Orientador: Masayoshi Tsuchida / Banca: José Manoel Balthazar / Banca: Cláudio Agnaldo Buzzi / Resumo: Este trabalho apresenta um estudo de um pêndulo eletromecânico com excitação vertical utilizando a teoria de perturbações. O objetivo é fazer um estudo analítico para verificar os efeitos de ressonância no estado estacionário do sistema, efeitos esses provocados por alguns valores de freqüência do sistema dinˆamico. As equações do sistema dinâmico estudado apresentam características que impedem a obtenção de soluções analíticas devido à presença de termos não lineares, e ainda exibem interações ressonantes entre bloco, motor e pêndulo. A análise feita considerou o sistema com ressonância entre o bloco e o motor, mas foi descartada a interação ressonante com o pêndulo. Como a excitação no suporte é vertical, em primeira aproximação a equação do pêndulo é a equação de Mathieu. Devido à presença de um termo não linear nesta equação, foi feito também um estudo com a teoria de perturbações para obter uma solução analítica aproximada, tomando como exemplo a equação de Mathieu analisada no estudo desenvolvido por Nayfeh. As equações para o estado estacionário do sistema foram obtidas através da aplicação de um método de perturbação. O estudo dessas equações foi baseado no trabalho desenvolvido por Kononenko, e os resultados obtidos são análogos, pois o sistema dinâmico deste estudo e o sistema dinâmico considerado por Kononenko guardam certa semelhança. / Abstract: In this work a study of an electromechanical pendulum with a vertical excitation is done using the Perturbation theory. The main objective is to make an approximate analytic study to verify the effects of resonance at the stationary state of the system, effects that are caused by some values of frequencies of the dynamic system. The equations of the system show characteristics that don't permit the analytic solutions because of presence of nonlinear terms and there are resonant interactions between the block, the eccentric mass and the pendulum. In this analysis the resonance between the block and the eccentric mass was considered, but the resonance with the pendulum was ignored. As the excitation of the support is vertical, the first approximation of the equation of the pendulum is a Mathieu equation. Due to the presence of one nonlinear term in this equation, a study with the perturbation theory was performed to get a solution at first approximation, following the study made by Nayfeh. The equations for the stationary state were taken through the application of one perturbation method. The study of these equations was based on the work developed by Kononenko and the results obtained are similar, because the dynamic system of this work and the system considered by Kononenko keep certain similarities. / Mestre

In this thesis we present some of the theory of parametric stability in linear Hamiltonian systems with one degree and a degree and a half of freedom. To this end, we provide de nitions and results on Hamiltonian systems, symplectic vector spaces and linear stability of Hamiltonian systems balances. This work ends with the description of Deprit-Hori method in order to apply it to the Mathieu equation and thus build the boundary curves of the regions of stability and instability. / Nesta disserta c~ao apresentamos um pouco da teoria acerca da estabilidade param etrica em sistemas Hamiltonianos lineares com um grau e com um grau e meio de liberdade. Para tanto, fornecemos de ni c~oes e resultados sobre sistemas Hamiltonianos, espa cos vetoriais simpl eticos e estabilidade de equil brios de sistemas Hamiltonianos lineares. Esse trabalho e nalizado com a descri c~ao do m etodo de Deprit-Hori com o objetivo de aplic a-lo a Equa c~ao de Mathieu e assim construir as curvas de fronteira das regi~oes de estabilidade e instabilidade.

Using the film La Haine (1995), directed by Mathieu Kassovitz, as an object of analysis, this paper explores culture as a tool of exclusion in France through sociological, architectural, and political contexts. It investigates La Haine as one of the first representations of the banlieue to mainstream French audiences, as well as the ways in which the film reveals how immigrants and children of immigrants struggle to find personal, cultural, and national identity in France.

