Cosmic ray environment model for Earth orbit

A set of computer codes, which include the effects of the Earth's magnetic field, used to predict the cosmic ray environment (atomic numbers 1 through 28) for a spacecraft in a near-Earth orbit is described. A simple transport analysis is used to approximate the environment at the center of a spherical shield of arbitrary thickness. The final output is in a form (a Heinrich Curve) which has immediate applications for single event upset rate predictions. The codes will culate the time average environment for an arbitrary number (fractional or whole) of circular orbits. The computer codes were run for some selected orbits and the results, which can be useful for quick estimates of single event upset rates, are given. The codes were listed in the language HPL, which is appropriate or a Hewlett Packard 9825B desk top computer. Extensive documentation of the codes is available from COSMIC, except where explanations have been deferred to references where extensive documentation can be found. Some qualitative aspects of the effects of mass and magnetic shielding are also discussed

The combinatorics of hyperbolized manifolds

A topological version of a longstanding conjecture of H. Hopf, originally proposed by W. Thurston, states that the sign of the Euler characteristic of a closed aspherical manifold of dimension $d=2m$ depends only on the parity of $m$. Gromov defined several hyperbolization functors which produce an aspherical manifold from a given simplicial or cubical manifold. We investigate the combinatorics of several of these hyperbolizations and verify the Euler Characteristic Sign Conjecture for each of them. In addition, we explore further combinatorial properties of these hyperbolizations as they relate to several well-studied generating functions