Thesis (Ph.D.)--Baylor University, 2009. / Includes bibliographical references (p. 141-147).

Orientador: Michelle Ferreira Zanchetta Morgado / Banca: Aldicio José Miranda / Banca: João Carlos Ferreira Costa / Resumo: Neste trabalho estudamos germes de funções sob a ação do grupo R_I dos germes de difeomorfismos em C^n que preservam um ideal I, descrevendo os conceitos de codimensão e determinação finita associados. Isso nos fornece ferramentas para caracterizar um tipo especial de germes com singularidades não isoladas, as chamadas singularidades do tipo D(q,p). Conseguimos ainda relacionar o conceito de R_I-estabilidade com estes germes, para o caso em que I é um ideal radical que define uma intersecção completa quase homogênea com singularidade isolada. Além disso, apresentamos um sistema de coordenadas através do qual obtemos uma fórmula explícita para alguns dos números de Lê destes germes / Abstract: In this work we study germs of functions under the action of the R_I group of diffeomorphisms of germs in C^n which preserving an ideal I, describing the concepts of codimension and finite determination associated. This provides the tools to characterize a particular type of germ with non isolated singularities, the so called D(q,p) singularities. We can still relate the concept of R_I-stability with these germs, in the case where I is a radical ideal that defines complete intersection with isolated singularity. Moreover, we present a coordinate system by which we obtain an explicit formula for some Lê numbers of these germs / Mestre

<p>A Hodge module on an algebraic variety may be viewed as a variation of Hodge structure  with singularities. Given an irreducible variety $X$, for any polarized variation of Hodge structure $\bold{H}$ on a smooth open subvariety $U\subset X,$ there exists a unique Hodge module $\cM \in HM_{X}(X)$ that extends $\bH.$ Conversely, for any Hodge module $\cM \in HM_{X}(X)$ with strict support on $X,$ there exists a polarized variation of Hodge structure $\bH$ on a smooth open subset $U \subset X$ such that $\cM \vert _{V} \cong \bH.$ In this thesis, we first study the singularities of a Hodge module $\cM \in HM_{X}(X)$ by using Morihiko Saito's theory of $S$-sheaves and duality. Then using local cohomology and the theory of mixed Hodge modules, we study the Hodge structure of $H^{i}(X, DR(\cM))$  when $X$ is a projective variety. Finally, we consider a variation of Hodge structure $\bH$ on $U$ as a Hodge module $\cN \in HM(U)$ on $U,$ and study the local cohomology of the complex $Gr^{F}_{p}DR(j_{!}\cN) \in D^{b}_{coh}(\cO_{X}),$ where $j: U \hookrightarrow X$ is the natural map.</p>

The topological entropy of a continuous map quantifies the amount of chaos observed in the map. In this dissertation we present computational methods which enable us to compute topological entropy for given time series data generated from a continuous map with a transitive attractor. A triangulation is constructed in order to approximate the attractor and to construct a multivalued map that approximates the dynamics of the linear interpolant on the triangulation. The methods utilize simplicial homology and in particular the Lefschetz Fixed Point Theorem to establish the existence of periodic orbits for the linear interpolant. A semiconjugacy is formed with a subshift of nite type for which the entropy can be calculated and provides a lower bound for the entropy of the linear interpolant. The dissertation concludes with a discussion of possible applications of this analysis to experimental time series. / by Mark Wess. / Thesis (Ph.D.)--Florida Atlantic University, 2008. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2008. Mode of access: World Wide Web.

Errata inserted opposite p.177. / Bibliography: p. 173-177. / x, 177 p. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / The classical dynamical structure of cosomological models in which the matter content of the universe consists of a scalar field with arbitrary non-negative potential is analyzed in full. (abstract) / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1996?

Thesis (Ph.D.)--Michigan State University. Dept. of Mathematics, 2008. / Title from PDF t.p. (viewed on July 24, 2009) Includes bibliographical references (p. 75-78). Also issued in print.

La modélisation numérique via la méthode des éléments finis utilise classiquement des fonctions de forme polynomiale qui de par leur régularité représentent difficilement des évolutions singulières telles que celles observées dans les phénomènes de localisation en mécanique. Pour pallier cette difficulté, ces travaux de thèse ont eu pour objectif de proposer un nouveau support d'approximation adaptatif couplant la méthode de représentation par ondelettes à la méthode des éléments finis classique. Dans le domaine du traitement du signal, la méthode des ondelettes montre un réel potentiel pour traiter les phénomènes singuliers. L'étude porte sur la création d'un support de discrétisation hybride, associant une interpolation polynomiale et une interpolation en ondelettes exprimée via la fonction d'échelle de l'ondelette de Daubechies. Ce couplage permet de représenter la partie régulière de la réponse via le support polynomial et les éventuelles singularités à l'aide du support en ondelettes. L'adaptation du support hybride est effectuée via l'apport multirésolution, qui ajuste le support en fonction de l'importance des singularités observées. Une méthodologie de détection et d'enrichissement automatique est réalisée ayant pour objectif d'obtenir le support optimum. L'ondelette de Daubechies n'étant connue qu'en des points discrets, une méthode d'intégration particulière est proposée. Une modification de l'interpolation naturellement non nodale de l'ondelette est également introduite, de manière à pouvoir imposer des conditions limites classiques nodales. Une illustration de la méthode et de son implémentation informatique est présentée via une étude académique 1D. / The numerical modelling with the finite element method conventionally uses functions of polynomial form which, by their regularity, hardly represent singular evolutions such as those observed in the phenomena of localization in mechanics. To solve the issue, the aim of this thesis was to propose a new adaptive approximation support coupling the wavelet representation with the classical finite element method. In the field of signal processing, the wavelet method shows a real capacity to treat singular phenomena. This research study deals with the creation of a hybrid discretisation support, including a polynomial interpolation and a wavelet interpolation formulated with the scaling function of the Daubechies wavelet. The regular part of the solution is represented with the polynomial support and the singularities are visualised with the wavelet support. The adaptation of the hybrid support is carried out with the multiresolution contribution, which adjusts the support according to the importance of observed singularities. An automatic detection and enrichment method is carried out in order to obtain the optimum support. The Daubechies wavelet being known only in discrete points, a particular integration method is proposed. A modification of the not nodal naturally interpolated wavelet interpolation is also introduced, in order to impose classical nodal boundary conditions. An illustration of the method and its computer implementation is presented via a 1D academic study.