La production littéraire de Claude Mathieu, s’étalant de 1957 à 1965, tranche avec les oeuvres de ses contemporains. Le plus souvent, ces derniers défendent un nationalisme moderne et mettent à l’avant-plan le territoire et la société québécoise. De son côté, Mathieu aborde des thèmes plus généraux, par exemple le temps, l’art ou l’érotisme, qui trahissent ses sources d’inspiration issues de la littérature française et des littératures étrangères. Cet aspect est plutôt inusité chez les écrivains québécois de la décennie 1960. Dans cette analyse intertextuelle, nous cherchons à montrer la singularité de l’écriture de Claude Mathieu. Nous exposons ses principales sources et influences littéraires afin de comprendre comment il s’en inspire et comment elles orientent sa poétique où domine le fantastique teintée d’images surréalistes. L’analyse est constituée de deux chapitres. Le premier est consacré au recueil Vingt petits écrits ou le mirliton rococo. Les textes étudiés sont regroupés en trois sections, selon l’époque des références qui les appuient, soit les littératures hellénique, classique et moderne. Le second chapitre traite de La mort exquise, l’oeuvre la plus importante de Claude Mathieu. En analysant les principaux textes de ce recueil, nous montrons comment l’influence d’André Pieyre de Mandiargues et de Jorge Luis Borges s’impose face à la multitude de références diverses convoquées dans le premier recueil de nouvelles de Mathieu. Nous montrons également comment ces influences sont absorbées et transformées pour créer une écriture originale. / Claude Mathieu’s literary production, spanning from 1957 to 1965, differs quite a lot from the work of his contemporaries. Most often, they defend a modern nationalism and bring to the forefront Quebec’s society and territory. For his part, Mathieu discusses more general topics, such as time, art or erotism, inspired by French and foreign literature. This is rather original among Quebec writers of the 1960s. With this intertextual analysis, we seek to show the singularity of Claude Mathieu’s writing. We outline its main literary sources and influences in order to understand how he is inspired and how they guide his poetics. The analysis consists of two chapters. The first is devoted to the collection Vingt petits écrits ou le mirliton rococo. The texts studied are grouped into three sections, depending on the time of the references that support them, either Hellenic, classical or modern literature. The second chapter deals with La mort exquise, the most important work of Claude Mathieu. By analyzing the main pieces of this collection, we show how the influence of André Pieyre de Mandiargues and Jorge Luis Borges became larger than all the various references convened in the first collection of Mathieu’s short stories. We also show how these influences are absorbed and transformed to create an original writing.

In this thesis, we will give our discovery of original symmetric presentations of several important groups. We have investigated permutation and monomial progenitors 2*8: (23: 22), 2*9: (32: 24), 2*10: (24: (2 × 5)), 5*4:m (23: 22), 7*8:m (32: 24), and 3*5:m (24: (2 × 5)). The finite images of the above progenitors include the Mathieu sporadic group M12, the linear groups L2(8) and L2(13), and the extensions S6 × 2, 28 : .L2(8) , and 27 : .A5. We will show our construction of the four groups S3 , L2(8), L2(13), and S6 × 2 over S3, 22, S3 : 2, and S5, by using the technique of double coset enumeration. We will also provide isomorphism types all of the groups that have appeared as finite homomorphic images. We will show that the group L2(8) does not satisfy the conditions of Iwasawas Lemma and that the group L2(13) is simple by Iwasawas Lemma. We give constructions of M22 × 2 and M22 as homomorphic images of the progenitor S6.

