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Showing 1 to 8 of 8 (0.055 seconds)Spelling suggestions: "subject:"compact support"" "subject:"kompact support""
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The Compact Support Property for Hyperbolic SPDEs: Two Contrasting EquationsIgnatyev, Oleksiy 18 July 2008 (has links)
No description available.
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Dualidade de Poincaré e invariantes cohomológicos /Cellini, Caroline Paula. January 2008 (has links)
Orientador: Ermínia de Lourdes Campello Fanti / Banca: Fernanda Soares Pinto Cardona / Banca: Maria Gorete Carreira Andrade / Resumo: Neste trabalho são abordados alguns aspectos da teoria de dualidade. Ele pode ser dividido em três partes principais. Na primeira demonstramos o teorema de Dualidade de Poincaré para variedades (sem bordo) orientáveis. Para tanto, fez-se necessário o uso do limite direto e cohomologia com suporte compacto. Na segunda definimos grupos de dualidade, em particular, grupo de dualidade de Poincaré, apresentamos alguns resultados e observações sobre a relação existente entre tais grupos e os grupos fundamentais de variedades asféricas fechadas, que é ainda um problema em aberto. Finalmente, alguns resultados envolvendo invariantes cohomológicos "ends" e grupos de dualidade são apresentados. / Abstract: In this work we consider some aspects of duality theory. It can be divided in three principal parts. In the first we prove the Poincaré Duality theorem for orientable manifolds (without boundary). For that, it is necessary the use of the direct limit and cohomology with compact supports. In the second part we de¯ne duality groups, in particular, Poincaré duality groups, we introduce some results and observations about the relationship between such groups and fundamental groups of aspherical closed manifolds, that still is an open problem. Finally, some results envolving the cohomological invariant "ends" and duality groups are presented. / Mestre
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Informação, velocidade da luz e pontos não analíticos / Information, light velocity and non-analytical pointsSilva, Wagner Ferreira da 01 March 2007 (has links)
The work begins with a review on the concept of group and phase velocity, and a discussion
about pulses propagation in dispersive media. After that, we are going to study
the Helmholtz equation, followed by Drude-Lorentz s model description of electric susceptibility.
In this study we have analyzed the relations between the real and imaginary part
of the dielectric constant, using Kramers-Kronig relations. Moreover, we have analyzed
the necessary conditions to obtain these relations, and the causality principle. We have
shown physical systems in which is possible to obtain anomalous dispersion. The systems
are population inversion, system with gain-assisted and photonic crystal.
To understand better about some mathematical methods used to study the propagation
of pulses, we have reviewed Fourier, Laplace and Green s methods. We used the
wave equation to show how the methods mentioned above became a problem simpler to
be solved. Finally, we have studied Cauchy-Riemann s conditions and the analyticity of
real and imaginary functions.
We have studied the propagation of Gaussian pulse and a compact support pulse, in
the anomalous dispersion region. We have shown that the Gaussian pulse can propagate
with a bigger group velocity than the speed of light in the vacuum, and these results are
the same when we use the whole expression for the refractive index or not. However, in
the case of the compact support pulse we have seen that is not true. On the other
hand, in the study of the compact support pulse propagation, it was observed that the non-analytical points never exceed the speed of light in the vacuum. Associating
the information to the non-analytical points we have observed the impossibility to send
information faster than light in the vacuum. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O trabalho inicia com uma revisão sobre o conceito de velocidade de grupo e de
fase, e uma breve discussão do que ocorre quando um pulso se propaga num meio dispersivo.
Em seguida, fazemos um estudo da equação de onda de Helmholtz, seguido por
uma descrição do modelo de Drude-Lorentz para a susceptibilidade elétrica. Durante
este estudo exploramos as relações que existem entre a parte real e imaginária da constante
dielétrica, através da relação de Kramers-Kronig. Além disso, discutimos o que é
necessário na obtenção deste tipo de relação além do princípio de causalidade. Apresentamos
os seguintes sistemas físicos nos quais é possível obter regiões com dispersão anômala:
sistema com inversão de população, com ganho assistido e cristal fotônico.
Com o objetivo de aprofundar o entendimento das ferramentas matemáticas usadas
no estudo da propagação de pulsos, revisamos os métodos de Fourier, de Laplace e de
Green. Aplicamos estes métodos na equação de onda para mostrar como os mesmos
tornam o problema mais simples de ser resolvido. Por fim, estudamos as condições de
Cauchy-Riemann e a analiticidade de funções reais e imaginárias.
