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The present paper is devoted to the fast solution of boundary integral equations on unstructured meshes by the Galerkin scheme. On the given mesh we construct a wavelet basis providing vanishing moments with respect to the traces of polynomials in the space. With this basis at hand, the system matrix in wavelet coordinates can be compressed to $\mathcal{O}(N\log N)$ relevant matrix coefficients, where $N$ denotes the number of unknowns. The compressed system matrix can be computed within suboptimal complexity by using techniques from the fast multipole method or panel clustering. Numerical results prove that we succeeded in developing a fast wavelet Galerkin scheme for solving the considered class of problems.

Let Γ be a crystallographic group acting on the n-dimensional Euclidean space. In this dissertation, the surgery obstruction groups of Γ are computed in terms of certain sheaf homology groups defined by F. Quinn, when Γ has no 2-torsion. The main theorem is : Theorem : If a crystallographic group Γ has no 2-torsion, there is a natural isomorphism a : H_*(Rⁿ /Γ; L(p)) → L_*^-∞(Γ). / Ph. D.

L’hydrogène liquide est un ergol utilisé en complément de l’oxygène liquide pour la propulsion de nombreux lanceurs en particulier ceux de la famille Ariane. Cependant, sa dangerosité interdit la réalisation d’essais, en particulier vibratoires, sur des réservoirs remplis. Cette thèse explore une piste d’étude permettant de réaliser ces essais vibratoires sur le réservoir rempli d’un matériau de substitution : un ensemble de billes pré-contraintes. L’objectif est d’obtenir un comportement modal similaire en termes de modes et de fréquences propres à celui du réservoir rempli d’hydrogène liquide pour l’étude des premiers modes. Pour répondre à cet objectif, cette étude est développée en deux parties. Dans la première partie, une approche analytique basée sur une méthode par équivalences fréquentielles est détaillée. Après avoir présenté les grandes lignes de la méthodologie utilisée et l’ensemble des modèles développés, la méthodologie est appliquée au cas étudié expérimentalement de manière à mettre en évidence l’influence des différents paramètres et de proposer une première méthode pour choisir un jeu de billes adapté. La seconde partie, traite principalement des aspects expérimentaux et numériques. Après avoir détaillé la caractérisation des billes utilisées, le montage expérimental conçu et réalisé pour effectuer des essais vibratoires sur un réservoir rempli de billes pré-contraintes est présenté. Les différents résultats obtenus avec ce montage sont étudiés au regard de l’approche analytique, mais aussi de modèles numériques utilisant des éléments-discrets et des éléments-finis. / Liquid hydrogen is a propellant alternatively used with liquid oxygen for the propulsion of many launchers, especially those of the Ariane family. However, its dangerousness prohibits vibration tests on filled tank. The aim of this PHD is to explore the possibility to carry out such vibration tests by filling these tanks with a substitute material : a set of pre-stressed balls. As further argued and developed in the report, the objective is to obtain a modal behavior similar in term of mode shapes and natural frequencies to those of the tank filled with liquid hydrogen for the first modes. In the first part, an analytical approach based on a method using frequency equivalences is detailed. After presenting the outlines of the methodology used and all the models developed, the methodology is applied to the experimentally studied case in order to highlight the influence of the different parameters as well as then to propose a first method to choose a set of well adapted balls. The second part deals mainly with experimental and numerical aspects. Firstly, the balls used in the thesis are characterized. Then, the experimental set-up designed and realized to carry out vibration tests on a tank filled with pre-stressed balls is presented. The different results obtained are compared with both analytical results and numerical based on discrete-elements and finite-elements results.

This thesis studies derived equivalences between total spaces of vector bundles and dg-quivers. A dg-quiver is a graded quiver whose path algebra is a dg-algebra. A quiver with superpotential is a dg-quiver whose differential is determined by a "function" Φ. It is known that the bounded derived category of representations of quivers with superpotential with finite dimensional cohomology is a Calabi- Yau triangulated category. Hence quivers with superpotential can be viewed as noncommutative Calabi- Yau manifolds. One might then ask if there are derived equivalences between Calabi-Yau manifolds and quivers with superpotential. In this thesis, we answer this question and, generalizing Bridgeland [15], give a recipe on how to construct such derived equivalences.

