Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Não consta / O objetivo desta dissertação é expor com detalhes o resultado de Gursky-Malchiodi. Dada uma variedade Riemanniana (M,g) de dimensão n>4 com curvatura escalar não negativa e Q-curvatura semipositiva, existe uma métrica conforme a g com Q-curvatura constante positiva. Com estas hipóteses mostra-se um princípio do máximo forte para o operador de Paneitz, que é um operador diferencial parcial não linear de quarta ordem. A partir daí define-se um fluxo não local e, utilizando funções testes, modificamos conformemente a métrica inicial tal que o fluxo converge sequencialmente para uma métrica conforme de Q-curvatura constante positiva e curvatura escalar positiva.

Fundação de Apoio a Pesquisa e à Inovação Tecnológica do Estado de Sergipe - FAPITEC/SE / The main objective of this work is to show the existence of metrics with positive Ricci curvature in the class as a Riemannian metric with positive scalar curvature on compact manifolds of dimension 3 and 4. Catino-Djadli [ 3 ] and Gursky-Viaclovsky [ 13 ] showed that bends climbing and Ricci of a metric g satisfies an integral inequality in a three-dimensional compact manifold, then g is according to some metric of positive Ricci curvature. In the first article the authors work in three-dimensional manifolds and second manifolds 4 / O objetivo principal deste trabalho consiste em mostrar a existˆencia de m ́etricas com curva- tura de Ricci positiva na classe conforme de uma m ́etrica Riemanniana com curvatura escalar positiva em variedades compactas de dimens ̃ao 3 e 4. Catino-Djadli [3] e Gursky-Viaclovsky [13] mostraram que se as curvaturas escalar e de Ricci de uma métrica g satisfazem a uma desigualdade integral em uma variedade compacta tridimensional, então g é conforme a al- guma métrica de curvatura de Ricci positiva. No primeiro artigo os autores trabalham em variedades tridimensionais e no segundo em variedades de dimensão 4.

Made available in DSpace on 2014-07-29T15:08:21Z (GMT). No. of bitstreams: 1 dissertacao wesley.pdf: 2546407 bytes, checksum: 1c1c0ce0780c785a8633268a8ba0eae0 (MD5) Previous issue date: 2008-06-06 / The present work proposes a numeric formulation for the determination of Carter's factor as a function of the geometry of the slot of electric machines. This task is made by the use of the Schwarz-Christoffel transformation. In order to reach the objective, there is the need to calculate the Schwarz-Christoffel inverse transformation. This represents a non-linear optimization problem. Therefore, it is proposed a methodology to calculate the parameters of the Schwarz-Christoffel inverse transformation using genetic algorithms. The assessment of Carter s factor is achieved considering polygonal domains with many vertices. The transformation leads to a rectangular domain approach. Moreover, some case studies are proposed and the methodology results are compared to traditional formulation results for the Carter s factor, yielding some disparities. / O presente trabalho propõe obter uma formulação numérica para a determinação do fator de Carter em função da geometria da ranhura de máquinas elétricas, utilizando o cálculo numérico da transformação de Schwarz-Christoffel. Com este objetivo, verifica-se a necessidade do cálculo da transformação inversa de Schwarz-Christoffel. Este problema representa um problema de otimização não linear. Desta forma, propõe-se uma metodologia que implementa um algoritmo genético para resolver o problema de cálculo dos parâmetros da Transformação inversa de Schwarz-Christoffel, considerando domínios poligonais com muitos vértices. Em seguida, obtém-se um domínio retangular para o qual o problema do cálculo do fator de Carter é resolvido. Desta forma, apresentam-se vários casos de estudos onde a metodologia proposta é comparada com as formulações tradicionalmente utilizadas para o cálculo do fator de Carter. Os resultados obtidos pelas diferentes metodologias são confrontados, mostrando certas disparidades.

