Detection of non-radial g-mode pulsations in the newly discovered PG1159 star HE 1429-1209

We performed time-series photometry of the PG1159-type star HE 1429-1209, which was recently discovered in the ESO SPY survey. We show that the star is a low-amplitude (about 0.05 mag) non-radial g-mode pulsator with a period of 919s. HE 1429-1209 is among the hottest known post-AGB stars (Teff=160000 K) and, together with the known pulsator RX J2117.1+3412, it defines empirically the blue edge of the GW Vir instability strip in the HRD at high luminosities.Comment: 4 pages, 4 figures, to be published in A&

On the capacity functional of excursion sets of Gaussian random fields on R2\R^2

When a random field $(X_t, \ t\in {\mathbb R}^2)$ is thresholded on a given level $u$, the excursion set is given by its indicator $~1_{[u, \infty)}(X_t)$. The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets, as e.g. the capacity functional as well as the second moment measure of the boundary length. It extends results obtained for the one-dimensional case to the two-dimensional case, with tools borrowed from crossings theory, in particular Rice methods, and from integral and stochastic geometry.Comment: 19 page