Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2016-08-24T17:57:59Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertaçãosuper_final_(1).pdf: 1088878 bytes, checksum: f1d95f7419b99281751c7ea750e47cf8 (MD5) / Made available in DSpace on 2016-08-24T17:57:59Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertaçãosuper_final_(1).pdf: 1088878 bytes, checksum: f1d95f7419b99281751c7ea750e47cf8 (MD5) Previous issue date: 2011-08-31 / CAPES / Nesta dissertação é apresentada uma solução estacionária para um modelo de dinâmica populacional de uma única espécie, considerando a dispersão da população num espaço heterogêneo e um crescimento logístico da população. No primeiro capítulo, para dar ao leitor alguma intimidade com os conceitos apresentados estudamos alguns modelos de dinâmica populacional de uma única espécie. Referimo-nos a uma única população para dizer que não analisamos aqui a interação entre diversas espécies. No segundo capítulo concentra-se a parte substancial do nosso trabalho. Na seção 1 apresentamos o modelo, na seção 2 apresentamos a solução estacionária para o problema e na seção 3 fazemos uma discussão sobre efeitos de isolamento para uma população. / This thesis presents a stationary solution to a model of population dynamics of a single species, considering the dispersion of biological population in a heterogeneous space and a logistic population growth. In the rst chapter, to give the reader some familiarity with the concepts presented study some models of population dynamics of a single species. We refer to a single population to say we do not analyze the interaction between di erent species. The second chapter focuses on the substantial part of our work. In Section 1 presents the problem and the model, section 2 presents the stationary solution to the problem and in Section 3 we make a discussion about isolation e ects on a population

La classification spectrale consiste à créer, à partir des éléments spectraux d'une matrice d'affinité gaussienne, un espace de dimension réduite dans lequel les données sont regroupées en classes. Cette méthode non supervisée est principalement basée sur la mesure d'affinité gaussienne, son paramètre et ses éléments spectraux. Cependant, les questions sur la séparabilité des classes dans l'espace de projection spectral et sur le choix du paramètre restent ouvertes. Dans un premier temps, le rôle du paramètre de l'affinité gaussienne sera étudié à travers des mesures de qualités et deux heuristiques pour le choix de ce paramètre seront proposées puis testées. Ensuite, le fonctionnement même de la méthode est étudié à travers les éléments spectraux de la matrice d'affinité gaussienne. En interprétant cette matrice comme la discrétisation du noyau de la chaleur définie sur l'espace entier et en utilisant les éléments finis, les vecteurs propres de la matrice affinité sont la représentation asymptotique de fonctions dont le support est inclus dans une seule composante connexe. Ces résultats permettent de définir des propriétés de classification et des conditions sur le paramètre gaussien. A partir de ces éléments théoriques, deux stratégies de parallélisation par décomposition en sous-domaines sont formulées et testées sur des exemples géométriques et de traitement d'images. Enfin dans le cadre non supervisé, le classification spectrale est appliquée, d'une part, dans le domaine de la génomique pour déterminer différents profils d'expression de gènes d'une légumineuse et, d'autre part dans le domaine de l'imagerie fonctionnelle TEP, pour segmenter des régions du cerveau présentant les mêmes courbes d'activités temporelles. / The Spectral Clustering consists in creating, from the spectral elements of a Gaussian affinity matrix, a low-dimension space in which data are grouped into clusters. This unsupervised method is mainly based on Gaussian affinity measure, its parameter and its spectral elements. However, questions about the separability of clusters in the projection space and the spectral parameter choices remain open. First, the rule of the parameter of Gaussian affinity will be investigated through quality measures and two heuristics for choosing this setting will be proposed and tested. Then, the method is studied through the spectral element of the Gaussian affinity matrix. By interpreting this matrix as the discretization of the heat kernel defined on the whole space and using finite elements, the eigenvectors of the affinity matrix are asymptotic representation of functions whose support is included in one connected component. These results help define the properties of clustering and conditions on the Gaussian parameter. From these theoretical elements, two parallelization strategies by decomposition into sub-domains are formulated and tested on geometrical examples and images. Finally, as unsupervised applications, the spectral clustering is applied, first in the field of genomics to identify different gene expression profiles of a legume and the other in the imaging field functional PET, to segment the brain regions with similar time-activity curves.

