This dissertation supplies the methodology of the measure (area) in the Earth model adopted for Geodesy. This model is the ellipsoid of revolution, in which the system of Cartesian coordinates, the curvilinear coordinate system and the polar coordinate system are described. The coordinate nature in the development of the surface measure calculation is discussed. The following demonstrations are illustrated: the ellipse equation, the eccentricity of the ellipse, the meridian section curvature radius equation, the meridian transversal section curvature radius equation and elliptic integral. It define algebraic geodesic line and geometrically. The juridical basis are the article 3º of Brazilian Federal Law 10.267/2001, which modify article 176 of the Brazilian Federal Law 6.015/1973 (Public Record Law) and adds to this article the paragraphs 3º and 4º, the paragraph 3º of article 225 of the Brazilian Law 6.015/1973 and the article 971 of the Código de Processo Civil (CPC), which require the coordinates of the corners of the real property on the Brazilian Geodetic System (SGB). The partitioning of the regular ellipsoid quadrilateral and the partitioning of the irregular ellipsoid quadrilateral located in the real property Pó de Serra is presented. To become this partitioning, it was used surface of the Lambert azimuthal equal-area projection, i. e., the curvilinear geodetic coordinates in plane coordinates has been transformed. The surface partitioning was determined using the method area equation of the Gauss trapezes connected with the equation of the straight line. The direct problem of the Lambert azimuthal equal-area projection and the inverse problem supply the methodology that become feasible the juridical exigence (articles 176 and 225 of Brazilian Federal Law 6.015/1973 and article 971 of the CPC). The methodology to the geodetic coordinates system with the purpose to calculate the partitioned areas of surface on the ellipsoid can be applied. The calculation of surface measure supplies the effective practice of the mencioned juridical basis. / O propósito deste trabalho é fornecer os fundamentos de cálculo de medida de superfície (área) no modelo de Terra adotado pela Geodésia. Esse modelo é o elipsóide de revolução ao qual se vincula o sistema de coordenadas cartesianas, o sistema de coordenadas curvilíneas e o sistema de coordenadas polares. Discute a natureza das coordenadas no desenvolvimento do cálculo da medida de superfície. Efetuam-se as seguintes demonstrações: equação da elipse, equação da excentricidade da elipse, equação do raio de curvatura da seção meridiana, equação do raio de curvatura da seção transversal meridiana e integral elíptica. Define linha geodésica algébrica e geometricamente. Apresentam-se os instrumentos legais que são o artigo 3º da Lei 10.267/2001, o qual altera o artigo 176, inciso II da Lei 6.015/1973 (Lei de Registros Públicos) e acrescenta a este artigo os parágrafos 3º e 4º, o parágrafo 3º do artigo 225 da Lei 6.015/1973 e o artigo 971 do Código de Processo Civil (CPC), os quais vinculam as coordenadas dos vértices do imóvel ao Sistema Geodésico Brasileiro (SGB). Efetuam-se a divisão do quadrilátero elipsóidico regular e também do quadrilátero elipsóidico irregular localizado na gleba Pó de Serra. Para se fazer esta divisão, usou-se a superfície da projeção azimutal equivalente de Lambert, ou seja, as coordenadas elipsóidicas curvilíneas foram transformadas em coordenadas planas desse sistema de projeção. A divisão destas superfícies foi efetuada pelo método da equação da área dos trapézios de Gauss em conjunto com a equação da reta. Os problemas direto e inverso da projeção azimutal equivalente de Lambert fornecem a metodologia que tornam exeqüíveis os dispositivos legais (artigos 176 e 225 da Lei 6.015/1973 e artigo 971 do CPC). A metodologia de cálculo proposto pode ser aplicada ao sistema de coordenadas geodésicas com a finalidade de calcular as áreas de uma divisão de superfície no elipsóide. Os fundamentos do cálculo de medida de superfície instrumentalizam o efetivo cumprimento dos dispositivos legais retrocitados.

