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Un manipulateur parallèle à mobilité réduite a moins de six degrés de liberté et présente généralement différents types de mouvement connus sous le nom de modes d'opération. Ainsi, ce type de manipulateur peut être classifié comme reconfigurable selon sa capacité de transition entre les différents modes d'opération. Cette thèse de doctorat s'articule principalement autour de l'analyse cinématique de manipulateurs parallèles à mobilité réduite, de manipulateurs parallèles en série obtenus à partir de leur empilement en série et de mécanismes conformes conçus à partir de leurs configurations singulières à contraintes. La transformation cinématique de Study est utilisée pour dériver les équations algébriques de contraintes. Ensuite, elles sont interprétées à l'aide d'outils de géométrie algébrique pour effectuer des analyses de mobilité, de cinématique et de singularité. Les techniques de ‘‘screw theory’’ et ‘‘line geometry’’ sont utilisées à côté de l'approche algébrique au besoin. / A lower mobility parallel manipulator has less than six degrees of freedom and usually exhibits different motion types known as operation modes. Thus, it can be classified as reconfigurable on account of its ability to transition between different operation modes. This doctoral thesis mainly revolves around the kinematic analysis of some lower-mobility parallel manipulators, series-parallel manipulators obtained from their serial stacking and compliant mechanisms designed using their constraint singular configurations. Study's kinematic mapping is used to derive the algebraic constraint equations. They are further interpreted using algebraic geometry tools to perform mobility, kinematic and singularity analysis. Screw theory and line geometry techniques are used adjacent to algebraic approach wherever necessary.

Dans cette thèse, nous interprétons géométriquement la torsion de l'algèbre symétrique d'un faisceau d'idéaux I_Z d'un schéma Z défini par n+1 équations dans une variété n-dimensionnelle. Ceci revient à étudier la géométrie de la projectivisation de I_Z. Les applications de ce point de vue concernent en particulier le domaine des transformations birationnelles de l'espace projectif de dimension 3 au sujet duquel nous construisons des transformations birationnelles explicites qui ont le même degré algébrique que leur inverse, le domaine des courbes libres et presque-libres au sujet duquel nous généralisons une caractérisation des courbes libres en étendant les notions de nombre de Milnor et de nombre de Tjurina. Nous abordons aussi le sujet des hypersurfaces homaloides, notre motivation initiale, au sujet duquel nous exhibons en particulier une courbe homaloide de degré 5 en caractéristique 3. La dernière application concerne le calcul de l'inverse d'une transformation birationnelle. / In this thesis, we interpret geometrically the torsion of the symmetric algebra of the ideal sheaf I_Z of a scheme Z defined by n+1 equations in an n-dimensional variety. This is equivalent to study the geometry of the projectivization of I_Z. The applications of this point of view concern, in particular, the topic of birational maps of the projective space of dimension 3 for which we construct explicit birational maps that have the same algebraic degree as their inverse, free and nearly-free curves for which we generalise a characterization of free curves by extending the notion of Milnor and Tjurina numbers. We tackle also the topic of homaloidal hypersurfaces, our original motivation, for which we produce in particular a homaloidal curve of degree 5 in characteristic 3. The last application concerns the computation of the inverse of a birational map.

Neste trabalho,estudamos o índice de Poincaré-Hopf, definido para singularidades isoladas de campos de vetores sobre variedades diferenciáveis. Além disso, investigamos algumas definições de índices de campos de vetores definido sem variedades singulares, como o índice de Schwartz e o índice GSV. Estudaremos estes invariantes no caso específico em que (V; 0) é um germe de uma interseção completa com singularidade isolada na origem / In this work, we study thePoincaré-Hopf index, defined for isolated singularities of vector fields on manifolds. Moreover, we investigate some definitions of indices of vector fields defined on singular varieties, as the Schwartz index and the GSV index. We study these invariants in the case where (V; 0) is a germ of a complete intersection with an isolated singularity at the origin

In 1976, Springer defined a correspondence making a link between the irreducible ordinary (characteristic zero) representations of a Weyl group and the geometry of the associated nilpotent variety. In this thesis, we define a modular Springer correspondence (in positive characteristic), and we show that the decomposition numbers of a Weyl group (for example the symmetric group) are particular cases of decomposition numbers for equivariant perverse sheaves on the nilpotent variety. We calculate explicitly the decomposition numbers associated to the regular and subregular classes, and to the minimal and trivial classes. We determine the correspondence explicitly in the case of the symmetric group, and show that James's row and column removal rule is a consequence of a smooth equivalence of nilpotent singularities obtained by Kraft and Procesi. The first chapter contains generalities about perverse sheaves with Z_l and F_l coefficients.

We establish elements of a new approach to ellipticity and parametrices within operator algebras on manifolds with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaes. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The "full" calculus involves two separate theories, one near the tip of the corner and another one at the conical exit to infinity. However, concerning the conical exit to infinity, we establish here a new concrete calculus of edge-degenerate operators which can be iterated to higher singularities. / Wir führen einen neuen Zugang ein zu Elliptizität und Parametrices in Operatorenalgebren auf Mannigfaltigkeiten mit höheren Singularitäten, nur basierend auf allgemeinen axiomatischen Voraussetzungen über parameter-abhängige Operatoren in geeigneten Skalen von Räumen. Die Idee besteht darin, ein iteratives Verfahren zu modellieren mit neuen Generationen von parameter-abhängigen Operatortheorien, zusammen mit neuen Skalen von Räumen, die analoge Voraussetzungen erfüllen wie die ursprünglichen Objekte, jetzt auf dem entsprechenden höheren Niveau. Der „volle“ Kalkül besteht aus zwei separaten Theorien, eine nahe der Spitze der Ecke und eine andere am konischen Ausgang nach Unendlich. Allerdings, bezüglich des konischen Ausgangs nach Unendlich, bauen wir hier einen neuen konkreten Kalkül von kanten-entarteten Operatoren auf, der für höhere Singularitäten iteriert werden kann.

Der Vortrag beschreibt numerische Singularitäten bei der h- und p-FEM, wie sie erkannt werden und welche Lösungen möglich sind bzw. was nicht vermieden werden kann.

This thesis is concerned with the finite element analysis and the a posteriori error estimation for eigenvalue problems for general operator pencils on two-dimensional manifolds. A specific application of the presented theory is the computation of corner singularities. Engineers use the knowledge of the so-called singularity exponents to predict the onset and the propagation of cracks. All results of this thesis are explained for two model problems, the Laplace and the linear elasticity problem, and verified by numerous numerical results.

No description available.

Magistro darbe nagrinėjami paprastųjų tiesinių antros eilės diferencialinių lygčių sistemos su ypatuma kraštiniai uždaviniai. Ištirta sprendinių asimptotika ypatingojo taško aplinkoje. Surasti lygčių sistemos sprendinio įverčiai. Nagrinėjamų diferencialinių uždavinių sprendiniai, konstruojami naudojant integralinius operatorius. Įrodyta sprendinių vienatis. / In this paper the some boundary value problems for a system of ordinary second order differential equations with singularity are considered. The asymptotic of solutions in the neighborhood of singular point are discussed. The estimates of the solution are given. The solutions of considered differential problems are constructed using some integral operators. The uniqueness of the solutions is proved.