O PDE Escola, objeto desta pesquisa, é um programa do Ministério da Educação, de apoio à gestão escolar baseado no planejamento participativo e destinado a auxiliar as escolas públicas a melhorar sua gestão, conforme informado em seus materiais. O enfoque de pesquisa foi na edição 2011, em que o programa priorizou as escolas cujo IDEB 2009 foi igual ou inferior à média nacional e que não tinham sido priorizadas entre 2008 e 2010. Em linhas gerais, esta pesquisa teve como objetivo compreender qual a representação de problemas da escola para o desenvolvimento da educação, por sua perspectiva, considerando o nível de distanciamento ou aproximação existente em relação à proposta da política pública educacional do PDE Escola. Para isso, serviram como fontes documentais, as publicações oficiais do Ministério da Educação, a partir de 2006, quando a política começou a se expandir envolvendo as escolas públicas com os IDEBs mais baixos em todo o país, até 2011, que é o período do grupo de escolas priorizadas no PDE Escola, selecionado para análise. As fontes ou referências principais para análise foram os Planos de Desenvolvimento de Escolas da Rede Estadual do Rio Grande do Sul, priorizadas em 2011, que faziam parte da última edição do programa, ainda disponível para acesso em sistema on line do MEC em 2013. Como amostra para esta pesquisa foi definido o grupo das 44 escolas que tiveram o PDE Escola aprovado em 2011, com execução do recurso financeiro em 2012. A abordagem do ciclo de políticas de Stephen J. Ball foi a perspectiva de análise utilizada, mas com enfoque no contexto da prática. Fizeram parte do aporte teórico as abordagens sobre: ideologia; sociologia da globalização; a educação e o estado capitalista; o novo gerencialismo; o modelo de gestão do bem-estar social e o novo gerencialismo; as políticas e gestão da educação básica e escolar no Brasil. Por fim, verificou-se por meio deste estudo, que as dimensões do diagnóstico do PDE Escola, das escolas da amostra com as médias percentuais maiores na indicação de problemas e problemas considerados críticos, foram as dos indicadores e taxas, e taxas de rendimento, seguidas das que tratam da infraestrutura e comunidade escolar, sendo que ao final, com as médias percentuais mais baixas, ficaram as de ensino e aprendizagem e por último a de gestão. Isso evidenciou a forte influência da proposta da política sobre o que as escolas consideram como problemas na educação, que repercute até hoje nas dimensões em que se concentram as médias percentuais de escolas mais elevadas, na indicação de problemas. A proposta da política pesquisada neste estudo demonstrou enfocar a necessidade de avanço sobre os resultados educacionais, por meio da responsabilização dos atores locais para o planejamento de ações que solucionem isso, mas a representação de problemas apresentados aponta contradições que revelam outras necessidades, apesar de até certo ponto a proposta da política se materializar na priorização de problemas pela maioria das escolas, nas dimensões que são o foco do MEC. / The PDE School, object of this research is a program of the Ministry of Education to support school management based on participatory planning and designed to assist the public schools to improve their management, as reported in their materials. The research focus was in the 2011 edition, in which the program prioritized schools whose IDEB 2009 was equal to or below the national average and that had not been prioritized between 2008 and 2010. In general, this research aimed to understand what the representation school problems for the development of education, in perspective, considering the level of detachment or existing approach to the proposal of public education policy of PDE school. For that, served as documentary sources, the official publications of the Ministry of Education, from 2006, when the policy began to expand involving public schools with the lowest IDEBs across the country by 2011, which is the period of group prioritized schools in PDE School, selected for analysis. The sources or major references for analysis were the Development Plans of Schools of State Network of Rio Grande do Sul, prioritized in 2011, which were part of the last edition of the program, still available for access online system MEC in 2013. As sample for this study was defined the group of 44 schools that had the PDE School approved in 2011, with implementation of financial resources in 2012. the approach of Stephen J. Ball policies cycle analysis perspective was used, but with a focus on context of practice. Were part of the theoretical framework approaches on: ideology; sociology of globalization; education and the capitalist state; the new managerialism; the social welfare management model and the new managerialism; policies and management in primary and school education in Brazil. Finally, it has been found by this study that the dimensions of the diagnosis of PDE School Schools of the sample with the highest percentage means the indication considered critical issues and problems, and the indicators were the rates and yields, followed by dealing with infrastructure and school community, and at the end, with the lowest percentage averages, were the teaching and learning and finally the management. This showed the strong influence of the proposed policy on what schools consider as problems in education that affects today in dimensions that concentrate the percentage means higher schools, the indication of problems. The proposed policy researched in this study demonstrated focus on the need to advance on educational outcomes, through the empowerment of local actors for planning actions that solve this, but the representation of the problems presented points contradictions that reveal other needs, although so some extent the policy proposal to materialize in prioritizing problems by most schools, dimensions that are the focus of MEC.

