A Primal-Dual Approach of Weak Vector Equilibrium Problems

In this paper we provide some new sufficient conditions that ensure the existence of the solution of a weak vector equilibrium problem in Hausdorff topological vector spaces ordered by a cone. Further, we introduce a dual problem and we provide conditions that assure the solution set of the original problem and its dual coincide. We show that many known problems from the literature can be treated in our primal-dual model. We provide several coercivity conditions in order to obtain solution existence of the primal-dual problems without compactness assumption. We pay a special attention to the case when the base space is a reflexive Banach space. We apply the results obtained to perturbed vector equilibrium problems.Comment: 20 page

Exploration of the brown dwarf regime around solar-like stars by CoRoT

Aims. A summary of the CoRoT brown dwarf investigations are presented. Methods. Transiting brown dwarfs around solar like stars were studied by using the photometric time-series of CoRoT, and ground based radial velocity measurements. Results. CoRoT detected three transiting brown dwarfs around F and G dwarf stars. The occurence rate of brown dwarfs was found to be 0.20 +/- 0.15% around solar-like stars which is compatible with the value obtained by Kepler-data.Comment: To be appeared in 'The CoroT legacy book', 2016, Scientific Editors: Annie Baglin et al., Publisher: EDP Sciences, ISBN: 978-2-7598-1876-