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.     

Chiral separation of the four stereoisomers of a novel antianginal agent using a dual cyclodextrin system in capillary electrophoresis

Reported here is an analytical method enabling the stereochemical resolution of a new antianginal compound possessing two stereogenic centers, leading to four stereoisomers. Only one of these isomers is currently under development as a novel antianginal agent and consequently, the other three isomers are considered as unwanted chiral impurities. Therefore, an enantioselective method is required in order to check its enantiomeric purity. This paper presents a method exploiting the high efficiency of capillary electrophoresis and the complexing properties of cyclodextrins to achieve the separation of the four stereoisomers of this weakly basic compound (pKa = 7.4). For this purpose, the combination of a neutral cyclodextrin, hydroxypropyl-gamma-cyclodextrin (HP-gamma-CD), and an anionic cyclodextrin, carboxymethyl-beta-cyclodextrin (CM-beta-CD), was added to the separation buffer running in an uncoated silica capillary. After selection of the suitable cyclodextrin system, satisfactorily separation conditions were as follows: 30 mM phosphate buffer (pH 6.4) containing 10 mM of HP-gamma-CD and 10 mM of CM-beta-CD, running voltage +30 kV. The resulting run time and resolutions were respectively about 17 min and between 1.95 and 2.84. Linearity curves (0.993 < r2 < 0.998) are also shown.     

Effect of time on the interfacial and foaming properties of beta-lactoglobulin/acacia gum electrostatic complexes and coacervates at pH 4.2

The electrostatic complexation between beta-lactoglobulin and acacia gum was investigated at pH 4.2 and 25 degrees C. The binding isotherm revealed a spontaneous exothermic reaction, leading to a DeltaHobs = -2108 kJ mol(-1) and a saturation protein to polysaccharide weight mixing ratio of 2:1. Soluble electrostatic complexes formed in these conditions were characterized by a hydrodynamic diameter of 119 +/- 0.6 nm and a polydispersity index of 0.097. The effect of time on the interfacial and foaming properties of these soluble complexes was investigated at a concentration of 0.1 wt % at two different times after mixing (4 min, referred as t approximately 0 h and t = 24 h). At t approximately 0 h, the mixture is mainly made of aggregating soluble electrostatic complexes, whereas after 24 h these complexes have already insolubilize to form liquid coacervates. The surface elasticity, viscosity and phase angle obtained at low frequency (0.01 Hz) using oscillating bubble tensiometry revealed higher fluidity and less rigidity in the film formed at t approximately 0 h. This observation was confirmed by diminishing bubble experiments coupled with microscopy of the thin film. It was thicker, more homogeneous and contained more water at t approximately 0 h as compared to t = 24 h (thinner film, less water). This led to very different gas permeability's of Kt approximately 0 h = 0.021 cm s(-1) and Kt=24 h) = 0.449 cm s(-1), respectively. Aqueous foams produced with the beta-lactoglobulin/acacia gum electrostatic complexes or coacervates exhibited very different stability. The former (t approximately 0 h) had a stable volume, combining low drainage rate and mainly air bubble disproportionation as the destabilization mechanism. By contrast, using coacervates aged for 24 h, the foam was significantly less stable, combining fast liquid drainage and air bubble destabilization though fast gas diffusion followed by film rupture and bubble coalescence. The strong effect of time on the air/water interfacial properties of the beta-lactoglobulin/acacia gum electrostatic complexes can be understood by their reorganization at the interface to form a coacervate phase that is more fluid/viscous at t approximately 0 h vs rigid/elastic at t = 24 h.     

Synthesis,coordination to Rh(I), and hydroformylation catalysis of new beta-aminophosphines bearing a dangling nitrogen group: an unusual inversion of a Rh-coordinated P center

Variants of the beta-aminophosphine L(1) [Ph(2)PCH(2)CH(Ph)NHPh] containing additional nitrogen donor functions have been prepared. These functions are branched off the C atom adjacent to the P atom, or the P atom itself. Ligand [Ph(2)PCH(o-C(6)H(4)NMe(2))CH(Ph)NHPh] has been obtained as a mixture of two diastereomers L(3A) and L(3B) by lithiation of L(2) [Ph(2)PCH(2)(o-C(6)H(4)NMe(2))] with n-BuLi followed by PhCH=NPh addition and hydrolysis. The diastereomers have been separated by fractional crystallization from ethanol. Ligand Et(2)NCH(2)P(Ph)CH(2)CH(Ph)NHPh has been obtained as a mixture of two diastereomers L(5A) and L(5B)(starting with P-Ph reductive cleavage of L(1) by lithium and subsequent hydrolysis to give PhP(H)CH(2)CH(Ph)NHPh (mixture of two diastereomers L(4A) and L(4B)). The latter reacts with diethylamine and formaldehyde to afford the L(5) diastereomeric mixture. Complexes RhCl(CO)(L) (L = L(3A), 1(A); L(3B), 1(B); L(5A/B), 2(A/B)) were obtained by reaction of [RhCl(CO)(2)](2) and the appropriate ligand or ligand mixture. Complexes 1(A), 1(B), and 2(A) have been isolated in pure form and characterized by classical techniques and by single-crystal X-ray diffraction. All structures exhibit a bidentate kappa-P,kappa-N(NHPh) mode similar to the complex containing L(1). While complexes 1(A) or 1(B) are stable in CDCl(3) solution, complex 2(A) slowly converts to its diastereomer 2(B). This unexpected epimerization appears to take place by inversion at the Rh-coordinated P center, an apparently unprecedented phenomenon. A mechanism based on a reversible P-C bond oxidative addition is proposed. The influence of the pendant nitrogen function of the diaminophosphines L(3A) and L(5A/B) on the rhodium catalytic activity in styrene hydroformylation has been examined and compared to that of the aminophosphines L(1) or L(2). The observed trends are related to the basicity of the dangling amine function and to its proximity to the metal center.     

1-Methoxycarbonyl-substituiertes 2,3-Dihydropyridin-4(1H)-on (= Methyl-1,2,3,4-tetrahydro-4-oxopyridin-1-carboxylat) als Chromophor für die photochemische [2 + 2]-Cycloaddition

1-Methoxycarbonyl-Substituted 2,3-Dihydropyridin-4(1H)-one(= Methyl 1,2,3,4-Tetrahydro-4-oxopyridine-1-carboxylate) as Chromophore for Photochemical [2 + 2]-Cycloadditions With olefins having an electron-acceptor as well as with olefins having an electron-donor substituent, 1-methoxycarbonyl-substituted dihydropyridinone 12 undergoes [2 + 2] cycloaddition in good preparative yields. The photochemical cycloaddition is highly regioselective. For preparative purposes, the ring junction can be equilibrated to the thermodynamically more stable cis-junction. Only the ‘endo’/‘exo’ selectivity at the C-atom bearing the olefin substituent cannot be controlled. The photodimerization of 12 is the only side reaction. Using a slight excess of the olefin, the photodimerization can be suppressed. The protecting group at the N-atom of the dihydropyridinone can be varied in order to introduce an internal sensitizer, as shown with 1-acyl-substituted compound 29 , which underwent the cycloaddition process even with sunlight.