Cette thèse porte sur des équations aux dérivées partielles hamiltoniennes à conditions initiales aléatoires. En effet, on étudie ici l'évolution de certaines mesures à travers le flot de telles équations. Cette étude suit deux axes.Premièrement, on considère le caractère globalement bien posé de l'équation d'onde non linéaire quand la donnée initiale est de faible régularité. Cette donnée initiale est une variable aléatoire et on obtient le caractère globalement bien posé de façon presque sûre par rapport à la mesure induite par cette variable. La faible régularité fait référence à l'espace auquel appartient les valeurs de la variable aléatoires et dénote une régularité moins contraignante que celle requise par la théorie déterministe.Dans certaines conditions, des propriétés d'invariance de la loi de la donnée initiale sont nécessaires à la démonstration du caractère bien posé. C'est pourquoi le deuxième axe comprend la question de l'invariance de mesures et leurs stabilités à travers le flot d'EDPs.On donne ainsi une loi invariante à travers le flot de l'équation d'onde cubique et une autre à travers celui de l'équation de Benjamin-Bona-Mahony (BBM). la mesure invariante pour BBM est telle que les amplitudes associées à chaque longueur d'onde de la solution sont des variables aléatoires indépendantes les unes des autres. On considère alors la stabilité de l'invariance pour BBM lorsqu'on ajoute des corrélations entre ces amplitudes.Enfin, en s'inspirant de la littérature physique à propos de la turbulence faible, on s'est demandé ce qu'il advenait de l'indépendance entre les amplitudes dans un contexte plus général. Plus précisément, on a cherché à si les covariances des amplitudes restent petites lorsque celles-ci sont initialement indépendantes et que le terme non quadratique de l'énergie associée à l'équation étudiée est très petit devant l'énergie totale. / This thesis is about Hamiltonian partial differential equations with random initial data. Indeed, the evolution of particular measures are studied here through the flow of such equations. This study is done along two axis.First, the global well-posedness with initial data with low regularity is considered for the non linear wave equation. The initial datum is a random variable and the global well-posedness is obtained almost surely wrt the measure induced by this variable. The low regularity refers to the space which the values of the random initial datum belong to and means a regularity under the one given by deterministic theory.Some properties of invariance of the law of the initial datum are required in the proof of the global well-posedness under certain conditions. Hence, the second axis is the invariance of measures through the flow of PDEs and their stability.An invariant law is given for the cubic non linear wave equation and for the Benjamin-Bona-Mahony equation (BBM). The invariant measure for BBM is such that the amplitudes associated to each wavelength of the solution are random variables independent from each other. The stability of the invariance for BBM is considered when one adds correlations between these amplitudes.Finally, inspired by the Physics literature about wave turbulence, the stability of the independence between the amplitudes is investigated about. Namely, we tried to know if the covariances of the amplitudes remain small when they are initially independent and when the quadratic term of the energy associated to the equation is small compared to the total energy.

