Orientador: Angela Maria Sitta / Banca: Maria Aparecida Soares Ruas / Banca: Claudio Aguinaldo Buzzi / Resumo: Neste trabalho classificamos problemas de bifurcação Z2-equivariantes de corank 2 até co- dimensão 3 via técnicas da Teoria de Singularidades. A abordagem para classificar tais problemas é baseada no processo de redução à forma normal de Birkhoff para estudar a interação de modos Hopf-Pontos de Equilíbrio. O comportamento geométrico das soluções dos desdobramentos das formas normais obtidas é descrito pelos diagramas de bifurcação e estudamos a estabilidade assintótica desses ramos. / Abstract: In this work we classify the Z2-equivariant corank 2 bifurcation problems up to codimension 3 via Singularity Theory techniques. The approach to classify such problems is based on the Birkhoff normal form to study Hopf-Steady- State mode interaction. The geometrical behavior of the solutions of the unfolding of the normal forms is described by the bifurcation diagrams and we study the asymptotic stability of such branches. / Mestre

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis we studied the theory of stability in equilibrium solutions of autonomous Hamiltonian systems with two degrees of freedom in degenerate cases. We specifically focusedour study on two cases, namely, when there are a first-order single resonance and a first-orderdouble resonance. After approaching standardization algorithms of the Hamiltonianquadratic part, the main technique used is to obtain the normal form of the Hamiltonian Lie up to a suitable order and,by using the theorem of Invariant Curve, we provided some conditions for stability of the new Hamiltonian coefficients. We studied the classical theorems of Chetaev, assuming that the origin of the phase space corresponds to the balance of that system. As an illustration, we resolved a partial reciprocal of Lagrange-Dirichlet theorem with two degrees of freedom, and made some comments regarding this reciprocal to one degree of freedom. / Nesta dissertação, estudamos a teoria de estabilidade em soluções de equilíbrios de sistemas Hamiltonianos autônomos com dois graus de liberdade em casos degenerados. Concentramos o estudo especificamente em dois casos, a saber, quando há uma ressonância de primeira ordem e dupla ressonância de primeira ordem. Após abordarmos algoritmos de normalização da parte quadrática do Hamiltoniano, a técnica principal utilizada consiste em obter a forma normal de Lei do Hamiltoniano até uma ordem adequada e usando o teorema da Curva Invariante, fornecemos algumas condições para estabilidade a partir dos coeficientes do novo Hamiltoniano. Estudamos os teoremas clássicos de Chetaev, supondo que a origem do espaço de fase corresponde ao equilíbrio desse sistema. Como ilustração, resolvemos uma recíproca parcial do teorema de Dirichlet-Lagrange, com dois graus de liberdade, tecendo ainda alguns comentários a respeito desta recíproca para um grau de liberdade.

This dissertation revolves around various mathematical aspects of nonlinear wave motion in viscoelasticity and free surface flows. The introduction is devoted to the physical derivation of the stress-strain constitutive relations from the first principles of Newtonian mechanics and is accessible to a broad audience. This derivation is not necessary for the analysis carried out in the rest of the thesis, however, is very useful to connect the different-looking partial differential equations (PDEs) investigated in each subsequent chapter. In the second chapter we investigate a multi-dimensional scalar wave equation with memory for the motion of a viscoelastic material described by the most general linear constitutive law between the stress, strain and their rates of change. The model equation is rewritten as a system of first-order linear PDEs with relaxation and the well-posedness of the Cauchy problem is established. In the third chapter we consider the Euler equations describing the evolution of a perfect, incompressible, irrotational fluid with a free surface. We focus on the Hamiltonian description of surface waves and obtain a recursion relation which allows to expand the Hamiltonian in powers of wave steepness valid to arbitrary order and in any dimension. In the case of pure gravity waves in a two-dimensional flow there exists a symplectic coordinate transformation that eliminates all cubic terms and puts the Hamiltonian in a Birkhoff normal form up to order four due to the unexpected cancellation of the coefficients of all fourth order non-generic resonant terms. We explain how to obtain higher-order vanishing coefficients. Finally, using the properties of the expansion kernels we derive a set of nonlinear evolution equations for unidirectional gravity waves propagating on the surface of an ideal fluid of infinite depth and show that they admit an exact traveling wave solution expressed in terms of Lambert’s W-function. The only other known deep fluid surface waves are the Gerstner and Stokes waves, with the former being exact but rotational whereas the latter being approximate and irrotational. Our results yield a wave that is both exact and irrotational, however, unlike Gerstner and Stokes waves, it is complex-valued.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第22582号 / 情博第719号 / 新制||情||123(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 矢ヶ崎 一幸, 教授 中村 佳正, 教授 梅野 健 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

In this paper, we discuss the deficiencies of normal form definitions based on Functional Dependency and introduce a new normal form concept based on Functional Independency. Functional Independency has not been systematically investigated while there is a very strong theoretical foundation for the study of Functional Dependency in relational database normalization. This paper will demonstrate that considering Functional Dependency alone cannot eliminate some common data anomalies and the normalization process can yield better database designs with the addition of Functional Independency.

This thesis examines the connections between Bézout domains and elementary divisor domains. I establish what both of these domains are, and I provide some clarifying examples of each. I state and prove some key results that have been established already in the literature. I describe a process by which I tried to show a distinction between Bézout domains and elementary divisor domains, and then provide an explicit example which shows that this process as formulated would not lead to an example of a Bézout domain which is not an elementary divisor domain. Throughout the thesis, I also state open questions that could lead to future research in this area.

No description available.

京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24038号 / 情博第794号 / 新制||情||134(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)准教授 辻本 諭, 教授 梅野 健, 教授 矢ヶ崎 一幸 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

This thesis presents the architecture and implementation of a query system resulted from a domain-specific conceptual data modeling and querying methodology. The query system is built for a high level conceptual query language that supports dynamically user-defined domain-specific functions and application-specific functions. It is DBMS-independent and can be translated to SQL and OQL through a normal form. Currently, it has been implemented in neuroscience domain and can be applied to any other domain.

Orientador: Marco Antonio Teixeira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-05T21:55:10Z (GMT). No. of bitstreams: 1 Lima_MauricioFirminoSilva_D.pdf: 1170094 bytes, checksum: 090e81187787a7a96591621e58ae7742 (MD5) Previous issue date: 2006 / Resumo: Neste trabalho tratamos de famílias a um-parâmetro de campos vetoriais R-reversíveis definidos em uma vizinhança de um ponto de equilíbrio ressonante em R2n. Focalizamos a atenção às 0:p:q-ressonâncias. Inicialmente estudamos a existência/bifurcação de órbitas periódicas simétricas para tais sistemas. A existência e rigidez de famílias de órbitas homoclínicas também são discutidas. Além disso, também analisamos, para n = 3, a rigidez de famílias de Cantor¿ de dois-toros invariantes por meio da Teoria KAM / Abstract: In this work we deal with one parameter families of R-reversible vector fields defined around a resonant equilibrium point in R2n. We focus our attention to 0:p:q resonances. First of all we study the existence/bifurcation of symmetric periodic orbits for such systems. The existence and rigidity of families of homoclinic orbits are also discussed. We also analyze for n = 3 the rigidity of ¿Cantor families¿ of invariant two-torus by means of KAM Theory / Doutorado / Sistemas Dinamicos / Doutor em Matemática