Théorème de l’Indice et Formule des Traces

Our purpose is to obtain a geometric formula as explicit as possible for the L ² index of a Dirac operator over a locally symmetric space of finite volume, generalizing Arthur’s formula for the Euler–Poincaré caracteristic (Arthur in Invent Math 97:257–290, 1989).     

New amicable four-cycles

Fifty new amicable four-cycles are discovered by the constructive method invented in 1969 by the second author.

     

Nonenzymatic protocol for Pseudomonas aeruginosa DNA preparation and rapid subtyping by mini pulsed-field gel electrophoresis.

The fastest protocol for Pseudomonas aeruginosa subtyping by contour clamped homogeneous electric field (CHEF) electrophoresis takes around 20 h. It includes enzymatic sample preparation, DNA restriction and fragment separation. Here, P. aeruginosa cells embedded in agarose miniplugs were lysed and deproteinized by incubating the miniplugs for 30 min in a single nonenzymatic solution. DNA molecules were digested for 2 h with 5 U of XbaI, and fragments were separated in 4.96 h by miniCHEF electrophoresis at 10 V/cm. Total time for P. aeruginosa subtyping was 8 h. Control experiments included DNA preparation by enzymatic or nonenzymatic protocols, different times of DNA restriction and comparisons of DNA separations done by miniCHEF or CHEF electrophoresis. Both methods and chambers gave similar results, but the rapid nonenzymatic method and the miniCHEF gave them in less time. Cells grown in broth or on plates were useful for nonenzymatic DNA preparation. Thirteen P. aeruginosa isolates were successfully fingerprinted using the protocol described here.     

Application of global Carleman estimates with rotated weights to an inverse problem for the wave equation

We establish geometrical conditions for the inverse problem of determining a stationary potential in the wave equation with Dirichlet data from a Neumann measurement on a suitable part of the boundary. We present the stability results when we measure on a part of the boundary satisfying a rotated exit condition. The proofs rely on global Carleman estimates with angle type dependence in the weight functions. To cite this article: A. Doubova, A. Osses, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Determination of the phenylurea herbicide linuron and its metabolites in environmental samples by HPLC with serial ultraviolet and amperometric detection

Summary Procedures were developed for the determination of the herbicide linuron and its main metabolites using reversed-phase high performance liquid chromatography with serial ultravoilet-amperometric detection. For the application to water and soil analysis solid-phase extraction with cyclohexyl cartridges was found to be useful for the separation and enrichment of these compounds at trace level. By amperometric detection at +1.3 V down to approximately 0.5 ng of the tested metabolites could be determined. This is about 5-times more sensitive than the ultraviolet detection by the selected wavelength of 247 nm. Only for linuron the UV-detection proved to be more sensitive under the described conditions; the detection limit was found to be 5 ng.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Asymptotic analysis of the lattice Boltzmann equation

In this article we analyze the lattice Boltzmann equation (LBE) by using the asymptotic expansion technique. We first relate the LBE to the finite discrete-velocity model (FDVM) of the Boltzmann equation with the diffusive scaling. The analysis of this model directly leads to the incompressible Navier–Stokes equations, as opposed to the compressible Navier–Stokes equations obtained by the Chapman–Enskog analysis with convective scaling. We also apply the asymptotic analysis directly to the fully discrete LBE, as opposed to the usual practice of analyzing a continuous equation obtained through the Taylor-expansion of the LBE. This leads to a consistency analysis which provides order-by-order information about the numerical solution of the LBE. The asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities, such as vorticity. It also justifies the use of Richardson’s extrapolation method. As an example, a two-dimensional Taylor-vortex flow is used to validate our analysis. The numerical results agree very well with our analytic predictions.