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-03-24T17:48:37Z No. of bitstreams: 2 Dissertação - Alan Henrique Ferreira Silva - 2016.pdf: 10881029 bytes, checksum: 1c411277f8b103cc8a55709053ed7f9b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-03-27T15:13:01Z (GMT) No. of bitstreams: 2 Dissertação - Alan Henrique Ferreira Silva - 2016.pdf: 10881029 bytes, checksum: 1c411277f8b103cc8a55709053ed7f9b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-03-27T15:13:01Z (GMT). No. of bitstreams: 2 Dissertação - Alan Henrique Ferreira Silva - 2016.pdf: 10881029 bytes, checksum: 1c411277f8b103cc8a55709053ed7f9b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-31 / This work proposes method to encode and decode imas using conformal mapping. Conformal mapping modifies domains without modifyung physical characteristics between them. Real images are processed between these domains using encoding keys, also called transforming functions. The advantage of this methodology is the ability to carry the message as an encoded image in printed media for posterior-decoding. / Este trabalho propõe método que utiliza transformações conformes para codificar e decodificar imagens. As transformações conformes modificam os domínios em estudos sem modificar as características físicas entre eles. As imagens reais são transformadas entre estes domínios utilizando chaves, que são funções transformadoras. o diferencial desta metodologia é a capacidade de transportar a mensagem contida na imagem em meio impresso codificado e depois, decodificá-la.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2017-04-24T22:03:45Z No. of bitstreams: 2 Dissertação - Hector Andrés Rosero García - 2017.pdf: 4670148 bytes, checksum: 8bc0d1f8d189cce09af8bc129ec5edcd (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-04-25T15:46:02Z (GMT) No. of bitstreams: 2 Dissertação - Hector Andrés Rosero García - 2017.pdf: 4670148 bytes, checksum: 8bc0d1f8d189cce09af8bc129ec5edcd (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-04-25T15:46:02Z (GMT). No. of bitstreams: 2 Dissertação - Hector Andrés Rosero García - 2017.pdf: 4670148 bytes, checksum: 8bc0d1f8d189cce09af8bc129ec5edcd (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-03-31 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this work we develop the basics of the concept of Isocurved Surface, introduced in [2] by Barroso and Roitman, that is, a surface immersed in a 3-dimensional manifold M and which have the same Gaussian curvature induced by two different metrics. Later on, we show a geometric method to generate non-trivial examples of elliptic and hyperbolic isocurved surfaces for the particular case of M = R3+ and the Euclidean and hyperbolic metrics induced on it. We also exhibit some examples coming from the geometric method above. / Neste trabalho, desenvolvemos as bases do conceito de Superfície Isocurvada, introduzido em [2] por Barroso e Roitman, isto é, uma superfície imersa numa variedade 3-dimensional M a qual tem a mesma curvatura Gaussiana induzida por duas métricas diferentes em M. Segundo isso, mostramos um método geométrico para a geração de exemplos não triviais de superfícies isocurvadas elípticas e hiperbólicas no caso particular de M = R^3_+ com as métricas conformes Euclidiana e hiperbólica. Também exibimos alguns exemplos subjacentes ao método acima.

Neste trabalho estabelecemos o Teorema Central do Limite para o modelo O(N) de Heisenberg hierárquico na criticalidade via equação a derivadas parciais no limite N -> infinito. Por simplicidade consideramos apenas o caso d = 4, sendo o teorema também válido para d > 4. Pelo estudo de uma dada equação a derivadas parciais (EDP) determinamos a temperatura inversa crítica do modelo esférico hierárquico contínuo para um d > 2 qualquer, havendo conexão entre criticalidade e o ponto fixo da EDP. Por meio de uma análise geométrica da trajetória crítica obtemos informações sobre a dinâmica e distribuição dos zeros de Lee-Yang. / In this work we stablish the Central Limit Theorem for the hierarchical O(N) Heisenberg model at criticality via partial differential equation in the limit N -> infinity. For simplicity we only treat the d = 4 case but the theorem is still valid for d > 4. By studying a given partial differential equation (PDE) we determine for any d > 2 the critical inverse temperature of the continuum hierarchical spherical model, and we show a connection between criticality and the fixed point of PDE. By means of a geometric analysis of the critical trajectory we obtain some informations about Lee-Yang zeros´s dynamics and distribution.

