For degenerate elliptic partial differential equations, it is often desirable to show that a weak solution is smooth. The first and most difficult step in this process is establishing local Hölder continuity. Sufficient conditions for establishing continuity have already been documented in [FP], [SW1], and [MRW], and their necessity in [R]. However, the complexity of the equations discussed in those works makes it difficult to understand the core structure of the arguments employed. Here, we present a harmonic-analytic method for establishing Hölder continuity of weak solutions in context of a simple linear equation div(Q?u) = f in a homogeneous space structure in order to showcase the form of the argument. Ad- ditionally, we correct an oversight in the adaptation of the John-Nirenberg inequality presented in [SW1], restricting it to a much smaller class of balls.

[pt] A tese intitulada O Plano de Desenvolvimento da Escola como instrumento de planejamento das escolas públicas municipais de Campos dos Goytacazes-RJ é uma investigação do PDE Escola em 2014, em duas escolas do primeiro segmento do ensino fundamental público municipal de Campos dos Goytacazes, município localizado no norte do estado do Rio de Janeiro. São adotados como subsídios para a investigação da política educacional em tela, os princípios da municipalização e descentralização político-administrativa, da autonomia dos entes federados e da participação institucional em âmbito local, bem como as teorias de planejamento estratégico e regulação das políticas educacionais. A partir de uma abordagem qualitativa, realizou-se uma análise do planejamento elaborado pelas escolas, relacionando os objetivos e problemas identificados pelas instituições escolares no processo de elaboração do PDE Escola tanto com os processos de execução das ações e aplicação dos recursos financeiros, didáticos e pedagógicos para melhoria do desempenho da escola, quanto com os resultados obtidos na Prova Brasil e no Ideb. Buscou-se, também, desvelar as percepções dos agentes escolares acerca de possíveis mudanças nas formas de gestão e nas ações pedagógicas propiciadas pela adesão ao PDE Escola. Os resultados apontam que a elaboração do PDE Escola nas escolas investigadas não resguardou os passos iniciais fundamentais requeridos pelo programa para a organização do ambiente institucional, o que envolve o planejamento com a participação da comunidade escolar, com destaque para a não efetivação do convite ao Conselho Escolar para elaborar o plano ou constituir um Grupo do Trabalho com a comunidade escolar e a falta de divulgação junto à comunidade escolar do planejamento da escola. Os dados dos planos gerados pelas escolas revelam uma forte canalização dos recursos do programa para ações de infraestrutura que é acompanhada pela quase inexistência de ações de resposta aos problemas pedagógicos, e que constituem a razão pela qual as escolas ingressaram no programa. Assim, compreende-se que a aplicação do PDE Escola nas escolas municipais investigadas no município de Campos dos Goytacazes não envolveu os elementos teórico-metodológicos do planejamento estratégico, e ainda, que os princípios da descentralização, participação institucional e autonomia das instituições escolares foram vivenciados na forma de um planejamento meramente formal. / [en] The doctoral thesis entitled O Plano de Desenvolvimento da Escola como instrumento de planejamento das escolas públicas municipais de Campos dos Goytacazes-RJ is a research of PDE Escola in 2014, in two schools of the first segment of municipal public elementary education of Campos dos Goytacazes, municipality located in the North of the state of Rio de Janeiro. It is utilized as subsidies of the investigation,the education policy principles of municipalization and political-administrative decentralization, federative autonomy, the institutional participation at the local level, and theories of strategic planning and regulation of educational policies. It was accomplished an analysis of the planning developed by the schools, relating the objectives and problems identified by school institutions in the elaboration process of PDE Escola with the actions executed, as well as didactic, pedagogical and financial resources applied, and relating the results obtained in Prova Brasil and Ideb. Is was subject of the investigation unveiling the perceptions of school agents about possible changes in the forms of management and pedagogical actions, provided by the inclusion in the PDE Escola, which was studied from a qualitative approach.The results indicate that the elaboration of the PDE Escola by investigated schools did not preserve the firsts fundamentals steps for the organization of the institutional environment and for the planning with the participation of the school community, as required in the program. In this case, it is important to note that the School Board was not invited to elaborate the school s plan, neither to form a Working Group including the school community. The data of schools planning documents reveals a strong channeling of program resources to mostly infrastructure actions and very few actions related to pedagogic problems, which led the school to join the program. It is comprehended in the research that the application of the PDE Escola in the municipal schools investigated in the municipality of Campos dos Goytacazes did not involve the theoretical-methodological elements of strategic planning, and that the principles of decentralization, institutional participation and autonomy of school institutions were not applied according with the theoretical-legal framework of the PDE Escola and with the theoretical-legal framework used in the research, because it was a purely formal form of planning.

