Normalisation holomorphe de structures de Poisson

We show that a Poisson structure whose linear part vanishes can be holomorphically normalized in a neighbourhood of its singular point $0\in \Bbb C^n$ if, on the one hand, a Diophantine condition on a Lie algebra associated to the quadratic part is satisfied and, on the other hand, the normal form satisfies some formal condition

Validating Virtual Reality as an effective Training Medium in the Security Domain

Virtual Reality (VR) training simulations are an idea which is being explored in numerous industries and professions. However, evidence purporting to the effectiveness of VR technology in relation to standard real-world exercises is still relatively thin. In this paper, we discuss our approach for validating the effectiveness of a VR training for law enforcement professionals in the context of the AUGGMED project, and present results of the validation study. Our study indicates that realistic VR-based trainings, either by themselves or in combination with the traditional hands-on training, can be as effective as highly resource-intensive practical training sessions

The spinorial geometry of supersymmetric heterotic string backgrounds

We determine the geometry of supersymmetric heterotic string backgrounds for which all parallel spinors with respect to the connection $\hat\nabla$ with torsion $H$, the NS$\otimes$NS three-form field strength, are Killing. We find that there are two classes of such backgrounds, the null and the timelike. The Killing spinors of the null backgrounds have stability subgroups K\ltimes\bR^8 in $Spin(9,1)$, for $K=Spin(7)$, SU(4), $Sp(2)$, $SU(2)\times SU(2)$ and $\{1\}$, and the Killing spinors of the timelike backgrounds have stability subgroups $G_2$, SU(3), SU(2) and $\{1\}$. The former admit a single null $\hat\nabla$-parallel vector field while the latter admit a timelike and two, three, five and nine spacelike $\hat\nabla$-parallel vector fields, respectively. The spacetime of the null backgrounds is a Lorentzian two-parameter family of Riemannian manifolds $B$ with skew-symmetric torsion. If the rotation of the null vector field vanishes, the holonomy of the connection with torsion of $B$ is contained in $K$. The spacetime of time-like backgrounds is a principal bundle $P$ with fibre a Lorentzian Lie group and base space a suitable Riemannian manifold with skew-symmetric torsion. The principal bundle is equipped with a connection $\lambda$ which determines the non-horizontal part of the spacetime metric and of $H$. The curvature of $\lambda$ takes values in an appropriate Lie algebra constructed from that of $K$. In addition $dH$ has only horizontal components and contains the Pontrjagin class of $P$. We have computed in all cases the Killing spinor bilinears, expressed the fluxes in terms of the geometry and determine the field equations that are implied by the Killing spinor equations.Comment: 73pp. v2: minor change

Holomorphic and sectorial normalization of structures of Poisson structures

TOULOUSE3-BU Sciences (315552104) / SudocSudocFranceF