The analytic torsion of a disc

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).

Reddenings of Cepheids

The aim of this work is to derive precise reddenings for 31 Cepheids using multiphase high-resolution spectroscopic observations and literature-derived colors. Each individual reddening value was determined as a difference between the observed (B - V) value and a calculated (B - V) value based on Castelli stellar model atmospheres and atmosphere parameters (effective temperature and gravity) previously determined through high-resolution spectroscopic analysis. This procedure was repeated for all pulsational phases at which spectra were obtained (typically 11 spectra for each star). After that, the mean reddening value for a given Cepheid was obtained. The reddening values derived were compared to values based on the use of distances and multiband photometry, reaching the general conclusion that reddening derived in this manner agrees with those from other methods.