Die vorliegende Arbeit befasst sich mit der Konvergenztheorie für die regularisierten Lösungen inkorrekter inverser Probleme bei A-priori-Parameterwahl im Hilbertraum. Zunächst werden bekannte Konvergenzratenresultate basierend auf verallgemeinerten Quelldarstellungen systematisch zusammengetragen. Danach wird sich mit dem Fall befasst, was getan werden kann, wenn solche Quellbedingungen nicht erfüllt sind. Man gelangt zur Analysis von Abstandsfunktionen, mit deren Hilfe ebenfalls Konvergenzraten ermittelt werden können. Praktisch wird eine solche Abstandsfunktion anhand der Betrachtung einer Fredholmschen Integralgleichung 2. Art abgeschätzt. Schließlich werden die Zusammenhänge zwischen bedingter Stabilität, Stetigkeitsmodul und Konvergenzraten erörtert und durch ein Beispiel zur Laplace-Gleichung untermauert. / This dissertation deals with the convergence theory of regularized solutions of ill-posed inverse problems in Hilbert space with a priori parameter choice. First, well-known convergence rate results based on general source conditions are brought together systematically. Then it is studied what can be done if such source conditions are not fulfilled. One arrives at the analysis of distance functions. With their help, convergence rates can be determined, too. As an example, a distance function is calculated by solving a Fredholm integral equation of the second kind. Finally, the cross-connections between conditional stability, the modulus of continuity and convergence rates is treated accompanied with an example concerning the Laplace equation.

This work explains the effect of failure on permeability anisotropy and dilation in sands. Shear failure is widely observed in field operations. There is incomplete understanding of the influence of shear failure in sand formations. Shear plane orientations are dependent on the stress anisotropy and that view is confirmed in this research. The effect of shear failure on the permeability is confirmed and calculated. Description of permeability anisotropy due to shear failure has also been discussed. In this work, three-dimensional discrete element modeling is used to model the behavior of uncemented and weakly cemented sand samples. Mechanical deformation data from experiments conducted on sand samples is used to calibrate the properties of the spherical particles in the simulations. Orientation of the failure planes (due to mechanical deformation) is analyzed both in an axi-symmetric stress regime (cylindrical specimen) and a non-axi-symmetric stress regime (right cuboidal specimen). Pore network fluid flow simulations are conducted before and after mechanical deformation to observe the effect of failure and stress anisotropy on the permeability and dilation of the granular specimen. A rolling resistance strategy is applied in the simulations, incorporating the stiffness of the specimens due to particle angularity, aiding in the calibration of the simulated samples against experimental data to derive optimum granular scale elastic and friction properties. A flexible membrane algorithm is applied on the lateral boundary of the simulation samples to implement the effect of a rubber/latex jacket. The effect of particle size distribution, stress anisotropy, and confining pressure on failure, permeability and dilation is studied. Using the calibrated micro-properties, simulations are extended to non-cylindrical specimen geometries to simulate field-like anisotropic stress regimes. The shear failure plane alignment is observed to be parallel to the maximum horizontal stress plane. Pore network fluid flow simulations confirm the increase in permeability due to shear failure and show a significantly greater permeability increase in the maximum horizontal stress direction. Using the flow simulations, anisotropy in the permeability field is observed by plotting the permeability ellipsoid. Samples with a small value of inter-granular cohesion depict greater shear failure, larger permeability increase and a greater permeability anisotropy than samples with a larger value of inter-granular cohesion. This is estimated by the number of micro-cracks observed. / text

The thesis unifies the most important author's results in the field of algorithms concerning zonotopes and their applications in optimization and statistics. The computational-geometric results consist of a new compact output-sensitive algorithm for enumerating vertices of a zonotope, which outperforms the rival algorithm with the same complexity-theoretic properties both theoretically and empirically, and a polynomial algorithm for arbitrarily precise approximation of a zonotope with the Löwner-John ellipsoid. In the application area, the thesis presents a result, which connects linear regression model with interval outputs with the zonotope matters. The usage of presented geometric algorithms for solving a nonconvex optimisation problem is also discussed.

