A strong form of almost differentiability

We present a uniformization of Reeken's macroscopic differentiability (see [5]), discuss its relations to uniform differentiability (see [6]) and classical continuous differentiability, prove the corresponding chain rule, Taylor's theorem, mean value theorem, and inverse mapping theorem. An attempt to compare it with the observability (see [1, 4]) is made too. © 2009 Springer Science+Business Media, Inc.CEOCFCTFEDER/POCT

Retroreflecting curves in nonstandard analysis

We present a direct construction of retroreflecting curves by means of Nonstandard Analysis. We construct non self-intersecting curves which are of class C(1), except for a hyper-finite set of values, such that the probability of a particle being reflected from the curve with the velocity opposite to the velocity of incidence, is infinitely close to 1. The constructed curves are of two kinds: a curve infinitely close to a straight line and a curve infinitely close to the boundary of a bounded convex set. We shall see that the latter curve is a solution of the problem: find the curve of maximum resistance infinitely close to a given curve.CEOCFCTFEDER/POCT

A model of the reflection distribution in the vacuum ultra violet region

A reflection model with three components, a specular spike, a specular lobe and a diffuse lobe is discussed. This model was successfully applied to describe reflection of xenon scintillation light (175 nm) by PTFE and other fluoropolymers and can be used for Monte Carlo simulation and analysis of scintillation detectors. The measured data favors a Trowbridge-Reitz distribution function of ellipsoidal micro-surfaces. The intensity of the coherent reflection increases with increasing angle of incidence, as expected, since the surface appears smoother at grazing angles. The total reflectance obtained for PTFE is about 70% for VUV light at normal incidence in vacuum and estimated to be up to 100% in contact with liquid xenon

Scintillation efficiency of liquid xenon for nuclear recoils with the energy down to 5 keV

The scintillation efficiency of liquid xenon for nuclear recoils has been measured to be nearly constant in the recoil energy range from 140 keV down to 5 keV. The average ratio of the efficiency for recoils to that for gamma-rays is found to be 0.19+-0.02.Comment: 13 pages, 5 figure

Metallicity of M dwarfs III. Planet-metallicity and planet-stellar mass correlations of the HARPS GTO M dwarf sample

Aims. The aim of this work is the study of the planet-metallicity and the planet-stellar mass correlations for M dwarfs from the HARPS GTO M dwarf subsample Methods. We use a new method that takes advantage of the HARPS high-resolution spectra to increase the precision of metallicity, using previous photometric calibrations of [Fe/H] and effective temperature as starting values. Results. In this work we use our new calibration (rms = 0.08 dex) to study the planet-metallicity relation of our sample. The well-known correlation for Giant planet FGKM hosts with metallicity is present. Regarding Neptunians and smaller hosts no correlation is found but there is a hint that an anti-correlation with [Fe/H] may exist. We combined our sample with the California Planet Survey late-K and M-type dwarf sample to increase our statistics but found no new trends. We fitted a power law to the frequency histogram of the Jovian hosts for our sample and for the combined sample, f_p = C10^\alpha[Fe/H], using two different approaches: a direct bin fitting and a bayesian fitting procedure. We obtained a value for C between 0.02 and 0.04 and for \alpha between 1.26 and 2.94. Regarding stellar mass, an hypothetical correlation with planets was discovered, but was found to be the result of a detection bias.Comment: Accepted for publication in A&A. 18 pages, 11 Figures, 12 Table