Estudamos a propagação de um pulso Gaussiano e de um pulso com suporte compacto,
na região de dispersão anômala. Mostramos que um pulso Gaussiano se propaga com uma
velocidade de grupo maior que a velocidade da luz no vácuo, e que o resultado obtido é o
mesmo se usarmos somente a parte real do índice de refração ou se usarmos a expressão
completa no estudo da propagação. No caso de um pulso com suporte compacto vimos que
isto não é verdade. Percebemos ainda que na propagação do pulso com suporte compacto
os pontos não analíticos nunca excedem a velocidade da luz no vácuo. Associando a
informação a pontos não analíticos mostramos ser impossível enviar informação mais
rápida que a luz no vácuo.
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Dualidade de Poincaré e invariantes cohomológicosCellini, Caroline Paula [UNESP] 31 March 2008 (has links) (PDF)
Made available in DSpace on 2014-06-11T19:30:22Z (GMT). No. of bitstreams: 0
Previous issue date: 2008-03-31Bitstream added on 2014-06-13T19:19:04Z : No. of bitstreams: 1
cellini_cp_me_sjrp.pdf: 781641 bytes, checksum: 70ed1b385d132f8255370c0014be09b4 (MD5) / Neste trabalho são abordados alguns aspectos da teoria de dualidade. Ele pode ser dividido em três partes principais. Na primeira demonstramos o teorema de Dualidade de Poincaré para variedades (sem bordo) orientáveis. Para tanto, fez-se necessário o uso do limite direto e cohomologia com suporte compacto. Na segunda definimos grupos de dualidade, em particular, grupo de dualidade de Poincaré, apresentamos alguns resultados e observações sobre a relação existente entre tais grupos e os grupos fundamentais de variedades asféricas fechadas, que é ainda um problema em aberto. Finalmente, alguns resultados envolvendo invariantes cohomológicos ends e grupos de dualidade são apresentados. / In this work we consider some aspects of duality theory. It can be divided in three principal parts. In the first we prove the Poincaré Duality theorem for orientable manifolds (without boundary). For that, it is necessary the use of the direct limit and cohomology with compact supports. In the second part we de¯ne duality groups, in particular, Poincaré duality groups, we introduce some results and observations about the relationship between such groups and fundamental groups of aspherical closed manifolds, that still is an open problem. Finally, some results envolving the cohomological invariant ends and duality groups are presented.
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Étude de quelques problèmes elliptiques et paraboliques quasi-linéaires avec singularités / Study of some quasilinear and singular elliptic and parabolic problemsSauvy, Paul 04 December 2012 (has links)
Cette thèse s’inscrit dans le domaine mathématique de l’analyse des équations aux dérivées partielles non-linéaires. Plus précisément, nous avons fait ici l’étude de problèmes quasi-linéaires singuliers. Le terme "singulier" fait référence à l’intervention d’une non-linéarité qui explose au bord du domaine où ’équation est posée. La présence d’une telle singularité entraîne un manque de régularité et donc de compacité des solutions qui ne nous permet pas d’appliquer directement les méthodes classiques de l’analyse non-linéaire pour démontrer l’existence de solutions et discuter des propriétés de régularité et de comportement asymptotique de ces solutions. Pour contourner cette difficulté, nous sommes amenés à établir des estimations a priori très fines au voisinage du bord du domaine en combinant diverses méthodes : méthodes de monotonie (reliée au principe du maximum), méthodes variationnelles, argument de convexité, méthodes de point fixe et semi-discrétisation en temps. A travers, l’étude de trois problèmes-modèle faisant intervenir l’opérateur p-Laplacien, nous avons montré comment ces différentes méthodes pouvaient être mises en œuvre. Les résultats que nous avons obtenus sont décrits dans les trois chapitres de cette thèse : Dans le Chapitre I, nous avons étudié un problème d’absorption elliptique singulier. En utilisant des méthodes de sur- et sous solutions et des méthodes variationnelles, nous établissons des résultats d’existence de solutions. Par des méthodes de comparaison locale, nous démontrons également la propriété de support compact de ces solutions, pour de fortes singularités. Dans le Chapitre II, nous étudions le cas d’un système d’équations quasi-linéaires singulières. Par des arguments de point fixe et de monotonie, nous démontrons deux résultats généraux d’existence de solutions. Dans un deuxième temps, nous faisons une analyse plus détaillée de systèmes du type Gierer-Meinhardt modélisant des phénomènes biologiques. Des résultats d’unicité ainsi que des estimations précises sur le comportement des solutions sont alors obtenus. Dans le Chapitre III, nous faisons l’étude d’un problème d’absorption, parabolique singulier. Nous établissons par une méthode de semi-discrétisation en temps des résultats d’existence de solutions. Grâce à des inégalités d’énergie, nous démontrons également l’extinction en temps fini de ces solutions. / This thesis deals with the mathematical field of nonlinear partial differential equations analysis. More precisely, we focus on quasilinear and singular problems. By singularity, we mean that the