La production littéraire de Claude Mathieu, s’étalant de 1957 à 1965, tranche avec les oeuvres de ses contemporains. Le plus souvent, ces derniers défendent un nationalisme moderne et mettent à l’avant-plan le territoire et la société québécoise. De son côté, Mathieu aborde des thèmes plus généraux, par exemple le temps, l’art ou l’érotisme, qui trahissent ses sources d’inspiration issues de la littérature française et des littératures étrangères. Cet aspect est plutôt inusité chez les écrivains québécois de la décennie 1960. Dans cette analyse intertextuelle, nous cherchons à montrer la singularité de l’écriture de Claude Mathieu. Nous exposons ses principales sources et influences littéraires afin de comprendre comment il s’en inspire et comment elles orientent sa poétique où domine le fantastique teintée d’images surréalistes. L’analyse est constituée de deux chapitres. Le premier est consacré au recueil Vingt petits écrits ou le mirliton rococo. Les textes étudiés sont regroupés en trois sections, selon l’époque des références qui les appuient, soit les littératures hellénique, classique et moderne. Le second chapitre traite de La mort exquise, l’oeuvre la plus importante de Claude Mathieu. En analysant les principaux textes de ce recueil, nous montrons comment l’influence d’André Pieyre de Mandiargues et de Jorge Luis Borges s’impose face à la multitude de références diverses convoquées dans le premier recueil de nouvelles de Mathieu. Nous montrons également comment ces influences sont absorbées et transformées pour créer une écriture originale. / Claude Mathieu’s literary production, spanning from 1957 to 1965, differs quite a lot from the work of his contemporaries. Most often, they defend a modern nationalism and bring to the forefront Quebec’s society and territory. For his part, Mathieu discusses more general topics, such as time, art or erotism, inspired by French and foreign literature. This is rather original among Quebec writers of the 1960s. With this intertextual analysis, we seek to show the singularity of Claude Mathieu’s writing. We outline its main literary sources and influences in order to understand how he is inspired and how they guide his poetics. The analysis consists of two chapters. The first is devoted to the collection Vingt petits écrits ou le mirliton rococo. The texts studied are grouped into three sections, depending on the time of the references that support them, either Hellenic, classical or modern literature. The second chapter deals with La mort exquise, the most important work of Claude Mathieu. By analyzing the main pieces of this collection, we show how the influence of André Pieyre de Mandiargues and Jorge Luis Borges became larger than all the various references convened in the first collection of Mathieu’s short stories. We also show how these influences are absorbed and transformed to create an original writing.

Thèse en recherche-création Cotutelle avec l'Université de Lorraine, Nancy, France / Cette thèse porte sur le récit de retour aux origines dans la littérature contemporaine française et se concentre sur des auteurs transclasses, c’est-à-dire qui ont quitté leur milieu d’origine et changé de statut social. Elle s’intéresse spécifiquement à un corpus d’auteurs originaires de régions non attractives de l’Hexagone. Elle concentre son analyse sur des textes de Nicolas Mathieu, Annie Ernaux, Didier Eribon, Édouard Louis et Raymond Depardon. Ce travail détermine d’abord ce qui est entendu par « récit de retour » en littérature, notamment lorsqu’il s’agit de représenter les campagnes qui intéressent ces auteurs. Il dégage des poétiques du retour chez chacun de ces auteurs, en observant l’hybridité générique qui les traverse : la photobiographie et le documentaire avec Depardon, le roman avec Ernaux et Mathieu, l’autobiographie avec Louis, l’essai avec Eribon. Dans un second temps, la thèse examine la temporalité et la géographie du retour, en particulier les motifs de la nostalgie et du déplacement. La thèse explore ensuite le point de vue de l’auteur, narrateur ou personnage transclasse sur son milieu d’origine, point de vue tantôt décalé, renouvelé ou surplombant. À cette recherche succède un texte de création, Je t’envoie des photos des primevères dans le sable, qui allie, en deux temps, fiction et enquête photolittéraire et qui questionne lui aussi le geste de retour aux origines en milieu rural. / This thesis focuses on the return to origins in contemporary French narratives. It examines the works of authors who left their hometown or their village and experienced social mobility. It specifically investigates the works of authors who come from post-industrial and non-touristy areas in France: Nicolas Mathieu, Annie Ernaux, Didier Eribon, Édouard Louis and Raymond Depardon. First, this work analyzes what the notion of return in literature implies, especially when French rural life is represented. The study aims to define a poetics of return for each of these texts, focusing on how these books are multi-genre or genre-bending: photobiography and documentary with Depardon, fiction with Ernaux and Mathieu, autobiography with Louis, essay with Eribon. In a second part, we examine the temporality and the geography of return, in particular nostalgia and displacement. This thesis also explores the author, narrator or character’s point of view on their background, as someone who left and changed their social status: the final chapter analyzes how this point of view has shifted, how it is renewed, but also how it can present itself as distant and apart. A creative text follows this research: titled I am sending you pictures of the primroses in the sand, it brings fiction and documentary (which includes photographs) together and reflects on the return gesture within rural areas.