Artificial neural networks (ANNs) are commonly considered as "black boxes": they can approximate any function without giving any interpretation. Novel research has observed that the laws of physics, which govern everything around us, can supplement the implementation of a neural network. For this purpose, we have physics-informed neural networks (PINNs): they are networks trained to consider the physics outlined in nonlinear partial differential equations (PDEs).  This thesis focuses on the thermal modelling of power transformers applying PINNs constrained to the heat diffusion equation. The aim is to estimate the top-oil temperature and the thermal distribution of a transformer. A solution of the equation will be provided by the Finite Volume Method (FVM), which will constitute a benchmark for the PINNs predictions. Differently from other works on PINNs, an additional challenge in this problem is the availability of field measurements. The results obtained show good accuracy in estimating the distribution and the top-oil temperature with PINN almost mimicking exactly FVM. Further improvements could be attained by rearranging the equation using more specific parameters to model the thermal behaviour of transformers and scaling the equation to dimensionless form. / Artificiella neurala nätverk (ANN) betraktas vanligtvis som "svarta lådor": de kan approximera vilken funktion som helst utan att tillhandahålla någon tolkning. Inom ny forskning har man sett att fysikens lagar, som styr allt runt omkring oss, kan komplettera implementeringen av ett neuralt nätverk. För detta ändamål har formulerats fysikinformerade neurala nätverk (PINN): de är nätverk som har tränats att ta hänsyn till den fysik som beskrivs i ickelinjära partiella differentialekvationer (PDE). Denna avhandling fokuserar på termisk modellering av transformatorer med tillämpning av PINN begränsat till värmeledningsekvationen. Syftet är att uppskatta en toppoljetemperatur och en transformators värmefördelning. Lösningen till ekvationen erhålls med finita volymmetoden (FVM), som används som en referenslösning för att utvärdera förutsägelserna från PINN. Implementeringen av PINN-algoritmen medförde en extra utmaning eftersom källtermen innefattade uppmätta värden. En metod att kringgå denna svårighet genom att approximera värdena på mätningarna i det neurala nätverket genom träning på motsvarande data presenteras. De erhållna resultaten visar god noggrannhet vid uppskattning av fördelningen och toppoljetemperaturen med PINN i jämförelse med FVM-lösningen. Ytterligare förbättringar kan uppnås genom att arrangera om ekvationen med mer specifika parametrar för att modellera transformatorernas termiska beteende och skalning av ekvationen till dimensionslös form.

In recent years, there has been an increasing interest in modeling crowd and evacuation dynamics. Pedestrian models are based on macroscopic or microscopic behavior. In this work, we are interested in developing models that can be used for evacuation control strategies. Hence, we use macroscopic modeling approach, where pedestrians are treated in an aggregate way and detailed interactions are overlooked. In this dissertation, we developed two-dimensional space crowd dynamic models to allow bi-directional low by modifying and enhancing various features of existing traffic and fluid dynamic models. In this work, four models based on continuum theory are developed, and conservation laws such as the continuity and momentum equations are used. The first model uses a single hyperbolic partial differential equation with a velocity-density relationship, while the other three models are systems of hyperbolic partial differential equations. For one of the system models presented, we show how it can be derived independently from a microscopic crowd model. The models are nonlinear, time-varying, hyperbolic partial differential equations, and the numerical simulation results given for the four macroscopic models were based on computational fluid dynamics schemes. We also started an initial control design that synthesizes the feedback linearization method for the one-dimensional traffic flow problem applied directly on the distributed parameter system. In addition, we suggest and discuss the information technology requirements for an evacuation system. This research was supported in part from the National Science Foundation through grant no. CMS-0428196 with Dr. S. C. Liu as the Program Director. This support is gratefully acknowledged. Any opinion, findings, and conclusions or recommendations expressed in this study are those of the writer and do not necessarily reflect the views of the National Science Foundation. / Ph. D.

