Nesta tese estudamos o conceito de grau de um morfismo irredutível em ${m mod}A$ relacionado ao conceito de teoria de partições pós-projetiva e pré-injetiva de uma álgebra de artin $A$. Introduzimos o conceito de grau de um morfismo irredutível em relação a uma categoria ${\\mathfrak D}$ de ${m ind}A$ e estudamos o caso em que ${\\mathfrak D}$ é um elemento da partição ${\\bf P_0}, \\cdots, {\\bf P_{\\infty}}$. Dentro do contexto de grau de um irredutível em relação a uma subcategoria resolvemos um problema proposto por Chaio, Le meur e Trepode em \\cite. Utilizando as partições pós-projetiva e pré-injetiva obtemos outra demonstração para a caracterização de álgebras de tipo finito obtida em \\cite e obtemos uma caracterização semelhante para subcategorias de módulos $\\Delta$-bons de tipo finito de ${m mod}A$ tal que $A$ é uma álgebra quasi-hereditária. Também utilizamos a teoria de partições para provar que, dada uma álgebra quasi-hereditária $A$ e ${\\cal F}(\\Delta) \\subseteq {m mod}A$, se $({m rad}_{\\Delta}^{\\infty})^2=0$ então ${\\cal F}(\\Delta)$ é de tipo finito. / In this thesis we analyse the concept of the degree of an irreducible morphism associated to the theory of postprojective and preinjective partitions. We introduce the idea of the degree of an irreducible morphism with respect to a subcategory ${\\mathfrak D}$ and we study the case in which ${\\mathfrak D}$ is an element of the postprojective partition ${\\bf P_0}, \\cdots, {\\bf P_{\\infty}}$. By using the concept of the degree of an irreducible morphism with respect to a subcategory ${\\mathfrak D}$ we present a solution to a problem recently proposed by Chaio, Le Meur and Trepode in \\cite. We also use the theory of postprojective and preprojective partitions to give another proof to the characterization of finite type algebras obtained by Chaio and Liu in \\cite and we apply similar techniques to obtain a characterization of finite type ${\\cal F}(\\Delta)$ subcategories where ${\\cal F}(\\Delta)$ is the subcategory of $\\Delta$-good modules of the category of finitely generated modules over a quasi-hereditary algebra. We also prove that given a quasi-hereditary algebra $A$ and ${\\cal F}(\\Delta) \\subseteq {m mod}A$, if $({m rad}_{\\Delta}^{\\infty})^2=0$ then ${\\cal F}(\\Delta)$ is of finite type.

Nesta tese estudamos o conceito de grau de um morfismo irredutível em ${m mod}A$ relacionado ao conceito de teoria de partições pós-projetiva e pré-injetiva de uma álgebra de artin $A$. Introduzimos o conceito de grau de um morfismo irredutível em relação a uma categoria ${\\mathfrak D}$ de ${m ind}A$ e estudamos o caso em que ${\\mathfrak D}$ é um elemento da partição ${\\bf P_0}, \\cdots, {\\bf P_{\\infty}}$. Dentro do contexto de grau de um irredutível em relação a uma subcategoria resolvemos um problema proposto por Chaio, Le meur e Trepode em \\cite. Utilizando as partições pós-projetiva e pré-injetiva obtemos outra demonstração para a caracterização de álgebras de tipo finito obtida em \\cite e obtemos uma caracterização semelhante para subcategorias de módulos $\\Delta$-bons de tipo finito de ${m mod}A$ tal que $A$ é uma álgebra quasi-hereditária. Também utilizamos a teoria de partições para provar que, dada uma álgebra quasi-hereditária $A$ e ${\\cal F}(\\Delta) \\subseteq {m mod}A$, se $({m rad}_{\\Delta}^{\\infty})^2=0$ então ${\\cal F}(\\Delta)$ é de tipo finito. / In this thesis we analyse the concept of the degree of an irreducible morphism associated to the theory of postprojective and preinjective partitions. We introduce the idea of the degree of an irreducible morphism with respect to a subcategory ${\\mathfrak D}$ and we study the case in which ${\\mathfrak D}$ is an element of the postprojective partition ${\\bf P_0}, \\cdots, {\\bf P_{\\infty}}$. By using the concept of the degree of an irreducible morphism with respect to a subcategory ${\\mathfrak D}$ we present a solution to a problem recently proposed by Chaio, Le Meur and Trepode in \\cite. We also use the theory of postprojective and preprojective partitions to give another proof to the characterization of finite type algebras obtained by Chaio and Liu in \\cite and we apply similar techniques to obtain a characterization of finite type ${\\cal F}(\\Delta)$ subcategories where ${\\cal F}(\\Delta)$ is the subcategory of $\\Delta$-good modules of the category of finitely generated modules over a quasi-hereditary algebra. We also prove that given a quasi-hereditary algebra $A$ and ${\\cal F}(\\Delta) \\subseteq {m mod}A$, if $({m rad}_{\\Delta}^{\\infty})^2=0$ then ${\\cal F}(\\Delta)$ is of finite type.

