Thesis (Ph. D.)--University of Adelaide, Dept. of Pure Mathematics. 1985. / Includes bibliographical references (leaves 225-227).

Thesis (Ph. D.)--University of Adelaide, Dept. of Pure Mathematics, 1992. / Includes bibliographical references (leaves 185-195).

Bibliography: leaves 185-195 / 195 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics, 1992

Bibliography: leaves 225-227 / v, 227, 37 leaves : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Pure Mathematics. 1985

<p> We look at methods to generate uniformly distributed points from the classical matrix groups, spheres, projective spaces, and Grassmannians. We motivate the discussion with a number of applications ranging from number theory to wireless communications. The uniformity of the samples and the efficiency of the algorithms are compared. </p> / Thesis / Master of Science (MSc)

This dissertation demonstrates a procedure to view any quasitoric manifold as a “minimal” sub-manifold of an ambient quasitoric manifold of codimension two via the wedge construction applied to the quotient polytope. These we term wedge quasitoric manifolds. We prove existence utilizing a construction on the quotient polytope and characteristic matrix and demonstrate conditions allowing the base manifold to be viewed as dual to the first Chern class of the wedge manifold. Such dualization allows calculations of KO characteristic classes as in the work of Ochanine and Fast. We also examine the Todd genus as it relates to two types of wedge quasitoric manifolds. Background matter on polytopes and toric topology, as well as spin and complex cobordism are provided.

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (leaf [106]).

We present (without proof) a version of Bott theorem for compact complex orbifolds with isolated singularities. Then we deduce some important consequences of this theorem, and nally we give some applications to holomorphic foliations on weighted projective spaces. / Presentamos (sin demostración) una versión del teorema de Bott para un orbifold complejo compacto y con singularidades aisladas. A continuación deducimos algunas consecuencias importantes de este teorema, y finalmente daremos algunas aplicaciones para foliaciones holomorfas en espacios proyectivos ponderados.

Orientador: Clésio Luis Tozzi / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-20T02:20:27Z (GMT). No. of bitstreams: 1 Gomes_MarceloMarques_M.pdf: 2920969 bytes, checksum: 0ae0c041b47241b92c32e9792f18d608 (MD5) Previous issue date: 2012 / Resumo: Este trabalho aborda a solução para o problema da recuperação da informação tridimensional somente a partir de imagens da cena ou do objeto que se deseja modelar desconhecidas as informações a respeito das câmeras utilizadas. A solução apresentada divide-se em duas partes: na primeira se estabelece a relação entre pares ou trios de câmeras utilizando matriz fundamental ou tensor trifocal, respectivamente e a partir dessas relações obtém-se por meio de triangulação uma reconstrução tridimensional da cena ou do objeto observado em função de uma transformação projetiva arbitrária. Na segunda parte determina-se uma transformação que leva a cena ou o objeto obtidos no espaço projetivo para o espaço métrico. Essa transformação que leva o objeto recuperado no espaço projetivo para o espaço métrico é encontrada por meio de autocalibração utilizando o plano no infinito e a cônica absoluta que apresentam a propriedade de serem invariantes a rotação, translação e escala, em relação a um referencial escolhido arbitrariamente. Dependendo do número de imagens disponíveis é necessário inserir restrições nos parâmetros intrínsecos das câmeras para viabilizar o cálculo da transformação. Essas restrições são inseridas na forma de suposições a respeito dos parâmetros intrínsecos das câmeras, como pontos principais conhecidos ou constantes entre as câmeras, skew nulo, relação de aspecto unitária etc. Os resultados da reconstrução no espaço projetivo obtidos com o uso da matriz fundamental e do tensor trifocal foram comparados em relação ao erro de reconstrução utilizando protótipo implementado em Matlab e imagens sintéticas. A solução geral foi avaliada em relação ao erro de reprojeção, reconstrução no espaço métrico com base em imagens sintéticas e imagens reais de objetos conhecidos, utilizando um protótipo desenvolvido na plataforma Embarcadero Delphi / Abstract: This work addresses a solution to the problem of recovering three-dimensional information from images of a scene or modeled object based only on images and without any information of the cameras parameters. The presented solution is divided in two parts: in the first part it is established the relationship between a pair or a triple of cameras using the fundamental matrix or trifocal tensor, respectively, and obtained by triangulation a three-dimensional reconstruction of the observed scene or object in function of an arbitrary projective transformation. In the second part it is determined a transformation to covert the obtained scene or object reconstruction from the projective space to the metric space. This transformation is found by auto-calibration using the plane at infinity and the absolute conic which have the property of being invariant to rotation, translation and scale in relation to an arbitrarily chosen reference frame. According to the number of available images, restrictions on the intrinsic parameters may be necessary in order to obtain a valid transformation. These restrictions are inserted in the form of assumptions about the values of the intrinsic parameters of the cameras or relations between then, like known principal points or constant values for the cameras, zero skew, unit aspect ratio and so on. Using synthetic images and a prototype implemented in Matlab, the results of reconstruction in projective space based on the fundamental matrix and trifocal tensor were compared in relation to the error of reconstruction. Based on synthetic images and real images of known objects and a prototype developed in the Embarcadero Delphi platform, the general solution was evaluated in relation to the reprojection error and the error of reconstruction in the metric space / Mestrado / Engenharia de Computação / Mestre em Engenharia Elétrica

Der Laplace-Operator auf kompakten Riemannschen Mannigfaltigkeiten besitzt eine natürliche Verallgemeinerung auf kompakte Riemannsche Orbifolds und das Spektrum des so gewonnenen Operators besteht ausschließlich aus Eigenwerten endlicher Vielfachheit. Die Feststellung, dass das Spektrum Informationen über die Geometrie einer Mannigfaltigkeit (oder, allgemeiner, einer Orbifold) enthält, begründete ein ganzes Teilgebiet der Mathematik. Es ist eine offene Frage der sogenannten Spektralgeometrie, ob eine Mannigfaltigkeit und eine singuläre Orbifold isospektral sein (d.h., dasselbe Spektrum mitsamt den Vielfachheiten der Eigenwerte besitzen) können. Angesichts diverser Obstruktionen zur Existenz eines solchen Beispiels für die bekannten Beispiele isospektraler guter Orbifolds, soll diese Arbeit die Spektralgeometrie schlechter Orbifolds erhellen. Zu diesem Zweck geben wir die ersten Beispiele für isospektrale Metriken auf schlechten Orbifolds an. Diese basieren auf bestimmten gewichteten projektiven Räumen, auf denen wir mittels einer Verallgemeinerung von Schüths Version der Torus-Methode nicht-trivial isospektrale Metriken konstruieren. / The Laplace Operator on compact Riemannian manifolds naturally generalizes to compact Riemannian orbifolds and the spectrum of the resulting operator consists only of eigenvalues with finite multiplicities. The observation that the spectrum contains information about the geometry of a manifold (and, more generally, an orbifold) gave rise to a whole field of mathematics. It is an open question of so-called spectral geometry, whether a manifold and a singular orbifold can be isospectral (i.e., have the same spectrum with the same multiplicities of the eigenvalues). Given the various obstructions to the existence of such an example for the known examples of isospectral good orbifolds, this work is an attempt to shed light on the spectral geometry of bad orbifolds by giving the first examples of isospectral Riemannian metrics on bad orbifolds. In our case these are particular fixed weighted projective spaces equipped with non-trivially isospectral metrics obtained by a generalization of Schüth''s version of the torus method.