[pt] O estudo analisa o processo de implementação do programa Plano de Desenvolvimento da Escola (PDE-Escola) no município do Rio de Janeiro, face ao contexto mais recente de políticas do governo federal com perspectiva de responsabilização, nos seus diferentes níveis de negociação, quais sejam: i) ao nível macro-político: as etapas de estruturação, negociação e implementação do programa, a partir do MEC e de agências internacionais de fomento; ii) ao nível meso-político: a estruturação do programa e seu desenvolvimento na rede municipal do Rio de Janeiro, através de suas instâncias de mediação (SME-Rio/ CREs-RJ); iii) ao nível Micro-institucional: as unidades escolares que implementam os processos técnico-gerenciais e político-financeiros do PDE-Escola. As análises ao nível macro envolvem dois momentos: em um primeiro momento se concentra na discussão sobre a introdução dos mecanismos de responsabilização na execução do PDE-Escola, no âmbito do PDE-Escola/ Plano de Metas. Para tanto, considera-se o contexto histórico que favoreceu a entrada desse tipo de política no cenário educacional brasileiro e são identificados que elementos da responsabilização se encontram nos documentos sobre o programa veiculados pelo MEC. Em um segundo momento, examina-se as mudanças que se configuraram no desenho do PDE-Escola ao longo dos últimos anos, destacando que tais mudanças refletem a conjuntura política de cada período, bem como os interesses e valores dos agentes responsáveis por sua formulação. A análise ao nível meso-político focaliza como o programa está sendo implementado no município do Rio de Janeiro, desde 2007, examinando a participação dos atores sociais das instâncias de mediação do programa no município (SME-Rio/ CREs-RJ) nesse processo, bem como investigando as percepções dos mesmos sobre o programa e suas reformulações. Por fim, a análise ao nível micro-institucional se centra nas escolas participantes do programa, identificando quem são estas escolas e seus processos institucionais. São investigadas as escolas pertencentes às duas primeiras listas de escolas prioritárias do município do Rio de Janeiro, ou seja, as primeiras escolas avaliadas como necessitando de melhorias, no contexto mais recente de políticas do governo com perspectiva de responsabilização (concernentes ao período de 2008-2012). Para a operacionalização do estudo, procedemos à análise documental e à realização de entrevistas semiestruturadas com representantes da SME-Rio/ CREs-RJ/. Os resultados indicam que houve uma paulatina e sistemática mudança de enfoque no programa após sua vinculação ao PDE/Plano de Metas, assumindo os pressupostos da responsabilização pelo resultado, em consonância com a política mais ampla do governo federal, e ensejando elementos da prestação de contas e da responsabilização em sua dinâmica técnico-operacional. / [en] This study analyzes the implementation process of the School Development Plan (PDE-Escola) program in the city of Rio de Janeiro, in view of the more recent context of the federal government s policies with the prospect of accountability, in its different levels of negotiation, namely: i) the macro-political level: the steps of structuring, negotiation, and implementation of the program, from the Ministry of Education (MEC) and from international development agencies; ii) the meso-political level: the structure of the program and its development in the municipal school network of Rio de Janeiro, through its bodies of mediations (SME-Rio / CREs-RJ); iii) the micro-institutional level: the school units that implement the technical-menagerial and political-financial processes of the PDE-Escola. The analyzes at the macro level involve two stages: at first, it focuses on the discussion of the introduction of accountability mechanisms in the implementation of PDE-Escola, related to the PDE-Escola / Goals Plan. For this, we consider the historical context that favored the entrance of this type of policy in the Brazilian educational scenario and identify which elements of the accountability are found in the documents about the program hand out by MEC. In a second stage, we examine the changes that have shaped the design of PDE-Escola over the last few years, highlighting that these changes reflect the political situation of each period, as well as the interests and ideals of the agents responsible for its formulation. The analysis at the meso-political level focuses on how the program is being implemented in the city of Rio de Janeiro since 2007, examining the involvement of the social characters in the mediation instances of the program in the city (SME-Rio / CREs-RJ) in this process, as well as investigating the perceptions of those characters on the program and its revisions. Finally, the analysis at the micro-institutional level focuses on the schools participating in the program, identifying who these schools are and their institutional processes. Schools belonging to the first two lists of priority schools in the city of Rio de Janeiro are investigated, in other words, the first schools assessed as in need of improvements in the most recent context of government policies with accountability perspective (concerning the 2008-2012 period). For the study operationalization, we performed a documental review and conducted semi-structured interviews with representatives of SME-Rio / CREs-RJ. The results indicate that there was a gradual and systematic change of focus in the program after its vinculation to the PDE / Goals Plan, taking on the assumptions of accountability by results, in consonance with the broader policy of the federal government, and entailing elements of accountability and account disclosure in its technical and operational dynamics.

