Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-13T11:21:20Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Cid Dias Ferraz Machado - 2014.pdf: 1785087 bytes, checksum: 2f0dd6f0844c3aa992b9eaf248f40ed4 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-13T11:22:09Z (GMT) No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Cid Dias Ferraz Machado - 2014.pdf: 1785087 bytes, checksum: 2f0dd6f0844c3aa992b9eaf248f40ed4 (MD5) / Made available in DSpace on 2015-01-13T11:22:10Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação - Cid Dias Ferraz Machado - 2014.pdf: 1785087 bytes, checksum: 2f0dd6f0844c3aa992b9eaf248f40ed4 (MD5) Previous issue date: 2014-03-07 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this work we present a study of a class of oriented hypersurfaces in hyperbolic space satisfying a special linear relation between the rth mean curvatures which is based on a Walterson Ferreira and Pedro Roitman’s article, where this class is characterized by a harmonic map derived from the two hyperbolic Gauss maps.We also show the relation of such hypersufaces with solutions of the equation Du+kun+2 n􀀀2 = 0, where k 2 f􀀀1;0;1g. / Neste trabalho apresentamos um estudo de uma classe de hipersuperfícies orientadas no espaço hiperbólico satisfazendo uma relação linear especial entre as r-ésimas curvaturas médias, baseado no trabalho de Walterson Ferreira e Pedro Roitman, onde esta classe é caracterizada por uma aplicação harmônica derivada das duas aplicações hiperbólicas de Gauss. Também mostramos a relação de tais hipersuperfícies com as soluções da equação Du+kun+2 n􀀀2 = 0, onde k 2 f􀀀1;0;1g.

Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-06-19T17:00:58Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) dissertação-Thiago Lucas-FINAL.pdf: 424556 bytes, checksum: 504bc5cad61e90dcf5cfc403f099b634 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-06-19T17:01:10Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) dissertação-Thiago Lucas-FINAL.pdf: 424556 bytes, checksum: 504bc5cad61e90dcf5cfc403f099b634 (MD5) / Made available in DSpace on 2018-06-19T17:01:10Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) dissertação-Thiago Lucas-FINAL.pdf: 424556 bytes, checksum: 504bc5cad61e90dcf5cfc403f099b634 (MD5) Previous issue date: 2016-12-14 / In this dissertation we will present a demonstration that a linear Weingarten translation surface in Euclidean space and Lorentz-Minkowski space should have constant mean curvature or constant Gaussian curvature. The work is based on the article "Translation surfaces of linear Weingarten type" Antonio Bueno and Rafael López. / Nesta dissertação apresentaremos uma demonstração de que uma superfície de translação Weingarten linear no espaço euclidiano e no espaço Lorentz- Minkowski deve ter curvatura média constante ou curvatura de Gauss constante. O trabalho é baseado no artigo "Translation surfaces of linear Weingarten type"de Antonio Bueno e Rafael López.

The topic of this thesis is motivated by recent developments in Architectural Geometry, namely Eike Schling’s asymptotic gridshells and progress in solutions for paneling freeform facades. An asymptotic gridshell is fabricated from flat straight lamellas of bendable material such as sheet metal. These strips are then arranged in a grid-like spatial structure, such that the lamellas are orthogonal to a reference surface, which however is not materialized. Differential geometry then tells us that the strips must follow asymptotic curves of that reference surface. The actual construction is simplified if angles at nodes are constant. If that angle is a right angle, one gets minimal surfaces as reference surfaces. If the angle is constant, one obtains negatively curved surfaces with a constant ratio of principal curvatures (CRPC surfaces). Their characteristic parameterizations are equi-angular asymptotic parameterizations. We are also interested in the positively curved CRPC surfaces. Due to the relation between curvatures, they have a one-parameter family of curvature elements, which facilitates cost-effective paneling solutions through mold-reuse. Our approach to positively curved CRPCS surfaces is again based on equi-angular characteristic parameterizations. These characteristic parameterizations are conjugate and symmetric with respect to the principal curvature directions. After a review of the required results from classical surface theory, we first present a derivation of rotational CRPC surfaces. By simple geometric considerations one can find their characteristic parameterizations. In this way we add some new insight to this known class of surfaces. However, it turns out to be very hard to come up with explicit results on non-rotational CRPC surfaces. This is in big contrast to the special case of minimal surfaces which are characterized be the constant principal curvature ratio -1. Due to the difficulties in handling smooth CRPC surfaces, we turn to discrete models in form of constrained quad meshes. The discrete models belong to the area of Discrete Differential Geometry. There, one does not discretize equations from the smooth theory, but fundamental concepts of the theory. We introduce the basic structures needed in this context: asymptotic nets, conjugate nets and principal symmetric nets. The latter are a recent development in discrete differential geometry and characterized by spherical vertex stars. This means that a vertex of the quad mesh and its four connected neighbors lie on a sphere. If that sphere degenerates to a plane at all vertices, one has the classical discrete asymptotic parameterization as an A-net. Several ways to discretize the constant intersection angle are presented. The actual computation of discrete CRPC surfaces is performed with numerical optimization with an appropriately regularized Gauss-Newton algorithm for solving a nonlinear least squares problem. Optimization requires initial configurations. Those can come from the known classes of CRPC surfaces such as rotational surfaces of minimal surfaces. The latter case yields some surprising results on negatively curves CRPC surfaces of nontrivial topology. In general, such discrete models can serve as a guiding line for future research on the theoretical side. This is briefly indicated in the final discussion on future research directions.