The content of this dissertation is divided into two main topics: 1) nonlinear profile monitoring and 2) an improved approximate distribution for the T² statistic based on the successive differences covariance matrix estimator. Part 1: Nonlinear Profile Monitoring In an increasing number of cases the quality of a product or process cannot adequately be represented by the distribution of a univariate quality variable or the multivariate distribution of a vector of quality variables. Rather, a series of measurements are taken across some continuum, such as time or space, to create a profile. The profile determines the product quality at that sampling period. We propose Phase I methods to analyze profiles in a baseline dataset where the profiles can be modeled through either a parametric nonlinear regression function or a nonparametric regression function. We illustrate our methods using data from Walker and Wright (2002) and from dose-response data from DuPont Crop Protection. Part 2: Approximate Distribution of T² Although the T² statistic based on the successive differences estimator has been shown to be effective in detecting a shift in the mean vector (Sullivan and Woodall (1996) and Vargas (2003)), the exact distribution of this statistic is unknown. An accurate upper control limit (UCL) for the T² chart based on this statistic depends on knowing its distribution. Two approximate distributions have been proposed in the literature. We demonstrate the inadequacy of these two approximations and derive useful properties of this statistic. We give an improved approximate distribution and recommendations for its use. / Ph. D.

Este trabalho trata do estudo de robôs de arquitetura paralela, focando na modelagem e otimização dos mesmos. Não foi construído nenhum tipo de protótipo físico, contudo os modelos virtuais poderão, no futuro, habilitar tal façanha. Após uma busca por uma aplicação que se beneficie do uso de um robô de arquitetura paralela, fez-se uma pesquisa por arquiteturas viáveis já existentes ou relatadas na literatura. Escolheu-se a mais apta e prosseguiu-se com os estudos e modelagem cinemática e dinâmica, dando uma maior ênfase na cinemática e dinâmica inversa, esta última utilizando a formulação de Newton - Euler. Foi construído um simulador virtual em ambiente MATLAB 6.5, dotado de várias capacidades como interpolação linear e circular, avanço e uso de múltiplos eixos coordenados. Seu propósito principal é o de demonstrar a funcionalidade e eficácia dos métodos utilizados. Depois foi incorporado ao simulador um algoritmo de cálculo do volume de trabalho da máquina que utiliza alguns dados do usuário para calcular o volume, que pode ser aquele atrelado a uma postura em particular ou o volume de trabalho de orientação total. Algoritmos para medir o desempenho da máquina quanto à uniformidade e utilização da força dos atuadores foram construídos e também incorporados ao simulador, que consegue mostrar o elipsóide de forças ao longo de quaisquer movimentos executados pela plataforma móvel. Quanto à otimização, parte do ferramental previamente construído foi utilizado para que se pudesse chegar a um modelo de uma máquina que respeitasse restrições mínimas quanto ao tamanho e forma de seu volume de trabalho, mas ainda mantendo o melhor desempenho possível dentro deste volume. / This work is about the study of parallel architecture robots, focusing in modeling and optimization. No physical prototypes were built, although the virtual models can help those willing to do so. After searching for an application that could benefit from the use of a parallel robot, another search was made, this time for the right architecture type. After selecting the architecture, the next step was the kinematics and dynamics analysis. The dynamics model is developed using the Newton ? Euler method. A virtual simulator was also developed in MATLAB 6.5 environment. The simulator?s main purpose was to demonstrate that the methods applied were correct and efficient, so it has several features such as linear and circular interpolations, capacity to use multiple coordinate systems and others. After finishing the simulator, an algorithm to calculate the machine workspace was added. The algorithm receives as input some desired requirements regarding the manipulator pose and then calculates the workspace, taking into consideration imposed constraints. Lastly, algorithms capable to measure the manipulator?s performance regarding to its actuator and end-effector force relationship were also incorporated into the simulator that calculates the machine?s force ellipsoid during any movement, for each desired workspace point. For the optimization procedures, some previously developed tools were used, so that the resulting model was capable to respect some workspace constraints regarding size and shape, but also maintaining the best performance possible inside this volume.