Inspiré par l'algèbre d’échange et birapport de rang n introduit par F. Labourie, nous construisons un anneau muni de la structure de Poisson--- l’algèbre d’échangée de rang n Zn(P) pour étudier les espaces de modules de birapports . Nous prouvons que Zn(P) hérite d'une structure de Poisson provenant de l’algèbre d’échangée. Pour tenir compte des “birapports” dans l’anneau de fraction, en interprétant Zn(P) par un modèle géométrique dans l'étude de la géométrie théorie des invariants, nous montrons que Zn(P) est intègre. Ensuite, nous considérons l'anneau Bn(P) engendreré par les birapports dans l'anneau de fraction de Zn(P). Pour n = 2,3, nous trouvons un homomorphisme injectif poissonienne de l'anneau engendré par coordonnées de Fock-Goncharovde sur l'espace des configurations de drapeaux dans Rn vers Bn(P). En étudiant le système intégrable discret pour l'espace des configurations de polygones N-tordus dans RP1, à une transformation de Fourier discrète, nous rapportons asymptotiquement l'algèbre d’échangée à l'algèbre de Virasoro sur une hypersurface de MN, 1. / Inspired by the swapping algebra and the rank n cross-ratio introduced by F. Labourie, we construct a ring equipped with the swapping Poisson structure---the rank n swapping algebra Zn(P) to study the moduli spaces of cross ratios. We prove that Zn(P) inherits a Poisson structure form the swapping bracket. To consider the "cross-ratios" in the fraction ring, by interpreting Zn(P) by a geometric model in the study of geometry invariant theory, we prove that Zn(P) is an integral domain. Then we consider the ring Bn(P) generated by the cross ratios in the fraction ring of Zn(P). For n = 2,3, we embed in a Poisson way the ring generated by Fock-Goncharov coordinates for configuration space of flags in Rn into Bn(P). By studying the discrete integrable system for the configuration space MN,1 of N-twisted polygons in RP1, up to a discrete Fourier transformation, we asymptotically relate the swapping algebra to the Virasoro algebra on a hypersurface of MN,1.

Nesta disertação estudamos algumas ferramentas básicas relacionadas aos espaços de Teichmüller. Introduzimos o espaço de Teichmüller de gênero g ≥ 1, denotado por Tg. O objetivo principal é construir as coordenadas de Fenchel-Nielsen ωG : Tg → R3g-3+ × R3g-3 para cada grafo trivalente marcado G. / In this dissertation we study some basic tools related to Teichmüller space. We introduce the Teichmüller space of genus g ≥ 1, denoted by Tg. The main goal is to construct the Fenchel-Nielsen coordinates ωG : Tg → R3g-3+ × R3g-3 to each marked cubic graph G.

Made available in DSpace on 2017-07-24T19:38:06Z (GMT). No. of bitstreams: 1 Renata Olegario.pdf: 5279781 bytes, checksum: 47c1e5b7166f5caec9a3a371cfe659e3 (MD5) Previous issue date: 2012-03-02 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / This study focused on the Cerium oxide (CeO2) based pigmenting systems, doped with Praseodymium oxide (Pr6O11) and hematite (Fe2O3 – iron oxide) synthesized through the solid state reaction (OM – oxide mixture) and the Pechini method. Simultaneously, CeO2-Pr6O11-Fe2O3 ternary system pigments were synthesized through OM, with the addition of mineralizers. The samples synthesized through OM were wet homogeneized, in isopropyl alcohol, in a horizontal ball mill for 18 hours and dried in oven at 110 C, then thermally treated at 1300 ºC for 3 hours. In samples synthesized through the Pechini method, the process started from the synthesis of the polymeric resin, formed by the citric acid reaction, glycol ethyl, water and the desired oxide salts, kept