Les surrénales sont des glandes endocrines permettant la réponse au stress de l’organisme. Alors que la medulla produit des catécholamines, la corticosurrénale sécrète des minéralocorticoïdes au niveau de la zone glomérulée, et des glucocorticoïdes grâce aux cellules de la zone fasciculée. Ces hormones sont notamment impliquées dans l’homéostasie hydrominérale, la réponse immunitaire et la maturation pulmonaire au cours de la vie fœtale. Les insuffisances surrénaliennes peuvent donc être très délétère en absence de traitement. Pour maintenir l’intégrité tissulaire au cours de la vie et pour mieux répondre aux variations des besoins de l’organisme, le cortex surrénalien est en renouvellement cellulaire constant. Des expériences de lignage ont mis en évidence que ce renouvellement repose sur le recrutement de cellules progénitrices capsulaires et situées dans la partie externe du cortex. Lorsqu’ils sont mobilisés, ces progéniteurs se différencient en cellules de la zone glomérulée, qui vont alors migrer de façon centripète le long du cortex et se différencier en cellules de la zone fasciculée après une conversion de lignage, au cours de leur migration. Cette conversion de lignage est orchestrée via un équilibre entre l’activation des voies Wnt/β-caténine, imposant une identité glomérulée, et PKA, permettant une différenciation fasciculée. Les facteurs épigénétiques jouent de nombreux rôles essentiels, du développement embryonnaire jusqu’à la tumorigenèse, en passant par l’homéostasie des tissus. Nous avons montré que la méthyltransférase EZH2 était le facteur épigénétique le plus surexprimé dans les carcinomes corticosurrénaliens et que cette surexpression était associée à l’agressivité de ces cancers. EZH2 est la sous-unité catalytique du complexe multi-protéique PRC2 qui permet, entre autres, la répression de la transcription de ses gènes cibles en posant la marque H3K27me3. L’objectif de ma thèse a été d’identifier les potentiels rôles physiologiques de EZH2 dans la surrénale, qui n’avaient jusque là, jamais été recherchés.En développant un modèle murin d’invalidation génétique de Ezh2 dans le cortex surrénalien, dès l’émergence de l’ébauche surrénalienne au cours du développement embryonnaire, nous avons pu mettre en évidence une hypoplasie corticosurrénalienne, résultant d’une forte atrophie de la zone fasciculée, et associé à une insuffisance primaire en glucocorticoïdes. Nos analyses nous ont permis de démontrer le rôle original et inattendu de Ezh2 dans le contrôle de la voie de signalisation PKA, en réprimant l’expression d’inhibiteurs de cette voie comme les phosphodiestérases (PDE) et la sous-unité régulatrice Prkar1b. EZH2 régule ainsi la zonation fonctionnelle du cortex surrénalien via son activité histone méthyltransférase. A l’inverse, on n’observe pas d’altération marquée de la voie Wnt/β-caténine, suggérant que Ezh2 n’est pas essentiel au contrôle de cette voie dans la surrénale. Nous avons également pu mettre en évidence une dédifférenciation de cellules corticales qui retrouvent, suite à la perte de Ezh2, une identité progénitrice en exprimant des marqueurs adréno-gonadique tels que Gata4 et Wt1. Cette dédifférenciation est un phénomène naturel que l’on retrouve avec le vieillissement et qui pourrait être associée avec la diminution progressive de l’expression de Ezh2 dans les cellules stéroïdogènes. L’ensemble de ces résultats, met en évidence une nouvelle fonction de Ezh2 dans le contrôle de la voie de signalisation PKA et de l’homéostasie de la glande surrénale. / Adrenals are endocrine glands allowing the stress response of the organism. While the medulla produces catecholamines, the adrenal cortex secretes mineralocorticoids in the glomerular zone, and glucocorticoids through cells in the fasciculated zone. These hormones are notably involved in hydromineral homeostasis, the immune response and pulmonary maturation during fetal life. Adrenal insufficiency can therefore be very deleterious in the absence of treatment. To maintain tissue integrity over the course of life and to better respond to the changing needs of the body, the adrenal cortex is in constant cell renewal. Lineage experiments have shown that this renewal is based on the recruitment of capsular progenitor cells and progenitors located in the outer part of the cortex. When mobilized, these progenitors differentiate into cells of the glomerular zone, which then migrate centripetally along the cortex and differentiate into cells of the fasciculated zone after lineage conversion, during their migration. This lineage conversion is orchestrated via a balance between the activation of the Wnt/β-catenin pathway, imposing a glomerular identity, and PKA pathway, allowing fasciculated differentiation. Epigenetic factors play many important roles, from embryonic development to tumorigenesis, passing by tissue homeostasis. We have shown that methyltransferase EZH2 is the most overexpressed epigenetic factor in adrenocortical carcinomas and this overexpression is associated with cancer agressivity. EZH2 is the catalytic subunit of the multiprotein complex PRC2 that allow, among others things, the repression of the transcription of its target genes by posing the mark H3K27me3. The aim of my thesis was to indentify the putative physiological roles of EZH2 in the adrenal, never investigated yet.By developing a murine model of genetic invalidation of Ezh2 in the adrenal cortex, from the emergence of the adrenal anlagen during embryonic development, we have been able to demonstrate adrenocortical hypoplasia, resulting from a strong atrophy of the zona fasciculata, and associated with primary glucocorticoid insufficiency. Our analyses allowed us to demonstate the original and unexpected role of EZH2 in the controle of the PKA pathway, by repressing expression of this pathway inhibitors such as phosphodiesterases (PDE) and regulatory subunit Prkar1b. EZH2 thus regulate functionel zonation of adrenal cortex via its histone methyltransferase activity. On the contrary, we don’t observe marked alteration of the Wnt/β-catenin pathway, suggesting EZH2 is not essential for the control of this pathway in the adrenal. We could also show a dedifferenciation of cortical cells which, after the loss of Ezh2, exhibit progenitors identity by expressing adreno-gonadal marks as Gata4 and Wt1. This dedifferenciation is a natural phenomenon that appear with ageing and could be associated with processive decrease of Ezh2 expression in steroidogenic cells. All of these results, highlights a new function of Ezh2 in the control of the PKA signaling pathway and in the homeostasis of the adrenal gland.

