We formulate an analogue of the conjecture of Birch and Swinnerton-Dyer for Abelian schemes with everywhere good reduction over higher dimensional bases over finite fields. We prove some conditional results for the p′-part on it, and prove the p′-part of the conjecture for constant or isoconstant Abelian schemes, in particular the p′-part for (1) relative elliptic curves with good reduction or ...

We determine all helical surfaces in three-dimensional Euclidean space which possess a constant ratio $$a:=\kappa _1/\kappa _2$$ of principal curvatures (CRPC surfaces), thus providing the first explicit CRPC beyond known rotational ones. Our approach is based on involution conjugate surface tangents and well chosen generating profiles such that characterizing differential equation sufficiently...

Abstract This is a follow-up paper of Goldner (Math Z 297(1–2):133–174, 2021), where rational curves in surfaces that satisfy general positioned point and cross-ratio conditions were enumerated. A suitable correspondence theorem provided Tyomkin (Adv Math 305:1356–1383, 2017) allowed us to use tropical geometry, and, particular, degeneration technique called floor diagrams . also holds higher d...

An accurate and robust EEG source localization algorithm is an asset in the understanding, diagnosis, and treatment of some neurological disorders. Two inverse algorithms, LORETA and the Borgiotti-Kaplan beamformer (BK Beam) are used to localize a single dipole source from a simulated EEG within a realistic head model. Compared over a range of SNR values and source locations, the BK Beam exhibi...