From fundamental forms to curvatures and geodesics, differential geometry has many special theorems and applications worth examining. Among these, the Gauss-Bonnet Theorem is one of the well-known theorems in classical differential geometry. It links geometrical and topological properties of a surface. The thesis introduced some basic concepts in differential geometry, explained them with examples, analyzed the Gauss-Bonnet Theorem and presented the proof of the theorem in greater detail. The thesis also considered applications of the Gauss-Bonnet theorem to some special surfaces.

[pt] Neste trabalho são estudados os moduladores delta desenvolvido a partir do conhecimento estatístico disponível sobre o sinal a ser transmitido. Estes moduladores são aqui chamados estruturados. Após uma rápida introdução à modulação delta, são descritos alguns sistemas mais conhecidos. Os sistemas estruturados são então formalmente caracterizados e uma análise teórica é desenvolvida, sendo apontadas as dificuldades analíticas envolvidas. A partir de uma configuração básica proposta por C.L. Song, são desenvolvidas equações gerais diferentes das por ele obtidas. A particularização destas equações para sinais Gauss Markov de primeira Ordem dá origem ao chamado sistema Song modificado. Resultados obtidos a partir da simulação digital do sistema de song, do sistema de Song modificado, e do sistema delta simples, são apresentados. Um processo adaptativo para aumentar a faixa dinâmica é proposto com base nos resultados de simulação. / [en] This work examines delta modulation systems in which statistical knowledge about the signal to be tranmitted is explicitly used in sistem design. These modulators are called here structured delta modulators. After a brief introduction to delta modulation some well-known systems are described. Structured systems are then formally defined and analytical difficulties in finding general solutions are pointed out. Starting from a system proposed by C.L. Song, general equations are derived. These equations, which are more complete than the ones obtained by Song are then specialized to first-order Gauss-Maarkov signals, leading to what has been called a modified Song modulators. Digital simulations results are then obtained for song modulators, modified Song modulators and linear delta modulators. An adptive producedure is finally suggested to improve the dynamic range of these systems.

Reproduction de : Thèse de doctorat : Mathématiques : Faculté des sciences de Paris : 1868. / Titre provenant de la page de titre du document numérisé.

Habilitationsschrift, Bonn, 1971; extra t.p. inserted. / Includes bibliographical references (p. [92-93]).

Habilitationsschrift, Bonn, 1971; extra t.p. inserted. / Includes bibliographical references (p. [92-93]).

University, Diss., 2007--Bonn.

En este artículo describimos exhaustivamente las superficies de traslación con curvatura gaussiana intrínseca K constante en el espacio hiperbólico H³. Al igual que las superficies de traslación en el espacio euclidiano, que son los cilindros generalizados, estas superficies son generadas por curvas planas, pasando por cada punto de la curva generatriz una curva equidistante de la geodésica invariante que es ortogonal al plano totalmente geodésico que contiene la curva. En el espacio euclidiano todas las superficies de este tipo poseen K=O. En el espacio hiperbólico existe amplia variedad de superficies con K ≠O y, en general, para casi todos los valores de K no se obtienen superficies completas. Una excepción notable aparece cuando -1≤ K < O. Indagamos también el comportamiento de estas superficies en el borde ∂∞H³ ofrecemos gráficos elaborados en computador para la mayoría de los ejemplos hallados.

Les grilles de calcul et les grille de PC sur Internet offrent des alternatives intéressantes pour le calcul scientifique à grande échelle, qui demande des ressources de calcul importantes. Toutefois, l’adaptation des applications pour ces systèmes est difficile à cause des facteurs nombreux tels que l'interface complexe de programmation. L'objectif de cette thèse est de trouver une solution pour faciliter le calcul scientifique à grande échelle. Pour ce faire, j’ai travaillé sur l’algorithme de Gauss Jordan et une nouvelle version d’un schéma de parallélisme. Ce schéma peut exploiter le maximum de parallélisme entre des opérations. Comme un exemple excellent, l'algorithme de Gauss Jordan est également utilisé pour évaluer des environnements expérimentaux et des outils différents. Les expérimentations avec YML, OmniRPC et XtremWeb sur les grilles et les grilles de PC montrent que YML peut être une bonne solution pour que les utilisateurs fassent du calcul scientifique à grande échelle, à cause des bonnes caractéristiques comme « l’interface d'abstraction de haut niveau», « les composants réutilisables » et «le surcoût acceptable». Pour obtenir les meilleures performances de cette plate-forme, les questions concernées, telles que la granularité des tâches, la persistance des données et le mécanisme d’ordonnancement, sont également abordés dans cette thèse. Selon les analyses faites ci-dessus et les caractéristiques communes des nuages informatiques ciblés, YML-PC, une architecture de référence basée sur les workflows pour les constructions de nuages informatiques privés scientifique est proposée. YML-PC hérite les bonnes caractéristiques présentées ci-dessus et des autres technologies clefs telles que « la persistance des données », « La prévision du temps disponible »  et « l'évaluation sur des nœuds de calcul hétérogènes » pour YML-PC, qui sont également abordées dans cette thèse. Les évaluations sur l'algorithme de Gauss Jordan sont réalisées sur les grilles, les grilles de PC et les nuages informatiques privés qui sont implantés sur la plate-forme Grid5000, la plateforme de calcul de Polytech Lille en France et la plateforme de calcul de Hohai, en Chine. / Grid computing and Desktop Grid computing provide interesting alternatives for large scale scientific computing which needs very large scale computing resources. However gridification is hard to develop because of series of factors such as complex programming interface. The aim of this dissertation is to find a solution to make large scientific computing in an easy way. To do that, research on Gauss Jordan algorithm is made and a new parallel programming version is presented. The parallel version can achieve maximum degree parallelism between operations. Also the Gauss Jordan algorithm as an excellent example is used to evaluate different experimental environments and tools. Experiments with YML, OmniRPC and XtremWeb on Grid and Desktop Grid environments testify YML can be a good solution for end users to make large scale scientific computing for its series of good features such as higher level interface, component reuse and acceptable overhead. To get better performance of platform, related issues such as task granularity, data persistence and schedule mechanism are also discussed in this dissertation. According to analysis made above and the common features of Clouds possessed, YML-PC a reference architecture based on workflow for building scientific Private Clouds is proposed. YML-PC inherits those good features presented above and some other key technologies such as “data persistence”, “available time prediction” and “evaluation on heterogeneous computing nodes” for YML-PC are also discussed in this dissertation. Evaluations are made based on Gauss Jordan algorithm on Grids, Desktop Grids and Private Clouds which build on Grid5000, Polytech Lille platform, France and Hohai platform, China.

No description available.

In this paper we study the Gauss map of minimal surfaces in the Heisenberg group, H₃. We obtain a representation formula for minimal surfaces in H₃ by means of the Gauss map. As consequence we conclude that: The Gauss map of a minimal surface of H₃ is antiholomorphic if the minimal surface is a plane.