problems that we have considered involve a nonlinearity in the equation which blows-up near the boundary. This singular pattern gives rise to a lack of regularity and compactness that prevent the straightforward applications of classical methods in nonlinear analysis used for proving existence of solutions and for establishing the regularity properties and the asymptotic behavior of the solutions. To overcome this difficulty, we establish estimations on the precise behavior of the solutions near the boundary combining several techniques : monotonicity method (related to the maximum principle), variational method, convexity arguments, fixed point methods and semi-discretization in time. Throughout the study of three problems involving the p-Laplacian operator, we show how to apply this different methods. The three chapters of this dissertation the describes results we get :– In Chapter I, we study a singular elliptic absorption problem. By using sub- and super-solutions and variational methods, we prove the existence of the solutions. In the case of a strong singularity, by using local comparison techniques, we also prove that the compact support of the solution. In Chapter II, we study a singular elliptic system. By using fixed point and monotonicity arguments, we establish two general theorems on the existence of solution. In a second time, we more precisely analyse the Gierer-Meinhardt systems which model some biological phenomena. We prove some results about the uniqueness and the precise behavior of the solutions. In Chapter III, we study a singular parabolic absorption problem. By using a semi-discretization in time method, we establish the existence of a solution. Moreover, by using differential energy inequalities, we prove that the solution vanishes in finite time. This phenomenon is called "quenching".
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Pathwise Uniqueness of the Stochastic Heat Equation with Hölder continuous o diffusion coefficient and colored noise / Pfadweise Eindeutigkeit der stochastischen Wärmeleitungsgleichung mit Hölder-stetigem Diffusionskoeffizienten und farbigem RauschenRippl, Thomas 29 October 2012 (has links)
No description available.
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Cohomologie d'espaces fibrés au-dessus de l'immeuble affine de GL(N) / Cohomology of fiber spaces over the affine building of GL(N)Rajhi, Anis 01 October 2014 (has links)
Cette thèse se compose de deux parties : dans la première on donne une généralisation d'espaces fibrés construit au-dessus de l'arbre de Bruhat-Tits du groupe GL(2) sur un corps p-adique. Plus précisément, on a construit une tour projective d'espaces fibrés au-dessus du 1-squelette de l'immeuble de Bruhat-Tits de GL(n) sur un corps p-adique. On a montré que toute représentation cuspidale π de GL(n) se plonge avec multiplicité 1 dans le premier espace de cohomologie à support compact du k-ième étage de la tour, où k est le conducteur de π. Dans la deuxième partie on a construit un espace W au-dessus de la subdivision barycentrique de l'immeuble de Bruhat-Tits de GL(n) sur un corps p-adique. Pour étudier les espaces de cohomologie à support compact d'un G-complexe simplicial propre X muni d'un recouvrement équivariant assez particulier, où G est un groupe localement compact totalement discontinu, on a montré l'existence d'une suite spactrale dans la catégorie des représentations lisses de G qui converge vers la cohomologie à support compact de X. En s'appuyant sur ce dernier résultat, on a calculé la cohomologie à support compact de l'espace W comme représentation lisse de GL(n) puis on a montrer que les types cuspidaux de niveau 0 de GL(n) apparaissent avec multiplicité fini dans la cohomologie de certain complexes fini construit au niveau résiduel. Comme conséquence, on montre que les représentations cuspidales de niveau 0 de GL(n) apparaissent dans la cohomologie de W. / This thesis consists of two parts: the first one gives a generalization of fiber spaces constructed above the Bruhat-Tits tree of the group GL(2) over a p-adic field. More precisely we construct a projective tower of spaces over the 1-skeleton of the Bruhat-Tits building of GL(n) over a p-adic field. We show that any cuspidal representation π of GL(n) embeds with multiplicity 1 in the first cohomology space with compact support of k-th floor of the tower, where k is the conductor of π. In the second part we constructed a space W above the barycentric subdivision of the Bruhat-Tits building of GL(n) over a p-adic field. To study the cohomology spaces with compact support of a proper G-simplicial complex X with a rather special equivariant covering, where G is a totally disconnected locally compact group, we show the existence of a spactrale sequence in the category of smooth representations of G that converges to the cohomology with compact support of X. Based on the latter results, we calculate the cohomology with compact support of W as smooth representation of GL(n), and then we show that the level zero cuspidal types of GL(n) appear with finite multiplicity in the cohomology of some finite simplicial complexes constructed in residual level. As a consequence, we show that the cuspidal representations of level 0 of GL(n) appear in the cohomology of W.
