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.     

First measurement of the ϱ spectral function in nuclear collisions

The NA60 experiment at the CERN SPS has studied low-mass muon pairs in 158 A GeV In–In collisions. A strong excess of pairs is observed above the yield expected from neutral meson decays. The unprecedented sample size close to 400000 events and the good mass resolution of about 2% made it possible to isolate the excess by subtraction of the decay sources. The shape of the resulting mass spectrum shows some non-trivial centrality dependence, but is largely consistent with a dominant contribution from π⁺π^-→ϱ→μ⁺μ^- annihilation. The associated ϱ spectral function exhibits considerable broadening, but essentially no shift in mass. The p_T-differential mass spectra show the excess to be much stronger at low p_T than at high p_T. The results are compared to theoretical model predictions; they tend to rule out models linking hadron masses directly to the chiral condensate. PACS 25.75.-q; 12.38.Mh; 13.85.Qk     

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.     

A New Differential Method Applied to the Study of Arbitrary Cross Section Microstructured Optical Fibers

The present work adapts a recent grating theory called “Fast Fourier factorization” to cylindrical coordinates in order to study microstructured optical fibers (MOFs). Compared with the classical differential method, this new differential method takes into account the truncation of Fourier series and the discontinuities of the fields across the diffracting surface with the help of new factorization rules. The main advantage of this method is that the directrix of the diffracting cylindrical surface is arbitrary and permits anisotropic and inhomogeneous media although its numerical application needs longer computation time, compared with other well-known numerical methods. The S-propagation algorithm is used to avoid numerical contaminations. The numerical results are validated and compared with the well-established Multipole method in the case of a MOF with six circular cylinders. Further, a new cross-sectional profile (with sectorial inclusions) that the Multipole method cannot consider is studied.     

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.     

Polarized light and X-ray precession study of the ferroelastic domains of YBa2Cu3O7-δ

The ferroelastic domains of the orthorhombic phase of YBa₂Cu₃O_7- have been observed in polarized light on ceramics and single crystals. By combining polarized light microscopy with the X-ray precession technique, the correlation of the orientation of the orthorhombica- andb-axes with that of thea-b-plane bireflectance, reflection dichroism, transmission dichroism (at a thickness of about 1m), reflection tints generated with compensators and upon uncrossing of polars, as well as the orientation of etch pits has been realized on ferroelastic single domains, bi-domains and more complicated domain patterns. Four ferroelastic orthorhombic domain states have been identified, at variance with former group theoretical considerations, predicting only two states. Ensembles of lamellar domains beyond optical resolution generate strong bireflectance with principal axes rotated by 45° relative to the truea, b-directions.     

Group additive values for the gas phase standard enthalpy of formation of hydrocarbons and hydrocarbon radicals

A complete and consistent set of 95 Benson group additive values (GAV) for the standard enthalpy of formation of hydrocarbons and hydrocarbon radicals at 298 K and 1 bar is derived from an extensive and accurate database of 233 ab initio standard enthalpies of formation, calculated at the CBS-QB3 level of theory. The accuracy of the database was further improved by adding newly determined bond additive corrections (BAC) to the CBS-QB3 enthalpies. The mean absolute deviation (MAD) for a training set of 51 hydrocarbons is better than 2 kJ mol(-1). GAVs for 16 hydrocarbon groups, i.e., C(C(d))(3)(C), C-(C(d))(4), C-(C(t))(C(d))(C)(2), C-(C(t))(C(d))(2)(C), C-(C(t))(C(d))(3), C-(C(t))(2)(C)(2), C-(C(t))(2)(C(d))(C), C-(C(t))(2)(C(d))(2), C-(C(t))(3)(C), C-(C(t))(3)(C(d)), C-(C(t))(4), C-(C(b))(C(d))(C)(H), C-(C(b))(C(t))(H)(2), C-(C(b))(C(t))(C)(H), C-(C(b))(C(t))(C)(2), C(d)-(C(b))(C(t)), for 25 hydrocarbon radical groups, and several ring strain corrections (RSC) are determined for the first time. The new parameters significantly extend the applicability of Benson's group additivity method. The extensive database allowed an evaluation of previously proposed methods to account for non-next-nearest neighbor interactions (NNI). Here, a novel consistent scheme is proposed to account for NNIs in radicals. In addition, hydrogen bond increments (HBI) are determined for the calculation of radical standard enthalpies of formation. In particular for resonance stabilized radicals, the HBI method provides an improvement over Benson's group additivity method.