in thermal blanket at 150 C, under constant agitation for 2 hours, following two thermal treatments at 300 C for 2 hours, and then one at 900 C for 3 hours. After the thermal treatment the pigmenting systems were characterized through XRD, UV-Vis reflectance spectroscopy, scanning electronic microscopy, Raman spectroscopy and thermal analysis, determining the phases present, the colorimetric parameters, band gap values, micro-structural agglomerations and thermal and chemical stability to glass enamel. Single phase pigments were obtained in the binary system CeO2-Pr6O11, with addition of up to 10% Pr6O11 synthesized through OM and up to 3% Pr6O11 synthesized through the Pechini method, whereas the binary system CeO2-Fe2O3, presented single phase only in OM synthesis, with concentrations up to 2% of Fe2O3. More intense shades were obtained in pigments with addition of up to 5% mol praseodymium oxide in the CeO2-Pr6O11 system, and with up to 3% mol iron oxide in the CeO2-Fe2O3 system. The ternary system CeO2-Pr6O11-Fe2O3 presented secondary phase PrFeo3, remaining this phase even with the addition of mineralizers. The pigments applied to low temperature frits (LTF) and windscreen glass (WSG) showed chemically and thermally resistant at 800 C, free of surface defects on the ceramic plates, presenting better dispersion and color homogeneity. / A presente pesquisa estudou os sistemas pigmentantes à base de óxido de cério (CeO2) dopados com óxido de praseodímio (Pr6O11) e hematita (Fe2O3 - óxido de ferro), sintetizados pelo método de reação de estado sólido (mistura de óxidos - MO) e pelo método Pechini. Paralelamente foram sintetizados pelo método MO, pigmentos do sistema ternário CeO2-Pr6O11-Fe2O3 com adição de mineralizadores. As amostras sintetizadas por MO foram homogeneizadas a úmido, em álcool isopropílico, em um moinho de bolas horizontal por 18 horas e secas em estufa a 110 C, e tratadas termicamente a 1300 C por 3 horas. Nas amostras sintetizadas pelo método Pechini partiu-se da síntese da resina polimérica, formada pela reação de ácido cítrico, etileno glicol, água e os sais contendo os íons metálicos dos óxidos pretendidos, mantida em manta térmica a 150 C, sob agitação constante, por 2 horas, sendo tratadas termicamente duas vezes a 300 C por 2 horas, e, na sequência, a 900 C por 3 horas. Após tratamento térmico os sistemas pigmentantes foram caracterizados por difração de raios X, espectroscopia de reflectância na região do UV-Vis, microscopia eletrônica de varredura, espectroscopia Raman e análise térmica, sendo determinadas as fases presentes, os parâmetros colorimétricos, valores de band gap, aglomerações micro estruturais e a estabilidade térmica e química frente à esmaltação vítrea. Pigmentos de fase única foram obtidos no sistema binário CeO2-Pr6O11, com adição de até 10% de Pr6O11 sintetizado por MO e com até 3% de Pr6O11 sintetizado por Pechini; já no sistema binário CeO2-Fe2O3, fase única somente em sínteses por MO, com concentrações até 2% de Fe2O3. Tonalidades mais intensas foram obtidas nos pigmentos com adição de até 5% mol de óxido de praseodímio no sistema CeO2-Pr6O11, e com adição de até 3% mol de óxido de ferro no sistema CeO2-Fe2O3. O sistema ternário CeO2-Pr6O11-Fe2O3 apresentou fase secundária PrFeO3, persistindo esta fase mesmo com adição de mineralizadores. Os pigmentos aplicados em frita de baixa temperatura (FBT) e vidro de pára-brisa (VPB) se mostraram resistentes química e termicamente a 800 ºC, sem presença de defeitos superficiais nas placas cerâmicas, apresentando melhor dispersão e homogeneidade da cor.