Made available in DSpace on 2017-07-21T20:31:20Z (GMT). No. of bitstreams: 1 Thamiris Mendes.pdf: 1073648 bytes, checksum: 7986020a8091de7e963600ec7a43284f (MD5) Previous issue date: 2015-02-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This research, whose theme is about being and remaining a teacher, has as object of investigation the teaching professional. Our premise is that to be an education professional in the contemporary society is not an easy task as there are many factors that influence the teaching professional practice, from his/her education to his/her professional constitution. Thus, we understand that there is a complexity about being a teacher as it is a vulnerable profession due to various transformations that have been happening in the contemporaneity. In this way, the objective of this study was to unveil what is to be a teacher and what keeps them in the profession. This is a qualitative research (BOGDAN; BIKLEN, 1994) whose study participants were teachers in continuing education through the Education Development Program (Programa de Desenvolvimento Educacional - PDE) of Paraná, in the Education Regional Centers of Ponta Grossa, Wenceslau Bras and Telemaco Borba. Data collection occurred in two phases: the first with a questionnaire (N=160) and the second included semi-structured interviews (N=6). Data were analyzed using the EVOC and SIMI softwares and also through discursive textual analysis (MORAES; GALIAZZI, 2011). We elected as theoretical framework of the research authors that deal with the teaching profession and teacher education, as Nóvoa (1995), Marcelo (2009), Fontana (2010), Imbernón (2011), among others. In addition, we held on some concepts of Psychoanalysis using scholars as Freud (1912; 1937), Lacan (1979a; 1979b) and Mrech (2003; 2005a; 2005b). On the one hand the results show that being a teacher moves between three evocations (commitment, dedication and education) and three representative categories (I - Teacher: Professional of transformation, II - Teacher: Professional of knowledge and III - Teacher: Professional of uncertainty). On the other hand remaining a teacher was proved markedly by the significant „transformation‟. Thus, it is possible to point out that being a teacher is not limited to the teaching and learning process, but beyond it. The investigated teachers demonstrate that they have other concerns and need to account for situations that transcend the classroom and remaining in the teaching profession goes through the desire to be recognized by the other. / Esta pesquisa, cujo tema é o ser e o manter-se professor, tem como objeto de investigação o profissional docente. Partiu-se da premissa de que ser profissional do ensino, na sociedade contemporânea, não é tarefa fácil visto que existem muitos fatores que influenciam no exercício profissional docente, desde sua formação até sua constituição profissional. Assim, entende-se que há uma complexidade em ser professor por conta de ser uma profissão vulnerável às diversas transformações que acontecem na contemporaneidade. Diante disso, o objetivo deste trabalho consistiu em desvelar o que é ser professor e o que os mantêm na profissão. Trata-se de uma pesquisa de abordagem qualitativa (BOGDAN; BIKLEN, 1994) em que os participantes do estudo foram professores em formação continuada pelo Programa de Desenvolvimento Educacional (PDE) do Paraná, dos Núcleos Regionais de Educação de Ponta Grossa, Wenceslau Brás e Telêmaco Borba. A coleta de dados aconteceu em duas etapas: a primeira com questionário (N=160), e a segunda contou com entrevistas semiestruturadas (N=6). Os dados foram analisados com auxílio dos softwares EVOC e SIMI e, também, por meio da análise textual discursiva (MORAES; GALIAZZI, 2011). Elegeu-se como aporte teórico da pesquisa autores que tratam da profissão docente e da formação de professores, como Nóvoa (1995), Marcelo (2009), Fontana (2010), Imbernón (2011), dentre outros. Além disso, amparou-se em alguns conceitos da Psicanálise utilizando estudiosos como Freud (1912; 1937), Lacan (1979a; 1979b) e Mrech (2003; 2005a; 2005b). Os resultados apontam que ser professor transita entre três evocações (comprometimento, dedicação e formação) e entre três categorias representativas (I - Professor: profissional da transformação, II - Professor: profissional do conhecimento e III - Professor: profissional da incerteza). Já o manter-se professor revelou-se marcadamente pelo significante “transformação”. Desse modo, é possível apontar que ser professor não se limita ao processo de ensino e aprendizagem, mas o ultrapassa. Os docentes investigados demonstram ter outras preocupações e necessitam dar conta de situações que transcendem a sala de aula, e o manter-se na profissão docente passa pelo desejo em ser reconhecido pelo outro.

