Orientador: Glaucia Amorim Faria / Resumo: O eucalipto é difundido em várias regiões brasileiras e no mundo. Os Estados brasileiros com maiores áreas de plantio do eucalipto são Minas Gerais, Mato Grosso do Sul, São Paulo e Paraná. Com crescente contribuição ao longo dos anos, o seu cultivo tem gerado empregos tanto na área rural quanto na área urbana. O que torna de suma importância maiores pesquisas que visem a melhoria das áreas de plantio, maiores informações para condução e melhoria de produção, o que acarretará em maiores ofertas para o mercado nacional. Neste cenário, estudos que auxiliem o pesquisador a conhecer a variabilidade desta cultura, definir o tamanho ideal de parcela e as curvas de crescimento que melhor representem o conjunto de dados ao longo do tempo, serão essenciais para que se faça a inferência correta, se tenha maior precisão e maximização das informações, garantindo maior eficiência do procedimento experimental, como redução do tempo de espera, permitindo ao pesquisador a comparação do comportamento da planta e seus componentes mais relevantes. Para tanto, o trabalho tem por objetivo: a recomendação de uma tabela de classificação de variação (utilizando os métodos de Garcia, Pimentel-Gomes e Costa, Seraphin e Zimmermann); o tamanho ótimo de parcelas (utilizando o método da máxima curvatura modificada) em experimentos em casa de vegetação; o modelo não-linear (Logístico, Gompertz e Von Bertalanffy) que melhor se adeque ao padrão de crescimento ao longo do tempo, em experimentos com a cultura d... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Eucalyptus is widespread in several Brazilian regions and in the world. The Brazilian states with the largest eucalyptus plantation areas are Minas Gerais, Mato Grosso do Sul, São Paulo, and Paraná. With growing contribution over the years, its cultivation has generated jobs in both rural and urban areas. This makes more important research to improve the planting areas, greater information for conducting and improving production, which will lead to greater offers for the domestic market. In this scenario, studies that help the researcher to know the variability of this crop, to define the ideal plot size and the growth curves that best represent the data set over time, will be essential for correct inference, if greater accuracy and maximization of information, guaranteeing greater efficiency of the experimental procedure, such as reduction of waiting time, allowing the researcher to compare the behavior of the plant and its most relevant components. To do so, the objective of the study is: to recommend a variation classification table (using the methods of Garcia, Pimentel-Gomes and Costa, Seraphin and Zimmermann); the optimal size of plots (using the modified maximum curvature method) in greenhouse experiments; the non-linear model (Logistic, Gompertz and Von Bertalanffy) that best fit the pattern of growth over time, in experiments with the Eucalyptus crop. / Mestre

Os modelos de Toda admitem uma representação de suas equações de movimento em termos da curvatura nula, isto é, existem potenciais que são funcionais dos campos da teoria e pertencem a uma álgebra de Kac-Moody tal que a condição de curvatura nula seja equivalente às equações de movimento. Para a construção das soluções solitônicas e cargas conservadas são necessários a gradação inteira da álgebra de Kac-Moody e a existência de soluções de vácuo, de forma que os potenciais assumam valores em uma subálgebra abeliana quando calculados nestas soluções de vácuo. A gradação da álgebra é de extrema importância pois garante que o potencial transformado tenha a mesma estrutura que o potencial de vácuo. As cargas conservadas são então construídas partindo de soluções da órbita do vácuo por meio de transformações de dressing, que consistem na aplicação da decomposição de Gauss para a produção de um potencial transformado a partir de duas transformações de Gauge. Nesta dissertação calculamos as infinitas cargas conservadas dos modelos de Toda sl(3) e também sl(N), avaliadas nas soluções pertencentes à órbita do vácuo sob transformações de dressing. As soluções de interesse físico, como sólitons e breathers pertencem a esta órbita, e as cargas conservadas para tais soluções são escritas como uma soma sobre os sólitons. Mostramos que a energia e o momento proveem de termos de superfície. / The Toda models admit a zero curvature representation of their equations of motion, i.e. there exist potentials, (A), wich are functionals of the fields of the theory and which belong to a Kac-Moody algebra G such that the zero curvature condition is equivalent to the equations of motion. For the construction of the solitons solutions and conserved charges is required an integer gradation of the Kac-Moody algebra and a ``vacuum solution\'\', such that the potentials evaluated on it belong to an abelian subalgebra. The gradation of the algebra is of extreme importance since it guarantees that the transformed potential have the same structure as the vacuum potential. The conserved charges are then constructed using the dressing method, that through the Gauss decomposition, leads to the transformed potentials by two gauge transformations. In this dissertation we calculate the infinite conserved charges of models Toda sl (3) and also sl (N) evaluated on the solutions belonging to the orbit of the vacuum under dressing transformations. The solutions of physical interest, like solitons and breathers belong to this orbit and the conserved charges for such solutions are written as a sum over the number the solitons. We show that the energy and momentum are boundary terms.

