W-superalgebras as truncation of super-Yangians

We show that some finite W-superalgebras based on gl(M|N) are truncation of the super-Yangian Y(gl(M|N)). In the same way, we prove that finite W-superalgebras based on osp(M|2n) are truncation of the twisted super-Yangians Y(gl(M|2n))^{+}. Using this homomorphism, we present these W-superalgebras in an R-matrix formalism, and we classify their finite-dimensional irreducible representations.Comment: Latex, 32 page

Near-UV to near-IR disk-averaged Earth's reflectance spectra

We report 320 to 1020nm disk-averaged Earth reflectance spectra obtained from Moon's Earthshine observations with the EMMI spectrograph on the NTT at ESO La Silla (Chile). The spectral signatures of Earth atmosphere and ground vegetation are observed. A vegetation red-edge of up to 9% is observed on Europe and Africa and ~2% upon Pacific Ocean. The spectra also show that Earth is a blue planet when Rayleigh scattering dominates, or totally white when the cloud cover is large.Comment: Proceeding of an oral prensentation at the UAI No200 Colloquiu

Kinematic Characterisation of Hexapods for Industry

International audiencePurpose-The aim of this paper is to propose two simple tools for the kinematic characterization of hexapods. The paper also aims to share the authors' experience with converting a popular commercial motion base (Stewart-Gough platform, hex-apod) to an industrial robot for use in heavy duty aerospace manufacturing processes. Design/methodology/approach-The complete workspace of a hexapod is a six-dimensional entity that is impossible to visualize. Thus, nearly all hexapod manufacturers simply state the extrema of each of the six dimensions, which is very misleading. As a compromise, we propose a special three-dimensional subset of the complete workspace, an approximation of which can be readily obtained using a CAD/CAM software suite, such as CATIA. While calibration techniques for serial robots are readily available, there is still no generally-agreed procedure for calibrating hexapods. We propose a simple calibration method that relies on the use of a laser tracker and requires no programming at all. Instead, the design parameters of the hexapod are directly and individually measured and the few computations involved are performed in a CAD/CAM software such as CATIA. Findings-The conventional octahedral hexapod design has a very limited workspace, though free of singularities. There are important deviations between the actual and the specified kinematic model in a commercial motion base. Practical implications-A commercial motion base can be used as a precision positioning device with its controller retrofit-ted with state-of-the-art motion control technology with accurate workspace and geometric characteristics. Originality/value-A novel geometric approach for obtaining meaningful measures of the workspace is proposed. A novel, systematic procedure for the calibration of a hexapod is outlined. Finally, experimental results are presented and discussed

Soliton surfaces associated with symmetries of ODEs written in Lax representation

The main aim of this paper is to discuss recent results on the adaptation of the Fokas-Gel'fand procedure for constructing soliton surfaces in Lie algebras, which was originally derived for PDEs [Grundland, Post 2011], to the case of integrable ODEs admitting Lax representations. We give explicit forms of the \g-valued immersion functions based on conformal symmetries involving the spectral parameter, a gauge transformation of the wave function and generalized symmetries of the linear spectral problem. The procedure is applied to a symmetry reduction of the static $\phi^4$-field equations leading to the Jacobian elliptic equation. As examples, we obtain diverse types of surfaces for different choices of Jacobian elliptic functions for a range of values of parameters.Comment: 14 Pages, 2 figures Conference Proceedings for QST7 Pragu

Near-UV to near-IR disk-averaged Earth's spectra from Moon's Earthshine observations

We discuss a series of Earthshine spectra obtained with the NTT/EMMI instrument between 320nm and 1020nm with a resolution of R~450 in the blue and R~250 in the red. These ascending and descending Moon's Earthshine spectra taken from Chile give disk-averaged spectra for two different Earth's phases. The spectra show the ozone (Huggins and Chappuis bands), oxygen and water vapour absorption bands, and also the stronger Rayleigh scattering in the blue. Removing the known telluric absorptions reveals a spectral feature around 700nm which is attributed to the vegetation stronger reflectivity in the near-IR, so-called vegetation red-edge.Comment: 2 pages, 1 figure, proceedings from a poster at 'Semaine de l'Astrophysique Francaise', 27th june-1st july 2005, Strasbour