Dans cette thèse, on s'intéresse à l'étude qualitative des solutions d'équations aux dérivées partielles hamiltoniennes par le biais de la théorie des mesures invariantes. L'existence d'une telle mesure pour une EDP fournit, en effet, des informations sur sa dynamique en temps long. Nous étudierons deux situations quelque peu "extrémales". Dans une première partie, nous nous intéressons aux équations ayant une infinité de lois de conservation et dans une seconde, aux équations dont on ne connaît qu'une seule loi de conservation non triviale.Nous étudions les premières équations par le biais de l'équation de Benjamin-Ono. Il s'agit d'un modèle de description des ondes internes dans un fluide de grande profondeur.Nous nous intéressons à la dynamique de cette équation sur l'espace C^infty(T) en lui construisant une mesure invariante sur cet espace. Par conséquent, une propriété de récurrence presque sûre (par rapport à cette mesure) est établie pour les solutions infiniment lisses de cette équation. Nous prouvons, ensuite, des propriétés de non-dégénérescence pour cette mesure. En effet, nous montrons que, via cette mesure, une infinité de fonctionnelles indépendantes ont des distributions absolument continues par rapport à la mesure de Lebesgue sur R. Enfin, nous montrons que cette mesure est de nature au moins $2$-dimensionnelle. Dans ce travail, nous avons utilisé l'approche Fluctuation-Dissipation-Limite (FDL) introduite par Kuksin-Shirikyan. Notons qu'une propriété de récurrence presque sûre a été établie pour les solutions de régularité Sobolev de l'équation de Benjamin-Ono, dans les travaux de Deng, Tzvetkov et Visciglia.Dans l'autre partie de la thèse, nous abordons l'équation de Klein-Gordon à non-linéarité cubique, c'est un exemple d'EDPs hamiltoniennes pour lesquelles il n'est connu qu'une seule loi de conservation non triviale. Cette équation modélise l'évolution d'une particule massive relativiste. Ici, nous considérons les cas où l'équation est posée sur le tore tri-dimensionnel ou sur un domaine borné de R^3 à bord assez régulier. Nous lui construisons une mesure invariante concentrée sur l'espace de Sobolev H^2, en utilisant toujours l'approche FDL. Un autre aspect de ce travail est d'étendre le cadre de cette approche au contexte des EDPs à une seule loi de conservation, en effet, dans les travaux antérieurs, l'approche FDL avait nécessité deux lois de conservation pour fonctionner. Puis nous établissons une propriété de non-dégénérescence pour la mesure construite. Par conséquent, une propriété de récurrence presque sûre, par rapport à la mesure construite, est prouvée. Notons que des travaux antérieurs dus à Burq-Tzvetkov, de Suzzoni, Bourgain-Bulut et Xu ont traité la question de mesure de Gibbs invariante pour des équations des ondes dans un contexte radial. / In this thesis, we are concerned with the qualitative study of solutions of Hamiltonian partial differential equations by the way of the invariant measures theory. Indeed, existence of such a measure provides some informations concerning the large time dynamics of the PDE in question. In this thesis we treat two "extremal" situations. In the first part, we consider equations with infinitely many conservation laws, and in the second, we study equations for which we know only one non-trivial conservation law.We study the first equations by considering the Benjamin-Ono equation. The latter is a model describing internal waves in a fluide of great depth.We are concerned with the dynamics of that equation on the space C^infty(T) by constructing for it an invariant measure on that space. Accordingly, an almost sure (w.r.t. this measure) recurrence property is established for infinitely smooth solutions of that equation. Then, we prove qualitative properties for the constructed measure by showing that there are infinitely many independent observables whose distributions via this measure are absolutely continuous w.r.t. the Lebesgue measure on R. Moreover, we establish that the measure is of at least 2-dimensional nature. In this work, we used the Fluctuation-Dissipation-Limit (FDL) approach introduced by Kuksin and Shirikyan. Notice that an almost sure recurrence property for the Benjamin-Ono equation was established on Sobolev spaces by Deng, Tzvetkov and Visciglia.In the second part of the thesis, we consider the cubic Klein-Gordon equation, which is an example of Hamiltonian PDEs for which we know only one conservation law. This equation models the evolution of a massive relativistic particle. Here, we consider both the case of the tri-dimensional periodic solutions and those defined on a bounded domain of R^3. In both settings, we construct an invariant measure concentrated on the Sobolev space H^2xH^1, again with use of the FDL approach. Another aspect of this work is to extend the FDL approach to the context of PDEs having only one conservation law; indeed, in previous works, this approach required two conservation laws. Qualitative properties for the measure and almost sure (w.r.t. this measure) recurrence for H^2-solutions are proven. Notice that previous works by Burq-Tzvetkov, de Suzzoni, Bourgain-Bulut and Xu have treated the invariant Gibbs measure problem in the radial symmetry context for waves equations.

