Famille de schémas implicites uniformément contrôlables pour l'équation des ondes 1-D

We present a parameterized family of finite difference schemes for the exact controllability of the 1-D wave equation. These schemes differ from the usual centered ones by additional terms of order to $h^2$, where h denotes the discretization step in space. Using a discrete version of Ingham's inequality for nonharmonic Fourier series, the spectral properties and dispersion diagrams of the schemes, we determine the parameters leading to a uniform controllability property with respect to h and an optimal stability CFL condition. To cite this article: A. Münch, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Upper bound for the size of quadratic Siegel disks

If is an irrational number, we let {p_n/q_n}_n0, be the approximants given by its continued fraction expansion. The Bruno series B() is defined as

Newton polygons and families of polynomials

We consider a continuous family (f_s), s[0,1] of complex polynomials in two variables with isolated singularities, that are Newton non-degenerate. We suppose that the Euler characteristic of a generic fiber is constant. We firstly prove that the set of critical values at infinity depends continuously on s, and secondly that the degree of the f_s is constant (up to an algebraic automorphism of ²).Mathematics Subject Classification (2000): 32S20 (Primary); 14M25 (Secondary)     

Une remarque sur les sommes de Ramanujan

We study the asymptotic behaviour of the function $A(q)={\sup }_{x,y}|{\sum }_{x<n?y}{c}_q(n)|$ where $c_q(n)$ denotes the Ramanujan sum. We prove that $q?A(q)?q\sqrt{{\log }_{2}q}$ and determine how sharp this estimation is. To cite this article: A. Chadozeau, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Pump-noise transfer in optical parametric chirped-pulse amplification

We report on direct observation of temporal contrast degradation of short pulses amplified by optical parametric chirped-pulse amplification. We show that, despite injection seeding, quantum-noise-induced fast modulations (< 50 ps) of the temporal profile of the pump pulse are imprinted on the spectrum of the amplified chirped pulse and give rise to a large picosecond pedestal in the time domain.     

Add-on extends the capability of a conventional NMR spectrometer

A spectrometer allowing the measurement of signals with spin-spin relaxation times as short as 0.5 micros has been developed. It consists of a transmitter based on a commercial spectrometer and a homemade receiver. The acquired signals are imported in the software of the commercial spectrometer. This is a simple and rather cheap way to transform a commercial rig into a spectrometer allowing measurements on systems with short T2 such as found in magnetic systems.     

Aggregation of metallo-supramolecular architectures by metallo-assembled hydrogen bonding sites

Metal-ligand interactions are used not only to design metallo-supramolecular architectures but also to assemble multiple hydrogen bond sites at the periphery of these architectures. The hydrogen bond sites aggregate the architectures into polymeric arrays with the selection of anion determining whether this is self H-bond aggregation or anion-mediated H-bond aggregation.     

Restoration of Gibbsianness for projected and FKG renormalized measures

We restore part of the thermodynamic formalism for some renormalized measures that are known to be non-Gibbsian. We determine a necessary and sufficient condition for consistency with a specification that is quasilocal only in a fixed direction. This condition is then applied to models with FKG monotonicity and to models with appropriate directional continuity rates, in particular to (noisy) decimations or projections of the Ising model. In this way we establish: (i) the validity of the second part of the variational principle for projected and FKG block-renormalized measures, and (ii) the almost quasilocality of FKG block-renormalized + and – measures.