Cette thèse porte sur l'étude des phénomènes d'explosion pour certaines équations aux dérivées partielles dispersives et plus particulièrement pour l'équation de Schrodinger non linéaire. Ces phénomènes ont été beaucoup étudiés et notamment dans le cas Euclidien. On s'intéresse ici à des cas où l'espace n'est plus l'espace Euclidien. Cela comprend en particulier l'étude des trois prototypes : domaine de l'espace Euclidien, tore (courbure nulle), sphère (courbure positive) et espace hyperbolique (courbure négative). Concernant l'équation de Schrodinger, plusieurs résultats ont montré que la métrique pouvait influencer le comportement qualitatif des solutions, en particulier les propriétés dispersives des solutions et le seuil critique d'existence locale pour le problème de Cauchy. Plusieurs résultats concernant l'explosion sont ensuite venus confirmer ces phénomèmes. Dans cette thèse, on se propose de poursuivre cette étude. / In this thesis, we study blow-up behavior of solutions for dispersive equations, more precisely for the nonlinear Schr"odinger equation. This has been studied essentially in the Euclidean case. In this work, we are interested in the case where the equation is posed on a general manifold; this includes the case of a domain of the Euclidean space, torus (zero curvature); the sphere (non negative curvature) and the hyperbolic space (negative curvature). For the Schr"odinger equation, several results proved that the metric could change the qualitative behavior of the solutions, in particular dispersive properties and the critical threshold of existence for the Cauchy problem. Then, some results showed that blow-up theory is also concerned. In this work, we continue this study.

O PDE Escola, objeto desta pesquisa, é um programa do Ministério da Educação, de apoio à gestão escolar baseado no planejamento participativo e destinado a auxiliar as escolas públicas a melhorar sua gestão, conforme informado em seus materiais. O enfoque de pesquisa foi na edição 2011, em que o programa priorizou as escolas cujo IDEB 2009 foi igual ou inferior à média nacional e que não tinham sido priorizadas entre 2008 e 2010. Em linhas gerais, esta pesquisa teve como objetivo compreender qual a representação de problemas da escola para o desenvolvimento da educação, por sua perspectiva, considerando o nível de distanciamento ou aproximação existente em relação à proposta da política pública educacional do PDE Escola. Para isso, serviram como fontes documentais, as publicações oficiais do Ministério da Educação, a partir de 2006, quando a política começou a se expandir envolvendo as escolas públicas com os IDEBs mais baixos em todo o país, até 2011, que é o período do grupo de escolas priorizadas no PDE Escola, selecionado para análise. As fontes ou referências principais para análise foram os Planos de Desenvolvimento de Escolas da Rede Estadual do Rio Grande do Sul, priorizadas em 2011, que faziam parte da última edição do programa, ainda disponível para acesso em sistema on line do MEC em 2013. Como amostra para esta pesquisa foi definido o grupo das 44 escolas que tiveram o PDE Escola aprovado em 2011, com execução do recurso financeiro em 2012. A abordagem do ciclo de políticas de Stephen J. Ball foi a perspectiva de análise utilizada, mas com enfoque no contexto da prática. Fizeram parte do aporte teórico as abordagens sobre: ideologia; sociologia da globalização; a educação e o estado capitalista; o novo gerencialismo; o modelo de gestão do bem-estar social e o novo gerencialismo; as políticas e gestão da educação básica e escolar no Brasil. Por fim, verificou-se por meio deste estudo, que as dimensões do diagnóstico do PDE Escola, das escolas da amostra com as médias percentuais maiores na indicação de problemas e problemas considerados críticos, foram as dos indicadores e taxas, e taxas de rendimento, seguidas das que tratam da infraestrutura e comunidade escolar, sendo que ao final, com as médias percentuais mais baixas, ficaram as de ensino e aprendizagem e por último a de gestão. Isso evidenciou a forte influência da proposta da política sobre o que as escolas consideram como problemas na educação, que repercute até hoje nas dimensões em que se concentram as médias percentuais de escolas mais elevadas, na indicação de