Made available in DSpace on 2014-06-11T19:26:56Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-04-27Bitstream added on 2014-06-13T19:55:23Z : No. of bitstreams: 1 elias_lj_me_sjrp.pdf: 456982 bytes, checksum: 012c9b4ab5b1b167819de6d4b46a698b (MD5) / Este trabalho apresenta um estudo de um pêndulo eletromecânico com excitação vertical utilizando a teoria de perturbações. O objetivo é fazer um estudo analítico para verificar os efeitos de ressonância no estado estacionário do sistema, efeitos esses provocados por alguns valores de freqüência do sistema dinˆamico. As equações do sistema dinâmico estudado apresentam características que impedem a obtenção de soluções analíticas devido à presença de termos não lineares, e ainda exibem interações ressonantes entre bloco, motor e pêndulo. A análise feita considerou o sistema com ressonância entre o bloco e o motor, mas foi descartada a interação ressonante com o pêndulo. Como a excitação no suporte é vertical, em primeira aproximação a equação do pêndulo é a equação de Mathieu. Devido à presença de um termo não linear nesta equação, foi feito também um estudo com a teoria de perturbações para obter uma solução analítica aproximada, tomando como exemplo a equação de Mathieu analisada no estudo desenvolvido por Nayfeh. As equações para o estado estacionário do sistema foram obtidas através da aplicação de um método de perturbação. O estudo dessas equações foi baseado no trabalho desenvolvido por Kononenko, e os resultados obtidos são análogos, pois o sistema dinâmico deste estudo e o sistema dinâmico considerado por Kononenko guardam certa semelhança. / In this work a study of an electromechanical pendulum with a vertical excitation is done using the Perturbation theory. The main objective is to make an approximate analytic study to verify the effects of resonance at the stationary state of the system, effects that are caused by some values of frequencies of the dynamic system. The equations of the system show characteristics that don’t permit the analytic solutions because of presence of nonlinear terms and there are resonant interactions between the block, the eccentric mass and the pendulum. In this analysis the resonance between the block and the eccentric mass was considered, but the resonance with the pendulum was ignored. As the excitation of the support is vertical, the first approximation of the equation of the pendulum is a Mathieu equation. Due to the presence of one nonlinear term in this equation, a study with the perturbation theory was performed to get a solution at first approximation, following the study made by Nayfeh. The equations for the stationary state were taken through the application of one perturbation method. The study of these equations was based on the work developed by Kononenko and the results obtained are similar, because the dynamic system of this work and the system considered by Kononenko keep certain similarities.

La présente étude propose une analyse langagière à travers certaines scènes d’un corpus de quatre films mosaïques du cinéaste français Arnaud Desplechin : Comment je me suis disputé… (« ma vie sexuelle ») (1996); Rois et reine (2004); Un conte de Noël (Roubaix!) (2008) et Trois souvenirs de ma jeunesse (nos arcadies) (2015). En premier lieu, elle se penche sur la qualification de ces temps volumineux accordés à un personnage bavard, la définition du monologue telle qu’on la rencontrera s’appliquant mal à ces longues tirades qui ne s’inscrivent pas non plus dans la logique du dialogue, puisque l’échange verbal n’existe pas véritablement et que la communication se voit mise en échec. Ce mémoire analyse par la suite l’avènement de ces soliloques et leurs effets sur la narration selon l’état physique ou mental du personnage ainsi que la crédibilité accordée à ce dernier. L’altération de la possibilité de discourir découle de différents facteurs chez le cinéaste : la maladie, l’insomnie, l’aphonie, la mort ou encore l’ébriété, la prise de stupéfiants, la névrose voire la psychose. Après avoir étudié les différentes brides possibles de la parole des personnages, cet essai focalise brièvement son attention sur le comique relatif découlant de ces tirades. Est ensuite étudiée la forme et la place singulières octroyées aux lettres, motif central dans ce corpus de films. Cette étude se penche sur l’écriture de ces pièces de paroles conséquentes et isolées du reste de la narration avec leur temporalité différente, leur diction proche de la récitation théâtrale, une mise en scène privilégiant le face caméra ainsi que les raisons d’avoir recours au biais