O presente trabalho trata do estudo, projeto, desenvolvimento, construção e medida de lentes discretas planares (DLAs). Estes dispositivos atuam como sistemas irradiantes, especialmente com características multi-feixes. A construção destas lentes utiliza tecnologias compatíveis com a fabricação de circuitos impressos, com alguns detalhes que são característicos da área de antenas e circuitos planares. O estudo aborda as equações de projeto e considerações gerais relativas ao atendimento de especificações técnicas preliminares. Foram desenvolvidas duas lentes discretas, uma na frequência de 8GHz (banda X) e outra na frequência de 40GHz (banda Ka- faixa de ondas milimétricas). São apresentados os resultados de medidas destas duas lentes, que comprovam a possibilidade de uso em aplicações multi-feixes, bem como seu efeito de foco, análogo ao observado em lentes óticas comuns. / The object of this work is the study, design, development, fabrication and measurement of discrete lens arrays (DLAs). These devices act as radiant systems, especially with multi-beam characteristics. Their construction follows the same procedures and techniques normally found in printed circuit fabrication, with some further details that are pertinent to the antenna and planar circuit field. This study contains the design equations and general remarks as to fulfill preliminary technical specifications. Two real designs were developed, one in the X-band (8GHz) and another in the millimeter range, Ka band (40GHz). Their respective measurement results are presented, which proved their possible application in multi-beam systems, as well as their focusing effect, which is analogous to that observed in common optical lenses.

Les variations du champ magnétique terrestre sont documentées par les observatoires au sol et les satellites en orbite basse, pour des échelles de temps de l'année au siècle.Sur ces périodes, la dynamique du noyau externe -- là où est principalement généré le champ magnétique -- est fortement influencée par la rotation terrestre, qui tend à imposer une invariance dans la direction parallèle à l'axe de rotation.Dans cette thèse, j'étudie un modèle s'appuyant sur cette hypothèse de bidimensionnalité du champ de vitesse, le modèle quasi-géostrophique.Je présente une nouvelle dérivation de ce modèle par une approche variationnelle, plus adaptée aux fortes pentes des frontières du domaine sphérique.Je présente une étude modale des ondes hydro-magnétiques, qui pour la première fois prend en compte l'impact d'un champ magnétique imposé non-zonal.Deux groupes d'ondes magnéto-hydrodynamiques apparaissent alors : les ondes magnéto-Coriolis (centennales) et les ondes d'Alfvéen de torsion (interannuelle).Je décris l'évolution des ondes à mesure que l'on intensifie l'effet de la rotation, jusqu'à atteindre des paramètres géophysiques.Je discute également dans quel mesure une version du modèle quasi-géostrophique où la force de Lorentz est représentée par des produits quadratiques du champ magnétique est adapté pour l'interprétation de calculs numériques tridimensionnels de la dynamo. J'observe que pour les paramètres aujourd'hui accessibles à ces calculs, les forces magnétiques sont faibles. À long terme, nous espérons utiliser le modèle quasi-géostrophique dans le contexte de l'assimilation de données satellitaires. / Variations of the Earth's magnetic field are documented by ground observatories and low-orbiting satellites, for time scales from year to century.On such periods, dynamics of the outer core -- where the creation of the magnetic field takes place -- is strongly influenced by the Earth rotation, which tends to impose invariance of the flow in the direction parallel to the rotation axis.In this thesis report, I study a model based on this bi-dimensional velocity field hypothesis, the quasi-geostrophic model.I present a new mathematical formulation of this model through a variational approach, better suited to steep slopes on the boundaries of the spherical domain.I present a modal study of hydromagnetic waves, taking into account for the first time the impact of a non-zonal imposed magnetic field.Two groups of hydromagnetic waves are present : centennial magneto-Coriolis waves and interannual torsional Alfvén waves.I describe evolution of those waves as the effect of rotation is intensified until Earth-like parameters are reached.I also discuss in what measure an other version of the quasi-geostrophic model, where Lorentz force is represented by quadratic products of the magnetic field, can be adapted to understand tridimensional dynamo numerical simulations.I observe that for parameters available today, magnetic forces are weak.In the future, we hope to use the Quasi-geostrophic model in the context of satellite data assimilation.

