Cette thèse de doctorat traite d’un cadre en géométrie complexe et de méthodes pouvant y être développées pour résoudre des ensembles d’équations différentielles compatibles venant de systèmes intégrables, classiques ou quantiques, dans le contexte de la géométrie d’espaces de modules de connexions au-dessus de courbes complexes, ou surfaces de Riemann. Elle vient de l’idée en physique mathématique que les symétries des systèmes intégrables imposent aux objets d’intérêt (fonctions de partitions ou de corrélations) des contraintes algébro-différentielles nommées équations de boucles. Le but est par la suite de résoudre ces contraintes par récurrence dans des régimes dits topologiques en utilisant une procédure nommée récurrence topologique. Leurs solutions sont en général les fonctions génératrices de quantités issues de problèmes de géométrie énumérative. Étant principalement déterminées par les conditions initiales de la récurrence, on produit au passage une classification algébro-géométrique de la famille de systèmes intégrables considérée. / This PhD thesis is about a framework in complex geometry and methods thereof for solving sets of compatible differential equations arising from integrable systems, classical or quantum, in the context of the geometry of moduli spaces of connections over complex curves, or Riemann surfaces. It is based on the idea in mathematical Physics that integrable systems posess symmetries that impose algebro-differential constraints, so-called loop equations, on the objects of interest (e.g. partition or correlation functions). In turn, we intend to solve these constraints recursively in certain topological regimes using a particular procedure called the topological recursion. Their solutions are in general generating functions of enumerative-geometric quantities. Since they are for the most part determined by the initial data of the recursive process, it realizes in the making an algebro-geometric classification of the family of integrable models under consideration.

Orientadores: Rubens Augusto Camargo Lamparelli, Jansle Vieira Rocha / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Agricola / Made available in DSpace on 2018-08-12T21:23:17Z (GMT). No. of bitstreams: 1 Ramme_FernandoLuizProchnow_D.pdf: 9393591 bytes, checksum: a6d5183861f5be0ab0ed23ba7a8838da (MD5) Previous issue date: 2008 / Resumo: O objetivo do trabalho foi avaliar a relação entre as fases do crescimento da cana-de-açúcar com as formas de curvas do perfil temporal do Índice de Vegetação por Diferença Normalizada - NDVI, obtidas a partir do sensor remoto orbital MODerate-resolution Imaging Spectroradiometer - MODIS, na região de estudo. A avaliação desta relação é realizada utilizando-se técnicas de sensoriamento remoto para a geração do perfil temporal do NDVI, ao longo do ciclo de desenvolvimento fenológico da cana-soca, nas maturações Precoce, Média e Tardia. Os talhões de cana-soca analisados foram agrupados de acordo com a variedade, solo, data de plantio e corte, e contigüidade. A visualização gráfica das formas de curvas analisadas é realizada através de aplicativo, desenvolvido neste trabalho na linguagem de programação Java, e do sistema gerenciador de banco de dados PostgreSQL. O aplicativo realiza a filtragem de ruídos presentes nas imagens, composição na resolução temporal de 8 dias, através dos dados da banda de controle de qualidade do produto MOD09Q1, realiza a eliminação de valores discrepantes ao longo do perfil temporal do NDVI para a safra analisada, corrige as influências dos períodos de corte e rebrota da cana-soca, e propicia a suavização da forma de curva através do filtro Savitzky-Golay. Três janelas temporais de monitoramento da cultura são apresentadas neste trabalho. Cada janela temporal é determinada em função do tipo de maturação da cultura, do coeficiente de cultura (Kc) ao longo do ciclo fenológico da cana-soca e do comportamento na evolução do perfil temporal do NDVI. Concluiu-se que na região de estudo, diferentes maturações são caracterizadas por diferentes formas de curvas do perfil temporal do NDVI / Abstract: The objective of the work was to evaluate the relationship among the phases of the growth of the sugarcane with the forms of curves of the Normalized Difference Vegetation Index - NDVI temporal profile, obtained from remote sensor orbital MODerate-resolution Imaging Spectroradiometer - MODIS, in the study area. The evaluation of this relationship is accomplished by using of the techniques of remote sensing to generate the NDVI profile, along the phenological development phase of stubble-cane, in the Carly, Medium and Late maturations. The fields of stubble-cane analyzed were contained in agreement with the variety, soil, planting date and cut, and proximity. The graphic visualization of curves shape analyzed is accomplished through application, developed in this work in the Java programming language, and of the PostgreSQL system database manager. The application accomplishes the filtering of present noises in the images, composition in the temporal resolution of 8 days, through the data of the band of quality control of the MOD09Q1 product, accomplishes the elimination of outliers along the NDVI temporal profile for the culture analyzed, corrects the influences of the cut periods and regrowth of the stubble-cane, and propitiates the smoothing in the curve shape through the filter Savitzky-Golay. Three temporal windows of culture monitoring are presented in this work. Each temporal window is determined in function of the type of crop maturation, of the culture coefficient (Kc) along the phenological development phase of stubble-cane and of the behavior in the evolution of the NDVI profile. It concluded that in the study area, different maturations are characterized by different forms of NDVI profile curves / Doutorado / Planejamento e Desenvolvimento Rural Sustentável / Doutor em Engenharia Agrícola

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