Orientador: Germán Jesus Lozada Cruz / Banca: Marcos Roberto Teixeira Primo / Banca: Andréa Cristina Prokopezyk Arita / Resumo: Neste trabalho vamos estudar a existência e unicidade de solução para equações da forma { u + Au = f(t,u) u(t0)= u0 ∈ X, (I) onde X é um espaço de Banach, A : D(A) ⊂ X → X é um operador linear, f é uma função não linear conhecida, u0 ∈ X é um dado inical conhecido e u : I ⊂ R → X é uma função desconhecida e t0 ∈ I. Faremos este estudo usando a Teoria dos Semigrupos de Operadores Lineares. Para melhor entendimento do estudo das equações (I), faremos duas aplicações. A primeira tratando de um modelo (linear) de divisão celular e a segunda, do modelo (não linear) de condução do calor. / Abstract: In this work we will study the existence and uniqueness of the solutions for the following equation { u + Au = f(t,u) u(t0)= u0 ∈ X, (I) where X is a Banach space, A : D(A) ⊂ X → X is a linear operator, f is a nonlinear function, u : I ⊂ R → X is unknown function. In this study we will use the theory of semigroup of linear operators. For a best understanding of the study of equations (I), we will do two applications. The first one, is a (linear) model of cellular division and the second one, is about the (nonlinear) model od conduction of the heat. / Mestre

Cette thèse porte sur l’étude d’équations d’évolution sur certains groupes hyperboliques, en particulier, nous étudions l’équation de la chaleur, l’équation de Schrödinger et l’équation des ondes modifiée, d’abord sur les arbres homogènes, ensuite sur des graphes symétriques. Sur les arbres homogènes, nous montrons que, sous une hypothèse d’invariance de jauge, on a existence globale des solutions de l’équation de Schrödinger ainsi qu’un phénomène de ’scattering’ pour des données arbitraires dans l’espace des fonctions de carré intégrable sans restriction sur le degré de la non-linéarité, contrairement au cas euclidien ou au cas hyperbolique. Nous généralisons ensuite ce résultat sur les graphes symétriques de degré (k − 1)(r − 1) sous la condition k < r. Un de nos principaux résultats sur les graphes symétriques est l’estimation du noyau de la chaleur associé au laplacien combinatoire. Pour finir, nous établissons une expression explicite des solutions de l’équation des ondes modifiée sur les graphes symétriques. / This thesis focuses on the study of evolution equations on certain hyperbolic groups, in particular, we study the heat equation, the Schrödinger equation and the modified wave equation first on homogeneous trees then on symmetric graphs. In the homogeneous trees case, we show that under a gauge invariance condition, we have global existence of solutions of the Schrödinger equation and scattering for arbitrary data in the space of square integrable functions without any restriction on the degree of the nonlinearity, in contrast to the euclidean and hyperbolic space cases. We then generalize this result on symmetric graphs of degree (k − 1)(r − 1) under the condition k < r . One of our main results on symmetric graphs is the estimate of the heat kernel associated to the combinatorial laplacian. Finally, we establish an explicit expression of solutions of the modified wave equation on symmetric graphs.