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Contribution à la théorie des ondelettes : application à la turbulence des plasmas de bord de Tokamak et à la mesure dimensionnelle de cibles / Contribution to the wavelet theory : Application to edge plasma turbulence in tokamaks and to dimensional measurement of targetsScipioni, Angel 19 November 2010 (has links)
La nécessaire représentation en échelle du monde nous amène à expliquer pourquoi la théorie des ondelettes en constitue le formalisme le mieux adapté. Ses performances sont comparées à d'autres outils : la méthode des étendues normalisées (R/S) et la méthode par décomposition empirique modale (EMD).La grande diversité des bases analysantes de la théorie des ondelettes nous conduit à proposer une approche à caractère morphologique de l'analyse. L'exposé est organisé en trois parties.Le premier chapitre est dédié aux éléments constitutifs de la théorie des ondelettes. Un lien surprenant est établi entre la notion de récurrence et l'analyse en échelle (polynômes de Daubechies) via le triangle de Pascal. Une expression analytique générale des coefficients des filtres de Daubechies à partir des racines des polynômes est ensuite proposée.Le deuxième chapitre constitue le premier domaine d'application. Il concerne les plasmas de bord des réacteurs de fusion de type tokamak. Nous exposons comment, pour la première fois sur des signaux expérimentaux, le coefficient de Hurst a pu être mesuré à partir d'un estimateur des moindres carrés à ondelettes. Nous détaillons ensuite, à partir de processus de type mouvement brownien fractionnaire (fBm), la manière dont nous avons établi un modèle (de synthèse) original reproduisant parfaitement la statistique mixte fBm et fGn qui caractérise un plasma de bord. Enfin, nous explicitons les raisons nous ayant amené à constater l'absence de lien existant entre des valeurs élevées du coefficient d'Hurst et de supposées longues corrélations.Le troisième chapitre est relatif au second domaine d'application. Il a été l'occasion de mettre en évidence comment le bien-fondé d'une approche morphologique couplée à une analyse en échelle nous ont permis d'extraire l'information relative à la taille, dans un écho rétrodiffusé d'une cible immergée et insonifiée par une onde ultrasonore / The necessary scale-based representation of the world leads us to explain why the wavelet theory is the best suited formalism. Its performances are compared to other tools: R/S analysis and empirical modal decomposition method (EMD). The great diversity of analyzing bases of wavelet theory leads us to propose a morphological approach of the analysis. The study is organized into three parts. The first chapter is dedicated to the constituent elements of wavelet theory. Then we will show the surprising link existing between recurrence concept and scale analysis (Daubechies polynomials) by using Pascal's triangle. A general analytical expression of Daubechies' filter coefficients is then proposed from the polynomial roots. The second chapter is the first application domain. It involves edge plasmas of tokamak fusion reactors. We will describe how, for the first time on experimental signals, the Hurst coefficient has been measured by a wavelet-based estimator. We will detail from fbm-like processes (fractional Brownian motion), how we have established an original model perfectly reproducing fBm and fGn joint statistics that characterizes magnetized plasmas. Finally, we will point out the reasons that show the lack of link between high values of the Hurst coefficient and possible long correlations. The third chapter is dedicated to the second application domain which is relative to the backscattered echo analysis of an immersed target insonified by an ultrasonic plane wave. We will explain how a morphological approach associated to a scale analysis can extract the diameter information
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