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You searched for subject:(Hodge Decomposition Theorem). Showing records 1 – 2 of 2 total matches.

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1. Sacchetto, Lucas Kaufmann. Fundamentos da geometria complexa: aspectos geométricos, topológicos e analiticos.

Degree: Mestrado, Matemática, 2012, University of São Paulo

Este trabalho tem como objetivo apresentar um estudo detalhado dos fundamentos da Geometria Complexa, ressaltando seus aspectos geométricos, topológicos e analíticos. Começando com materiais preliminares, como resultados básicos sobre funções holomorfas de uma ou mais variáveis e a definição e primeiros exemplos de variedades complexas, passamos a uma introdução à teoria de feixes e sua cohomologia, ferramenta indispensável para o restante do trabalho. Após um estudo sobre fibrados de linha e divisores damos atenção à Geometria de Kähler e alguns de seus resultados centrais, como por exemplo o Teorema da Decomposição de Hodge, o Teorema ``Difícil\'é o Teorema das (1,1)-classes de Lefschetz. Em seguida, nos dedicamos ao estudo dos fibrados vetoriais complexos e sua geometria, abordando os conceitos de conexões, curvatura e Classes de Chern. Terminamos o trabalho descrevendo alguns aspectos da topologia de variedades complexas, como o Teorema dos Hiperplanos de Lefschetz e algumas de suas consequências.

The main goal of this work is to present a detailed study of the foundations of Complex Geometry, highlighting its geometric, topological and analytical aspects. Beginning with a preliminary material, such as the basic results on holomorphic functions in one or more variables and the definition and first examples of a complex manifold, we move on to an introduction to sheaf theory and its cohomology, an essential tool to the rest of the work. After a discussion on divisors and line bundles we turn attention to Kähler Geometry and its central results, such as the Hodge Decomposition Theorem, the Hard Lefschetz Theorem and the Lefschetz Theorem on (1,1)-classes. After that, we study complex vector bundles and its geometry, focusing on the concepts of connections, curvature and Chern classes. Finally, we finish by describing some aspects of the topology of complex manifolds, such as the Lefschetz Hyperplane Theorem and some of its consequences.

Advisors/Committee Members: Gorodski, Claudio.

Subjects/Keywords: Chern Classes; Classes de Chern; Cohomologia de Feixes; Complex Geometry; Geometria Complexa; Hard Lefschetz Theorem; Hodge Decomposition Theorem; Kähler Manifolds; Lefschetz Theorem on (1 1)-classes; Leschetz Hyperplane Theorem.; Sheaf Cohomology; Teorema da Decomposição de Hodge; Teorema das (1 1) -classes de Lefschetz; Teorema dos Hiperplanos de Lefschetz; Teorema ``Difícil'' de Lefschetz; Variedades de Kähler

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Sacchetto, L. K. (2012). Fundamentos da geometria complexa: aspectos geométricos, topológicos e analiticos. (Masters Thesis). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/45/45131/tde-18062012-194224/ ;

Chicago Manual of Style (16th Edition):

Sacchetto, Lucas Kaufmann. “Fundamentos da geometria complexa: aspectos geométricos, topológicos e analiticos.” 2012. Masters Thesis, University of São Paulo. Accessed September 24, 2019. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-18062012-194224/ ;.

MLA Handbook (7th Edition):

Sacchetto, Lucas Kaufmann. “Fundamentos da geometria complexa: aspectos geométricos, topológicos e analiticos.” 2012. Web. 24 Sep 2019.

Vancouver:

Sacchetto LK. Fundamentos da geometria complexa: aspectos geométricos, topológicos e analiticos. [Internet] [Masters thesis]. University of São Paulo; 2012. [cited 2019 Sep 24]. Available from: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-18062012-194224/ ;.

Council of Science Editors:

Sacchetto LK. Fundamentos da geometria complexa: aspectos geométricos, topológicos e analiticos. [Masters Thesis]. University of São Paulo; 2012. Available from: http://www.teses.usp.br/teses/disponiveis/45/45131/tde-18062012-194224/ ;


Université de Montréal

2. Rioux-Lavoie, Damien. Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre .

Degree: 2017, Université de Montréal

L’objectif de ce mémoire est d’introduire une nouvelle méthode smoothed particle hydrodynamics (SPH) implicite purement lagrangienne, pour la résolution des équations de Navier- Stokes incompressibles bidimensionnelles en présence d’une surface libre. Notre schéma de discrétisation est basé sur celui de Kéou Noutcheuwa et Owens [19]. Nous avons traité la surface libre en combinant la méthode multiple boundary tangent (MBT) de Yildiz et al. [43] et les conditions aux limites sur les champs auxiliaires de Yang et Prosperetti [42]. Ce faisant, nous obtenons un schéma de discrétisation d’ordre 𝓞(Δ t 2) et 𝓞(Δ x 2), selon certaines contraintes sur la longueur de lissage h. Dans un premier temps, nous avons testé notre schéma avec un écoulement de Poiseuille bidimensionnel à l’aide duquel nous analysons l’erreur de discrétisation de la méthode SPH. Ensuite, nous avons tenté de simuler un problème d’extrusion newtonien bidimensionnel. Malheureusement, bien que le comportement de la surface libre soit satisfaisant, nous avons rencontré des problèmes numériques sur la singularité à la sortie du moule. Advisors/Committee Members: Owens, Robert Gwyn (advisor).

Subjects/Keywords: Smoothed particle hydrodynamics (SPH); Écoulement incompressible; Méthode de projection; Théorème de décomposition de Helmholtz-Hodge; Méthode lagrangienne; Surface libre; Multiple boundary tangent (MBT); Problème d’extrusion newtonien; Incompressible flow; Projection method; Helmholtz-Hodge decomposition theorem; Lagrangian method; Free surface; Newtonian extrusion problem

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Rioux-Lavoie, D. (2017). Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre . (Thesis). Université de Montréal. Retrieved from http://hdl.handle.net/1866/19377

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Rioux-Lavoie, Damien. “Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre .” 2017. Thesis, Université de Montréal. Accessed September 24, 2019. http://hdl.handle.net/1866/19377.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Rioux-Lavoie, Damien. “Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre .” 2017. Web. 24 Sep 2019.

Vancouver:

Rioux-Lavoie D. Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre . [Internet] [Thesis]. Université de Montréal; 2017. [cited 2019 Sep 24]. Available from: http://hdl.handle.net/1866/19377.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Rioux-Lavoie D. Méthode SPH implicite d’ordre 2 appliquée à des fluides incompressibles munis d’une frontière libre . [Thesis]. Université de Montréal; 2017. Available from: http://hdl.handle.net/1866/19377

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.