Spectral analysis of the background in ground-based, long-slit spectroscopy

This paper examines the variations, because of atmospheric extinction, of broad-band visible spectra, obtained from long-slit spectroscopy, in the vicinity of some stars, nebulae, and one faint galaxy.Comment: 12 figure

General considerations on the illumination of galactic nebulae

The interpretation of observations over different wavelength domains, which now exist over a large fraction of the sky, will be used to determine relationships between a nebula and its' illuminating source. The illuminating source of a high latitude nebula must be behind the cloud and e.g. at close angular distance. It is either a point source behind the nebula or the average radiation field created by all the background stars. In the latter case it is possible to estimate the maximum surface brightness a nebula can reach. Illumination by the galactic plane is always negligible in up to date observations. The red color of some nebulae, when they are not HII regions, is more likely to be due to large column densities than to an emission process. Concerning interstellar grain properties, the same data will be used to support the well known property that grains scatter starlight in forward direction.Comment: 14 pages, 2 figure

Reddening law and interstellar dust properties along Magellanic sight-lines

This study establishes that SMC, LMC and Milky Way extinction curves obey the same extinction law which depends on the 2200A bump size and one parameter, and generalizes the Cardelli, Clayton and Mathis (1989) relationship. This suggests that extinction in all three galaxies is of the same nature. The role of linear reddening laws over all the visible/UV wavelength range, particularly important in the SMC but also present in the LMC and in the Milky Way, is also highlighted and discussed.Comment: accepted for publication in Astrophysics and Space Science. 16 pages, 12 figures. Some figures are colour plot

Unitary expansion of the time evolution operator

We propose an expansion of the unitary evolution operator, associated to a given Schr\"odinger equation, in terms of a finite product of explicit unitary operators. In this manner, this unitary expansion can be truncated at the desired level of approximation, as shown in the given examples.Comment: 6 pages, 7 figures. Updated version, minor final change

Single observable concurrence measurement without simultaneous copies

We present a protocol that allows us to obtain the concurrence of any two qubit pure state by performing a minimal and optimal tomography of one of the subsystems through measuring a single observable of an ancillary four dimensional qudit. An implementation for a system of trapped ions is also proposed, which can be achieved with present day experimental techniques.Comment: 4 pages, 1 figur