Ce travail de thèse a pour objectif de fournir un outil de modélisation rapide de l'interaction d'une source électromagnétique 3D avec une pièce de géométrie ou de propriétés physiques complexes dans le domaine des basses fréquences (régime quasi-statique). La principale application est la simulation d'un procédé de Contrôle Non Destructif (CND) d'une pièce conductrice présentant une surface ou des propriétés physiques perturbées. La plateforme logicielle CIVA, comportant un module dédié à la simulation des procédés de CND par courants de Foucault intègre à l’heure actuelle des modèles semi-analytiques limités aux géométries canoniques : pièces planes, cylindriques. Afin de lever ce verrou, le formalisme des équations de Maxwell covariantes, déjà très utilisé dans le domaine optique pour la caractérisation des réseaux de diffraction (méthode des coordonnées curvilignes) est étendu au régime quasi-statique. L’utilisation d’un nouveau système de coordonnées curvilignes non-orthogonal associé à la géométrie de la pièce conduit à écrire très facilement et de manière analytique les conditions de passage aux interfaces de formes complexes. La résolution numérique des équations de Maxwell sous leur forme covariante est abordée par une approche modale qui repose sur le calcul préalable de solutions propres d’un système d’équations différentielles en absence de source. La représentation des composantes du champ électromagnétique à partir de deux fonctions de potentiels du second ordre (SOVP) ou potentiels de Hertz dans des systèmes de coordonnées canoniques est d’abord étendue au système de coordonnées curvilignes. On obtient alors les expansions modales des composantes covariantes et contra-variantes du champ électromagnétique. Les coefficients de ces expansions modales sont déterminés ensuite en introduisant le champ d’excitation et en imposant les conditions de passage adéquates entre les différents milieux. Cette approche est ensuite couplée d'une part à un algorithme récursif (les paramètres S) afin de prendre en compte la présence d'interfaces internes complexes dans la pièce, et d'autre part à une méthode numérique d'ordre élevé (Méthode pseudo-Spectrale) afin de prendre en compte de façon rigoureuse des variations des propriétés physiques (perméabilité magnétique et/ou conductivité électrique...) du matériau avec la profondeur. La validation de la méthode numérique proposée s’appuie sur des comparaisons avec des données simulées à l'aide d'un logiciel commercial de calcul par éléments finis et des données expérimentales obtenues au laboratoire. En outre, les codes développés ont été intégrés à une version de développement de la plateforme CIVA afin de répondre aux besoins des partenaires dans le cadre du projet européen SIMPOSIUM. / This PhD work concerns the development of fast numerical tools, dedicated to the computation of the electromagnetic interaction between a low frequency 3D current source and a complex conductor, presenting rough interfaces and/or conductivity (and/or permeability) variations. The main application is the simulation of the Eddy Current non-destructive testing process applied to complex specimens. Indeed, the existing semi-analytical models currently available in the CIVA simulation platform are limited to canonical geometries. The method we propose here is based on the covariant Maxwell equations, which allow us to consider the physical equations and relationships in a non-orthogonal coordinate system depending on the geometry of the specimen. Historically, this method (cf. C-method) has been developed in the framework of optical applications, particularly for the characterization of diffraction gratings. Here, we transpose this formalism into the quasi-static regime and we thus develop an innovative formulation of the Second Order Vector Potential formalism, widely used for the computation of the quasi-static fields in canonical geometries. Then, we determine numerically a set of modal solutions of the source-free Maxwell equations in the coordinate system introduced, and this allows us to represent the unknown fields as modal expansions in source-free domains. Then, the coefficients of these expansions are computed by introducing the source fields and enforcing the boundary conditions that the total fields must verify at the interfaces between media. In order to tackle the case of a layered conductor presenting rough interfaces, the generalized SOVP formalism is coupled with a recursive algorithm called the S-matrices. On the other hand, the application case of a complex shape specimen with depth-varying physical properties is treated by coupling the modal method we developed with a high-order numerical method: pseudo-spectral method. The validation of these codes is carried out numerically by comparison with a commercial finite element software in some particular configurations. Besides, the homogeneous case is also validated by comparison with experimental data.