problemas. A proposta da política pesquisada neste estudo demonstrou enfocar a necessidade de avanço sobre os resultados educacionais, por meio da responsabilização dos atores locais para o planejamento de ações que solucionem isso, mas a representação de problemas apresentados aponta contradições que revelam outras necessidades, apesar de até certo ponto a proposta da política se materializar na priorização de problemas pela maioria das escolas, nas dimensões que são o foco do MEC. / The PDE School, object of this research is a program of the Ministry of Education to support school management based on participatory planning and designed to assist the public schools to improve their management, as reported in their materials. The research focus was in the 2011 edition, in which the program prioritized schools whose IDEB 2009 was equal to or below the national average and that had not been prioritized between 2008 and 2010. In general, this research aimed to understand what the representation school problems for the development of education, in perspective, considering the level of detachment or existing approach to the proposal of public education policy of PDE school. For that, served as documentary sources, the official publications of the Ministry of Education, from 2006, when the policy began to expand involving public schools with the lowest IDEBs across the country by 2011, which is the period of group prioritized schools in PDE School, selected for analysis. The sources or major references for analysis were the Development Plans of Schools of State Network of Rio Grande do Sul, prioritized in 2011, which were part of the last edition of the program, still available for access online system MEC in 2013. As sample for this study was defined the group of 44 schools that had the PDE School approved in 2011, with implementation of financial resources in 2012. the approach of Stephen J. Ball policies cycle analysis perspective was used, but with a focus on context of practice. Were part of the theoretical framework approaches on: ideology; sociology of globalization; education and the capitalist state; the new managerialism; the social welfare management model and the new managerialism; policies and management in primary and school education in Brazil. Finally, it has been found by this study that the dimensions of the diagnosis of PDE School Schools of the sample with the highest percentage means the indication considered critical issues and problems, and the indicators were the rates and yields, followed by dealing with infrastructure and school community, and at the end, with the lowest percentage averages, were the teaching and learning and finally the management. This showed the strong influence of the proposed policy on what schools consider as problems in education that affects today in dimensions that concentrate the percentage means higher schools, the indication of problems. The proposed policy researched in this study demonstrated focus on the need to advance on educational outcomes, through the empowerment of local actors for planning actions that solve this, but the representation of the problems presented points contradictions that reveal other needs, although so some extent the policy proposal to materialize in prioritizing problems by most schools, dimensions that are the focus of MEC.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-07-14T12:01:58Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese_Fabiana corrigida.pdf: 10988390 bytes, checksum: 0f7ed97ccd1c58e803213e43db1e6a2c (MD5) / Made available in DSpace on 2016-07-14T12:01:58Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese_Fabiana corrigida.pdf: 10988390 bytes, checksum: 0f7ed97ccd1c58e803213e43db1e6a2c (MD5) Previous issue date: 2015-07-29 / FACEPE / O Sildenafil é um inibidor potente e seletivo da fosfodiesterase-5 (PDE5). Este fármaco foi aprovado para uso terapêutico na disfunção erétil e, atualmente, vem sendo usado também no tratamento da hipertensão pulmonar. Embora mantenha um excelente nível de segurança e perfil de tolerabilidade, poucos estudos avaliaram os possíveis efeitos colaterais do tratamento crônico com Sildenafil sobre o sistema reprodutor masculino, especialmente na próstata visando o relaxamento da uretra e alívio