On s'intéresse dans cette thèse à l'étude de variables aléatoires sur les groupes de Lie compacts classiques. On donne une déformation du calcul de Weingarten tel qu'il a été introduit par B. Collins et P. Sniady. On fait une étude asymptotique du mouvement brownien sur les groupes de Lie compacts de grande dimension en obtenant des nouveaux résultats de fluctuations. Deux nouveaux objets, que l'on appelle champ maître gaussien planaire et champ maître orienté planaire, sont introduits pour décrire le comportement asymptotique des mesures de Yang-Mills pour des groupes de structure de grande dimension.

Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-23T11:16:42Z No. of bitstreams: 1 arquivototal.pdf: 1343904 bytes, checksum: dfca90c2164204a1513fc4a55eca4527 (MD5) / Made available in DSpace on 2016-03-23T11:16:43Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1343904 bytes, checksum: dfca90c2164204a1513fc4a55eca4527 (MD5) Previous issue date: 2015-05-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Our purpose is to study the geometry of Riemannian immersions in certain semi- Riemannian manifolds. Initially, considering linearWeingarten hypersurfaces immersed in locally symmetric manifolds and, imposing suitable constraints on the scalar curvature, we guarantee that such a hypersurface is either totally umbilical or isometric to a isoparametric hypersurface with two distinct principal curvatures, one of them being simple. In higher codimension, we use a Simons type formula to obtain new characterizations of hyperbolic cylinders through the study of submanifolds having parallel normalized mean curvature vector field in a semi-Riemannian space form. Finally, we investigate the rigidity of complete spacelike hypersurfaces immersed in the steady state space via applications of some maximum principles. / Nos propomos estudar a geometria de imersões Riemannianas em certas variedades semi-Riemannianas. Inicialmente, consideramos hipersuperfícies Weingarten lineares imersas em variedades localmente simétricas e, impondo restrições apropriadas à curvatura escalar, garantimos que uma tal hipersuperfície é totalmente umbílica ou isométrica a uma hipersuperfície isoparamétrica com duas curvaturas principais distintas, sendo uma destas simples. Em codimensão alta, usamos uma fórmula do tipo Simons para obter novas caracterizações de cilindros hiperbólicos a partir do estudo de subvariedades com vetor curvatura média normalizado paralelo em uma forma espacial semi-Riemanniana. Finalmente, investigamos a rigidez de hipersuperfícies tipo-espaço completas imersas no steady state space via aplicações de alguns princípios do máximo.

Made available in DSpace on 2015-05-15T11:46:04Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 816279 bytes, checksum: 28c5081e37dbd539abb463a0ed89b87c (MD5) Previous issue date: 2012-07-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this paper we studied surfaces with constant mean curvature and surfaces with constant Gaussian curvature in the Sol space which are invariant under the action of two one-parameter subgroups of isometries of the ambient space. Furthermore, we classify the surfaces that satisfy a relationship of type k1 = mk2, where k1 and k2 are the principal curvatures of the surface and m ∈ R. / O presente trabalho aborda um estudo das superfícies com curvatura média constante e das superfícies com curvatura Gaussiana constante no espaço Sol que são invariantes sob a ação de dois grupos a 1-parâmetro de isometrias do espaço ambiente. Além disso, classificamos as superfícies que satisfazem uma relação do tipo k1 = mk2, onde k1 e k2 são as curvaturas principais da superfície e m ∈ R.

