Universal Deformation Formulae, Symplectic Lie groups and Symmetric Spaces

We apply methods from strict quantization of solvable symmetric spaces to obtain universal deformation formulae for actions of a class of solvable Lie groups. We also study compatible co-products by generalizing the notion of smash product in the context of Hopf algebras

Universal Deformation Formulae for Three-Dimensional Solvable Lie groups

We apply methods from strict quantization of solvable symmetric spaces to obtain universal deformation formulae for actions of every three-dimensional solvable Lie group. We also study compatible co-products by generalizing the notion of smash product in the context of Hopf algebras. We investigate in particular the dressing action of the `book' group on SU(2)

A mi-chemin entre analyse complexe et superanalyse

In the framework of superanalysis we get a functions theory close to complex analysis, under a suitable condition (A) on the real superalgebras in consideration (this condition is a generalization of the classical relation 1 + i^2 = 0 in C). Under the condition (A), we get an integral representation formula for the superdifferentiable functions.We give a result of Hartogs type of separated superdifferentiability, a continuation theorem of Hartogs-Bochner type and a Liouville theorem for the superdifferentiable functions.Comment: version 2 : \`a para\^itre dans Publicacions Matem\`atiques (compl\'ements par rapport \`a la version 1 : commentaires sur les conditions alg\'ebriques

Entre analyse complexe et superanalyse

In the framework of superanalysis we get a functions theory close to complex analysis, under a suitable condition (A) on the real superalgebras in consideration. Under the condition (A), we get an integral representation formula for the superdifferentiable functions.We give a result of Hartogs type of separated superdifferentiability and a continuation theorem of Hartogs-Bochner type for the superdifferentiable functions.Comment: v2 correspond \`a l'article d\'etaill\'e pour une note aux CRAS (v3) parue en 200

Almost holomorphic curves in real analytic hypersurfaces

Using the theory of exterior differential systems, we study the existence of germ of pseudo-holomorphic disk in a real analytic hypersurface locally defined in a complex manifold equipped with J a real analytic almost complex structure. The integrable case in C n with J the multiplication by i has been intensively studied by several authors [DF], [DA1] and [DA2] for example. The non integrable case is drastically different essentially due to the following fact : in generic case, there is no J-invariant objects of dimension bigger than one. This simple observation leads to the non existence of some equivalents of Segree varieties or ideals of holomorphic functions which play a fundamental role in the complex case. Nevertheless in the almost complex case, we adopt the exterior differential system point of view of E.Cartan developed and clarified in [BCGGG]

Flexible G1 Interpolation of Quad Meshes

International audienceTransforming an arbitrary mesh into a smooth G1 surface has been the subject of intensive research works. To get a visual pleasing shape without any imperfection even in the presence of extraordinary mesh vertices is still a challenging problem in particular when interpolation of the mesh vertices is required. We present a new local method, which produces visually smooth shapes while solving the interpolation problem. It consists of combining low degree biquartic Bézier patches with minimum number of pieces per mesh face, assembled together with G1-continuity. All surface control points are given explicitly. The construction is local and free of zero-twists. We further show that within this economical class of surfaces it is however possible to derive a sufficient number of meaningful degrees of freedom so that standard optimization techniques result in high quality surfaces

PISCO2: the new speckle camera of the Nice 76-cm refractor

We present the new speckle camera PISCO2 made in 2010-2012, for the 76-cm refractor of C\^ote d'Azur Observatory. It is a focal instrument dedicated to the observation of visual binary stars using high angular resolution speckle interferometry techniques to partly overcome the degradation caused by the atmospheric turbulence. Fitted with an EMCCD detector, PISCO2 allows the acquisition of short exposure images that are processed in real time by our specially designed software. Two Risley prisms are used for correcting the atmospheric dispersion. All optical settings are remotely controlled. We have already been able to observe faint, close binary stars with angular separations as small as 0".16, and visual magnitudes of about 16. We also have measured some particularly difficult systems with a magnitude difference between the two components of about 4 magnitudes. This level of performance is very promising for the detection and study of large sets of yet unknown (or partly measured) binaries with close separation and/or large magnitude difference.Comment: 13 pages, 12 figure