Made available in DSpace on 2014-07-29T16:02:23Z (GMT). No. of bitstreams: 1 DISSERTACAO.pdf: 293631 bytes, checksum: 5c813b219dd91ac79277b83be339ffcd (MD5) Previous issue date: 2008-03-28 / In this work we study some results from the article of Tomas E. Cecil, On the Lie curvature of Dupin hypersurfaces [4]. We study the basic concepts of Lie sphere geometry, which given the framework for the study of Dupin hypersurfaces in the Lie sphere geometry. We construct example of a non-compact proper Dupin hypersurface immersed in Sn on which the Lie curvature &#936; = 1/2 which is not Lie equivalent to an open subset of an isoparametric hypersurface in Sn. We also produce example on which Lie curvature &#936; has a constant value c, 0 < c < 1. / Neste trabalho estudamos alguns resultados do artigo de Tomas E. Cecil, On the Lie curvature of Dupin hypersurfaces [4]. Estudamos os conceitos básicos da geometria de Lie, que fornece as ferramentas necessárias para o estudo das hipersuperfícies de Dupin na geometria de Lie. Construímos exemplos de uma hipersuperfície de Dupin própria não compacta mergulhada em Sn, com curvatura de Lie &#936; = 1/2 e que não é Lie equivalente a um subconjunto aberto de uma hipersuperfície isoparamétrica em Sn. Também construímos exemplos onde a curvatura de Lie &#936; tem valor constante c, 0 < c < 1.

Orientadores: Mário Jorge Dias Carneiro, Marco Antonio Teixeira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-19T10:54:43Z (GMT). No. of bitstreams: 1 Damasceno_JosueGeraldo_D.pdf: 1045427 bytes, checksum: 2cb1e5f51924e8667d69ad7267aeaa4e (MD5) Previous issue date: 2011 / Resumo: Descrevemos algumas propriedades dinâmicas de uma família de aplicações bilhares sobre curvas convexas (ovais) as quais são deformadas pelo fluxo de curvatura. Quando a mesa se deforma, a razão entre as curvaturas mínima e máxima converge a 1 e por um resultado clássico de Gage e Hamilton, depois de uma normalização, as curvas tendem a um círculo. Como conseqüência, a região de Lazutkin, isto é, a região que contém cáusticas convexas, cresce gradualmente. Descreveremos algumas bifurcações dinâmicas nesse processo, em particular, descreveremos o que acontece com a família de órbitas de período dois e as órbitas "zig-zag" / Abstract: We describe some dynamical properties of one parameter families of billiards on convex curves (ovals) which are deformed by the curvature flow. As the billiard table deforms, the ratio between minimal and maximal curvature converges to 1 and by a classical result of Gage and Hamilton [GH], after a normalization, the curves tend to a circle. As a consequence, the Lazutkin region, i.e. the region that contains convex caustics, gradually increases. We describe some dynamical bifurcations in this process, in particular, we describe what happens with the family of period two orbits and the "zig-zag"orbits / Doutorado / Matematica / Doutor em Matemática

[pt] Muitas aplicações em processamento de imagens e computação gráfica recaem em propriedades geométricas de curvas, particularmente suas curvaturas. Uma outra propriedade importante mas menos explorada é a torção, sendo esta para curvas no espaço. Vários métodos para estimar curvaturas de curvas planas são conhecidos, a maioria deles para curvas digitais. Nesta dissertação fazemos um levantamento desses métodos e propomos um novo método baseado em aproximações por parábolas e cúbicas paramétricas. Apresentamos uma análise teórica do método e também estudamos a influência do ruído no cálculo da curvatura e da torção. O novo estimador foi comparado com outros estimadores e mostrou-se bastante robusto. / [en] Many applications in image processing and computer vision rely on geometric properties of curves, in particular their curvatures. Another important, but less exploited, property is the torsion for curves in space. Several methods of estimating the curvature of plane curves are known, most of them for digital curves. In this dissertation we survey these methods and propose a new method based on approximations by parabolic and cubic curves. We present a theoretical analysis of this method and also study the effect of noise. The new estimator is compared to other estimators and is seen to be very robust.