dos Sintomas do Trato Urinário Inferior (STUI). Desta forma, avaliamos o efeito do tratamento, em camundongos C57Bl/6, através de análise morfológica, ultraestrutural e expressão molecular de guanilato ciclase solúvel-sGC, Óxido nítrico sintase endotelial-eNOS, Antígeno prostático específico-PSA e Fator de crescimento transformador beta-TGF- no tecido prostático. Foi-se observado que o tratamento com Sildenafil não induz danos evidentes na próstata. Além disso, tem sido demonstrado que Sildenafil tem eficácia terapêutica em doenças inflamatórias crônicas, podendo apresentar uma eficácia terapêutica potencial em diferentes doenças. Entre elas, uma atenção especial tem sido dada para as patologias relacionadas ao trato urogenital masculino, como a Hiperplasia Prostática Benigna (HPB), Câncer de próstata e Prostatites. A inflamação tem sido considerada como um fator etiológio da HPB e STUI. Assim, foi proposto um modelo de lesão prostática com injeção intrauretral de LPS (1mg/ml), em camundongos machos Swiss e C57Bl/6, desenvolvido durante 3, 7, 10 e 14 dias. A análise dos resultados mostrou que a indução intrauretral com lipopolisacarideo-LPS atua como importante agente da HPB, além de promover o aumento de fatores de crescimento (FGF-7 e FGF- β), α-actina e citocinas pró-inflamatórias (IL-1, IL-6, IL-17), tanto no estroma como no epitélio. Uma vez que o Sildenafil tem potencial anti-inflamatório, este estudo se propôs a analisar a ação do Sildenafil em um modelo de lesão prostática experimental, induzido por injeção intrauretral de LPS em camundongos C57BL/6. O tratamento com Sildenafil (25mg/kg) dos animais com prostatite apresentaram redução significativa de -actina, COX-2, NFK- B, IL-6, IL-17 e FGF-7. Por não induzir danos na próstata , o Sildenafil, por não induzir a longo prazo danos evidentes na próstata pode representar uma estratégia farmacológica para o tratamento de doenças inflamatórias crônicas do trato urogenital. / Sildenafil is a potent and selective inhibitor of phosphodiesterase-5 (PDE5). This drug has been approved for therapeutic use in erectile dysfunction and currently has been also used to treat pulmonary hypertension. While maintaining an excellent level of safety and tolerability profile, few studies have evaluated the possible side effects of chronic treatment with Sildenafil on the male reproductive system, especially in prostate aimed at relaxing the urethra and relief of symptoms of Lower Urinary Tract (LUTS). Therefore, we assessed the treatment effect in C57Bl/6 mice, using morphological analysis, ultrastructural and molecular expression of soluble guanylate cyclase-sGC, endothelial nitric oxide synthase, eNOS, prostate-specific antigen PSA and transforming growth factor beta TGF- in prostate tissue. It is observed that the treatment with sildenafil does not induce apparent damage to the prostate. Furthermore, Sildenafil has been shown to have therapeutic efficacy in chronic inflammatory diseases, which have a potential therapeutic efficacy in various diseases. Among them, special attention has been given to the pathologies related to the male urogenital tract, such as Benign Prostatic Hyperplasia (BPH), prostate cancer and Prostatitis. Inflammation has been considered as a factor etiológio of BPH and LUTS. Thus, it has been proposed a prostatic intraurethral injection injury model of LPS (1mg/ml) in male Swiss mice and C57Bl /6 developed for 3, 7, 10 and 14 days. The results showed that the intraurethral induction with lipopolysaccharide-LPS acts as an important agent of HPB, and to promote the increase of growth factors (FGF-7 and FGF- ), -actin and proinflammatory cytokines (IL- 1, IL-6, IL-17), both in the stroma and the epithelium. Since Sildenafil has potential anti-inflammatory, this study aimed to analyze the action of Sildenafil in an experimental prostate injury model induced by intraurethral injection of LPS in C57Bl/6 mice. Treatment with sildenafil (25 mg/kg) of animals with prostatitis showed a significant reduction of -actin, COX-2 NFK-kB, IL-6, IL-17 and FGF-7. By not induce damage to the prostate, Sildenafil, not to induce long term damage evident in the prostate may represent a pharmacologic strategy for the treatment of chronic inflammatory diseases of the urogenital tract.

