Dissertations / Theses on the topic 'Espace des Quaternions'
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Guillard, Gwenaël. "Un espace de représentation pour l'étude conjointe de la morphologie et de la fonctionnalité des surfaces articulaires." Rennes 1, 2005. http://www.theses.fr/2005REN1S148.
Full textDufour, Quentin. "Une construction de métriques quaternion-kählériennes à partir du groupe G2." Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066142/document.
Full textThe main theorem of this thesis is a construction of quaternionic Kählerian metrics over a 8-manifolds modelled on the non-compact Riemannian symmetric space G2/SO(4). This construction is in line with LeBrun?s construction (1989) and Biquard?s construction (2000) for which, on one side, the quaternionic Kählerian manifolds constructed have a homogeneous model which is a non-compact Riemannian symmetric space G/K , and in the other side, the initial data can be seen as deformations of a Furstenberg boundary G/P with P a parabolic sub-group of G. These constructions lead us to think about a general correspondence between the deformations of Furstenberg boundaries and quaternionic Kählerian manifolds. Those deformation of G/P space are manifolds with parabolic geometries. After a presentation of the theory of parabolic geometries given in the first part, we will focus on the previous supposed correspondence in the second part. Observing LeBrun?s construction (1989), we will reduce the candidates for a generalisation of this construction to two cases among which the one of the space G2/SO(4) with the parabolic sub-group P stabilizing an isotropic line in R^{3,4}. In the last part, we will precisely give the construction of quaternionic Kählerian metrics with initial data some parabolic geometries of type (G2,P). This construction begins with the construction of twistor spaces where we will deform some double curve named ribbon. The quaternionic Kählerian manifolds constructed will be some open set in the space of deformation of these curves
Denis, Patrice. "Quaternions et Algèbres Géométriques, de nouveaux outils pour les images numériques couleur." Phd thesis, Université de Poitiers, 2007. http://tel.archives-ouvertes.fr/tel-00277993.
Full textZenteno, Torres Jazmin. "Sliding mode control with fault tolerance capacities : application to a rendezvous mission in a circular orbit." Thesis, Bordeaux, 2020. http://www.theses.fr/2020BORD0063.
Full textIncreasing attention has grown with regards to Sliding Mode Controllers (SMC). In order to reduce the so-called chattering effect, the Super-Twisting Algorithm (STA) has been proposed, recently. In this work, a controller based on the STA in a backstepping setup, is proposed for spacecraft rendezvous in a circular orbit. A key feature is that the chaser is not treated as a point mass, given that the effects of the flexible modes and propellant sloshing phenomena are considered. The results obtained are taken further, given that the guarantee of robustness against perturbations is not enough when it comes to critical systems, through the second ordersliding mode controllers technique. It is shown that the technique enables to solve to problem of fault tolerant control. The solution is based on the Generalized Super-Twisting Algorithm (GSTA) with an anti-windup strategy and a nonlinear observer and the dual quaternion formalism. The main reason of employing a GSTA is because it offers more robustness against state dependentperturbations (sloshing phenomena and flexible modes) than the STA. In addition, with the help of the anti-windup strategy, the control law does not saturate the thrusters, avoiding instablity when faults occur. The proposed solution is evaluated through a simulation campaign in a high-fidelity non-linear simulator, and mission oriented criteria demonstrate its potential
Bouzzit, Aziz. "Ellipsométrie acoustique pour le suivi et la caractérisation de matériaux complexes." Electronic Thesis or Diss., CY Cergy Paris Université, 2024. http://www.theses.fr/2024CYUN1304.
