Uniqueness of the electrostatic solution in Schwarzschild space

In this Brief Report we give the proof that the solution of any static test charge distribution in Schwarzschild space is unique. In order to give the proof we derive the first Green's identity written with p-forms on (pseudo) Riemannian manifolds. Moreover, the proof of uniqueness can be shown for either any purely electric or purely magnetic field configuration. The spacetime geometry is not crucial for the proof.Comment: 3 pages, no figures, uses revtex4 style file

Transport on randomly evolving trees

The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to nodes. By using the method of the age-dependent branching processes we derive the joint distribution function of the number of living and dead nodes, and determine the correlation between these node numbers as a function of time. Also analyzed are the stochastic properties of the end-nodes; and the correlation between the numbers of living and dead end-nodes is shown to change its character suddenly at the very beginning of the evolution process. The survival probability of random trees is investigated and expressions are derived for this probability.Comment: 16 pages, 8 figures, published in Phys. Rev. E 72, 051101 (2005

The HATNet and HATSouth Exoplanet Surveys

The Hungarian-made Automated Telescope Network (HATNet) has been in operation since 2003, with the key science goal being the discovery and accurate characterization of transiting extrasolar planets (TEPs) around bright stars. Using six small, 11\,cm\ aperture, fully automated telescopes in Arizona and Hawaii, as of 2017 March, it has discovered and accurately characterized 67 such objects. The HATSouth network of telescopes has been in operation since 2009, using slightly larger, 18\,cm diameter optical tubes. It was the first global network of telescopes using identical instrumentation. With three premier sites spread out in longitude (Chile, Namibia, Australia), the HATSouth network permits round-the-clock observations of a 128 square arcdegree swath of the sky at any given time, weather permitting. As of this writing, HATSouth has discovered 36 transiting exoplanets. Many of the altogether ~100 HAT and HATSouth exoplanets were the first of their kind. They have been important contributors to the rapidly developing field of exoplanets, motivating and influencing observational techniques, theoretical studies, and also actively shaping future instrumentation for the detection and characterization of such objects.Comment: Invited review chapter, accepted for publication in "Handbook of Exoplanets", edited by H.J. Deeg and J.A. Belmonte, Springer Reference Work