À son retour en France en 1946, André Breton reçoit avec enthousiasme des pièces de théâtre qui parviennent à renouveler les pratiques dramatiques de l'époque. Ionesco, Schehadé, Gracq, mais aussi Adamov, Arrabal, Audiberti, Limbour, Obaldia, Vian et Weingarten, créent entre 1945 et la fin des années soixante des pièces audacieuses qui ont tout pour séduire le chef de file du surréalisme.Même si la plupart des auteurs n'entretiennent qu'un lien tenu voire inexistant avec le mouvement surréaliste, ils héritent de certaines préoccupations du premier surréalisme par le truchement de dramaturges et théoriciens de théâtre (tels que Artaud et Jarry), de penseurs (philosophes ou psychanalystes) mais aussi de metteurs en scènes. Les vingt pièces étudiées ici questionnent l'existence humaine en analysant tantôt la perception de l'absurdité du monde, l'incapacité à communiquer, tantôt la perte des valeurs et de repères, poussant les personnages à s'interroger sur leur identité, leurs souvenirs et leurs désirs.Au-delà de ces réflexions caractéristiques de la production dramatique de l'après-guerre, les dramaturges de notre corpus explorent de nouvelles voies dramatiques. Les uns proposent un travail linguistique qui vise à retrouver la poésie au sein des conversations quotidiennes. D'autres interrogent les certitudes établies par le biais de l'humour et de l'ironie. Enfin, d'autres encore se tournent vers l'exploration de l'inconscient, des rêves et de la folie. Ces trois démarches nées d'initiatives individuelles des dramaturges s'inscrivent dans une esthétique surréaliste, mais il n'est pas sûr qu'elles suffisent à résumer la diversité des entreprises dramatiques ni à définir a posteriori une nouvelle conception du théâtre surréaliste / When André Breton comes back to France in 1946, he's thrilled with theatre plays which manage to renew the dramatic practices of the time. Between 1945 and the late sixties, Ionesco, Schehadé, Gracq, and also Adamov, Arrabal, Audiberti, Limbour, Obaldia, Vian and Weingarten create daring plays which have everything to allure the leader of surrealism.Even if most authors only have a tenuous or even non-existent link with the surrealist movement, they inherit certain notions of first surrealism through playwrights and theatre theorists - such as Artaud and Jarry-, thinkers -philosophers or psychoanalysts- but also stage directors.The twenty plays studied here question human existence by either analyzing the perception of the nonsense of the world and the incapacity to communicate, or the loss of values and reference markers, leading the characters to wonder about their identities, their memories and their desires. Beyond these reflections characteristic of the dramatic production of the post-war period, the playwrights of our corpus explore new dramatic paths. Some propose a linguistic work which aims at finding poetry within daily conversations. Others question what we take for granted through humour and irony. Finally, others turn to the exploration of one’s unconscious, dreams and madness.These three approaches born of individual initiatives of the playwrights get close to a surrealist aesthetics, but they may not by themselves summarize the diversity of dramatic attempts nor define a posteriori a new idea of surrealist theatre.

On s'intéresse dans cette thèse à l'étude de variables aléatoires sur les groupes de Lie compacts classiques. On donne une déformation du calcul de Weingarten tel qu'il a été introduit par B. Collins et P. Sniady. On fait une étude asymptotique du mouvement brownien sur les groupes de Lie compacts de grande dimension en obtenant des nouveaux résultats de fluctuations. Deux nouveaux objets, que l'on appelle champ maître gaussien planaire et champ maître orienté planaire, sont introduits pour décrire le comportement asymptotique des mesures de Yang-Mills pour des groupes de structure de grande dimension. / In the following text, we are interested in the study of Lie-groups valued random variables. We give a deformation of the Weingarten calculus introduced by Benoît Collins and Piotr Sniady. We study the asymptotic behavior of Brownian motion on compact Lie groups in high dimensions and obtain new fluctuations results. Two new objects called the planar gaussian master field and the planar oriented master field are introduced here to describe the asymptotic behavior of the Yang-Mills measure as the dimension of the structure group is large.

This thesis investigates a technique to estimate the risk of the mean-variance (MV) portfolio optimization problem. We call this technique the Scaling technique. It provides a better estimator of the risk of the MV optimal portfolio. We obtain this result for a general estimator of the covariance matrix of the returns which includes the correlated sampling case as well as the independent sampling case and the exponentially weighted moving average case. This gave rise to the paper, [CMcS]. Our result concerning the Scaling technique relies on the moments of the inverse of compound Wishart matrices. This is an open problem in the theory of random matrices. We actually tackle a much more general setup, where we consider any random matrix provided that its distribution has an appropriate invariance property (orthogonal or unitary) under an appropriate action (by conjugation, or by a left-right action). Our approach is based on Weingarten calculus. As an interesting byproduct of our study - and as a preliminary to the solution of our problem of computing the moments of the inverse of a compound Wishart random matrix, we obtain explicit moment formulas for the pseudo-inverse of Ginibre random matrices. These results are also given in the paper, [CMS]. Using the moments of the inverse of compound Wishart matrices, we obtain asymptotically unbiased estimators of the risk and the weights of the MV portfolio. Finally, we have some numerical results which are part of our future work.

This thesis investigates a technique to estimate the risk of the mean-variance (MV) portfolio optimization problem. We call this technique the Scaling technique. It provides a better estimator of the risk of the MV optimal portfolio. We obtain this result for a general estimator of the covariance matrix of the returns which includes the correlated sampling case as well as the independent sampling case and the exponentially weighted moving average case. This gave rise to the paper, [CMcS]. Our result concerning the Scaling technique relies on the moments of the inverse of compound Wishart matrices. This is an open problem in the theory of random matrices. We actually tackle a much more general setup, where we consider any random matrix provided that its distribution has an appropriate invariance property (orthogonal or unitary) under an appropriate action (by conjugation, or by a left-right action). Our approach is based on Weingarten calculus. As an interesting byproduct of our study - and as a preliminary to the solution of our problem of computing the moments of the inverse of a compound Wishart random matrix, we obtain explicit moment formulas for the pseudo-inverse of Ginibre random matrices. These results are also given in the paper, [CMS]. Using the moments of the inverse of compound Wishart matrices, we obtain asymptotically unbiased estimators of the risk and the weights of the MV portfolio. Finally, we have some numerical results which are part of our future work.