Thesis (Ph. D.)--Catholic University of America, 1927. / Biographical sketch.

Thesis (Ph. D.)--State University of New York at Binghamton, Department of Mathematical Sciences, 2005. / Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2001. / Includes bibliographical references. Also available on the Internet.

Made available in DSpace on 2014-06-11T19:27:09Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-10-09Bitstream added on 2014-06-13T20:55:47Z : No. of bitstreams: 1 castro_rb_me_rcla.pdf: 774630 bytes, checksum: b9499068a589a33827880e026c206fd9 (MD5) / Neste projeto tratamos da Geometria Projetiva advinda da generalização da Geometria Afim do Plano Euclidiano. Estabelecemos um Sistema Axiomático para a Geometria Projetiva e provamos resultados de sustentabilidade para esta geometria, sobretudo resultados sobre Perspectivas e Projeções. Também exploramos Cônicas dentro deste contexto. O principal livro usado como referência deste trabalho foi [1] de Judith Cederberg e como textos auxiliares consultaremos [2] e [3] / This project dealt with the Projective Geometry arising from the generalization of the Affine Geometry of the Euclidean Plane. Established an Axiomatic System for Projective Geometry and prove sustainability outcomes for this geometry, particularly on results Prospects and Projections. We also explored conics within this context

Orientador: Marcos Vieira Teixeira / Resumo: O presente trabalho discorre a respeito de dois textos do arquiteto e matemático francês Girard Desargues. As obras que aqui chamamos de Método de Perspectiva (1636) e Brouillon Project (1639), foram desenvolvidas em um período com ampla produção teórica relacionada a técnicas de representação. No trabalho de 1636 Desargues descreveu o processo necessário para representar uma gaiola em perspectiva. No trabalho, Brouillon Project, ele trata de propriedades geométricas envolvendo feixe de retas aproximando-se dos conceitos existentes no campo das projeções de figuras, contudo parte das referências utilizadas, como Chasles, Poudra, Taton, entre outros, consideraram que o Brouillon Project foi um trabalho relacionado as seções cônicas. Nosso objetivo é apresentar uma análise envolvendo os conteúdos geométricos explorados nas duas obras citadas com o intuito de relacioná-las com o campo da perspectiva e projeção de figuras. Para isso, desenvolvemos uma pesquisa em história da matemática envolvendo história perspectiva, história da geometria, forma de produção do conhecimento daquele período, em conjunto com teorias que estavam sendo produzidas até o séc. XVII / Abstract: The present work deals with two texts of the French architect and mathematician Girard Desargues. The works that we call the Method of Perspective (1636) and Brouillon Project (1639) were developed in a period with a large theoretical production related to representations of figures in perspective. In the work of 1636 Desargues described the process necessary to represent a cage in perspective. At work, Brouillon Project, he dealt with geometric properties involving beam of straight lines approaching the existing concepts in the field of projections of figures. However, some of the references used, such as Chasles, Poudra, Taton, and others, consider that the Brouillon Project was a work related to the conic sections. Our objective is to present a study involving the geometric contents explored in the two works mentioned, seeking to relate them to the field of perspective and projection of figures. For this, we developed a research in history of mathematics involving history, perspective, history of geometry, form of knowledge production of that period, together with theories that were being produced until the century. XVII / Mestre

Orientador: Elíris Cristina Rizziolli / Banca: Grazielle Feliciani Barbosa / Banca: Carina Alves / Resumo: Neste projeto tratamos da Geometria Projetiva advinda da generalização da Geometria Afim do Plano Euclidiano. Estabelecemos um Sistema Axiomático para a Geometria Projetiva e provamos resultados de sustentabilidade para esta geometria, sobretudo resultados sobre Perspectivas e Projeções. Também exploramos Cônicas dentro deste contexto. O principal livro usado como referência deste trabalho foi [1] de Judith Cederberg e como textos auxiliares consultaremos [2] e [3] / Abstract: This project dealt with the Projective Geometry arising from the generalization of the Affine Geometry of the Euclidean Plane. Established an Axiomatic System for Projective Geometry and prove sustainability outcomes for this geometry, particularly on results Prospects and Projections. We also explored conics within this context / Mestre

This thesis is concerned with the theory of invariant bilinear differential pairings on parabolic geometries. It introduces the concept formally with the help of the jet bundle formalism and provides a detailed analysis. More precisely, after introducing the most important notations and definitions, we first of all give an algebraic description for pairings on homogeneous spaces and obtain a first existence theorem. Next, a classification of first order invariant bilinear differential pairings is given under exclusion of certain degenerate cases that are related to the existence of invariant linear differential operators. Furthermore, a concrete formula for a large class of invariant bilinear differential pairings of arbitrary order is given and many examples are computed. The general theory of higher order invariant bilinear differential pairings turns out to be much more intricate and a general construction is only possible under exclusion of finitely many degenerate cases whose significance in general remains elusive (although a result for projective geometry is included). The construction relies on so-called splitting operators examples of which are described for projective geometry, conformal geometry and CR geometry in the last chapter. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1339548 / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2008

Thesis (Ph.D.)--University of Delaware, 2009. / Principal faculty advisor: Gary L. Ebert, Dept. of Mathematical Sciences. Includes bibliographical references.

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

Includes bibliography. / 281 p ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--Dept. of Pure Mathematics, University of Adelaide, 1978