In this thesis, the symmetry structure of gravitational theories at null infinity is studied further, in the case of pure gravity in four dimensions and also in the case of Einstein-Yang-Mills theory in d dimensions with and without a cosmological constant.<p><p>The first part of this thesis is devoted to the presentation of asymptotic methods (symmetries, solution space and surface charges) applied to gravity in the case of the BMS gauge in three and four spacetime dimensions.<p><p>The second part of this thesis contains the original contributions.<p>Firstly, it is shown that the enhancement from Lorentz to Virasoro algebra also occurs for asymptotically flat spacetimes defined in the sense of Newman-Unti. As a first application, the transformation laws of the Newman-Penrose coefficients characterizing solution space of the Newman-Unti approach are worked out, focusing on the inhomogeneous terms that contain the information about central extensions of the theory. These transformations laws make the conformal structure particularly transparent, and constitute the main original result of the thesis.<p>Secondly, asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner in $d$ dimensions. In agreement with a recent conjecture, a Virasoro-Kac-Moody type algebra is found not only in three dimensions but also in the four dimensional asymptotically flat case.<p><p>These two parts of the thesis are supplemented by appendices. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

La fonction de partition de théories de jauge supersymétriques avec quatre supercharges sur la sphere à deux dimensions est calculée exactement grâce à la localisation supersymétrique. Pour certaines théories de jauge, les expressions explicites sont égales à des corrélateurs dans la théorie conforme des champs de Toda de dimension deux. Ces égalités trouvent leur place ausein de la correspondance AGT, qui relie des théories de jauge supersymétriques de dimension quatre avec huit supercharges à des corrélateurs de la théorie de Toda. En effet, les théories de jauge à deux dimensions peuvent être insérées le long d’une surface dans une théorie à quatre dimensions, formant ainsi un opérateur de surface à moitié BPS. Une telle insertioncorrespond à l’ajout d’un opérateur local particulier (un opérateur de vertex dégénéré) dans le corrélateur de Toda.Cette correspondance enrichie a plusieurs conséquences. D’une part, les symétries des corrélateurs de Toda impliquent des analogues des dualités de Seiberg et de Kutasov–Schwimmer pour les théories de jauge à deux dimensions avec quatre supercharges. D’autre part, les résultats exacts en théorie de jauge fournissent de nouvelles données dans la théorie de Toda.Cela mène à une proposition concrète pour l’échange de deux opérateurs de vertex semi-dégénérés dans la théorie de Toda, qui contient des informations importantes concernant la S-dualité à quatre dimensions. / The sphere partition function of two-dimensional supersymmetric gauge theories with four supercharges is computed exactly using supersymmetric localization. For some gauge theories, explicit expressions are found to match with correlators in the two-dimensional Toda conformal field theory. This fits into the AGT correspondence, which relates supersymmetric fourdimensionalgauge theories with eight supercharges to correlators in the Toda theory. More precisely, the two-dimensional gauge theories can be inserted along a surface in a four-dimensional theory, thus forming half-BPS surface operators: such an insertion corresponds to the addition of a particular local operator (a degenerate vertex operator) in the Toda correlator.This enriched correspondence has several consequences. On the one hand, symmetries of Toda correlators imply analogues of Seiberg and Kutasov–Schwimmer dualities for two-dimensional gauge theories with four supercharges. On the other hand, exact gauge theory results yield previously unknown data in the Toda theory. This leads to a concrete proposal for the Toda braiding kernel of two semi-degenerate vertex operators, which holds important information about four-dimensional S-duality.

