The complex gradient inequality with parameter

We prove that given a holomorphic family of holomorphic functions with isolated singularities at zero and constant Milnor number, it is possible to obtain the gradient inequality with a uniform exponent.Comment: A remark was added at the end and some misprints were correcte

Identified kaon production in Ar+Sc collisions at SPS energies

NA61/SHINE is a fixed target experiment at the CERN Super Proton Synchrotron. The main goals of the experiment are to discover the critical point of strongly interacting matter and to study the properties of the onset of deconfinement. In order to reach these goals, a study of hadron production properties is performed in nucleus-nucleus, proton-proton and proton-nucleus interactions as a function of collision energy and size of the colliding nuclei. In this talk, the newest preliminary results on kaon spectra produced in Ar+Sc collisions at three beam momenta (30A, 40A and 75A) will be shown. The distributions of transverse mass and rapidity will be compared with results of NA61/SHINE (p+p, Be+Be) and NA49 (Pb+Pb, C+C, Si+Si), as well as with available world data

The Kuratowski convergence of medial axes and conflict sets

This paper consists of two parts. In the first one we study the behaviour of medial axes (skeletons) of closed, definable (in some o-minimal structure) sets in {\Rz}^n under deformations. The second one is devoted to a similar study of conflict sets in definable families. We apply a new approach to the deformation process. Instead of seeing it as a `jump' from the initial to the final state, we perceive it as a continuous process, expressed using the Kuratowski convergence of sets (hence, unlike other authors, we do not require any regularity of the deformation). Our main `medial axis inner semi-continuity' result has already proved useful, as it was used to compute the tangent cone of the medial axis with application in singularity theory.Comment: The preprint has been extended to include also the study of the behaviour of the conflict set of a continuous family of definable sets performed with a new co-author. Therefore the title has slightly been changed, too. Besides that, the references have also been updated and in the last version we strengthened the statement of Theorem 5.1