Relation-based Galois connections: towards the residual of a relation

Inma P. Cabrera, Pablo Cordero, Manuel Ojeda-Aciego, Relation-based Galois connections: towards the residual of a relation, CMMSE 2017: Proceedings of the 17th International Conference on Mathematical Methods in Science and Engineering ( ISBN: 978-84-617-8694-7) , pp. 469--475We explore a suitable generalization of the notion of Galois connection in which their components are binary relations. Many different approaches are possible depending both on the (pre-)order relation between subsets in the underlying powerdomain and the chosen type of relational composition.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Limits to the presence of transiting circumbinary planets in CoRoT data

The CoRoT mission during its flight-phase 2007-2012 delivered the light-curves for over 2000 eclipsing binaries. Data from the Kepler mission have proven the existence of several transiting circumbinary planets. Albeit light-curves from CoRoT have typically lower precision and shorter coverage, CoRoT's number of targets is similar to Kepler, and some of the known circumbinary planets could potentially be detected in CoRoT data as well. The aim of this work has been a revision of the entire CoRoT data-set for the presence of circumbinary planets, and the derivation of limits to the abundances of such planets. We developed a code which removes the light curve of the eclipsing binaries and searches for quasi-periodic transit-like features in a light curve after removal of binary eclipses and instrumental features. The code needs little information on the sample systems and can be used for other space missions as well, like Kepler, K2, TESS and PLATO. The code is broad in the requirements leading to detections, but was tuned to deliver an amount of detections that is manageable in a subsequent, mainly visual, revision about their nature. In the CoRoT sample we identified three planet candidates whose transits would have arisen from a single pass across the central binary. No candidates remained however with transit events from multiple planetary orbits. We calculated the upper limits for the number of Jupiter, Saturn and Neptune sized planets in co-planar orbits for different orbital period ranges. We found that there are much less giant planets in short-periodic orbits around close binary systems than around single stars.Comment: Accepted for publication in A&A, 11 pages, 4 figures and 4 tables. Updated to fix error in acknowledgemen