We present the final part of the proof of the Kepler Conjecture.

Abstract Inferring planetary parameters from transit timing variations (TTVs) is challenging for small exoplanets because their transits may be so weak that determination of individual difficult or impossible. We implement a useful combination tools together provide numerically fast global photodynamical model. This used to fit the TTV-bearing light curve, in order constrain masses transiting l...

Let n ≥ 2 be a positive integer. To each irreducible representation σ of U(1), a U(1)-Kepler problem in dimension (2n − 1) is constructed and analyzed. This system is super integrable and when n = 2 it is equivalent to a MICZ-Kepler problem. The dynamical symmetry group of this system is e U(n, n), and the Hilbert space of bound states H (σ) is the unitary highest weight representation of e U(n...

In this paper we survey results on packings of congruent spheres in 3-dimensional spaces of constant curvature. The topics discussed are as follows: Hadwiger numbers of convex bodies and kissing numbers of spheres; Touching numbers of convex bodies; Newton numbers of convex bodies; One-sided Hadwiger and kissing numbers; Contact graphs of finite packings and the combinatorial Kepler problem; Is...

Peham is credited (Burket and Abell, 1944) with the report of the first case in 1899 in Germany, but there was no typical masculinization in his case. Bovin (Kepler, Dokerty and Priestly, 1944) reported the first case in America in 1908 and Blair and Bell (Searle et al., 1948) reported the first case in England in 1915. By 1944, Kepler et al. collected 13 cases from the literature and added one...

We present an automated method of identifying background eclipsing binaries masquerading as planet candidates in the Kepler planet candidate catalogs. We codify the manual vetting process for Kepler Objects of Interest (KOIs) described in Bryson et al. (2013) with a series of measurements and tests that can be performed algorithmically. We compare our automated results with a sample of manually...

A model of computation (MoC) is a formal abstraction of execution in a computer. There is a need for composing 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 demonstrates t...