This thesis is broadly divided in two parts. In the first part we give a survey of various distances between metric spaces, namely the uniform distance, Lipschitz distance, Hausdor distance and the Gramoz Hausdor distance. Here we talk about only the most basic of their properties and give a few illustrative examples. As we wish to study collections of metric measure spaces, which are triples (X; d; m) consisting of a complete separable metric space (X; d) and a Boral probability measure m on X, there are discussions about some distances between them. Among the three that we discuss, the transportation and distortion distances were introduced by Sturm. The later, denoted by 2, on the space X2 of all metric measure spaces having finite L2-size is the focus of the second part of this thesis. The second part is an exposition based on the work done by Sturm. Here we prove a number of results on the analytic and geometric properties of (X2; 2). Beginning by noting that (X2; 2) is a non-complete space, we try to understand its completion. Towards this end, the notion of a gauged measure space is useful. These are triples (X; f; m) where X is a Polish space, m a Boral probability measure on X and f a function, also called a gauge, on X X that is symmetric and square integral with respect to the product measure m2. We show that, Theorem 1. The completion of (X2; 2) consists of all gauged measure spaces where the gauges satisfy triangle inequality almost everywhere. We denote the space of all gauged measure spaces by Y. The space X2 can be embedded in Y and the transportation distance 2 extends easily from X2 to Y. These two spaces turn out to have similar geometric properties. On both these spaces 2 is a strictly intrinsic metric; i.e. any two members in them can be joined by a shortest path. But more importantly, using a description of the geodesics in these spaces, the following result is proved. Theorem 2. Both (X2; 2) and (Y; 2) have non-negative curvature in the sense of Alexandrov.

[pt] Um resultado clássico no âmbito de equações diferenciais parciais e de geometria diferencial é o seguinte: Dada uma constante a existe uma condição da fronteira do domínio (Omega) de maneira que o problema de Dirichlet para a equação da curvatura média a no espaço Euclidiano é sempre solúvel. Este é um teorema devido a Serrin (1969). Além disso, se a condição de Serrin não for satisfeita, há um resultado de não-existência. A partir disso foi perguntado se um resultado similar valeria no espaço Hiperbólico. A finalidade desta tese é dar uma resposta afirmativa a esta pergunta, exibindo uma condição tipo Serrin. De maneira que obtém-se existência de superfícies cujo gráfico tenha curvatura média hiperbólica pré-determinada H(x) no espaço hiperbólico. O resultado é sharp no sentido que se tal condição for negada então não-existência pode ser estabelecida. O ponto central é uma estimativa a priori do gradiente de uma tal solução. / [en] A classical result in Partial Differential Equations and Differential Geometrydue to Serrin (1969) is the following: Given a constant (alfa) there exists a condition on the boundary of the domain (omega)such that the Dirichlet problem for the mean equation (alfa)is solvable. Besides, if Serrin's condition fails there is a non-existence result. Taking into account this classical result one may ask if a similar theorem holds in hyperbolic space. The goal of this thesis is to give a positive answer to this question establishing a certain Serrin type condition. Thus we obtain existence of surfaces whose graphs has prescribed mean curvature H(x) in hyperbolic space. This result is sharp because if the condition is not satisfied then a non- existence result can be inferred. The main point of the argument is some a priori gradient estimate and degree theory.

Drawing sketches is certainly one of the most important but at the same time elaborate parts of archaeological work. Currently, 3D scanning technology is affording a number of new applications, and only one of them is using virtual copies instead of the originals as the basis for documentation. Our major contribution are methods for automatically generating stylized images from 3D models. These are not only intuitive and easy to read but also more objective and accurate than traditional drawings. Besides some other useful tools we show several examples from our daily work proving that the system accelerates the whole documentation process considerably.

This thesis considers linear perturbations to the steady flow of a compressible inviscid perfect gas along a cylindrical or annular duct. Particular consideration is given to the model of the duct boundary, and to the effect of curvature of the duct centreline. For a duct with a straight centreline and a locally-reacting boundary, the acoustic duct modes can be segregated into ordinary duct modes and surface modes. Previously-known asymptotics for the surface modes are generalized, and the generalization is shown to provide a distinctly better approximation in aeroacoustically relevant situations. The stability of the surface modes is considered, and previous stability analyses are shown to be incorrect, as their boundary model is illposed. By considering a metal thin-shell boundary, this illposedness is explained, and stability analysed using the Briggs-Bers criterion. The stability of a cylindrical thin shell containing compressible fluid is shown to differ significantly from the stability for an incompressible fluid, even for parameters for which the fluid would otherwise be expected to behave incompressibly. The scattering of sound by a sudden hard-wall to thin-shell boundary change is considered, using the Wiener-Hopf technique. The causal acoustic field is derived analytically, without the need to apply a Kutta-like condition or to include an instability wave, as had previously been necessary. Attention is then turned to a cylindrical duct with a curved centreline and either hard or locally-reacting walls. The centreline curvature (which is not assumed small) and wall radii vary slowly along the duct, enabling an asymptotic multiple scales analysis. The duct modes are found numerically at each axial location, and interesting characteristics are explained using ray theory. This analysis is applied to a hard-walled RAE 2129 duct, and frequency-domain solutions are convolved to give a time-domain example of a pulse propagating along this duct. Finally, some numerical work on the nonlinear propagation of a large-amplitude pulse along a curved duct is presented. This is aimed at modelling a surge event in an aeroengine with a convoluted intake.