This thesis presents a joint experimental and theoretical study of vector correlations in the electronically, vibrationally, and rotationally inelastic collisions of simple molecules with rare-gas atoms. In the first instance, empirical and calculated data are presented for rotationally inelastic scattering in the NO(X)+Ar and ND₃(X̃)+Ar systems at collision energies in the range 405-2210 cm^-1. These experiments - the first to be conducted on a newly commissioned crossed-molecular beam machine - measured the k-k' correlation, i.e. that between the vectors describing the relative velocities before and after collision, respectively. The empirical data were subjected to rigorous comparison with both quantum-mechanical and quasi-classical trajectory (QCT) calculations. For both the NO(X)+Ar and ND₃(X̃)+Ar systems, there is generally good agreement between experiment and theory at all four collision energies investigated. Two chapters of this thesis focus on the development of trajectory surface-hopping (TSH) QCT models of the OH(A, v = 0)+Kr and OH(A, v = 0)+Xe systems. Experimental data relating to scalar quantities (rotational energy transfer (RET) and electronic quenching) and to the j-j' correlation (which quantifies the depolarisation of the angular momentum of the OH(A) radical) are compared to variable-collision-energy TSH QCT calculations in which the length of the OH bond is fixed. The algorithms involve all three PESs of the OH(A/X)+Kr system, and the full range of electrostatic and roto-electronic mechanisms that couple them, for the first time. The most complete model succeeded in accounting for 93% of experimentally observed quenching. For the OH(A/X)+Xe system, coupling matrix elements were estimated from those of OH(A/X)+Kr, and the most complete model recovered 63% of experimentally observed quenching. This thesis also presents a novel theoretical study of rotationally inelastic dynamics in the OH(A, v = 1)+Kr system. Provisional results from adiabatic calculations in which the OH bond length is allowed to vary over the course of a trajectory are presented alongside experimental data that were reported previously. To date, these calculations continue to underestimate the extent of empirical RET data. Reasons for the observed discrepancy, and suggestions to resolve it, are outlined in detail.

On utilise la théorie de Floquet-Lin pour des systèmes différentiels linéaires quasi- périodiques pour établir des résultats d'existence et d'unicité et de dépendance continue des systèmes différentiels non linéaires quasi-périodiques. Et dans un second temps on établit un résultat de réductibilité d'un système différentiel linéaire presque-périodique en un système différentiel linéaire triangulaire supérieur avec conservation du nombre des solutions presque-périodiques indépendantes. Ensuite, un résultat d’existence et d’unicité et de dépendance continue des systèmes différentiels non linéaires presque-périodiques par rapport au terme du contrôle. / We use a Floquet theory for quasi-periodic linear ordinary differential equations due to Zhensheng Lin to obtain results, of existence, unicity, continuous and differentiable dependence, on the quasi-periodic solutions of quasi-periodic nonlinear ordinary differential equations. in a second time we establish the reducibility of linear systems of almost periodic differential equations into upper triangular systems of a. p. differential equations. This is done while the number of independent a. p. solutions is conserved. We prove existence and uniqueness of a. p. solutions of a nonlinear system with an a. p. linear part. Also we prove the continuous dependence of a. p. solutions of a nonlinear system with respect to an a. p. control term.