Orientador: Luzia Aparecida Trinca / Resumo: A classe dos modelos de regressão incorporando polinômios fracionários - FPs (Fractional Polynomials), proposta por Royston & Altman (1994), tem sido amplamente estudada. O uso de FPs em modelos mistos constitui uma alternativa muito atrativa para explicar a dependência das medidas intra-unidades amostrais em modelos em que há não linearidade na relação entre a variável resposta e variáveis regressoras contínua. Tal característica ocorre devido aos FPs oferecerem, para a resposta média, uma variedade de formas funcionais não lineares para as variáveis regressoras contínuas, em que se destacam a família dos polinômios convencionais e algumas curvas assimétricas e com assíntotas. A incorporação dos FPs na estrutura dos modelos mistos tem sido investigada por diversos autores. Porém, não existem publicações sobre: a exploração da problemática da modelagem na parte fixa e na parte aleatória (principalmente na presença de várias variáveis regressoras contínuas e categóricas); o estudo da influência dos FPs na estrutura dos efeitos aleatórios; a investigação de uma adequada estrutura para a matriz de covariâncias do erro; ou, um ponto de fundamental importância para colaborar com a seleção do modelo, a realização da análise de diagnóstico dos modelos ajustados. Uma contribuição, do nosso ponto de vista, de grande relevância é a investigação e oferecimento de estratégias de ajuste dos modelos polinômios fracionários com efeitos mistos englobando os pontos citados acima com o objetiv... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The class of regression models incorporating Fractional Polynomials (FPs), proposed by Royston & Altman (1994), has been extensively studied. The use of FPs in mixed models is a very attractive alternative to explain the within-subjects’ measurements dependence in models where there is non-linearity in the relationship between the response variable and continuous covariates. This characteristic occurs because the FPs offers a variety of non-linear functional forms for the continuous covariates in the average response, in which the family of the conventional polynomials and some asymmetric curves with asymptotes stand out. The incorporation of FPs into the structure of the mixed models has been investigated by several authors. However, there are no works about the following issues: the modeling of the fixed and random effects (mainly in the presence of several continuous and categorical covariates), the study of the influence of the FPs on the structure of the random effects, the investigation of an adequate structure for the covariance of the random errors, or, a point that has central importance to the selection of the model, to perform a diagnostic analysis of the fitted models. In our point of view, a contribution of great relevance is the investigation and the proposition of strategies for fitting FPs with mixed effects encompassing the points mentioned above, with the goals of filling these gaps and to awaken the users to the great potential of mixed models, now even mor... (Complete abstract click electronic access below) / Doutor

Orientador: Sueli Irene Rodrigues Costa / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-09-11T21:20:45Z (GMT). No. of bitstreams: 1 Bressan_JoaoPaulo_D.pdf: 1164660 bytes, checksum: 4825edafe6fbea5e3bc43934bc528376 (MD5) Previous issue date: 2012 / Resumo: A partir das desigualdades de Hamming e Gilbert-Varshamov obtém-se um limitante superior e um limitante inferior para o número de pontos de um código numa variedade flag geométrica. Isto é feito tomando-se uma estimativa para o volume de bolas geodésicas, que resulta de cálculos envolvendo a curvatura seccional destas variedades. Em particular, são derivados limitantes para empacotamentos de esferas numa variedade de Grassmann complexa. Um limitante superior para a distância mínima também é obtido através da inversa da função que calcula o volume de um chapéu esférico. Esta técnica geométrica também é aplicada no estudo de limitantes para empacotamentos em alguns casos particulares de variedades flag maximais. Através de procedimentos computacionais, tais limitantes são implementados numericamente em alguns exemplos. Uma motivação para este trabalho foi à busca de possíveis extensões de alguns resultados sobre as grassmanianas complexas, cujo interesse na área de comunicações vem de uma interpretação que pode ser feita da transmissão em canais MIMO não coerentes via códigos em tais variedades / Abstract: Upper and lower bounds for the number of points of codes in geometric flag manifolds are obtained from Hamming and Gilbert-Varshamov inequalities. This is done by taking an estimate for the volume of geodesic balls, as a result of calculations involving the sectional curvature of such manifolds. As a particular case, sphere packing bounds in complex Grassmann manifolds are derived. An upper bound on the minimum distance is also obtained through the inverse mapping for the volume of spherical caps. This geometric technique is also applied in the study of sphere packing bounds in some particular cases of full-flag manifolds. Such bounds are numerically implemented in some examples. One motivation for this work was the search for possible extensions of some results on complex Grassmann manifolds, which interest in communications comes from a model for the transmition on non-coherent MIMO channels via codes in such manifolds / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