Cette thèse s'inscrit dans le cadre des travaux sur l'acquisition des langues étrangères. L'objectif principal est de déterminer les structurations linguistiques transitoires employées par les apprenants francophones pour exprimer l'espace en mandarin langue étrangère. La procédure utilisée est l'analyse d'un corpus de productions orales issues d'une étude expérimentale de vingt mois menée auprès d'apprenants adultes francophones du mandarin de niveau débutant, intermédiaire et avancé. Pour atteindre l'objectif fixé, nous nous penchons d'abord sur l'acquisition des verbes directionnels en mandarin, puis sur les calculs des coordonnées spatiales qui impliquent l'« habitual thought » du mandarin concernant les verbes lái (venir) et qù (aller). L'analyse des expressions spatiales par les apprenants nous permettra ensuite de détailler le processus d'acquisition des ensembles spécifiques de la relation forme/fonction du mandarin et, plus précisément, la façon dont les options linguistiques façonnent la production des apprenants à chaque niveau de l'apprentissage. L'étude de l'acquisition des verbes de repérage ainsi que du calcul des coordonnées spatiales, quant à elles, nous dévoileront le processus cognitif de la conceptualisation du domaine spatial. / This thesis intervenes in the field of foreign language acquisition. The main objective is to determine the transient language structuring used by French-speaking learners to express space in Mandarin. The procedure used is the analysis of an oral corpus from an experimental study during twenty months with French-speaking adult learners of three different Mandarin levels: beginner, intermediate and advanced. To achieve our goal, we focus primarily on the acquisition of directional verbs in Mandarin, then on the calculation of spatial coordinates that involve the "habitual thought" about Mandarin verbs lái (come) and qù (go). The analysis of spatial expressions by French learners will detail the process of acquiring specific sets of the form/function relationship in Mandarin; to be more precise, we will show how the language options shape the learners production at each level of learning. The acquisition of the verbs lái (come) and qù (go) and of the calculation of spatial coordinates, in turn, will reveal the cognitive process of space conceptualization by the French learners.

My thesis is about functions, like linear functions, quadratic functions, goniometric functions etc. Goal of my work ist to design appropriate tasks with focus on function links. Students can with help of matematic program GeoGebra discover and adopt needed properties of functions. In this work you can find Cartesian coordinates and overview of basic properties of functions too.

The estimation of motion of multi-camera systems is one of the most important tasks in computer vision research. Recently, some issues have been raised about general camera models and multi-camera systems. Using many cameras as a single camera is studied [60], and the epipolar geometry constraints of general camera models is theoretically derived. Methods for calibration, including a self-calibration method for general camera models, are studied [78, 62]. Multi-camera systems are an example of practically implementable general camera models and they are widely used in many applications nowadays because of both the low cost of digital charge-coupled device (CCD) cameras and the high resolution of multiple images from the wide field of views. To our knowledge, no research has been conducted on the relative motion of multi-camera systems with non-overlapping views to obtain a geometrically optimal solution. ¶ In this thesis, we solve the camera motion problem for multi-camera systems by using linear methods and convex optimization techniques, and we make five substantial and original contributions to the field of computer vision. First, we focus on the problem of translational motion of omnidirectional cameras, which are multi-camera systems, and present a constrained minimization method to obtain robust estimation results. Given known rotation, we show that bilinear and trilinear relations can be used to build a system of linear equations, and singular value decomposition (SVD) is used to solve the equations. Second, we present a linear method that estimates the relative motion of generalized cameras, in particular, in the case of non-overlapping views. We also present four types of generalized cameras, which can be solvable using our proposed, modified SVD method. This is the first study finding linear relations for certain types of generalized cameras and performing experiments using our proposed linear method. Third, we present a linear 6-point method (5 points from the same camera and 1 point from another camera) that estimates the relative motion of multi-camera systems, where cameras have no overlapping views. In addition, we discuss the theoretical and geometric analyses of multi-camera systems as well as certain critical configurations where the scale of translation cannot be determined. Fourth, we develop a global solution under an L∞ norm error for the relative motion problem of multi-camera systems using second-order cone programming. Finally, we present a fast searching method to obtain a global solution under an L∞ norm error for the relative motion problem of multi-camera systems, with non-overlapping views, using a branch-and-bound algorithm and linear programming (LP). By testing the feasibility of LP at the earlier stage, we reduced the time of computation of solving LP.¶ We tested our proposed methods by performing experiments with synthetic and real data. The Ladybug2 camera, for example, was used in the experiment on estimation of the translation of omnidirectional cameras and in the estimation of the relative motion of non-overlapping multi-camera systems. These experiments showed that a global solution using L∞ to estimate the relative motion of multi-camera systems could be achieved.

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