Submitted by HERACLIO LEDGAR LÓPEZ LÁZARO null (herack_11@hotmail.com) on 2016-03-21T12:48:28Z No. of bitstreams: 1 Heracliodissertação.pdf: 1074830 bytes, checksum: eacc291c2e8f474bef30477ea2c47a2f (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-03-22T14:20:35Z (GMT) No. of bitstreams: 1 lazaro_hll_me_sjrp.pdf: 1074830 bytes, checksum: eacc291c2e8f474bef30477ea2c47a2f (MD5) / Made available in DSpace on 2016-03-22T14:20:35Z (GMT). No. of bitstreams: 1 lazaro_hll_me_sjrp.pdf: 1074830 bytes, checksum: eacc291c2e8f474bef30477ea2c47a2f (MD5) Previous issue date: 2016-03-07 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / The problem that we are going to study in this work, is motivated by the dynamics of differential equations nonautonomous. We will establish the existence and uniqueness of solution for a class of parabolic semilineares equations with Dirichlet boundary condition, in a family of domains that varies with time. In addition, certain hypotheses about the non-linearity, we will show the existence of a family of attractors pullback. / O problema que vamos estudar neste trabalho é motivado pela dinâmica de equações diferenciais não autônomas. Vamos estabelecer a existência e unicidade de solução para uma classe de equaçõoes parabólicas semilineares com condição de fronteira de Dirichlet, em uma família de domínios que varia com o tempo. Além disso, sob certas hipóteses sobre a não linearidade, mostraremos a existência de uma família de atratores pullback.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this dissertation, we will use the techniques established in [2] to analyze the existence and uniqueness of classical solution to the nonlinear heat equation in ; provided u0 2 Lq() with some conditions on 1 q 1, where RN is a smooth bounded domain and p > 1. / Nesta dissertação, vamos utilizar as técnicas vistas em [2] para analisar a existência e unicidade de solução clássica para a equação do calor não-linear quando uo E Lq com algumas condições sobre 1<q<, onde RN é um domínio limitado suave e p>1.

Orientador: Lucas Catão de Freitas Ferreira / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-24T06:33:09Z (GMT). No. of bitstreams: 1 Mesquita_ClaudiaAlineAzevedodosSantos_D.pdf: 1141685 bytes, checksum: a65a24d1917c5f998314d01970bb86e3 (MD5) Previous issue date: 2013 / Resumo: Nesta tese, estudamos dois tipos de EDPs com potenciais singulares críticos, a saber, uma equação elíptica com operador poliharmônico e a equação do calor linear. Para a primeira, pesquisamos existência e propriedades qualitativas das soluções no espaço $\mathcal{H}_{k,\vec{\alpha}}$ que é uma soma de espaços $L^{\infty}$ com peso, o qual parece ser um espaço mínimo para o tipo de potencial singular considerado. Investigamos um conceito de simetria para soluções que estende o de simetria radial e satisfaz uma ideia de invariância em torno das singularidades. Para a segunda, uma estratégia baseada na transformada de Fourier é empregada para obter resultados de boa-colocação global e comportamento assintótico de soluções, sem hipóteses de pequenez e sem utilizar a desigualdade de Hardy. Em particular, obtemos boa-colocação de soluções para o caso do potencial monopolar $V(x)=\frac{\lambda}{\left\vert x\right\vert ^{2}}$ com $\left\vert \lambda\right\vert <\lambda_{\ast}=\frac{(n-2)^{2}}{4}$. Este valor limiar é o mesmo obtido em resultados de boa-colocação global em $L^2$ que utilizam desigualdades de Hardy e estimativas de energia. Desde que não existe uma relação de inclusão entre $L^{2}$ e $PM^{k}$, nossos resultados indicam que $\lambda_{\ast}$ é intrínseco da EDP e independe de uma particular abordagem. Palavras-chave: Equações elípticas, equação do calor, potencial singular, existência, simetria, autossimilaridade, comportamento assintótico / Abstract: In this thesis, we study two types of PDEs with critical singular potentials, namely, an elliptic equation with polyharmonic operator and the linear heat equation. For the first, we obtain existence and qualitative properties of solutions in $\mathcal{H}_{k,\vec{\alpha}}$-spaces which are a sum of weighted $L^{\infty}$-spaces, and seem to be a minimal framework for the potential profile of interest. We investigate a concept of symmetry for solutions which extends radial symmetry and carries out an idea of invariance around singularities. For the second, a strategy based on the Fourier transform is employed to obtain results of global well-posedness and asymptotic behavior of solutions, without smallness hypotheses and without using Hardy inequality. In particular, well-posedness of solutions is obtained for the case of the monopolar potential $V(x)=\frac{\lambda}{\left\vert x\right\vert ^{2}}$ with $\left\vert \lambda\right\vert <\lambda_{\ast}=\frac{(n-2)^{2}}{4}$. This threshold value is the same one obtained for the global well-posedness of $L^{2}$-solutions by means of Hardy inequalities and energy estimates. Since there is no inclusion relation between $L^{2}$ and $PM^{k}$, our results indicate that $\lambda_{\ast}$ is intrinsic of the PDE and independent of a particular approach. Keywords: Elliptic equation, heat equation, singular potential, existence, symmetry, self-similarity, asymptotic behavior / Doutorado / Matematica / Doutora em Matemática