L'objet de cette thèse est l'étude de la régularité des solutions d'énergie infinie d'une équation de transport non locale. Plus précisément, nous nous sommes intéressés à deux équations de transport dont la vitesse est donnée par un opérateur non local. La première équation est l'équation dissipative surface quasi-géostrophique (SQG) et la seconde est un modèle 1D qui peut être vu comme la version 1D de l'équation quasi-géostrophique non écrite sous forme divergence. Une autre motivation du modèle 1D est le lien qu'a cette équation avec l'équation de Birkoff-Rott modélisant l'évolution d'une poche de tourbillon. Ces deux équations ont été introduites par Constantin, Majda et Tabak pour (SQG) et par Constantin, Lax, Majda pour le modèle 1D dans le but de mieux comprendre l'étude de la régularité des solutions de l'équation d'Euler tridimensionnelle écrite en terme de la vorticité. Dans une première partie, nous nous sommes attachés à étudier l'équation quasi géostrophique (SQG) lorsque la donnée initiale est dans l'espace de Morrey-Campanato non homogène $L^{2}_{uloc}(mathbb{R}^2)$. Le manque de décroissance à l'infini du noyau de convolution de l'opérateur de Riesz ne permet pas de considérer le cas d'une donnée intiale $L^{2}_{uloc}(mathbb{R}^2)$. Cependant, en donnant plus de décroissance au noyau de l'opérateur de Riesz, ou de façon équivalente, en donnant plus d'oscillations à la donnée initiale nous rendons possible l'étude de l'équation dans des espaces de Morrey-Camapanato. Nous montrons alors un théorème d'existence globale dans le cas d'oscillations suffisamment grandes et local dans le cas de petites oscillations. Dans une seconde partie, nous nous sommes intéressés à l'étude de l'équation de transport 1D dont la vitesse est non locale. Contrairement à l'équation (SQG), l'approche Morrey-Campanato pour l'équation 1D ne marche pas aussi bien. Le caractère non locale de cette équation associé au fait qu'elle ne soit pas écrite sous forme divergence introduit de grandes difficultés. Cependant, l'étude dans les espaces à poids est possible et nous obtenons un résultat d'existence globale à condition de prendre un poids appartenant à la classe A_2 de Muckenhoupt. Enfin, nous terminons en montrant que la condition de positivité de la donnée initiale n'est pas nécessaire si l'on désire uniquement avoir un contrôle globale de solutions faibles dont l'énergie ne décroit pas. Comme cela a été remarqué dans l'article de Cordoba, Cordoba et Fontelos, la décroissance de l'énergie n'est valable que sous l'hypothèse de positivité de la donnée initiale. Ceci rejoint un résultat établi récemment par Hongjie Dong / In this thesis, we adress the study of weak infinite energy solutions for the critical dissipative quasi geostrophic (SQG) equation. We also study a 1D transport equation with non local velocity. More precisely, we consider the (SQG) equation equation with data in Morrey-Camapanto type spaces and the other equation in a weighted Lebesgue spaces. Both spaces generate infinite energy solutions. Regarding the 1D equation with non local velocity, the existence of weak Morrey solutions is not easy to obtain, this is due to the fact that the non linearity is not written in a divergence form. Nevertheless, we are able to adress the study this 1D equation in a weigted Lebesgue space and this also provides infinite energy solutions. In a first part, we show that for any initial data lying in a Morrey-Campanato space for large enough oscillations, we have global existence of weak solutions. The proof is based on the study of the truncated equation (on a ball of radius $R>0$ centered at the origin) associated with a truncated et regularized initial data (by making a convolution with a standard mollifer). We obtain emph{a priori} estimates that give rise to an energy inequality. Then, we treat the case of small oscillations, namely $0<s<1/4$. More precisely, we show that for all initial data lying in $Lambda^{s} (dot H^{s}_{uloc} (mathbb{R}^{2}))cap L^infty(mathbb{R}^{2})$ we have local existence of solutions.In a second part, we study a 1D model equation driven by a non local velocity. This equation have been considered by Cordoba, Cordoba and Fontelos in a paper where the authors show that for all positive initial data in $H^{2} (mathbb{R}^{2})$ we have global existence of weak solutions. We first make some remarks regarding the positivity condition of the initial data by showing that this condition is not necessary for keeping the global control but we actually lost the $L^2$ maximum principle and the $L^{2}$ decay at inifinity. In the second part of the chapter, we show a global existence result of weak solutions for all positive initial data belonging to the weighted Lebesgue spaces $L^{2}(w)$ where $w$ is a weight of the $mathcal{A}_{2}$ class of Muckenhoupt. The method we used may easily be extend to other active scalar equations such as the surface quasi geostrophic equation

Made available in DSpace on 2014-06-11T19:22:34Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-08-17Bitstream added on 2014-06-13T18:49:37Z : No. of bitstreams: 1 campanha_ps_me_bauru.pdf: 713465 bytes, checksum: 80f1a0cfec7a9f0dda4e30ae9f1786ab (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Nesse trabalho propõe-se uma adaptação do método barreira penalidade quasi-Newton apresentado por P. Armand em 2003, para a resolução do problema do Fluxo de Potência Ótimo (FPO). Este método é denominado de método da função langrangiana barreira penalidade adaptada. Neste método as restrições de desigualdade são transformadas em igualdade pelo uso de variáveis de folga positivas. Estas variáveis são relaxadas, utilizando-se variáveis positivas, as quais, são incorporadas na função objetivo através de um termo de penalização. O novo problema restrito é então transformado em irrestrito associando a uma função lagrangiana às restrições de igualdade e uma função barreira penalidade às restrições de desigualdade. o algoritmo é composto por um ciclo interno e um externo. No ciclo interno é utilizado um método quasi-Newton para o cálculo das direções de busca e é determinado o tamanho do passo. No ciclo externo os parâmetros de barreira e penalidade são atualizados através de regras pré-definidas até que as condições de KKT sejam satisfeitas. Testes computacionais foram realizados utilizando problemas matemáticos e o problema de FPO, os quais demonstram a eficiência da adaptação proposta / This work proposes an adaptation of the quasi-Newton penalty barrier method presented by P. Armand in 2003. for the solution of the Optimal Power Flow (OPD) problem. This method is called method adapted penalty barrier lagrangian function. In this method the inequalities constraint are transformed in equality by adding non-negative slack variable. These variables are relaxed by positive auxiliary variables which are incorporated in the objective function through a penalty term. The new constraint problem is transformed in unconstraint by associating an lagrangian function for handling the equality constraint and an penalty barrier function for treating the inequality constraints. The algorithm is composed by an internal and external cycle. In the interanal cycle is used the quasi-Newton method to determine the search directions and the step size is calculated. In the external cycle the barrier parameters are updated through predefined rules until the KKT conditions are satisfied. Computational tests were accomplished using mathematical problems and the OPF problem which demonstrate the efficiency of the propose adaptation

