Arbitrary high-order schemes for the linear advection and wave equations: application to hydrodynamics and aeroacoustics

We present here an extension to any order of accuracy of the schemes proposed in Daru and Tenaud [J. Comput. Phys. 193 (2) (2004) 563–594] for the linear advection equation in 1D. Such schemes are then used for a high-order generalization of the Godunov method in the case of the wave equation and the locally linearized Euler equations. To cite this article: S. Del Pino, H. Jourdren, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

From social welfare ordering to acyclic aggregation of preferences

One way to overcome Arrow's impossibility theorem is to drop the requirement that the collective preference be transitive. If it is quasi-transitive (strict preferences are transitive) an oligarchy emerges. If it is only acyclic, many non-oligarchic aggregation rules are available, yet the resulting decision rules are poorly decisive: Nakamura's theorem characterizes acyclic and neutral Arrowian aggregators. We propose a parallel characterization of acyclic and anonymous aggregation methods.     

Catalyse par transfert de phase solide-liquide sans solvant : application a la reaction de michael

Solid-liquid phase transfer catalysis without added organic solvent efficiently promotes MICHAEL reactions. The method is applied here to the addition of acetylacetone, methylacetoacetate and fluorene anions on hindered acceptors.     

Heterogeneous wires made of martensitic materials

In this paper we present a direct derivation of a theory of heterogeneous wires starting from three-dimensional nonlinear hyperelasticity augmented by an interfacial energy term. The derivation involves no a priori choice of asymptotic expansion or ansatz. It yields a wire theory with two Cosserat vector fields. The theory is applied to multiwell energy functions appropriate for martensitic materials. A formal derivation of higher theories of homogeneous wires is given, which yields three additional Cosserat vector fields and an explicit form for the bending and torsion energy. To cite this article: H. Le Dret, N. Meunier, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Facteurs de transfert pour les intégrales de Kloosterman

We compute the transfer factors which relate absolute Klosterman integrals and Kloosterman integrals relative to a quadratic extension. To cite this article: H. Jacquet, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

A new example of a uniformly Levi degenerate hypersurface in <Emphasis Type="Bold">C</Emphasis><Superscript>3</Superscript>

The purpose of this erratum is to point out a mistake in a previous article by the authors and to explain how this affects the results of that article. The online version of the original article can be found at     

Fundamentals of the interferometric fiber-optic gyroscope

This paper reviews the basics of the interferometric fiber-optic gyroscope: fundamental principle based on Sagnac effect, importance of reciprocity and single-mode propagation, analysis of coherence and polarization problems, signal processing techniques. It also describes the technological progresses of guided-wave components (single-mode optical fiber, semi-conductor diode source, integrated optics, in-line fiber components). Finally, recent trends like multi-axis configurations and rare-earth doped fiber source are presented.     

Looking for SUSY with EDELWEISS-I and-II

The latest results obtained by the EDELWEISS WIMP (weakly interacting massive particles) direct detection experiment using three heat-and-ionization 320-g germanium bolometers are given. Presently the most sensitive WIMP direct detection experiment for WIMP mass >30 GeV, EDELWEISSI is testing a first region of SUSY models compatible with accelerator constraints. The status and main characteristics of EDELWEISS-II, involving in a first stage 28 germanium bolometers and able to accommodate up to 120 detectors, are briefly presented, together with neutron background estimates.     

Cantor spectrum and singular continuity for a hierarchical Hamiltonian

We study the spectrum of the HamiltonianH onl ₂() given by (H)(n)=(n+1)+(n–1)+V(n)(n) with the hierarchical (ultrametric) potentialV(2 ^m (2l+1))=(1–R ^m )/(1–R), corresponding to 1-, 2-, and 3-dimensional Coulomb potentials for 0<R<1,R=1 andR>1, respectively, in a suitably chosen valuation metric. We prove that the spectrum is a Cantor set and gaps open at the eigenvaluese _n (1)<e _n (2)<...<e _n (2 ⁿ –1) of the Dirichlet problemH=E, (0)=(2 ⁿ )=0,n1. In the gap opening ate _n (k) the integrated density of states takes on the valuek/2 ⁿ . The spectrum is purely singular continuous forR1 when the potential is unbounded, and the Lyapunov exponent vanishes in the spectrum. The spectrum is purely continuous forR<1 in (H)[–2, 2] and =0 here, but one cannot exclude the presence of eigenvalues near the border of the spectrum. We also propose an explicit formula for the Green's function.Work supported by the Fonds National Suisse de la Recherche Scientifique, Grant No. 2.042-0.86 (H.K. and R.L.) and 2.483-0.87 (A.S.)On leave from the Dipartimento di Fisica, Università degli Studi di Firenze, Largo E. Fermi 2, I-50125 Firenze, Italy     

The quadratic convergence of the topological epsilon algorithm for systems of nonlinear equations

In this work we consider the topological epsilon algorithm for solving systems of nonlinear equations. In section 2, a sufficient condition for its quadratic convergence is given. In section 3, some geometrical remarks about this condition are made.