Improved intermediate asymptotics for the heat equation

This letter is devoted to results on intermediate asymptotics for the heat equation. We study the convergence towards a stationary solution in self-similar variables. By assuming the equality of some moments of the initial data and of the stationary solution, we get improved convergence rates using entropy/entropy-production methods. We establish the equivalence of the exponential decay of the entropies with new, improved functional inequalities in restricted classes of functions. This letter is the counterpart in a linear framework of a recent work on fast diffusion equations; see Bonforte et al. (2009) [18]. The results extend to the case of a Fokker–Planck equation with a general confining potential.     

Equations of motion of compact binaries at the third post-Newtonian order

The equations of motion of two point masses in harmonic coordinates are derived through the third post-Newtonian (3PN) approximation. The problem of selffield regularization (necessary for removing the divergent self-field of point particles) is dealt with in two separate steps. In the first step the extended Hadamard regularization is applied, resulting in equations of motion which are complete at the 3PN order, except for the occurrence of one and only one unknown parameter. In the second step the dimensional regularization (ind dimensions) is used as a powerful argument for fixing the value of this parameter, thereby completing the 3-dimensional Hadamard-regularization result. The complete equations of motion and associated energy at the 3PN order are given in the case of circular orbits.     

Effective signal-to-noise ratio improvement by parametric image amplification

We show experimentally that parametric optical preamplification greatly improves the signal-to-noise ratio of an image if the detector has a poor quantum efficiency and/or a great level of readout noise. Results are fully consistent with the theory of quantum-noise-limited amplification.     

Chiral 3-aminopyrrolidines as a rigid diamino scaffold for organocatalysis and organometallic chemistry

Over 20 new and easily prepared diamines were screened for the asymmetric Morita–Baylis–Hillman reaction. Chiral non-racemic 3-(N,N-dimethylamino)-1-methylpyrrolidine was found to promote efficiently the reaction of methyl vinyl ketone and substituted benzaldehydes. Enantiomeric excesses up to 73% were reached with electron-deficient benzaldehyde derivatives. After a simple deprotonation, one of these diamines was transformed into a chiral mixed aggregate for the enantioselective synthesis of (R)-1-o-tolylethanol with 76% ee.     

Remarks on existence and uniqueness of Cournot–Nash equilibria in the non-potential case

This article is devoted to various methods (optimal transport, fixed-point, ordinary differential equations) to obtain existence and/or uniqueness of Cournot–Nash equilibria for games with a continuum of players with both attractive and repulsive effects. We mainly address separable situations but for which the game does not have a potential, contrary to the variational framework of Blanchet and Carlier (Optimal transport and Cournot–Nash equilibria, 2012). We also present several numerical simulations which illustrate the applicability of our approach to compute Cournot–Nash equilibria.     

Vibrational modes of oxygen on W(110)

Electron energy loss measurements of the vibrational modes of oxygen on W(110) as a function of coverage up to 0.5 monolayer are presented and analyzed. A single loss at 67 meV is observed initially; with increasing exposure this loss shifts to 72 meV and another loss appears at 47 meV. These data indicate coexistence of two species on the surface with a coverage-dependent conversion. Angular profiles of the specular elastic beam show a dramatic increase in width with initial oxygen coverage; this is possibly due to an oxygen-induced static disordering of the W surface layer.     

Long term sleep disturbance due to traffic noise

This contribution to the evaluation of the effects of traffic noise on sleep disturbance is focused on the responses of people living near a main road. Experiments were carried out in the homes of subjects who had habitually been exposed to noise for periods of more than four years. The chronic changes in overall sleep patterns and the temporary sleep responses to particular noise events caused by traffic are demonstrated. Young people show mainly stage 3 and 4 deficits whilst older people show REM sleep deficits. The cardiac response to noise during sleep was also examined. These results highlight that both long term average and peak levels are important in assessing sleep disturbance. The threshold levels, measured inside the bedroom and above which sleep quality starts to become impaired, are 37 L_eq(A) and 45 dB (A)L_{p max}, respectively. For the type of traffic studied these two levels are coherent and it is therefore possible that a single noise index, L_eq(A), is sufficient to scale sleep disturbance.     

Chemistry of 2-bromo 3-trichloromethyl succinic anhydride and dimethyl ester : preparation of various halogenated succinic,maleic, fumaric and malic acid derivatives

Various reactions of the readily available adducts of bromotrichloromethane with maleic anhydride and dimethyl maleate and fumarate leading to halogenated derivatives of succinic, maleic, fumaric or malic acids and/or esters are described.