O objetivo desta pesquisa é estudar a variabilidade e tendência dos elementos climáticos pluviosidade e temperatura, em quatro localidades do estado de São Paulo - Pirassununga, Rio Claro, São Carlos e São Simão -, que constituem parte da área de treinamento de voo da Academia da Força Aérea, para confirmar a hipótese de que essas alterações indicam indícios de mudanças climáticas de curto prazo, em escala local e que essas mudanças poderão afetar, no futuro, o planejamento das missões de treinamento de voo na AFA. Para isso foram utilizados, primeiramente, os dados mensais e anuais de temperatura e pluviosidade de uma série temporal de 34 anos (1976 a 2009) e, depois, de uma série mais curta, de 16 anos (1994 a 2009). Para a análise das condições climáticas de São Carlos, Rio Claro e São Simão foram utilizados os dados mensais e anuais de temperatura e pluviosidade de uma série temporal de 16 anos (1994 a 2009). Para efeito da análise estatística da variabilidade climática da temperatura e pluviosidade dentro da série temporal escolhida, foram aplicados os cálculos da média aritmética, do desvio padrão, do coeficiente de variação e da amplitude térmica. Para a análise da tendência, aplicou-se a técnica da regressão linear e os testes estatísticos não-paramétricos, conhecidos como testes de Mann-Kendall e Curvatura de Sen. Os resultados da pesquisa mostraram que a variabilidade mensal e anual da pluviosidade para as quatro localidade é semelhante e bem acentuada e que não existem tendências significativas para essa variável nas quatro localidades. Para as temperaturas em Pirassununga, a temperatura média apresentou grande variabilidade mensal. Para Rio Claro, São Carlos e São Simão a variabilidade anual das temperaturas foi baixa, próxima da estabilidade, com exceção da temperatura mínima, que apresentou grande variabilidade para as três localidades. Quanto à tendência para Pirassununga, apenas a temperatura média apresentou tendência decrescente e significativa. Os resultados obtidos para as temperaturas de Rio Claro, São Carlos e São Simão indicam tendências crescentes e/ou decrescentes, mas todas insignificantes. / The aim of this research is to study the variability and tendency in climatic elements, rainfall and temperature in four cities in the state of São Paulo: Pirassununga, Rio Claro, São Carlos and São Simão which are part of the flight training area of the Air Force Academy, in order to confirm the hypothesis that those alterations indicate signs of climatic variations in the short term, according to the local parameters and that those variations may change the schedule of the flight training missions at AFA. Monthly and annual data regarding to temperature and rainfall, recorded during a period of 34 years (1976-2009) were firstly considered during the study, followed by a shorter period of 16 years (1994-2009). In order to analyze the climatic conditions in São Carlos, Rio Claro and São Simão, monthly and annual data about temperature and rainfall collected during a period of 16 years (1994-2009) were considered. For purposes of statistical analysis of the climatic variability of temperature and rainfall within the chosen period of time, calculation of the arithmetic mean, standard deviation, coefficient of variation and temperature range were applied. In order to analyze such tendency, the linear regression model and non-parametric statistical tests, known as Mann-Kendall and Sen Curvature were applied. The results of the research showed that the monthly and annual variability of the rainfall in the four cities is similar and well marked and that there are not significant tendencies in that variable in the four cities. Relating to temperature in Pirassununga, the average temperature showed large monthly variability. In Rio Claro, São Carlos and São Simão, the annual temperature variability was low, tending to be stable, except for the minimum temperature which showed a large variability. Concerning to Pirassununga, just the average temperature tended to be decreasing and significant. The results obtained for the temperatures in Rio Claro, São Carlos and São Simão tended to be increasing and/or decreasing, but such tendencies were irrelevant.

Neste trabalho mostramos que dado um domínio exterior de classe C0 contido em uma superfície umb lica de H3; com curvatura média constante H 2 [0; 1); existe uma família de gracos de Killing com curvatura média constante H: O bordo de cada um destes gracos está contido nesta superfície umbílica e a norma do gradiente da função no bordo pode ser prescrita por um certo valor s 0. / In this paper we show that given an exterior domain of class C0 contained in an umbilical surface of H3; with constant mean curvature H 2 [0; 1); there exists a family of Killing graphs with constant mean curvature H: The boundary of each of these graphs is contained in this umbilical surface and the norm of the gradient of the function in the boundary can be prescribed by a certain value s 0:

Today is on products from the perspective of quality placed an increasing emphasis. This work is focused to the analyze of cross roll straghtening of long semifinished products with a circular cross-section. This process increased quality of semifinished products from the perspective of their curvature, because they do not reach the required limit values. Curvature of the semifinished product is due to residual stress, which is during straghtening using plastic deformation of the material redistributed and the semifinished product is leveled. This work analyzes the effect of rotation of straightening rolls on the distributiom of contact pressure between the straightening semifinished product and the roll of straightener. Author then analyzes effect of input parameters of program to straightening at the final curvature of the semifinished product. With the experience gained, then try to adjust some input parameters.