épistolaire, en évaluant en creux l’importance et le danger du silence tantôt subi, tantôt imposé par le personnage à travers le discours. Puisque cette étude analyse l’écriture langagière portée à l’oral et à l’écran et la complexité de filmer la parole, elle se conclut sur l’état de la recherche aujourd’hui, mais aussi sur les nombreuses pistes qu’il reste encore à explorer dans les études cinématographiques en ce qui concerne le langage à l’écran. / This present study’s aim is suggesting a linguistic analysis throughout different scenes in a medley of four films by the french director Arnaud Desplechin: Comment je me suis disputé… (« ma vie sexuelle ») (1996); Rois et reine (2004); Un conte de Noël (Roubaix!) (2008) et Trois souvenirs de ma jeunesse (nos arcadies) (2015). First of all, it looks into the qualifications of long periods of time granted to a very talkative character. The definition of soliloquy, such as described previously cannot be applied to these long speeches since they cannot be included in the dialogue logic. There is almost no real oral exchange. Communication cannot be established. Then this study will also analyze the different soliloques and their influence on the narration, according to the character’s physical or mental state together with his credibility. His disability to talk depends on different causes for the film maker : sickness, insomnia, aphonia, death, intoxication, drugs, neurosis, even psychosis. After exploring the different restrictions to the character’s communication, this essay will shortly focus on the comical side effects of these speeches. Then we will examine the special importance of letters which are essential in this film corpus. This essay also deals with the writing of these important words. They are separated from the rest of the story. They have a different temporality, their speech delivery is close to theatrical reciting. The production chooses filming front the front, explaining the reasons of rising the means of correspondance, pondering over the danger of silence which is, at times, either undergone or induced by the character through the speech. Since this analysis concerns the linguistic writing, both oral and filmed, the complexity of filming speech appears. As a conclusion, numerous new paths need to be explored when studying film making as far as filming speech is concerned.

[ES] Esta tesis trata sobre la integración numérica de sistemas hamiltonianos con potenciales explícitamente dependientes del tiempo. Los problemas de este tipo son comunes en la física matemática, porque provienen de la mecánica cuántica, clásica y celestial. La meta de la tesis es construir integradores para unos problemas relevantes no autónomos: la ecuación de Schrödinger, que es el fundamento de la mecánica cuántica; las ecuaciones de Hill y de onda, que describen sistemas oscilatorios; el problema de Kepler con la masa variante en el tiempo. El Capítulo 1 describe la motivación y los objetivos de la obra en el contexto histórico de la integración numérica. En el Capítulo 2 se introducen los conceptos esenciales y unas herramientas fundamentales utilizadas a lo largo de la tesis. El diseño de los integradores propuestos se basa en los métodos de composición y escisión y en el desarrollo de Magnus. En el Capítulo 3 se describe el primero. Su idea principal consta de una recombinación de unos integradores sencillos para obtener la solución del problema. El concepto importante de las condiciones de orden se describe en ese capítulo. En el Capítulo 4 se hace un resumen de las álgebras de Lie y del desarrollo de Magnus que son las herramientas algebraicas que permiten expresar la solución de ecuaciones diferenciales dependientes del tiempo. La ecuación lineal de Schrödinger con potencial dependiente del tiempo está examinada en el Capítulo 5. Dado su estructura particular, nuevos métodos casi sin conmutadores, basados en el desarrollo de Magnus, son construidos. Su eficiencia es demostrada en unos experimentos numéricos con el modelo de Walker-Preston de una molécula dentro de un campo electromagnético. En el Capítulo 6, se diseñan los métodos de Magnus-escisión para las ecuaciones de onda y de Hill. Su eficiencia está demostrada en los experimentos numéricos con varios sistemas oscilatorios: con la ecuación de Mathieu, la ec. de Hill matricial, las ecuaciones de onda y de Klein-Gordon-Fock. El Capítulo 7 explica cómo el enfoque algebraico y el desarrollo de Magnus pueden generalizarse a los problemas no lineales. El ejemplo utilizado es el problema de Kepler con masa decreciente. El Capítulo 8 