In this thesis, we investigate various problems in the representation theory of finite groups of Lie type. In Chapter 2, we hope to make sense of the last statement - we will introduce some background and notation that will be useful for the remainder of the thesis. In Chapter 3, we find bounds for the largest irreducible representation degree of a finite unitary group. In Chapter 4, we describe the block distribution and Brauer characters in cross characteristic for Sp₆(2ᵃ) in terms of the irreducible ordinary characters. This will be useful in Chapter 5 and Chapter 7, which focus primarily on the group Sp₆(2ᵃ) and contain the main results of this thesis, which we now summarize. Given a subgroup H ≤ G and a representation V for G, we obtain the restriction V|H of V to H by viewing V as an FH-module. However, even if V is an irreducible representation of G, the restriction V|H may (and usually does) fail to remain irreducible as a representation of H. In Chapter 5, we classify all pairs (V, H), where H is a proper subgroup of G = Sp₆(q) or Sp₄(q) with q even, and V is an l-modular representation of G for l ≠ 2 which is absolutely irreducible as a representation of H. This problem is motivated by the Aschbacher-Scott program on classifying maximal subgroups of finite classical groups. The local-global philosophy plays an important role in many areas of mathematics. In the representation theory of finite groups, the so-called "local-global" conjectures would relate the representation theory of G to that of certain proper subgroups, such as the normalizer of a Sylow subgroup. One might hope that these conjectures could be proven by showing that they are true for all simple groups. Though this turns out not quite to be the case, some of these conjectures have been reduced to showing that a finite set of stronger conditions hold for all finite simple groups. In Chapter 7, we show that Sp₆(q) and Sp₄(q), q even, are "good" for these reductions.

Les amplifications optimales d'énergie de structures quasiment alignées dans le sens de l'écoulement sont calculées dans le cas d'un sillage parallèle, d'un sillage synthétique faiblement non-parallèle et du sillage d'un cylindre. Il a été observé que de très grandes amplifications d'énergie peuvent être supportés par ces sillages. L'amplification d' énergie s'accroît avec la longueur d'onde des perturbations en envergure à l'exception du sillage du cylindre pour lequel l'accroissement d'énergie est maximal pour λz ≈ 5 − 7 D. Les structures amplifiées de manière optimale sont les streaks fluctuant dans le sens de l’écoulement. Il est montré que ces streaks sont capables de supprimer complètement l'instabilité absolue d'un sillage parallèle lorsqu'ils sont déclenchés avec une amplitude finie. L'instabilité globale d'un sillage faiblement non-parallèle et celle du sillage d'un cylindre peuvent être complètement supprimées par des streaks d'amplitude modeste. L'énergie de contrôle requise pour stabiliser le sillage est très faible lorsque les perturbations optimales sont utilisées, et il est montré qu'elle est toujours plus faible que celle qui devrait être utilisée pour un contrôle uniforme en envergure (2D). Il est aussi montré que la dépendance du taux de croissance est quadratique et que, par conséquent, les classiques analyses de sensibilité au premier ordre ne permettent pas de prédire la grande efficacité de la technique de contrôle par streaks. La dernière partie de ce travail livre des résultats préliminaires sur l'étude expérimentale du contrôle par streaks dans le cas du sillage turbulent d'un corps 3D. Il est montré que les streaks forcés artificiellement dans la zone d'instabilité absolue de l'écoulement sont capables de modifier la dynamique du sillage. / We compute optimal energy growths leading to streamwise streaks in parallel, weakly non-parallel and the circular cylinder wakes. We find that very large energy amplifications can be sustained by these wakes. The energy amplifications increase with the spanwise wavelength of the perturbations except in the circular cylinder wake where maximum energy growths are reached for λz ≈ 5 − 7 D. The optimally amplified structures are streamwise streaks. When forced with finite amplitudes these streaks are shown, in parallel wakes, to be able to completely suppress the absolute instability. The global instability of the weakly non-parallel and the circular cylinder wakes can be completely suppressed with moderate streaks amplitudes. The energy required to stabilize the wake is much reduced when optimal perturbations are used, and it is shown to be always smaller than the one that would be required if a 2D control was used. It is also shown that the sensitivity of the global mode growth rate is quadratic and that therefore usual first order sensitivity analyses are unable to predict the high efficiency of the control-by-streaks strategy.