Full textComplex materials are at the heart of major societal challenges in most major fields such as energy, transport, environment, heritage conservation/restoration, health and safety. Because of the opportunities for innovation offered in terms of features, these materials are giving rise to new problems of multi-physical and multi-scale analysis and understanding. The same applies to the instrumentation needed to characterize them.Acoustic methods, which are widely used in the non-destructive characterization of complex media, make use of the propagation properties of mechanical waves in these materials, which can be heterogeneous and anisotropic.In a multi-scale approach, the advantage of ultrasonic methods is that they are particularly sensitive to mechanical properties such as elasticity, rigidity and viscosity. The heterogeneous and multiphase nature of a complex medium thus leads to the notion of a viscoelastic medium, characterized by generalized complex Lamé coefficients (��∗, ��∗) and their variation as a function of frequency.The objective of this thesis is to develop a method for characterizing these complex viscoelastic materials that simultaneously measures the variation of the two generalized complex Lamé coefficients (��∗, ��∗) versus the frequency. The proposed approach is to follow, in space and in time, the propagation of the Rayleigh wave and to extract its ellipsometric parameters (ellipticity χ and orientation θ) in addition to the propagation parameters (k' and k'') conventionally determined. Based on the wave detection by 3D laser vibrometry at the surface of the complex material, and by means of 2D Gabor analysis in Quaternion space, the estimation of propagation and ellipsometric parameters gives access to the complete characterization of the complex material only by studying the interaction of a Rayleigh wave with the medium.The theoretical developments proposed in this work, together with experimental and simulation results, confirm the value of acoustic ellipsometry for characterizing these complex materials
Casteill, Pierre-Yves. "Renormalisation perturbative et T-dualité : nouvelles métriques d'Einstein et super-espace harmonique." Paris 7, 2002. https://tel.archives-ouvertes.fr/tel-00002166.
Full textCasteill, Pierre-Yves. "Renormalisation perturbative et T-dualite - Nouvelles metriques d'Einstein et super-espace harmonique." Phd thesis, Université Paris-Diderot - Paris VII, 2002. http://tel.archives-ouvertes.fr/tel-00002166.
Full textMorchid, Mohamed. "Représentations robustes de documents bruités dans des espaces homogènes." Thesis, Avignon, 2014. http://www.theses.fr/2014AVIG0202/document.
Full textIn the Information Retrieval field, documents are usually considered as a "bagof-words". This model does not take into account the temporal structure of thedocument and is sensitive to noises which can alter its lexical form. These noisescan be produced by different sources : uncontrolled form of documents in microbloggingplatforms, automatic transcription of speech documents which are errorprone,lexical and grammatical variabilities in Web forums. . . The work presented inthis thesis addresses issues related to document representations from noisy sources.The thesis consists of three parts in which different representations of content areavailable. The first one compares a classical representation based on a term-frequencyrepresentation to a higher level representation based on a topic space. The abstractionof the document content allows us to limit the alteration of the noisy document byrepresenting its content with a set of high-level features. Our experiments confirm thatmapping a noisy document into a topic space allows us to improve the results obtainedduring different information retrieval tasks compared to a classical approach based onterm frequency. The major problem with such a high-level representation is that it isbased on a space theme whose parameters are chosen empirically.The second part presents a novel representation based on multiple topic spaces thatallow us to solve three main problems : the closeness of the subjects discussed in thedocument, the tricky choice of the "right" values of the topic space parameters and therobustness of the topic-based representation. Based on the idea that a single representationof the contents cannot capture all the relevant information, we propose to increasethe number of views on a single document. This multiplication of views generates "artificial"observations that contain fragments of useful information. The first experimentvalidated the multi-view approach to represent noisy texts. However, it has the disadvantageof being very large and redundant and of containing additional variability associatedwith the diversity of views. In the second step, we propose a method based onfactor analysis to compact the different views and to obtain a new robust representationof low dimension which contains only the informative part of the document whilethe noisy variabilities are compensated. During a dialogue classification task, the compressionprocess confirmed that this compact representation allows us to improve therobustness of noisy document representation.Nonetheless, during the learning process of topic spaces, the document is consideredas a "bag-of-words" while many studies have showed that the word position in a7document is useful. A representation which takes into account the temporal structureof the document based on hyper-complex numbers is proposed in the third part. Thisrepresentation is based on the hyper-complex numbers of dimension four named quaternions.Our experiments on a classification task have showed the effectiveness of theproposed approach compared to a conventional "bag-of-words" representation
Louro, Donizetti Fermino. "Hipercomplexos: dos tripletos ao espaço." Pontifícia Universidade Católica de São Paulo, 2014. https://tede2.pucsp.br/handle/handle/13296.