This thesis focuses on the problem of determining appropriate skeletal configurations for which a virtual animated character moves to desired positions as smoothly, rapidly, and as accurately as possible. During the last decades, several methods and techniques, sophisticated or heuristic, have been presented to produce smooth and natural solutions to the Inverse Kinematics (IK) problem. However, many of the currently available methods suffer from high computational cost and production of unrealistic poses. In this study, a novel heuristic method, called Forward And Backward Reaching Inverse Kinematics (FABRIK), is proposed, which returnsvisually natural poses in real-time, equally comparable with highly sophisticated approaches. It is capable of supporting constraints for most of the known joint types and it can be extended to solve problems with multiple end effectors, multiple targets and closed loops. FABRIK wascompared against the most popular IK approaches and evaluated in terms of its robustness and performance limitations. This thesis also includes a robust methodology for marker prediction under multiple marker occlusion for extended time periods, in order to drive real-time centre of rotation (CoR) estimations. Inferred information from neighbouring markers has been utilised, assuming that the inter-marker distances remain constant over time. This is the firsttime where the useful information about the missing markers positions which are partially visible to a single camera is deployed. Experiments demonstrate that the proposed methodology can effectively track the occluded markers with high accuracy, even if the occlusion persists for extended periods of time, recovering in real-time good estimates of the true joint positions. In addition, the predicted positions of the joints were further improved by employing FABRIK to relocate their positions and ensure a fixed bone length over time. Our methodology is tested against some of the most popular methods for marker prediction and the results confirm that our approach outperforms these methods in estimating both marker and CoR positions. Finally, an efficient model for real-time hand tracking and reconstruction that requires a minimumnumber of available markers, one on each finger, is presented. The proposed hand modelis highly constrained with joint rotational and orientational constraints, restricting the fingers and palm movements to an appropriate feasible set. FABRIK is then incorporated to estimate the remaining joint positions and to fit them to the hand model. Physiological constraints, such as inertia, abduction, flexion etc, are also incorporated to correct the final hand posture. A mesh deformation algorithm is then applied to visualise the movements of the underlying hand skeleton for comparison with the true hand poses. The mathematical framework used for describing and implementing the techniques discussed within this thesis is Conformal GeometricAlgebra (CGA).

Le présent travail de thèse décrit le développement d'un protocole d'irradiation stéréotaxique combinée à une radiothérapie conformationnelle avec modulation d'intensité. Ce projet a été initiée dans le service de radiothérapie-oncologie du Centre Hospitalier Lyon Sud. La première partie de ce travail fait état d'une revue de littérature sur les techniques d'irradiation du cancer de la prostate. Trois grands thèmes de recherche ont été identifiés et developpés : un premier thèse de recherche portant sur la définition optimale des volumes à irradier lors d'une irradiation stéréotaxique de la prostate et la fiabilité d'uin repérage de l'oragane par des marqueurs intra-prostatiques. La deuxième thématique de recherche était dédiée à la planification du traitement stéréotaxique de la prostate avec pour principal objectif une protection optimale de la paroi rectale avec deux approches différentes : a) une augmentation focalisée de la dose d'irradiation uniquement sur la tumeur macroscopiquement visible, ou b) l'utilisation d'un gel injecté entre la paroi du rectum et la prostate. Le nombre optimal de faisceaux à utiliser ainsi que l'énergie la mieux adaptée ont été évalués dans le cadre de la première approche avec uin boost intégré.. La trosième thématique portait sur les contrôles qualité à réaliser dans le cadre de la mise en route de cette technique d'irradiation. Trois détecteur dédiés aux contrôles de la distribution de dose sous l'accélarateur ont été évalués. L'ensemble de ces travaux serviront de supports à la réalisation d'une étude de phase II intégrant une irradiation stéréotaxique des cancers de la prostate avec injection de gel d'acide hyaluronique entre le rectum et la prostate / The current work decribes the implementation of a protocol for stereotactic body radiotherapy (SBRT) combined with an intensity-modulated radiation therapy technique (IMRT). the project was initiated in the Department of Radiation-Oncology from Lyon Sud Hospital. The first part summarizes the state of the art of prostate cancer with a literature review on irradiation techniques. Three research themes were described and developped : The first theme discusses the optimal definition of the volumes to be irradiated during a prostate SBRT and the accuracy of the target localization using intraprostatic markers. The second theme of research describes the treatment planning for prostate SBRT having as main purpose an optimal protection of the rectal-wall with two different approaches: a) an augmentation of the dose with simultaneous integrated boost only into visible macroscopic tumor, or b) the use of a gel injected between the rectal-wall and the prostate. The optimal number of fields, as well as the most favorable energy, was evaluated in the context of the first approach with a simultaneous integrated boost. The third theme discusses the quality assurance (QA) that needs to be performed for an IMRT-SBRT technique. Three detectors that ara dedicated to the QA of dose distribution under accelerator were evaluated. The results of all these studies will be used for the implementation of a phase II study for prostate SBRT with an injection of hyaluronic acid between the rectum and the prostate.