Made available in DSpace on 2015-03-26T13:45:37Z (GMT). No. of bitstreams: 1 texto completo.pdf: 2634733 bytes, checksum: 3cb7c76ba150aef3f051776bae4f9a1a (MD5) Previous issue date: 2014-02-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In the 1990s, mathematicians Peter Giblin and Guillermo Sapiro have introduced the theory of affine invariant symmetry sets of plane curves. This dissertation is devoted to the study of some of these symmetry sets centre symmetry sets (CSS), affine distance symmetry set (ADSS) and affine envelope symmetry set (A6'SS) of a a simple closed convex smooth curve. We study these symmetry sets of through the locus of centers of conics and as an envelope of curves. We analyze the conditions of singularities, studying some in particular. We also study conditions of contact of the curve and of the conics that defined this symmetry sets. / No final dos anos 1990, os matemáticos Peter Giblin e Guillermo Sapiro introduziram a teoria sobre conjuntos de simetria de curvas planas invariantes por transformações afins. Esta dissertação é dedicada ao estudo de alguns destes conjuntosz 0 conjunto de simetria centml (CSS), 0 conjunto de simetria da distância afim(ADSS) e 0 conjunto de simetria da envolvente afim (A6'SS) de uma curva plana diferenciável fechada e convexa. Estudamos os conjuntos de simetria através do local geométrico dos centros de cônicas e como envolvente de curvas. Analisamos as condições de singularidades de cada um, estudando algumas em particular. Também estudamos condições de contato da curva e das cônicas que definem conjuntos de simetria. O estudo está baseado principalmente nos artigos [16] e [14].

Orientadores: Marco Antonio Teixeira, Alain Guy Jacquemard / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-05T23:50:08Z (GMT). No. of bitstreams: 1 Pereira_WeberFlavio_D.pdf: 1832947 bytes, checksum: 58bb202e90151fc6830fbc0cd1cf430e (MD5) Previous issue date: 2006 / Resumo: De acordo com a classificação feita por Anosov em 1959, obtemos diferentes tipos topológicos de sistemas "semi-lineares" descontínuos em JR4. Esta pré-classificação é feita através da apresentação das respectivas formas normais. Neste trabalho, consideramos perturbações não lineares de tais formas normais. As singularidades típicas são genericamente classificadas e o comportamento dos sistemas em torno destes pontos é analisado. Nosso foco é encontrar condições para a existência de uma família a l-parâmetro de órbitas periódicas terminando em singularidades no sentido do Teorema Centro de Lyapounov. As técnicas principais usadas são elementos do cálculo simbólico e da Teorida das Singularidades de Aplicações / Abstract: According to the classification made by Anosov in 1959, we derive several different topological types of semi-linear"discontinuous systems in R4. This pre-classification is done via pre-sentation of the respective normal forms. In this work, we consider non-linear perturbations of such normal forms. The typical singularities are generically classified and the behavior of the systems around these points is analyzed. Our focus is find conditions for the existence of 1-parameter family of periodic orbit terminating at the singularities in the sense of Lya- pounov Center Theorem. The main techniques used are elements of Symbolic Computation and Theory of Singularities of Mappings / Doutorado / Doutor em Matemática

Orientador: Sueli Irene Rodrigues Costa / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-11T17:03:12Z (GMT). No. of bitstreams: 1 Hoffman_AntonioRemiKieling_M.pdf: 1394491 bytes, checksum: bdb922cb72d13f5594d1bb3cc5517f23 (MD5) Previous issue date: 2008 / Resumo: Neste trabalho estudamos uma das curvas descritas por processos mecânicos: A Conchóide. Apresentamos breve relato sobre o surgimento da Conchóide de Nicomedes como uma forma de se "solucionar" um dos três clássicos problemas da geometria grega - o da trissecção do ângulo e abordamos o uso desta nos primórdios da Geometria analítica e do Cálculo no século XVII. Introduzimos a conchóide geral e analisamos com detalhes propriedades geométricas das conchóides de uma parábola. Discutimos a existência de singularidades - cúspides e pontos múltiplos, relacionando-os à evoluta e às curvas paralelas a uma parábola. Utilizamos o computador e programas livres de geometria dinâmica e cálculo simbólico para visualizar, experimentar e conjecturar os resultados a serem provados. / Abstract: We approach here one of the mechanical curves: The Conchoid. A brief description of the historical background of the Nicomedes'Conchoid, introduced to "solve" the angle trisection, one of the three classical problems of Greek geometry is presented and its use in the early times of the Calculus and Analytic Geometry in the XVII century is also described. We introduce the general conchoid and analyse the conchoids of a parabola. The existence of singularities such as cusps and multiple points is discussed and related to the evolute and parallel curves of a parabola. We have used the computer and free symbolic calculus and geometry software in visualising, experiencing and conjecturing results to be proved. / Mestrado / Geometria / Mestre em Matemática