Full textThe historiography of triplets of Hamilton aims to address the mathematical reasoning that preceded the development of quaternions and their contribution to the study of three-dimensional objects. The study of triplets as geometrical representation of square roots and negative quantities prior to the formalization of hypercomplex numbers, in particular the algebra of quaternions. The origin and the quaternion's fundaments based on triplets, applied in the rotational motion of threedimensional objects in space, evokes further study of their complex structures, a priori. The search of Hamilton for a hypercomplex number able to represent rotations in space presented geometrical concerns, as well as, a vector approach of plane, then their applications determine isometries that still underlie the mathematical morphology of the digital dynamic image
A historiografia dos tripletos de Hamilton pretende abordar o raciocínio matemático que antecedeu o desenvolvimento dos quaternions e sua contribuição ao estudo de objetos tridimensionais. O estudo dos tripletos como representação geométrica das raízes quadradas e quantidades negativas antecedeu a formalização dos números hipercomplexos, em específico da álgebra de quaternions. A origem e os fundamentos dos quaternions baseados nos tripletos, aplicados no movimento rotacional de objetos tridimensionais no espaço suscitam um estudo mais aprofundado de suas estruturas complexas, a priori. A busca de Hamilton por um número hipercomplexo capaz de representar rotações do espaço apresentava preocupações geométricas, assim como uma abordagem vetorial do plano, logo suas aplicações determinariam isometrias que ainda fundamentam a morfologia da imagem digital dinâmica
Silva, Rênad Ferreira da. "Transformações Geométricas no Plano e no Espaço." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7476.
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Abstract: In this work we study some geometric transformations in the plane and the space. Initially, we present some special types of transformations in the plane and find the matrix of each of these transformations. In the second part we discourse the transformations in the space, emphasizing the rotations. We will use the angles of Euler to determine a rotation in the space around the Cartesian axes and define an equation which allows to rotate a vector around any axis. We also discuss the homogeneous spaces aiming the matrix representation of transformations of translation. Finally, we use the structure of the quaternions group to present a second form to rotation vectors and composition of rotations in the space. We emphasize that this study is essential to describe the motion of objects in the plane and in the space.
Neste trabalho estudamos algumas das transformações geométricas no Plano e no Espaço. Inicialmente, apresentamos alguns tipos de transformações especiais no Plano e encontramos a matriz de cada uma destas transformações. Na segunda parte abordamos as transformações no Espaço, dando ênfase as rotações. Utilizamos os ângulos de Euler para determinar uma rotação no espaço em torno dos eixos cartesianos e definimos uma equação que permite rotacionar um vetores em torno de um eixo qualquer. Também abordamos os espaços homogêneos objetivando a representa ção matricial da transformação de translação. Por último, usamos a estrutura do grupo dos Quatérnios para apresentar uma segunda forma de fazer rotações de vetores e composição de rotações no espaço. Ressaltamos que este estudo é fundamental para descrever o movimento de objetos no plano e no espaço.
Lezowski, Pierre. "Questions d’euclidianité." Thesis, Bordeaux 1, 2012. http://www.theses.fr/2012BOR14642/document.
Full textWe study norm-Euclideanity of number fields and some of its generalizations. In particular, we provide an algorithm to compute the Euclidean minimum of a number field of any signature. This allows us to study the norm-Euclideanity of many number fields. Then, we extend this algorithm to deal with norm-Euclidean classes and we obtain new examples of number fields with a non-principal norm-Euclidean class. Besides, we describe the complete list of pure cubic number fields admitting a norm-Euclidean class. Finally, we study the Euclidean property in quaternion fields. First, we establish its basic properties, then we study some examples. We provide the complete list of Euclidean quaternion fields, which are totally definite over a number field with degree at most two
Adorno, Bruno. "Two-arm Manipulation : from Manipulators to Enhanced Human-Robot Collaboration." Thesis, Montpellier 2, 2011. http://www.theses.fr/2011MON20064/document.
