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 IV. A high-precision [Fe/H] and Teff technique from high-resolution optical spectra for M dwarfs

Aims. In this work we develop a technique to obtain high precision determinations of both metallicity and effective temperature of M dwarfs in the optical. Methods. A new method is presented that makes use of the information of 4104 lines in the 530-690 nm spectral region. It consists in the measurement of pseudo equivalent widths and their correlation with established scales of [Fe/H] and $T_{eff}$. Results. Our technique achieves a $rms$ of 0.08$\pm$0.01 for [Fe/H], 91$\pm$13 K for $T_{eff}$, and is valid in the (-0.85, 0.26 dex), (2800, 4100 K), and (M0.0, M5.0) intervals for [Fe/H], $T_{eff}$ and spectral type respectively. We also calculated the RMSE$_{V}$ which estimates uncertainties of the order of 0.12 dex for the metallicity and of 293 K for the effective temperature. The technique has an activity limit and should only be used for stars with $\log{L_{H_{\alpha}}/L_{bol}} < -4.0$. Our method is available online at \url{http://www.astro.up.pt/resources/mcal}.Comment: Accepted in Astronomy and Astrophysics. Updated one important reference in the introduction. Some typos correcte