concluye la tesis, reseña los resultados y traza las posibles direcciones de la investigación futura. / [CA] Aquesta tesi tracta de la integració numèrica de sistemes hamiltonians amb potencials explícitament dependents del temps. Els problemes d'aquest tipus són comuns en la física matemàtica, perquè provenen de la mecànica quàntica, clàssica i celest. L'objectiu de la tesi és construir integradors per a uns problemes rellevants no autònoms: l'equació de Schrödinger, que és el fonament de la mecànica quàntica; les equacions de Hill i d'ona, que descriuen sistemes oscil·latoris; el problema de Kepler amb la massa variant en el temps. El Capítol 1 descriu la motivació i els objectius de l'obra en el context històric de la integració numèrica. En Capítol 2 s'introdueixen els conceptes essencials i unes ferramentes fonamentals utilitzades al llarg de la tesi. El disseny dels integradors proposats es basa en els mètodes de composició i escissió i en el desenvolupament de Magnus. En el Capítol 3, es descriu el primer. La seua idea principal consta d'una recombinació d'uns integradors senzills per a obtenir la solució del problema. El concepte important de les condicions d'orde es descriu en eixe capítol. El Capítol 4 fa un resum de les àlgebres de Lie i del desenvolupament de Magnus que són les ferramentes algebraiques que permeten expressar la solució d'equacions diferencials dependents del temps. L'equació lineal de Schrödinger amb potencial dependent del temps està examinada en el Capítol 5. Donat la seua estructura particular, nous mètodes quasi sense commutadors, basats en el desenvolupament de Magnus, són construïts. La seua eficiència és demostrada en uns experiments numèrics amb el model de Walker-Preston d'una molècula dins d'un camp electromagnètic. En el Capítol 6 es dissenyen els mètodes de Magnus-escissió per a les equacions d'onda i de Hill. El seu rendiment està demostrat en els experiments numèrics amb diversos sistemes oscil·latoris: amb l'equació de Mathieu, l'ec. de Hill matricial, les equacions d'onda i de Klein-Gordon-Fock. El Capítol 7 explica com l'enfocament algebraic i el desenvolupament de Magnus poden generalitzar-se als problemes no lineals. L'exemple utilitzat és el problema de Kepler amb massa decreixent. El Capítol 8 conclou la tesi, ressenya els resultats i traça les possibles direccions de la investigació futura. / [EN] The present thesis addresses the numerical integration of Hamiltonian systems with explicitly time-dependent potentials. These problems are common in mathematical physics because they come from quantum, classical and celestial mechanics. The goal of the thesis is to construct integrators for several import ant non-autonomous problems: the Schrödinger equation, which is the cornerstone of quantum mechanics; the Hill and the wave equations, that describe oscillating systems; the Kepler problem with time-variant mass. Chapter 1 describes the motivation and the aims of the work in the historical context of numerical integration. In Chapter 2 essential concepts and some fundamental tools used throughout the thesis are introduced. The design of the proposed integrators is based on the composition and splitting methods and the Magnus expansion. In Chapter 3, the former is described. Their main idea is to recombine some simpler integrators to obtain the solution. The salient concept of order conditions is described in that chapter. Chapter 4 summarises Lie algebras and the Magnus expansion ¿ algebraic tools that help to express the solution of time-dependent differential equations. The linear Schrödinger equation with time-dependent potential is considered in Chapter 5. Given its particular structure, new, Magnus-based quasi-commutator-free integrators are build. Their efficiency is shown in numerical experiments with the Walker-Preston model of a molecule in an electromagnetic field. In Chapter 6, Magnus-splitting methods for the wave and the Hill equations are designed. Their performance is demonstrated in numerical experiments with various oscillatory systems: the Mathieu equation, the matrix Hill eq., the wave and the Klein-Gordon-Fock eq. Chapter 7 shows how the algebraic approach and the Magnus expansion can be generalised to non-linear problems. The example used is the Kepler problem with decreasing mass. The thesis is concluded by Chapter 8, in which the results are reviewed and possible directions of future work are outlined. / Kopylov, N. (2019). Magnus-based geometric integrators for dynamical systems with time-dependent potentials [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/118798