In this paper matrix compression techniques in the context of wavelet Galerkin schemes for boundary integral equations are developed and analyzed that exhibit optimal complexity in the following sense. The fully discrete scheme produces approximate solutions within discretization error accuracy offered by the underlying Galerkin method at a computational expense that is proven to stay proportional to the number of unknowns. Key issues are the second compression, that reduces the near field complexity significantly, and an additional a-posteriori compression. The latter one is based on a general result concerning an optimal work balance, that applies, in particular, to the quadrature used to compute the compressed stiffness matrix with sufficient accuracy in linear time. The theoretical results are illustrated by a 3D example on a nontrivial domain.

We establish multiresolution norm equivalences in weighted spaces <i>L²_w</i>((0,1)) with possibly singular weight functions <i>w(x)</i>&ge;0 in (0,1). Our analysis exploits the locality of the biorthogonal wavelet basis and its dual basis functions. The discrete norms are sums of wavelet coefficients which are weighted with respect to the collocated weight function <i>w(x)</i> within each scale. Since norm equivalences for Sobolev norms are by now well-known, our result can also be applied to weighted Sobolev norms. We apply our theory to the problem of preconditioning <i>p</i>-Version FEM and wavelet discretizations of degenerate elliptic problems.

As shown by Dahmen, Harbrecht and Schneider, the fully discrete wavelet Galerkin scheme for boundary integral equations scales linearly with the number of unknowns without compromising the accuracy of the underlying Galerkin scheme. The supposition is a wavelet basis with a sufficiently large number of vanishing moments. In this paper we present several constructions of appropriate wavelet bases on manifolds based on the biorthogonal spline wavelets of A. Cohen, I. Daubechies and J.-C. Feauveau. By numerical experiments we demonstrate that it is worthwhile to spent effort on their construction to increase the performance of the wavelet Galerkin scheme considerably.

<p>This thesis describes how social work language practice circulates around the implementation process of an evidence based structured assessment tool – Savry. The purpose is to examine and understand the social workers language practice in a working group that uses this structured assessment tool in their work with youth. The purpose is also to look for dimensions of identity in terms of discourse. The ontological viewpoint is post-structuralism where language is in focus. The theoretical framework is discourse theory based upon the work of Ernesto Laclau and Chantal Mouffe. This theory is used as a basis of the creation of an analytical toolkit which emphasises the concept chains of equivalence and nodal points. The study is based upon qualitative interviews with social workers in a group in the social services for children and youth, who uses the evidenced based structured assessment tool - Savry. The study concerns the structuring around two identities. Theese identities circulate around the nodal point “knowledge” and defines it in two different ways through chains of equivalence. One of the identities equivalates scientific research to the nodal point knowledge, the other equivalates the unique experience to the same nodal point. Theese identities seames to be the result of a hegemonic strategy articulated by one of the two. The purpose of the strategy seams to be the incorporation of as many discursive elements as possible into one dominating discourse. This is also done through the principal exclusion of certain discursive elements, witch is the characterisation of power in discursive theory. The character of the struggle for dominance is not equal. It is instead characterised by the expansion of the chains of equivalence by the scientific knowledge based identity to incorporate discursive elements form other discourses. This is identified as a hegemonic strategy with the purpose of organising consent around the definition of the concept of knowledge and its consequences for social work practice.</p>

This thesis describes how social work language practice circulates around the implementation process of an evidence based structured assessment tool – Savry. The purpose is to examine and understand the social workers language practice in a working group that uses this structured assessment tool in their work with youth. The purpose is also to look for dimensions of identity in terms of discourse. The ontological viewpoint is post-structuralism where language is in focus. The theoretical framework is discourse theory based upon the work of Ernesto Laclau and Chantal Mouffe. This theory is used as a basis of the creation of an analytical toolkit which emphasises the concept chains of equivalence and nodal points. The study is based upon qualitative interviews with social workers in a group in the social services for children and youth, who uses the evidenced based structured assessment tool - Savry. The study concerns the structuring around two identities. Theese identities circulate around the nodal point “knowledge” and defines it in two different ways through chains of equivalence. One of the identities equivalates scientific research to the nodal point knowledge, the other equivalates the unique experience to the same nodal point. Theese identities seames to be the result of a hegemonic strategy articulated by one of the two. The purpose of the strategy seams to be the incorporation of as many discursive elements as possible into one dominating discourse. This is also done through the principal exclusion of certain discursive elements, witch is the characterisation of power in discursive theory. The character of the struggle for dominance is not equal. It is instead characterised by the expansion of the chains of equivalence by the scientific knowledge based identity to incorporate discursive elements form other discourses. This is identified as a hegemonic strategy with the purpose of organising consent around the definition of the concept of knowledge and its consequences for social work practice.