L’objectif de cette thèse est de proposer deux approches complémentaires de modélisation et de simulation numériques des procédés de mise en forme de structures minces. La première est une approche inverse multi-pas, délibérément simplifiée, pour simuler et "optimiser" rapidement et à moindre coût des procédés d’emboutissage de tôles minces, tout en maintenant une bonne précision dans le calcul des contraintes. Un solveur statique implicite est développé en introduisant plusieurs configurations intermédiaires construites efficacement en utilisant une technique de programmation quadratique avec projection. La deuxième approche, de nature incrémentale, repose sur (i) une formulation d’équations de bilan et d’équations de comportement multi-physiques fortement couplés formulées dans le cadre des milieux micromorphes ; (ii) une discrétisation spatiale par EF et temporelle par DF avec un solveur global dynamique explicite et une intégration locale itérative implicite. Une attention particulière est accordée aux aspects thermiques avec l’introduction d’une microtempérature et ses premiers gradients conduisant à l’obtention de deux équations thermiques fortement couplées généralisant de nombreux modèles non locaux proposés dans la littérature. L'approche inverse multi-pas a été implémentée dans le code maison KMAS et l’approche incrémentale non locale a été implémentée dans ABAQUS/Explicit. Des études paramétriques sont menées et des validations sur des exemples simples et sur des procédés d’emboutissage sont réalisées / The aim of this thesis is to propose two complementary approaches for modeling and numerical simulations of thin sheet metal forming processes. The first one is a deliberately simplified multi-step inverse approach to simulate and "optimize" rapidly and inexpensively thin-sheet stamping processes while maintaining good accuracy in the stress calculation. An implicit static solver is developed by introducing several efficiently constructed intermediate configurations using a quadratic programming technique with projection. The second approach, which is of an incremental nature, is based on (i) a formulation of equilibrium equations and strongly coupled multiphysical behavior equations formulated in the context of micromorphic continua; (ii) spatial discretization by FEM and time discretization by FD with an explicit dynamic global solver and implicit iterative local integration scheme. Particular attention is paid to the nonlocal thermal aspects with the introduction of a micro-temperature and its first gradients leading to two strongly coupled thermal equations generalizing several thermal nonlocal models proposed in the literature. The multi-step inverse approach was implemented in the KMAS in house code while the nonlocal incremental approach was implemented in ABAQUS/Explicit. Parametric studies are performed and validations are carried out on simple examples and on deep drawing processes

We employ two efficient parallel approaches to reduce a model arising from a semi-discretization of a controlled heat transfer process for optimal cooling of a steel profile. Both algorithms are based on balanced truncation but differ in the numerical method that is used to solve two dual generalized Lyapunov equations, which is the major computational task. Experimental results on a cluster of Intel Xeon processors compare the efficacy of the parallel model reduction algorithms.

This study focuses on the numerical solution of a fourth-order cell problem obtained through a two- scale expansion approach applied to a higher gradient heat equation microscopic problem involving temperature distributions. The main objective is to investigate the temperature field within the macroscale domain and compute the effective conductivity using finite element methods. The research utilizes numerical techniques, specifically finite element methods, to solve the fourth-order cell problem and obtain the temperature distribution.