que la qualité de l’information rapportée dans les articles. Nous avons montré que leur utilisation est rare, que 15% des articles correspondent à des situations d’opportunité où ces méthodes auraient pu être implémentées, que 34% des case-crossover et 13% des self-controlled case-series étaient appliqué de façon inapproprié, et que pour 16% des articles la méthode aurait pu être adaptée pour être valide. Un usage plus approprié permettrait de contribuer à l’investigation en pharmacoépidémiologie tout en bénéficiant des avantages de ces méthodes en particulier sur bases de données de santé. / Pharmacoepidemiology consists in the study of efficacy or safety of drugs in real life, with the use more and more frequently of medico-administrative databases. Study designs are generally observational, thus they are prone to confounding bias. Confounders are not systematically collected in databases, which are implemented for other purposes than research. Self-controlled designs (mainly represented by case-crossover and self-controlled case-series, and in which the patient acts as his own control), have been developed for the study of intermittent exposure with short-term effect on abrupt onset event. They require that validity assumptions being fulfilled. They consist in the comparison over different periods, rather than different groups of patients, thus allowing for confounding factors, also if not measured, which are invariant over observed periods. Such designs have been proved useful in observational studies in the absence of randomization, and their implementation is recommended in case of validity assumptions are fulfilled. We studied their frequency of use in pharmacoepidemiology in healthcare databases, missed opportunities for use, inappropriate use with respect to validity assumptions, as well as quality of reporting. We showed that self-controlled designs are rarely used, that opportunity for use was founds in 15% of articles where such methods could have been implemented, that 34% of case-crossover and 13% of self-controlled case series were inappropriately used, and that the method could have been adapted to be valid in 16% of articles. A more appropriate use of self-controlled designs could contribute to improve investigation in pharmacoepidemiology, while beneficiating from their advantages, especially in healthcare databases.