Submitted by Leonardo Cavalcante (leo.ocavalcante@gmail.com) on 2018-05-22T12:23:29Z No. of bitstreams: 1 Arquivototal.pdf: 8409790 bytes, checksum: c50e50e576eae80e24c3733e2ed0170f (MD5) / Made available in DSpace on 2018-05-22T12:23:29Z (GMT). No. of bitstreams: 1 Arquivototal.pdf: 8409790 bytes, checksum: c50e50e576eae80e24c3733e2ed0170f (MD5) Previous issue date: 2017-10-10 / In this study, we looked at Educational Policies in the macro and micro contexts of these policies in order to analyze the Federal School Development Plan - PDE Escola, in the municipality of Santa Rita/PB. The interest in this subject is justified by our understanding that this program is involved in the development of school management. Thus, we highlight the public policies, especially, PDE Escola. Our general objective was to analyze the effects of the PDE Escola for the development of school management in the criterion of teaching and learning effectiveness of the Municipal Teaching System of Santa Rita/PB. We analyze the local context in the organized and articulated Curriculum categories and Effective Practices within the classroom. The study was carried out in a school that composes said system. The guiding thread to address this theme was focused on Brazilian public policies aimed at improving schools at the municipal level. Our research has emphasized the official documents that govern public educational policies in Brazil, more specifically, in relation to the PDE Escola program. In addition, we refer to the Federal Constitution (CF, 1988), the Law on Guidelines and Bases of National Education (LDBEN Law No. 9.394/1996), National Education Plan Law No. 13,005/2014 (PNE), Municipal Education Plan Law No 1666/2014 (SMEs). In addition, we focus on the data analysis approach in the continuous policy cycle of authors such as Ball, (1989); Ball, Gold and Bowe (1992); Ball, (1994); Ball, Maguire and Braun (2016). To support our methodological choice, we chose (BOGDAN, BIKLEN, 1994), whose assumptions point to the need for qualitative research, in which the direct source of data is the natural environment, the researcher being the main instrument. From this perspective, we conducted a case study supported by the authors Stake (2012) and Yin (2010). The data that constituted the corpus of the research were collected through the application of semi-structured interviews and participant observation. Our initial objectives sought to understand the PDE Escola's process of action in the Dimension of Teaching and Learning; identify the development of the actions targeted by the PDE Escola; to show which elements of the PDE Escola are announced based on the performance of the professionals of the education professionals surveyed; identify in the criterion of school effectiveness teaching and learning. Based on the requirements organized; articulated curriculum and effective practices within the classroom to improve the processes of school management of the Municipal Teaching System of Santa Rita/PB. In the dimension of Teaching and Learning, we conclude that, faced with the actions carried out by the actors involved in the process, there were positive effects, given the discourses of the subjects studied, in these discourses, the most important are financial and pedagogical autonomy, reorganization and application of resources in a correct way and as a negative point, there is an increase in insufficient work and resources, as well as the lack of involvement on the part of some. Therefore, the research revealed, based on the statements analyzed, that school management is democratic and participatory when it comes to the context of results/effects, education professionals are the main actors in this arena of results pressure, since they are the ones who recreate and reinvent politics, in the moments of acting/staging, translation and interpretation. / Nesse estudo, lançamos um olhar sobre as Políticas Educacionais nos contextos macro e micro destas políticas a fim de analisamos o Programa Federal Plano de Desenvolvimento da Escola ─ PDE Escola, no município de Santa Rita/PB. O interesse por essa temática justifica-se por compreendermos que, o referido programa atua no desenvolvimento da gestão das escolas. Assim, evidenciamos as políticas públicas, sobretudo, PDE Escola. Nosso objetivo geral foi analisar os efeitos do PDE Escola para o desenvolvimento da gestão escolar no critério de eficácia ensino e aprendizagem do Sistema Municipal de Ensino de Santa Rita/PB. Analisamos o contexto local nas categorias do Currículo organizado e articulado e Práticas efetivas dentro de sala de aula. O estudo foi realizado em uma escola que compõem o referido sistema. O fio norteador para abordarmos tal tema foi voltado às políticas públicas brasileiras destinadas à melhoria das escolas no âmbito municipal. Nossa pesquisa deu ênfase aos documentos oficiais que regem as políticas públicas educacionais no Brasil, mais especificamente, em relação ao programa PDE Escola. Além disso, nos referimos a Constituição Federal (CF, 1988), a Lei de Diretrizes e Bases da