Dans toutes sortes de milieux industriels comme l'aéronautique, l'industrie spatiale, l'industrie pétrolière et tant d'autres, il est indispensable d'effectuer des calculs numériques pour simuler des phénomènes intervenant dans des systèmes naturels ou artificiels modélisables par la mécanique des milieux continus. Nous nous sommes intéressés à la question scientifique suivante: Comment, pour une simulation donnée et des moyens de calcul donnés, obtenir la plus grande précision de prédiction ? Le but de cette thèse est de faire le lien entre deux techniques de simulation numérique : les méthodes multigrilles et les nouvelles méthodes adaptatives anisotropes récemment développées. On résout une équation aux dérivées partielles elliptique. L'adaptation des maillages au problème donné repose sur une minimisation d'une grandeur donnée suivant la méthode d'adaptation employée: l'erreur d'interpolation pour l'adaptation basée-hessiens, une pondération de l'erreur d'approximation pour la méthode goal-oriented et la norme de l'erreur d'approximation pour la méthode norm-oriented. La méthode multigrille permet d'accelérer la convergence sur chaque maillage. Plusieurs cas tests ont été effectués pour s'assurer de l'efficacité des différentes méthodes. / In many industrial activities such as aeronautics, space industry, oil industry and many others, it is essential to carry out numerical computations to simulate phenomena occurring in natural or artificial systems modelisable by mechanical Continuum. This thesis focuses on the following scientific question: how, for a given simulation and computing means given, obtain the highest prediction accuracy? Our contribustion makes the link between two numerical simulation techniques: multigrid methods and new recently developed anisotropic adaptative methods. We solve an elliptic partial differential equation. The adaptation of the mesh to the given problem is based on minimization of a given magnitude following the adaptation method employed: the interpolation error for the Hessian-based adaptation, a weighting of the approximation error for goal-oriented method and the norm of the approximation error for the norm-oriented method. The multigrid method permits to accelerate convergence on each mesh. Several tests cases were carried out to ensure the effectiveness of the different methods.

Cette thèse étudie le modèle elliptique de l'équation d'osmose et plusieurs de ses applications, en particulier la texturation de modèles 3Ds à partir d'image satellite multi-dates. L'équation d'osmose est similaire à l'équation de Poisson mais est invariante aux changements d'illuminations. Elle a été introduite dans le cadre du traitement d'image dans un modèle parabolique et résolue pour un domaine avec conditions au bord de Neumann.Le premier chapitre expose le modèle elliptique et donne des résultats théoriques pour plusieurs des problèmes au bord associés : conditions de Dirichlet, de Neumann et conditions mixtes. Sont prouvés en particulier l'existence et unicité d'une solution à ces problèmes, à une constante multiplicative près dans le cas de conditions de Neumann. Ces résultats sont étendus au cas de variétés ayant une seule carte locale.Le deuxième chapitre donne ces mêmes résultats pour le cas discret. Il est difficile pour un domaine arbitraire d'implémenter des conditions de Neumann ou des conditions mixtes avec la méthode des différences finies classique. Une formulation par graphe est par conséquent proposée qui facilite considérablement la manipulation des différentes conditions au bord. Cette formulation a également l'avantage de pouvoir être applicable sans changements à un maillage triangulaire.Le troisième chapitre présente différentes applications de l'équation d'osmose : le seamless cloning, la suppression d'ombres et la fusion d'images. Pour le seamless cloning, les résultats sont comparés à ceux obtenus avec Poisson editing. Ils montrent l'intérêt de l'invariance aux changements d'illumination dans le cas d'images d'entrées à contrastes très différents. Cette partie montre aussi les raisons de préférer résoudre l'équation localement avec conditions de Dirichlet plutôt que sur toute l'image avec conditions de Neumann.C'est pour le cas de la suppression d'ombres que l'importance des conditions mixtes apparaît comme elles permettent de traiter à la fois les ombres propres et les ombres portées.Ce chapitre propose aussi plusieurs méthodes pour la fusion de plus de deux images. Sont comparés en particulier les résultats obtenus par une fusion directe des couleurs et ceux obtenus par une fusion à base d'EDPs.Les méthodes développées pour le seamless cloning et la suppression d'ombres sont ensuite appliquées au cas particulier de la restoration digitale d'enluminures médiévales censurées. Cette application est présentée dans le quatrième chapitre et nécessite elle aussi l'usage de conditions au bord mixtes. Ce chapitre propose également une méthode à base d'inpainting pour la restauration d'enluminures endommagées.Le dernier chapitre propose une chaîne de traitement pour la création et la texturation d'un maillage à partir d'images satellites multi-dates. Les ombres sont automatiquement détectées pour un traitement différent