Made available in DSpace on 2014-06-12T18:30:53Z (GMT). No. of bitstreams: 2 arquivo6738_1.pdf: 1322957 bytes, checksum: a77dfa59ea2e61dc7f17b01f14df78a4 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2006 / Universidade Federal Rural de Pernambuco / Esta dissertação tem como principal objetivo expor o bem sucedido projeto de entender a aritmética das curvas algébricas a partir de sua geometria. Estaremos interessados em características qualitativas do conjunto dos pontos K-racionais (K corpo de números) da curva tais como existência, finitude e estrutura algébrica. Para curvas de gênero zero, mostramos o principio local-global (para quádricas) que garante a existência de um ponto em K baseado na existência de pontos em todos seus completamentos . Para curvas de gênero um que possuem um ponto K-racional, o método da tangente e da secante fornece ao conjunto dos pontos K-racionais da curva uma estrutura algébrico-geométrica de grupo abeliano, o principal resultado é o teorema de Mordell-Weil que garante que tal grupo é finitamente gerado, mostraremos mais geralmente o teorema de Mordell-Weil para variedades abelianas. A última classe de curvas que iremos considerar são as curvas de gênero maior ou igual a dois, para tais curvas o conjunto dos pontos K-racionais é sempre finito. Este é o teorema de Faltings (que não daremos uma demonstração completa)

Object trajectory tracking is an important topic in many different areas. It is widely used in robot technology, traffic, movie industry, and others. Optical flow is a useful method in the object tracking branch and it can calculate the motion of each pixel between two frames, and thus it provides a possible way to get the trajectory of objects. There are numerous papers describing the implementation of optical flow. Some results are acceptable, but in many projects, there are limitations. In most previous applications, because the camera is usually static, it is easy to apply optical flow to identify the moving targets in a scene and get their trajectories. When the camera moves, a global motion will be added to the local motion, which complicates the issue. In this thesis we use a combination of optical flow and image correlation to deal with this problem, and have good experimental results. For trajectory estimation, we incorporate a Kalman Filter with the optical flow. Not only can we smooth the motion history, but we can also estimate the motion into the next frame. The addition of a spatial-temporal filter improves the results in our later process.

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Made available in DSpace on 2016-04-28T18:24:10Z (GMT). No. of bitstreams: 1 Patricia Urvinis.pdf: 819816 bytes, checksum: cb3cbefd97bf61fdefb7a31a9e586891 (MD5) Previous issue date: 2009-08-07 / Secretaria da Educação do Estado de São Paulo / This research aims at investigating the local-global knowledge which emerges from the discoursive practices of two teachers of English who have just started the course Reflection on Action: the teacher of English learning and teaching and two other ones who have already finished the same course. Our theoretical construct is based on Contemporary Applied Linguistics on the perspective of Moita Lopes (2006a; 2006b; 2002); Kumaravadivelu (2006) and Celani (2005). This study is grounded on the binominal local-global knowledge (Canagarajah, 2005); on the official documents that guide the practice of teachers of English in the Brazilian educational context (São Paulo, 2008; Brasil, 2002; 2000; 1998) and on Vygotsky s Sociocultural and Historical Theory of teaching and learning (Vygotsky, 1930/1989; 1934/2001, among others). The research is conducted by an interpretative methodology (Myers, 1997; Moita Lopes; 1996; Erickson; 1986, among others) and the data has been collected through two instruments: a questionnaire and a semi-structured interview (Rizzini, Castro and Sartor, 1999). For analyzing and interpreting the data, three categories of analysis have been established: the category of thematic content, the observation of how the participants place their enunciates and deontic modalizations (Bronckart, 1997/1999). The study concentrates on three areas of analysis (a) senses, meanings and aims of teachinglearning English in the educational context; (2) planning and criteria for curriculum content selection; and (3) pedagogical practices. The results showed that the teachers who were taking the first module of the course Reflection on Action presented a discourse strongly supported by local knowledge, but heading to a dialogue with a global one. On the other hand, the teachers who have already finished the course achieved more autonomy to reflect about the global knowledge in their relationship to local one to promote the teaching-learning English for specific contexts / Esta pesquisa tem por objetivo investigar os saberes locais-globais que emergem nas práticas discursivas de duas professoras de inglês iniciantes do curso Reflexão sobre a ação: o professor de inglês aprendendo e ensinando e de duas professoras egressas do referido curso. Este estudo foi realizado dentro da perspectiva da Linguística Aplicada Contemporânea, com base em Moita Lopes (2006a; 2006b; 2002); Kumaravadivelu (2006) e Celani (2005). Apoia-se nos conceitos de saber local e global (Canagarajah, 2005), nos documentos oficiais que orientam a prática dos professores de inglês no contexto educacional (São Paulo, 2008; Brasil, 2002; 2000; 1998) e na teoria de ensino e aprendizagem sócio-histórico-cultural (Vygotsky, 1930/1989; 1934/2001; 1934/2003; dentre outros). A metodologia de pesquisa utilizada foi a interpretativista (cf. Myers, 1997; Moita Lopes; 1996; Erickson; 1986, dentre outros) e a coleta dos dados foi feita por meio de dois instrumentos: um questionário e uma entrevista semi-estruturada (Rizzini, Castro e Sartor, 1999). Para a análise e interpretação dos dados foram utilizadas três categorias: conteúdo temático, observação do posicionamento enunciativo dos participantes e modalizações deônticas (Bronckart, 1997/1999). Três foram os eixos de análise: (a) sentidos, significados e finalidades de ensinar e aprender inglês no contexto educacional; (b) planejamento e critérios utilizados para a seleção de conteúdos; e (c) ações pedagógicas. Os resultados obtidos a partir da análise dos dados revelaram que as professoras ingressantes do curso Reflexão sobre a Ação apresentaram um discurso fortemente apoiado em conhecimentos locais, mas já apontando para um diálogo com os globais; por outro lado, as egressas adquiriram mais autonomia para dialogar com as teorias globais para promover o ensino-aprendizagem de inglês para contextos locais