Educação Nacional (LDBEN Lei nº 9.394/1996), Plano Nacional de Educação Lei nº13.005/2014(PNE), Plano Municipal de Educação lei nº 1666/2014(PME). Além disso, pautamo-nos na abordagem de análise dos dados no ciclo contínuo de políticas de autores como Ball, (1989); Ball, Gold e Bowe (1992); Ball, (1994); Ball, Maguire e Braun (2016). Para fundamentar nossa escolha metodológica, optamos por (BOGDAN, BIKLEN, 1994), cujos pressupostos apontam para a necessidade de uma investigação qualitativa, na qual a fonte direta de dados é o ambiente natural, consistindo o investigador o instrumento principal. Nessa perspectiva, realizamos um estudo de caso respaldados nos autores Stake (2012) e Yin (2010). Os dados que constituíram o corpus da pesquisa foram coletados através de aplicação de entrevistas semiestruturadas e observação participante. Os nossos objetivos iniciais buscaram compreender o processo de atuação do PDE Escola na Dimensão de Ensino e Aprendizagem; identificar o desenvolvimento das ações objetivadas pelo PDE Escola; evidenciar quais os elementos do PDE Escola são anunciados a partir da atuação dos profissionais dos profissionais da educação pesquisados; identificar no critério de eficácia escolar ensino e aprendizagem. A partir dos requisitos currículo organizado e articulado e práticas efetivas dentro de sala de aula para melhoria dos processos da gestão escolar do Sistema Municipal de Ensino de Santa Rita/PB. Na dimensão do Ensino e Aprendizagem, concluímos que, diante das ações realizadas pelos atores envolvidos no processo, houve efeitos positivos, diante dos discursos dos sujeitos pesquisados, nestes discursos, destacam-se a autonomia financeira e pedagógica, a reorganização e a aplicação de recursos de forma correta e como ponto negativo, ressaltam-se o aumento de trabalho e recursos insuficientes, além da falta de envolvimento por parte de alguns. Portanto, a pesquisa nos revelou, com base nas falas analisadas, que a gestão escolar é democrática e participativa quando se refere ao contexto dos resultados/efeitos, os profissionais da educação são os atores principais nesta arena de pressões por resultados, pois são eles que recriam e reinventam a política, nos momentos de atuação/encenação, tradução e interpretação.

Cette thèse porte sur l’homogénéisation quantitative d’équations aux dérivées partielles paraboliques, et de problèmes elliptiques discrets. Dans l’introduction, nous voyons comment de tels problèmes, même lorsque les coefficients sont déterministes, résultent d’un modèle aléatoire. Nous donnons ensuite une notion de ce qu’est l’homogénéisation : que se passe-t-il lorsque les coefficients eux-mêmes sont aléatoires, est-il possible de considérer qu’un environnement présentant des inhomogénéités sur de très petites échelles, se comporte d’une manière proche d’un environnement fictif qui serait homogène ?Nous donnons ensuite une interprétation de cette question en terme de marche aléatoire en conductances aléatoires, puis donnons une idée des outils utilisés dans les preuves des deux chapitres suivants. Dans le chapitre II, nous démontrons un résultat d’homogénéisation quantitative pour une équation parabolique – l’équation de la chaleur par exemple – dans un environnement admettant des coefficients aléatoires et dépendant du temps. La méthode utilisée consiste à considérer les solutions d’un tel problème comme optimiseurs de fonctionnelles qui seront définies au préalable, puis d’utiliser la propriété cruciale de sous-additivité de ces quantités, afin d’en déduire une convergence puis un résultat de concentration, qui permettra d’en déduire une vitesse de convergence des solutions vers la solution du problème homogénéisé, Dans le chapitre III, nous adaptons ces méthodes pour un problème elliptique sur le graphe Zd. / This thesis deals with quantitative stochastic homogenization of parabolic partial differential equations, and discrete elliptic problems. In the introduction, we see how can such problems come from random models, even when the coefficients are deterministic. Then, we introduce homogenization : what happen if the coefficients themselves are random ? Could we consider that an environment with microscopical random heterogeneities behaves, at big scale, as a fictious deterministic homogeneous environment ? Then, we give a random walk in random environment interpretation and the sketch of the proofs in the two following chapters. In chapter II, we prove a quantitative homogenization result for parabolic PDEs, such as heat equation, in environment admitting time and space dependent coefficients. The method of the proof consists in considering solutions of such problems as minimizers of variational problems. The first step is to express solutions as minimizers, and then to use the capital property of subadditivity of the corresponding quantities, in order to deduce convergence and concentration result. From that, we deduce a rate of convergence of the actual solutions to the homogenized solution. In chapter III, we adapt these methods to a discrete elliptic problem on the lattice Zd.