des ombres propres et des ombres portées. La texture finale est une fusion l'aide de l'équation d'osmose des images satellites pondérée par la présence d'ombres et l'orientation du satellite. / This thesis deals with the elliptic osmosis equation and several of itsapplications. One application in particular is the texturation of 3D modelswith multi-date satellite images. The osmosis equation is similar to Poissonequation but with an illumination-invariant data term. It was first introduced forimage editing in a parabolic formulation for a domain with Neumann boundaryconditions.The first chapter describes the elliptic formulation of the osmosis model andseveral of its associated boundary-value problems: Dirichlet, Neumann and mixedboundary-value conditions. Theoretical results for the existence and uniquenessof solutions to these problems are proved for regular domains. These resultsare extended to manifolds with one local chart. The second chapter gives thesame results for the discrete case. For arbitrary domains, Neumann and mixedboundary conditions are difficult to implement with a classic finite differencescheme. For this reason a graph formulation of the problem is introduced thatallows much more flexibility for the manipulation of these boundary conditions.Unlike a finite difference scheme this formulation can be directlyapplied to triangular meshes.The third chapter presents applications of the elliptic osmosis model to theproblems of seamless cloning, shadow removal and image fusion. For seamlesscloning the results are compared to the ones obtained with Poisson editing. Thisshows the interest of having an illumination-invariant term when dealing withinput images whose contrasts are very different. The experiments also presenttheadvantages of solving the problem locally with Dirichlet conditions instead ofon the whole image domain with Neumann boundary conditions.The illumination-invariance of the equation encourages its use for the problemof shadow removal. This application showcases the interest of using mixed boundaryconditions as it allows the user to deal with both cast and attached shadows.This chapter also shows several methods to fuse more than two images of ascene. Several aggregator functions are proposed and the results of thedifferent fusions are compared. It illustrates the interest of PDE-based fusionover the simple fusion of the colour information.A more concrete application related to art is presented in the fourth chapter:the digital restoration of censored medieval illuminations when infraredreflectograms are provided along with the colour images. This applicationneeds the use of the methods already described for seamless cloning andshadow removal. It also showcases the importance of mixed boundary conditions.The last chapter proposes a pipeline to texture a given 3D model frommulti-date satellite images. We automatically detect the shadows,distinguishing the cast and attached shadows. The final texture is a PDE basedfusion of the satellite images weighted by the presence of shadows and theorientation of the satellite sensor.

This thesis deals with the practical usability of the PDE Toolbox in the MATLAB. It brieflydescribes the mathematical fundamentals of solution. The thesis presents the possibilitiesof PDE Toolbox in the creation of the model, geometry, boundary conditions, mesh and displayof results. The PDE Toolbox results from selected tasks from static, modal and transientmechanics and thermomechanics are compared with the analytical solution or with the FEMsimulation from the ANSYS. The main part deals with the evaluation and generalizationof results.

This dissertation is a summary of the graduate study in the past few years. In first part, we develop efficient spectral methods for the spectral fractional Laplacian equation and parabolic PDEs with spectral fractional Laplacian on rectangular domains. The key idea is to construct eigenfunctions of discrete Laplacian (also referred to Fourier-like basis) by using the Fourierization method. Under this basis, the nonlocal fractional Laplacian operator can be trivially evaluated, leading to very efficient algorithms for PDEs involving spectral fractional Laplacian. We provide a rigorous error analysis for the proposed methods, as well as ample numerical results to show their effectiveness.<div><br>In second part, we propose a method suitable for the computation of quasiperiodic interface, and apply it to simulate the interface between ordered phases in Lifschitz-Petrich model, which can be quasiperiodic. The function space, initial and boundary conditions are carefully chosen such that it fix the relative orientation and displacement, and we follow a gradient flow to let the interface and its optimal structure. The gradient flow is discretized by the scalar auxiliary variable (SAV) approach in time, and spectral method in space using quasiperiodic Fourier series and generalized Jacobi<br>polynomials. We use the method to study interface between striped, hexagonal and dodecagonal phases, especially when the interface is quasiperiodic. The numerical examples show that our method is efficient and accurate to successfully capture the interfacial structure.</div>

No description available.