Este trabalho trata do estudo de robôs de arquitetura paralela, focando na modelagem e otimização dos mesmos. Não foi construído nenhum tipo de protótipo físico, contudo os modelos virtuais poderão, no futuro, habilitar tal façanha. Após uma busca por uma aplicação que se beneficie do uso de um robô de arquitetura paralela, fez-se uma pesquisa por arquiteturas viáveis já existentes ou relatadas na literatura. Escolheu-se a mais apta e prosseguiu-se com os estudos e modelagem cinemática e dinâmica, dando uma maior ênfase na cinemática e dinâmica inversa, esta última utilizando a formulação de Newton - Euler. Foi construído um simulador virtual em ambiente MATLAB 6.5, dotado de várias capacidades como interpolação linear e circular, avanço e uso de múltiplos eixos coordenados. Seu propósito principal é o de demonstrar a funcionalidade e eficácia dos métodos utilizados. Depois foi incorporado ao simulador um algoritmo de cálculo do volume de trabalho da máquina que utiliza alguns dados do usuário para calcular o volume, que pode ser aquele atrelado a uma postura em particular ou o volume de trabalho de orientação total. Algoritmos para medir o desempenho da máquina quanto à uniformidade e utilização da força dos atuadores foram construídos e também incorporados ao simulador, que consegue mostrar o elipsóide de forças ao longo de quaisquer movimentos executados pela plataforma móvel. Quanto à otimização, parte do ferramental previamente construído foi utilizado para que se pudesse chegar a um modelo de uma máquina que respeitasse restrições mínimas quanto ao tamanho e forma de seu volume de trabalho, mas ainda mantendo o melhor desempenho possível dentro deste volume. / This work is about the study of parallel architecture robots, focusing in modeling and optimization. No physical prototypes were built, although the virtual models can help those willing to do so. After searching for an application that could benefit from the use of a parallel robot, another search was made, this time for the right architecture type. After selecting the architecture, the next step was the kinematics and dynamics analysis. The dynamics model is developed using the Newton ? Euler method. A virtual simulator was also developed in MATLAB 6.5 environment. The simulator?s main purpose was to demonstrate that the methods applied were correct and efficient, so it has several features such as linear and circular interpolations, capacity to use multiple coordinate systems and others. After finishing the simulator, an algorithm to calculate the machine workspace was added. The algorithm receives as input some desired requirements regarding the manipulator pose and then calculates the workspace, taking into consideration imposed constraints. Lastly, algorithms capable to measure the manipulator?s performance regarding to its actuator and end-effector force relationship were also incorporated into the simulator that calculates the machine?s force ellipsoid during any movement, for each desired workspace point. For the optimization procedures, some previously developed tools were used, so that the resulting model was capable to respect some workspace constraints regarding size and shape, but also maintaining the best performance possible inside this volume.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-10-22T19:41:10Z No. of bitstreams: 4 Dissertação - Douglas Hilário da Cruz - 2013 - PARTE 01.pdf: 20946472 bytes, checksum: 1f5cc7eeda54593cff53f3c563b23faa (MD5) Dissertação - Douglas Hilário da Cruz - 2013 - PARTE 02.pdf: 20125557 bytes, checksum: 9c30c03de1a6b7fb3f356cc931d61534 (MD5) Dissertação - Douglas Hilário da Cruz - 2013 - PARTE 03.pdf: 266901 bytes, checksum: 97410256533198e3a3b180056a740526 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2014-10-22T20:18:04Z (GMT) No. of bitstreams: 4 Dissertação - Douglas Hilário da Cruz - 2013 - PARTE 01.pdf: 20946472 bytes, checksum: 1f5cc7eeda54593cff53f3c563b23faa (MD5) Dissertação - Douglas Hilário da Cruz - 2013 - PARTE 02.pdf: 20125557 bytes, checksum: 9c30c03de1a6b7fb3f356cc931d61534 (MD5) Dissertação - Douglas Hilário da Cruz - 2013 - PARTE 03.pdf: 266901 bytes, checksum: 97410256533198e3a3b180056a740526 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-10-22T20:18:04Z (GMT). No. of bitstreams: 4 Dissertação - Douglas Hilário da Cruz - 2013 - PARTE 01.pdf: 20946472 bytes, checksum: 1f5cc7eeda54593cff53f3c563b23faa (MD5) Dissertação - Douglas Hilário da Cruz - 2013 - PARTE 02.pdf: 20125557 bytes, checksum: 9c30c03de1a6b7fb3f356cc931d61534 (MD5) Dissertação - Douglas Hilário da Cruz - 2013 - PARTE 03.pdf: 266901 bytes, checksum: 97410256533198e3a3b180056a740526 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-04-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study asymptotic lines in the neighborhood of a singular point, lines of curvature in the neighborhood of singular curves of ellipsoid wave fronts and the lines of curvature in the neighborhood of the Darbouxian umbilic points. / Neste trabalho estudamos as linhas assintóticas na vizinhança de um ponto singular, as linhas de curvatura na vizinhança das curvas de pontos singulares das frentes de ondas do elipsóide e as linhas de curvatura na vizinhança dos pontos umbílicos Darbouxianos das frentes de ondas de uma superfície regular.