Dans cette thèse, on étudie les représentations 2-dimensionnelles continues du groupe de Galois absolu d'une clôture algébrique fixée de Q sur les corps finis qui sont modulaires et leurs images. Ce manuscrit se compose de deux parties.Dans la première partie, on étudie un problème local-global pour les courbes elliptiques sur les corps de nombres. Soit E une courbe elliptique sur un corps de nombres K, et soit l un nombre premier. Si E admet une l-isogénie localement sur un ensemble de nombres premiers de densité 1 alors est-ce que E admet une l-isogénie sur K ? L'étude de la repréesentation galoisienne associéee à la l-torsion de E est l'ingrédient essentiel utilisé pour résoudre ce problème. On caractérise complètement les cas où le principe local-global n'est pas vérifié, et on obtient une borne supérieure pour les valeurs possibles de l pour lesquelles ce cas peut se produire.La deuxième partie a un but algorithmique : donner un algorithme pour calculer les images des représentations galoisiennes 2-dimensionnelles sur les corps finis attachées aux formes modulaires. L'un des résultats principaux est que l'algorithme n'utilise que des opérateurs de Hecke jusqu'à la borne de Sturm au niveau donné n dans presque tous les cas. En outre, presque tous les calculs sont effectués en caractéristique positive. On étudie la description locale de la représentation aux nombres premiers divisant le niveau et la caractéristique. En particulier, on obtient une caractérisation précise des formes propres dans l'espace des formes anciennes en caractéristique positive.On étudie aussi le conducteur de la tordue d'une représentation par un caractère et les coefficients de la forme de niveau et poids minimaux associée. L'algorithme est conçu à partir des résultats de Dickson, Khare-Wintenberger et Faber sur la classification, à conjugaison près, des sous-groupes finis de $\PGL_2(\overline{\F}_\ell)$. On caractérise chaque cas en donnant une description et des algorithmes pour le vérifier. En particulier, on donne une nouvelle approche pour les représentations irréductibles avec image projective isomorphe soit au groupe symétrique sur 4 éléments ou au groupe alterné sur 4 ou 5 éléments. / In this thesis we investigate $2$-dimensional, continuous, odd, residual Galois representations and their images. This manuscript consists of two parts.In the first part of this thesis we analyse a local-global problem for elliptic curves over number fields. Let $E$ be an elliptic curve over a number field $K$, and let $\ell$ be a prime number. If $E$ admits an $\ell$-isogeny locally at a set of primes with density one then does $E$ admit an $\ell$-isogeny over $K$? The study of the Galois representation associated to the $\ell$-torsion subgroup of $E$ is the crucial ingredient used to solve the problem. We characterize completely the cases where the local-global principle fails, obtaining an upper bound for the possible values of $\ell$ for which this can happen.In the second part of this thesis, we outline an algorithm for computing the image of a residual modular $2$-dimensional semi-simple Galois representation. This algorithm determines the image as a finite subgroup of $\GL_2(\overline{\F}_\ell)$, up to conjugation, as well as certain local properties of the representation and tabulate the result in a database. In this part of the thesis we show that, in almost all cases, in order to compute the image of such a representation it is sufficient to know the images of the Hecke operators up to the Sturm bound at the given level $n$. In addition, almost all the computations are performed in positive characteristic.In order to obtain such an algorithm, we study the local description of the representation at primes dividing the level and the characteristic: this leads to a complete description of the eigenforms in the old-space. Moreover, we investigate the conductor of the twist of a representation by characters and the coefficients of the form of minimal level and weight associated to it in order to optimize the computation of the projective image.The algorithm is designed using results of Dickson, Khare-Wintenberger and Faber on the classification, up to conjugation, of the finite subgroups of $\PGL_2(\overline{\F}_\ell)$. We characterize each possible case giving a precise description and algorithms to deal with it. In particular, we give a new approach and a construction to deal with irreducible representations with projective image isomorphic to either the symmetric group on $4$ elements or the alternating group on $4$ or $5$ elements.