Made available in DSpace on 2015-04-22T22:16:06Z (GMT). No. of bitstreams: 1 Geziel Damasceno.pdf: 743020 bytes, checksum: 0001ac62bcb357c87e266dd4d0de7a3b (MD5) Previous issue date: 2012-12-31 / FAPEAM - Fundação de Amparo à Pesquisa do Estado do Amazonas / Admits that in a complete surface, connected and oriented immersed in R3 with non-zero constant mean curvature, there is a geodesic triangle whose interior angles satisfy a relationship involving the integral mean curvature and the angle formed by unit vector parallel to a coordinate axis of either R3 and the unit vector normal to the surface, and in such cases shows that the immersion is a surface of revolution, ie, a surface Delaunay. Then give a characterization of the sphere is changing some hypotheses on the previous result. / Admite-se que, numa superfície completa, conexa e orientada imersa no espaço euclidiano tri-dimensional com curvatura média constante não nula, existe um triângulo geodésico cujos ângulos internos satisfazem uma relação integral envolvendo a curvatura média e o ângulo formado pelo vetor unitário paralelo a um eixo coordenado qualquer do espaço ambiente e o vetor unitário normal a superfície, e sob tais hipóteses mostra-se que a imersão é uma superfície de revolução, ou seja, uma superfície de Delaunay. Em seguida darse uma caracterização da esfera alterando-se algumas hipóteses no resultado anterior.

Thin films and multilayers are widely used in many applications, ranging from X-ray optics to microelectronic devices. In service, the X-ray optics elements are exposed to the X-ray beam, which heats up the structure resulting in the thermal deformations, and consequently in distortions of the reflective surface. In addition, the excessive heating may activate interdiffusion in the multilayers coatings and result in degradation of their reflective performance and even film cracking. Therefore, analysis of the thermally-induced deformations and stresses in the X-ray optical elements is important. The presented work is organized in two major parts. The first part examines formation of the peculiar periodic crack patterns observed in the thermally loaded Mo/Si multilayers. Film stress evolution during thermal cycling of the multilayers on Si substrate is analyzed. Results of the high-speed microscopic observations of crack propagation in the annealed Mo/Si multilayers are presented. The observations provide experimental evidence of the mechanism underlying formation of the periodic crack patterns. In the second part, thermal deformations and the resulting surface curvature changes in the X-ray optics elements are analyzed. Finite element modeling is used to assess the potential to thermally control curvature in the X-ray mirrors consisting of the Mo/Si multilayers on a Si substrate. Influence of heating due to the X-ray beam irradiation on thermal deformations in the X-ray mirror bonded to a thick substrate is analyzed in-depth. The detailed consideration includes analysis of the thermal and structural mechanics simulations. Based on simulations of different model configurations, influence of structural composition on thermal distortions of the optics elements is addressed. Results of this analysis can be used to mitigate distortions of the X-ray optics caused by the X-ray beam and provide basis for further studies of thermally controlling surface curvature in the optical elements.

The Black-Scholes model is one of the most important concepts in modern financial theory. It was developed in 1973 by Fisher Black, Robert Merton and Myron Scholes and is still widely used today, and regarded as one of the best ways of determining fair prices of options. In the classical Black-Scholes model for the market, it consists of an essentially riskless bond and a single risky asset. So far there is a number of straightforward extensions of the Black-Scholes analysis. Here we consider more complex products where each component in a portfolio entails several variables with constraints. This leads to elegant models based on multivariable stochastic integration, and describing several securities simultaneously. We derive a general asymptotic solution in a short time interval using the heat kernel expansion on a Riemannian metric. We then use our formula to predict the better price of options on multiple underlying assets. Especially, we apply our method to the case known as the one of two-color rainbow ptions, outperformance option, i.e., the special case of the model with two underlying assets. This asymptotic solution is important, as it explains hidden effects in a class of financial models.