Die vorliegende Arbeit befasst sich mit der Konvergenztheorie für die regularisierten Lösungen inkorrekter inverser Probleme bei A-priori-Parameterwahl im Hilbertraum. Zunächst werden bekannte Konvergenzratenresultate basierend auf verallgemeinerten Quelldarstellungen systematisch zusammengetragen. Danach wird sich mit dem Fall befasst, was getan werden kann, wenn solche Quellbedingungen nicht erfüllt sind. Man gelangt zur Analysis von Abstandsfunktionen, mit deren Hilfe ebenfalls Konvergenzraten ermittelt werden können. Praktisch wird eine solche Abstandsfunktion anhand der Betrachtung einer Fredholmschen Integralgleichung 2. Art abgeschätzt. Schließlich werden die Zusammenhänge zwischen bedingter Stabilität, Stetigkeitsmodul und Konvergenzraten erörtert und durch ein Beispiel zur Laplace-Gleichung untermauert. / This dissertation deals with the convergence theory of regularized solutions of ill-posed inverse problems in Hilbert space with a priori parameter choice. First, well-known convergence rate results based on general source conditions are brought together systematically. Then it is studied what can be done if such source conditions are not fulfilled. One arrives at the analysis of distance functions. With their help, convergence rates can be determined, too. As an example, a distance function is calculated by solving a Fredholm integral equation of the second kind. Finally, the cross-connections between conditional stability, the modulus of continuity and convergence rates is treated accompanied with an example concerning the Laplace equation.

L’étude topologique des variétés algébriques réelles remonte au moins aux travaux de Harnack, Klein, et Hilbert au 19éme siecle; en particulier, la classification des types d’isotopie réalisés par les courbes algébriques réelles d’un degré fixé dans RP2 est un sujet qui a connu un essor considérable jusqu'à aujourd'hui. En revanche, en dehors des études concernants les surfaces de Hirzebruch et les surfaces de degré au plus 3 dans RP3, à peu près rien n’est connu dans le cas de surfaces ambiantes plus générales. Cela est du en particulier au fait que les variétés construites en utilisant le "patchwork" sont des hypersurfaces de variétés toriques. Or, il existe de nombreuses autre surfaces algébriques réelles. Parmi celles-ci se trouvent les surfaces rationnelles réelles, et plus particulièrement les surfaces rèelles minimales. Dans cette thèse, on élargit l’étude des types d’isotopie réalisés par les courbes algébriques réelles aux surfaces réelles minimales de del Pezzo de degré 1 et 2. En outre, on termine la classification des types topologiques réalisés par les courbes algébriques réelles séparantes et non-séparantes de bidegré (5,5) sur la quadrique ellipsoide. / The study of the topology of real algebraic varieties dates back to the work of Harnack, Klein and Hilbert in the 19th century; in particular, the isotopy type classification of real algebraic curves with a fixed degree in RP2 is a classical subject that has undergone considerable evolution. On the other hand, apart from studies concerning Hirzebruch surfaces and at most degree 3 surfaces in RP3, not much is known for more general ambient surfaces. In particular, this is because varieties constructed using the patchworking method are hypersurfaces of toric varieties. However, there are many other real algebraic surfaces. Among these are the real rational surfaces, and more particularly the $mathbb{R}$-minimal surfaces. In this thesis, we extend the study of the topological types realized by real algebraic curves to the real minimal del Pezzo surfaces of degree 1 and 2. Furthermore, we end the classification of separating and non-separating real algebraic curves of bidegree $(5,5)$ in the quadric ellipsoid.

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