Made available in DSpace on 2014-12-17T15:14:58Z (GMT). No. of bitstreams: 1 ManoelSV_TESE_capa_ate_pag67.pdf: 3395617 bytes, checksum: 7b8445696b35d33ae99c6f6fe1c1b75d (MD5) Previous issue date: 1999-07-12 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / Neste trabalho investigamos as propriedades dos espectros de polariton de plasmons e de ondas de luz em super-redes semicondutoras e em multicamadas diel?tricas, respectivamente, arranjadas em um padr?o quasi-peri?dico. Esta quasi-periodicidade pode ser do tipo das chamadas sequ?ncias substitucionais. Elas s?o caracterizadas pela natureza de seus espectros de Fourier, que pode ser do tipo dense pur? point (sequ?ncia de Fibonacci), singular continuous (sequ?ncias de Thue-Morse e duplo-per?odo) e absolutely continuous ( sequ?ncia de Rudin-Shapiro). Com o objetivo de estudar o espectro de polariton de plasmon, usamos um conveniente modelo te?rico baseado no tratamento da matriz-transfer?ncia, com as camadas caracterizadas por uma fun??o diel?trica dependente da frequ?ncia, incluindo efeitos de retardamento. Encontramos um espectro fractal caracterizado por uma lei de pot?ncia para a distribui??o de bandas em cada tipo de estrutura quasi-peri?dica. Para a propaga??o das ondas de luz em multicamadas diel?tricas, os coeficientes de transmiss?o s?o derivados atrav?s da determina??o da matriz-transfer?ncia ?ptica. Uma compara??o entre a incid?ncia obl?qua e a incid?ncia normal, nos mostra comportamentos bastante diferentes do espectro de transmit?ncia para um intervalo particular de frequ?ncia. No caso da incid?ncia normal, apresentamos resultados num?ricos que ilustram o aspecto auto-similar destes espectros, assim como mostram suas impress?es digitais ?pticas que s?o determinadas atrav?s dos mapas de retorno de seus coeficientes de transmiss?o. Finalmente, investigamos tamb?m as propriedades multifractais destes espectros (polariton de plasmons e ondes de luz)

Estudamos a evolução temporal de perturbações escalares na vizinhança de uma estrela com densidade uniforme que colapsa em um buraco negro. O trabalho começa com um estudo básico de gravitação e modos quasi-normais. O objetivo principal é resolver a equação de Klein-Gordon sem massa para a perturbação escalar, cuja solução depende de métodos numéricos. Com este objetivo, tratamos os aspectos teóricos de buracos negros e estrelas a partir da solução prevista pela Relatividade Geral para um buraco negro, estrelas com densidade uniforme e estrelas em colapso. Estudamos também uma maneira de reduzirmos a Equação de Klein-Gordon para uma forma conveniente de ser integrada, assim como os métodos numéricos necessários para resolver essa equação. Encontramos soluções para os modos variando a massa M, o raio inicial R e o rótulo do momento angular l. Essas soluções são irregulares em muitas situações, mas em geral elas são crescentes, de acordo com o comportamente observado de explosões de Supernovas. / This work is a study on the time evolution of scalar perturbations around a star collapsing to a black hole. It starts with a basic study of gravitation and quasi-normal modes. The aim is to derive the solution of the massless Klein-Gordon equation, that depends on numerical methods. Aiming at this goal, we studied theoretical aspects of stars, black holes and gravitational collapse. The methods include coordinate substitutions to modify the Klein-Gordon equation to a simple form. We also studied numerical methods for partial differential equations. Solutions of the quasi-normal modes were found with different values of M, R and l. The solutions are irregular in several situations, but some of them display increasing modes, that could be explained by the explosive behavior of Supernovas.