Invariants of the dihedral group D2pD_{2p} in characteristic two

We consider finite dimensional representations of the dihedral group $D_{2p}$ over an algebraically closed field of characteristic two where $p$ is an odd integer and study the degrees of generating and separating polynomials in the corresponding ring of invariants. We give an upper bound for the degrees of the polynomials in a minimal generating set that does not depend on $p$ when the dimension of the representation is sufficiently large. We also show that $p+1$ is the minimal number such that the invariants up to that degree always form a separating set. As well, we give an explicit description of a separating set when $p$ is prime.Comment: 7 page

Reproductive behaviour of migrant women in Germany: Data, patterns and determinants

This paper examines the fertility of female migrants in Germany. After introducing major hypotheses on migrant fertility we give an overview on German datasets that are available for migrant fertility research. Finally, descriptive and multivariate analyses based on the "Sample Survey of Selected Migrant Groups in Germany (RAM)" are presented. Migrant fertility in Germany differs according to the country of origin: among major migrant groups analysed, Turkish women show the highest and Polish women the lowest fertility level. Multivariate analysis shows that the existence of children born in the country of origin has a strong increasing effect on migrant fertility. Besides, migrant women with German partners have a lower fertility than women with non-German partners. Furthermore, the fertility of Muslim women is elevated when compared with other religious groups. In contrast, emotional ties with the country of origin and the level of native and German language skills show no influence on migrants' fertility.

Solving k-Set Agreement with Stable Skeleton Graphs

In this paper we consider the k-set agreement problem in distributed message-passing systems using a round-based approach: Both synchrony of communication and failures are captured just by means of the messages that arrive within a round, resulting in round-by-round communication graphs that can be characterized by simple communication predicates. We introduce the weak communication predicate PSources(k) and show that it is tight for k-set agreement, in the following sense: We (i) prove that there is no algorithm for solving (k-1)-set agreement in systems characterized by PSources(k), and (ii) present a novel distributed algorithm that achieves k-set agreement in runs where PSources(k) holds. Our algorithm uses local approximations of the stable skeleton graph, which reflects the underlying perpetual synchrony of a run. We prove that this approximation is correct in all runs, regardless of the communication predicate, and show that graph-theoretic properties of the stable skeleton graph can be used to solve k-set agreement if PSources(k) holds.Comment: to appear in 16th IEEE Workshop on Dependable Parallel, Distributed and Network-Centric System

HST observations of the limb polarization of Titan

Titan is an excellent test case for detailed studies of the scattering polarization from thick hazy atmospheres. We present the first limb polarization measurements of Titan, which are compared as a test to our limb polarization models. Previously unpublished imaging polarimetry from the HST archive is presented which resolves the disk of Titan. We determine flux-weighted averages of the limb polarization and radial limb polarization profiles, and investigate the degradation and cancelation effects in the polarization signal due to the limited spatial resolution of our observations. Taking this into account we derive corrected values for the limb polarization in Titan. The results are compared with limb polarization models, using atmosphere and haze scattering parameters from the literature. In the wavelength bands between 250 nm and 2000 nm a strong limb polarization of about 2-7 % is detected with a position angle perpendicular to the limb. The fractional polarization is highest around 1 micron. As a first approximation, the polarization seems to be equally strong along the entire limb. The detected polarization is compatible with expectations from previous polarimetric observations taken with Voyager 2, Pioneer 11, and the Huygens probe. Our results indicate that ground-based monitoring measurements of the limb-polarization of Titan could be useful for investigating local haze properties and the impact of short-term and seasonal variations of the hazy atmosphere of Titan. Planets with hazy atmospheres similar to Titan are particularly good candidates for detection with the polarimetric mode of the upcoming planet finder instrument at the VLT. Therefore, a good knowledge of the polarization properties of Titan is also important for the search and investigation of extra-solar planets.Comment: 13 pages, 13 figures, accepted for publication in Astronomy & Astrophysic

Measurement of the earthshine polarization in the B, V, R, and I band as function of phase

The characterization of the polarimetric properties of the planet Earth is important for the interpretation of expected observations and the planning of future instruments. We present a multi-wavelengths and multi-phase set of benchmark values for the polarization signal of the integrated light from the planet Earth derived from new polarimetric observations of the earthshine back-scattered from the Moon's dark side. Using a new, specially designed wide field polarimeter we measured the fractional polarization of the earthshine in the B, V, R and I filters for Earth phase angles alpha between 30{\deg} and 110{\deg}. The phase dependence of the earthshine polarization is fitted by a function p x sin(alpha)^2. To determine the polarization of the planet Earth we correct our earthshine measurements by a polarization efficiency function for the lunar surface derived from measurements of lunar samples from the literature. The polarization of the earthshine decreases towards longer wavelengths and is about a factor 1.3 lower for the higher albedo highlands. For mare regions the measured maximum polarization is about 13 % at quadrature in the B band. The resulting fractional polarizations for Earth are 24.6 % for the B band, 19.1 % for the V band, 13.5 % for the R band, and 8.3 % for the I band. Together with literature values for the spectral reflectivity of Earth we obtain a contrast between the polarized flux of the Earth and the (total) flux of the Sun with an uncertainty of less than 20 % and we find that the best phase to detect an Earth twin is around an Earth phase alpha=65{\deg}. The polarimetric models of Earth-like planets from Stam (2008) are in qualitative agreement with our results but there are also significant differences which might guide more detailed computations.Comment: 14 pages, 14 figures, accepted for publication in Astronomy & Astrophysic

A simple optimized amplitude pupil mask for attempting to direct imaging of Proxima b with SPHERE/ZIMPOL at VLT

Proxima b is a terrestrial exoplanet orbiting in the habitable zone of our closest star Proxima Centauri. The separation between the planet and the star is about 40 mas and this is with current instruments only reachable with direct imaging, using a visual extreme AO system like SPHERE/ZIMPOL. Unfortunately, the planet falls under the first airy ring at 2$\lambda$/D in the I band, which degrades achievable contrast. We present the design, optical simulations and testing of an amplitude pupil mask for ZIMPOL that reshapes the PSF, increasing the contrast at $r = 2\lambda$/D about an order of magnitude. The simple mask can be inserted directly into the current setup of SPHERE.Comment: 11 pages, 8 figures, Poster presented at SPIE Astronomical Telescopes and Instrumentation 201