Full textThis thesis is devoted to the study of robotic two-arm coordination/manipulation from a unified perspective, and conceptually different bimanual tasks are thus described within the same formalism. In order to provide a consistent and compact theory, the techniques presented herein use dual quaternions to represent every single aspect of robot kinematic modeling and control.A novel representation for two-arm manipulation is proposed—the cooperative dual task-space—which exploits the dual quaternion algebra to unify the various approaches found in the literature. The method is further extended to take into account any serially coupled kinematic chain, and a case study is performed using a simulated mobile manipulator. An original application of the cooperative dual task-space is proposed to intuitively represent general human-robot collaboration (HRC) tasks, and several experiments were performed to validate the proposed techniques. Furthermore, the thesis proposes a novel class of HRC taskswherein the robot controls all the coordination aspects; that is, in addition to controlling its own arm, the robot controls the human arm by means of functional electrical stimulation (FES).Thanks to the holistic approach developed throughout the thesis, the resultant theory is compact, uses a small set of mathematical tools, and is capable of describing and controlling a broad range of robot manipulation tasks
Philippe, Zoe. "Invariants globaux des variétés hyperboliques quaterioniques." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0453/document.
Full textIn the first part of this thesis, we derive explicit universal – that is, depending only on the dimension – lower bounds on three global invariants of quaternionic hyperbolic sapces : their maximal radius, their volume, and their Euler caracteristic. We also exhibit an upper bound on their Margulis constant, showing that this last quantity decreases at least like a negative power of the dimension. In the second part, we study a specific lattice of isometries of the quaternionic hyperbolic plane : the Hurwitz modular group. In particular, we show that this group is generated by four elements, and we construct a fundamental domain for the subgroup of isometries of this lattice stabilising a point on the boundary of the quaternionic hyperbolic plane
Ruiz, Echartea Maria Elisa. "Pairwise and Multi-Component Protein-Protein Docking Using Exhaustive Branch-and-Bound Tri-Dimensional Rotational Searches." Electronic Thesis or Diss., Université de Lorraine, 2019. http://www.theses.fr/2019LORR0306.
Full textDetermination of tri-dimensional (3D) structures of protein complexes is crucial to increase research advances on biological processes that help, for instance, to understand the development of diseases and their possible prevention or treatment. The difficulties and high costs of experimental methods to determine protein 3D structures and the importance of protein complexes for research have encouraged the use of computer science for developing tools to help filling this gap, such as protein docking algorithms. The protein docking problem has been studied for over 40 years. However, developing accurate and efficient protein docking algorithms remains a challenging problem due to the size of the search space, the approximate nature of the scoring functions used, and often the inherent flexibility of the protein structures to be docked. This thesis presents an algorithm to rigidly dock proteins using a series of exhaustive 3D branch-and-bound rotational searches in which non-clashing orientations are scored using ATTRACT. The rotational space is represented as a quaternion “π-ball”, which is systematically sub-divided in a “branch-and-bound” manner, allowing efficient pruning of rotations that will give steric clashes. The contribution of this thesis can be described in three main parts as follows. 1) The algorithm called EROS-DOCK to assemble two proteins. It was tested on 173 Docking Benchmark complexes. According to the CAPRI quality criteria, EROS-DOCK typically gives more acceptable or medium quality solutions than ATTRACT and ZDOCK. 2)The extension of the EROS-DOCK algorithm to allow the use of atom-atom or residue-residue distance restraints. The results show that using even just one residue-residue restraint in each interaction interface is sufficient to increase the number of cases with acceptable solutions within the top-10 from 51 to 121 out of 173 pairwise docking cases. Hence, EROS-DOCK offers a new improved search strategy to incorporate experimental data, of which a proof-of-principle using data-driven computational restraints is demonstrated in this thesis, and this might be especially important for multi-body complexes. 3)The extension of the algorithm to dock trimeric complexes. Here, the proposed method is based on the premise that all of the interfaces in a multi-body docking solution should be similar to at least one interface in each of the lists of pairwise docking solutions. The algorithm was tested on a home-made benchmark of 11 three-body cases. Seven complexes obtained at least one acceptable quality solution in the top-50. In future, the EROS-DOCK algorithm can evolve by integrating improved scoring functions and other types of restraints. Moreover, it can be used as a component in elaborate workflows to efficiently solve complex problems of multi-protein assemblies
Adorno, Bruno Vilhena. "Contribution à la manipulation à deux bras : des manipulateurs à la collaboration homme-robot." Phd thesis, Université Montpellier II - Sciences et Techniques du Languedoc, 2011. http://tel.archives-ouvertes.fr/tel-00641678.
Full textPlouhinec, Jean-Baptiste. "Théorie des noeuds et espaces de représentations." Mémoire, 2006. http://www.archipel.uqam.ca/2017/1/M9262.pdf.
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