Cohomology of osp(1∣2)\mathfrak {osp}(1|2) acting on linear differential operators on the supercircle $S^{1|1}

We compute the first cohomology spaces $H^1(\mathfrak{osp}(1|2);\mathfrak{D}_{\lambda,\mu})$ ($\lambda, \mu\in\mathbb{R}$) of the Lie superalgebra $\mathfrak{osp}(1|2)$ with coefficients in the superspace $\mathfrak{D}_{\lambda,\mu}$ of linear differential operators acting on weighted densities on the supercircle $S^{1|1}$. The structure of these spaces was conjectured in \cite{gmo}. In fact, we prove here that the situation is a little bit more complicated. (To appear in LMP.

Decomposition of symmetric tensor fields in the presence of a flat contact projective structure

Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up by those vector fields that preserve the contact structure. If we consider symmetric tensor fields with coefficients in tensor densities, the vertical cotangent lift of contact form $\alpha$ is a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symmetric density valued tensor fields. This generalized Hamiltonian operator on the symbol space is invariant with respect to the action of the projective contact algebra $sp(2n+2)$. The preceding invariant operators lead to a decomposition of the symbol space (expect for some critical density weights), which generalizes a splitting proposed by V. Ovsienko

A numerical approach to large deviations in continuous-time

We present an algorithm to evaluate the large deviation functions associated to history-dependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm, valuable for systems with multiple time scales, thus extending the work of Giardin\`a, Kurchan and Peliti (PRL 96, 120603 (2006)). The procedure is supplemented with a thermodynamic-integration scheme, which improves its efficiency. We also show how the method can be used to probe large deviation functions in systems with a dynamical phase transition -- revealed in our context through the appearance of a non-analyticity in the large deviation functions.Comment: Submitted to J. Stat. Mec

Assimilation of reprocessed ERS scatterometer data into ECMWF weather analysis on the Mediterranean Sea

International audienceSince the launch of ERS-1 in 1991 and ERS-2 in 1995, carrying a C-band Scatterometer, a data set of more than thirteen years of backscattered signal from the Earth surface is available for exploitation. With its global coverage, day or night and all-weather operation, ERS Scatterometer data offer unique opportunity for long-term studies and research. To fulfill the needs of the scientific community, the European Space Agency (ESA) has developed the project: Advanced Scatterometer Processing System (ASPS). Main scope of the project is to provide with state-of-the-art algorithm, high quality and homogenous Scatterometer measurements (sigma nought) of the Earth surface and high quality wind field over the Oceans by re-processing the entire ERS mission. Additional scope is to provide on experimental basis scientific products in high resolution tailored for the emerging Scatterometer application on Ice and Land. The ASPS project is now in a pre-operational phase and the scope of the paper is to give to the scientific community an overview of the ASPS data and show the assimilation of the data into the ECMWF weather analysis system. ASPS data hopefully will help the scientific community to better understand and monitor the Earth's climate changes and to protect our environment

Differential operators on supercircle: conformally equivariant quantization and symbol calculus

We consider the supercircle $S^{1|1}$ equipped with the standard contact structure. The conformal Lie superalgebra K(1) acts on $S^{1|1}$ as the Lie superalgebra of contact vector fields; it contains the M\"obius superalgebra $osp(1|2)$. We study the space of linear differential operators on weighted densities as a module over $osp(1|2)$. We introduce the canonical isomorphism between this space and the corresponding space of symbols and find interesting resonant cases where such an isomorphism does not exist

On sl(2)-equivariant quantizations

By computing certain cohomology of Vect(M) of smooth vector fields we prove that on 1-dimensional manifolds M there is no quantization map intertwining the action of non-projective embeddings of the Lie algebra sl(2) into the Lie algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear Mathematical Physic

Maladie du hêtre. Bilan chiffré de la situation à l'été 2001

Durant l'été 2001, un inventaire des dégâts occasionnés par la maladie du hêtre à été réalisé. Les résultats de cette étude ont été publiés dans la revue Silva belgica. Nous en reprenons ici la conclusion ainsi que quelques-uns des nombreux graphiques et tableaux qui y sont présentés. Nous invitons le lecteur intéressé à se référer à l'article original