The abstract boundary construction of Scott and Szekeres has proven a practical classification scheme for boundary points of pseudo-Riemannian manifolds. It has also proved its utility in problems associated with the re-embedding of exact solutions containing directional singularities in space-time. Moreover it provides a model for singularities in space-time - essential singularities. However the literature has been devoid of abstract boundary results which have results of direct physical applicability.¶ This thesis presents several theorems on the existence of essential singularities in space-time and on how the abstract boundary allows definition of optimal em- beddings for depicting space-time. Firstly, a review of other boundary constructions for space-time is made with particular emphasis on the deficiencies they possess for describing singularities. The abstract boundary construction is then pedagogically defined and an overview of previous research provided.¶ We prove that strongly causal, maximally extended space-times possess essential singularities if and only if they possess incomplete causal geodesics. This result creates a link between the Hawking-Penrose incompleteness theorems and the existence of essential singularities. Using this result again together with the work of Beem on the stability of geodesic incompleteness it is possible to prove the stability of existence for essential singularities.¶ Invariant topological contact properties of abstract boundary points are presented for the first time and used to define partial cross sections, which are an generalization of the notion of embedding for boundary points. Partial cross sections are then used to define a model for an optimal embedding of space-time.¶ Finally we end with a presentation of the current research into the relationship between curvature singularities and the abstract boundary. This work proposes that the abstract boundary may provide the correct framework to prove curvature singularity theorems for General Relativity. This exciting development would culminate over 30 years of research into the physical conditions required for curvature singularities in space-time.

My dissertation focuses on the existence of metrics of non-positive curvature for the simplicial complexes constructed recently by Tom Brady and Daan Krammer for the braid groups and other Artin groups of finite type. In particular, for each Artin group of finite type, there is a recently constructed finite simplicial Eilenberg-Mac Lane space known as its Brady-Krammer complex. The Brady-Krammer complexes are highly symmetric objects. Prior work on the relationship between the Brady-Krammer complexes and the theory of CAT(0)spaces has produced some positive results in low-dimensions. More specifically, the Brady-Krammer complexes of dimension at most 3 have been shown to support piecewise Euclidean metrics of non-positive curvature. Similarly, the 4dimensional Brady-Krammer complexes of type A4 and type B4 also support such metrics. In every instance, the metrics assigned respect all of the symmetries alluded to above. The main results of my dissertation show that this pattern does not extend to the Brady-Krammer complexes of type F4 and D4. These are the first negative results known about the curvature of these Brady-Krammer complexes. The proofs of my main theorems involve a combination of combinatorial results and computer calculations. These negative results are particularly striking since Ruth Charney, John Meier and Kim Whittlesey have shown that a particular complex closely related to each Brady-Krammer complex admits an asymmetric metric satisfying a weak version of non-positive curvature. Thus, one corollary of my results is that the weak asymmetric version of a CAT(0) metric (initially defined by Mladen Bestvina) is strictly weaker than the traditional version.

Simulation and modelling of turbulent flows under influence of streamline curvature and system rotation have been considered. Direct numerical simulations have been performed for fully developed rotating turbulent channel flow using a pseudo-spectral code. The rotation numbers considered are larger than unity. For the range of rotation numbers studied, an increase in rotation number has a damping effect on the turbulence. DNS-data obtained from previous simulations are used to perform a priori tests of different pressure-strain and dissipation rate models. Furthermore, the ideal behaviour of the coefficients of different model formulations is investigated. The main part of the modelling is focused on explicit algebraic Reynolds stress models (EARSMs). An EARSM based on a pressure strain rate model including terms that are tensorially nonlinear in the mean velocity gradients is proposed. The new model is tested for a number of flows including a high-lift aeronautics application. The linear extensions are demonstrated to have a significant effect on the predictions. Representation techniques for EARSMs based on incomplete sets of basis tensors are also considered. It is shown that a least-squares approach is favourable compared to the Galerkin method. The corresponding optimality aspects are considered and it is deduced that Galerkin based EARSMs are not optimal in a more strict sense. EARSMs derived with the least-squares method are, on the other hand, optimal in the sense that the error of the underlying implicit relation is minimized. It is further demonstrated that the predictions of the least-squares EARSMs are in significantly better agreement with the corresponding complete EARSMs when tested for fully developed rotating turbulent pipe flow. / QC 20100825