Sur l'existence des opérateurs d'onde pour l'équation de Wigner dans les espaces L2,pExistence of wave operators for the Wigner equation in L2,p spaces

Basing on the formalism established by Markovich, we show the completeness of wave operators for the Wigner equation in L². In the second part, using estimations proved by Castella and Perthame on the one hand, and the L^p→L^q estimations for the Schrödinger group on the other hand, we prove the existence of the wave operators in L^2,p spaces. To cite this article: H. Emamirad, P. Rogeon, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 811–816.     

Complex polymer architectures through dimethoxymethyl 1,1‐diphenylethylene derivatives

The reactions of polystyryllithium and potassium on dimethoxymethyl 1,1‐diphenylethylene derivatives were studied in different solvents. In a polar medium, A₃ and A₆ star types were formed according to the stoichiometry, whereas in a nonpolar medium, hyperbranched structures were synthesized. Extensions of an already proposed mechanism in polar and nonpolar media were examined. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3329–3335, 2003     

Analysis of a Poisson system with boundary conditions

We consider a class of problems originating from a Raman laser amplification model, for which the equations can be written as a Poisson system with boundary conditions. Once reformulated, this system becomes an integro-differential equation that we study here in some detail. In particular, we show the existence of a smooth solution under general assumptions, and prove its uniqueness for boundary values that are not too far apart. Eventually, we completely solve the question of uniqueness for systems of dimensions one and two. To cite this article: F. Castella et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Une note sur les lemmes div–curl

Let $\text{Ω}$ be a strongly Lipschitz domain of $\text{R}{}^{\mathrm{n}}$ (n?2). We give endpoint versions of div–curl lemmata on $\text{Ω}$, for a given function f on $\text{Ω}$ whose gradient belongs to a Hardy space on $\text{Ω}$. To cite this article: P. Auscher et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Influence de la longue mémoire sur le comportement asymptotique d'estimateurs fonctionnelsInfluence of long memory on the asymptotic behaviour of functional estimators

This Note gives asymptotic results for kernel estimators of several functionals (density, failure rate and distribution functions) of a long-memory process. The results are presented in such a way as to highlight the influence of the long dependence on the rates of convergence. To cite this article: G. Estevez-Perez, P. Vieu, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 271–274.     

Comprehensive study on the formation of polyelectrolyte complexes from (quaternized) poly[2‐(dimethylamino)ethyl methacrylate] and poly(2‐acrylamido‐2‐methylpropane sodium sulfonate)

Polyelectrolyte complexes (PECs) have been prepared from well‐defined (quaternized) poly[2‐(dimethylamino)ethyl methacrylate] (PDMAEMA) and high molecular weight poly(2‐acrylamido‐2‐methylpropane sodium sulfonate) (PAMPSNa) after a thorough study of their viscometric properties. The effect of pH and quaternization degree of PDMAEMA on PECs stoichiometry has been examined. PEC‐based materials have been characterized in terms of thermal stability, equilibrium swelling degree, and free/bound water composition. The stoichiometry and swellability of the physically crosslinked hydrogels obtained from fully quaternized PDMAEMA/PAMPSNa complexes do not depend on pH. In contrast, PECs made of non quaternized PDMAEMA and PAMPSNa are highly affected by pH, and could reversibly disintegrate at pH ≥ 9. Partially quaternized PDMAEMA/PAMPSNa PECs exhibit intermediate properties and form stable loose structures in the whole investigated pH range. Finally, stable dispersions of PECs nanoparticles have been successfully produced from dilute solutions of the complementary polyelectrolytes. The nanoparticle average diameter as determined by dynamic light scattering proved to depend on the molar fraction of DMAEMA‐based subunits and on the initial polyelectrolyte concentration. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5468–5479, 2006     

Soluble models for dynamics driven by a super-diffusive noise

We explicitly discuss scalar Langevin type of equations where the deterministic part is linear, but where the integrated noise source is a non-linear diffusion process exhibiting superdiffusive behavior. We calculate transient and stationary probabilities and study the possibility of noise induced transitions from a unimodal to a bimodal probability shape. Illustrations from finance and dynamical systems are given.     

Bell's theorem based on a generalized EPR criterion of reality

First, the demonstration of Bell's theorem, i.e., of the nonlocal character of quantum theory, is spelled out using the EPR criterion of reality as premises and a gedankenexperiment involving two particles. Then, the EPR criterion is extended to include quantities predicted almostwith certainty, and Bell's theorem is demonstrated on these new premises. The same experiment is used but in conditions that become possible in real life, without the requirements of ideal efficiencies and zero background. Very high efficiencies and low background are needed, but these requirements may be met in the future.     

MECHANISM OF PHOTOREDUCTION OF THIAZINE DYES BY EDTA STUDIED BY FLASH PHOTOLYSIS-II. pH DEPENDENCE OF ELECTRON ABSTRACTION RATE CONSTANT OF THE DYES IN THEIR TRIPLET STATE

Abstract— The pH dependence of the apparent reactivity of thiazine dyes in their triplet states has been studied in aqueous solutions, using as electron donor HY^-3, the trianionic species of ethylene diamine tetraacetic acid (EDTA), in the pH range 4–8. The pH dependence is found to be related to a change in the degree of protonation of the triplet excited dye. The apparent reactivity and lifetime of two differently protonated forms of thionine, azur B and methylene blue were determined by classical and dye-laser flash techniques, making it possible to evaluate the rate constant for electron abstraction of these molecules in their triplet states. It is found that: (a) protonation on the ring nitrogen increases the electron-abstraction rate constant of the triplet-state species about twenty-fold, and (b) methylation on the side amino groups decreases it.     

Glass and polymeric membrane electrodes for the measurement of pH in milk and cheese

While there is a considerable interest in the food industry in determining various analytes using ion-selective electrodes (ISEs), only few reports describe their use for direct measurements in food. In this study, the suitability of glass electrodes and ionophore-based solvent polymeric ISEs for the determination of pH in Process cheese, Cheddar cheese and milk was investigated. The liquid junction potential between a 3 M KCl bridge electrolyte and diluted as well as undiluted Process cheese was found to be negligible. Reference electrodes with ceramic plug and sleeve-type junctions performed well, although precautions needed to be taken to prevent plugging at the junctions. While the protein rennet casein posed no problems in pH measurements, the extraction of neutral lipophilic compounds or hydrophobic peptides into solvent polymeric membranes was evident, resulting in some loss of selectivity for monovalent cations upon exposure to cheese. However, it was found that ISEs based on tridodecylamine (R₃N) as ionophore and o-nitrophenyl octyl ether (oNPOE) as plasticizer can be used to accurately measure the pH of milk and, after desensitization of the electrodes in a cheese emulsion, of diluted Process cheese. Since pH measurements with a glass electrode showed that emulsions of cheese moderately diluted to a cheese content of 70% have the same pH as undiluted cheeses, it is possible to determine the pH in cheese with ionophore-based ISEs. R₃N membranes also performed well in undiluted milk.