Computational electromagnetic modeling involves generating system matrices by discretizing integral equations and solving the resulting system of linear equations. Many methods of solving the system of linear equations exist and one such method is the factorization of the matrix using the so called local-global solution (LOGOS) modes. Computer codes to perform the discretization of the integral equations, filling of the matrix, and the subsequent LOGOS factorization have previously been developed by others. However, these codes are limited to complex double precision arithmetic only. This thesis extends and expands the existing computer by creating a more general implementation that is able to analyze a problem not only in complex double precision but also in real double precision and both complex and real single precision. The existing code is expanded using "templates" in Fortran 90 and the resulting generic code is used test the performance of the LOGOS (both OL- and NL-LOGOS) factorization on matrices generated by discretization of the volume integral equation. As part of this effort, we demonstrate for the first time that the LOGOS factorization provides an O(N log N) complexity solution to the volume integral equation formulation of low-frequency electromagnetic problems.

Les Sursauts de Rayonnement Gamma (GRBs) sont des flashs émanant du cosmos qui sont classés en deux groupes : les longs/doux et les courts/durs. Le lancement du satellite Swift a ouvert une nouvelle ère dans la recherche sur les GRBs. Cette thèse présente une étude détaillée du GRB 141221A qui montre une forte et inhabituelle hausse des valeurs des courbes de lumière dans le domaine optique lors de l'émission rémanente alors que dans le domaine des rayons X ces valeurs sont plus normales. GRB 141221A est un des GRBs qui mettent à l'épreuve les modèles car il exclut tout vent stellaire du progéniteur. Un regroupement des courbes de lumière dans le domaine X lors de l'émission rémanente GRBs a été observé avant le lancement de Swift. Cette classification a été débattue après le lancement de Swift. Nous avons construit un échantillon de 254 GRBs qui montre un éparpillement des distributions du flux à un jour. Cette distribution a été normalisée avec un décalage vers le rouge de 1. Nous avons investigué ce problème selon trois directions: un problème instrumental, un problème de calibration des données ou l'absence de regroupement. Coté instrument, le problème pourrait être observationnel, nous avons en effet observé des effets saisonniers durant les solstices et les équinoxes. Coté calibration des données, un tel problème pourrait avoir une influence sur les résultats de l'étude. La comparaison entre analyse manuelle et automatique des données telle que disponible sur le dépôt Swift-XRT montre de sérieux aléas sur les résultats. Les cas où l'analyse manuelle est judicieuse sont exposés. La dernière possibilité de l'absence de regroupement pourrait être un effet de sélection. / GRBs are ashes of gamma-rays coming from cosmos. They are one of the most mysteriousevents we have been able to observe since their discovery. GRBs are classified into two groups: long/soft GRBs and short/hard GRBs. Their emission mechanism consists of two phases: prompt emission and afterglow emission. The launch of the Swift satellite opened a New Era in the GRBs research. Swift is able to provide accurate position for more GRBs than previous missions, thanks to its fast capabilities of slewing. Furthermore, the Swift shows that GRBs have a canonical behaviour for the X-ray afterglow light curves. The data analysis process remains the key point of GRBs studies. I present a detailed study of the peculiar GRB 141221A at different wavelengths. GRB 141221A shows an unusual steep rise in the optical light curve of the afterglow. The broad band spectral energy distribution, taken near the maximum of the optical emission, presents either a thermal component or a behaviourbreak. This burst displays unusual feature in the optical band, whereas the X-ray data is more common. GRB 141221A is one of the challenging bursts that excludes a stellar wind from the progenitor of the GRBs. A clustering in the X-ray afterglow light curves was observed before the launch of the Swift satellite. This feature has been debated after the launch of the Swift. We have built a sample which consists of 254 GRBs that shows a scattering of the data for the flux distribution at one day. This distribution was investigated with a normalization of light curves at redshift one. We have investigated the problem into three different directions