We derive and present a fast and accurate solution of the initial value problem for Keplerian motion in universal variables that does not use the Stumpff series. We find that it performs better than methods based on the Stumpff series.

The Award Committee – Peter Kritzer, Johannes Kepler University Linz, Austria and Jan Vybiral, Charles University, Czech Republic – determined that the following paper exhibits exceptional merit and therefore awarded the prize to: Bernd Carl, Aicke Hinrichs, and Philipp Rudolph for their paper ‘‘Entropy numbers of convex hulls in Banach spaces and applications’’, which appeared in October, 2014...

We discuss the generalizations of the MICZ-Kepler system (the system describing the motion of the charged particle in the field of Dirac dyon), to the curved spaces, arbitrary potentials and to the multi-dyon background. The integrable system describing the motion of the charged particle in the field of Dirac dyon (magnetic monopole carrying the electric charge) has been suggested independently...

A model of computation (MoC) is a formal abstraction of execution in a computer. There is a need for composing diverse MoCs in e-science. Kepler, which is based on Ptolemy II, is a scientific workflow environment that allows for MoC composition. This paper explains how MoCs are combined in Kepler and Ptolemy II and analyzes which combinations of MoCs are currently possible and useful. It demons...

We trace the history of atmospheric refraction from the ancient Greeks up to the time of Kepler. The concept that the atmosphere could refract light entered Western science in the second century B.C. Ptolemy, 300 years later, produced the first clearly defined atmospheric model, containing air of uniform density up to a sharp upper transition to the ether, at which the refraction occurred. Alha...

Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenbergerstrasse 69, A-4040 Linz, Austria, Zentrum für Oberflächenund Nanoanalytik, Johannes Kepler University Linz, Altenbergerstrasse 69, A-4040 Linz, Austria, L-NESS, Dipartimento di Fisica, Politecnico di Milano, Polo di Como, via Anzani 42, I-22100 Como, Italy, Charles University, Department of Condensed...

www.sciencemag.org SCIENCE VOL 344 18 APRIL 2014 COVER Artist’s concept of Kepler-186f, a planet located ~500 light-years from Earth in the constellation Cygnus. The discovery of Kepler-186f confi rms that Earth-sized planets exist in the habitable zone of other stars (that is, the range of distances from a star wherein liquid water might pool on the surface of an orbiting planet) and signals a...

The asymptotics of Rydberg states, i.e., highly excited bound states of the hydrogen atom Hamiltonian, and various expectations involving these states are investigated. We show that suitable linear combinations of these states, appropriately rescaled and regarded as functions either in momentum space or con guration space, are highly concentrated on classical momentum space or con guration spac...

We show that the exact integrator for the classical Kepler motion, recently found by Kozlov (J. Phys. A: Math. Theor. 40 (2007) 4529-4539), can be derived in a simple natural way (using well known exact discretization of the harmonic oscillator). We also turn attention on important earlier references, where the exact discretization of the 4-dimensional isotropic harmonic oscillator has been app...