NUMBER OF NEIGHBORLY D-POLYTOPES WITH D+3 VERTICES

In this paper is proved a formula for the number of neighbourly d-polytopes with d + 3 vertices, when d is odd

Valuations and tensor weight on polytopes

Let V be a finite-dimensional vector space over a square-root closed ordered field F (this restriction permits an inner product with corresponding norm to be imposed on V)

A dice probability problem

Two different approaches to a probability problem involving convex polytopes lead to a geometric proof of an integral geometric result about mixed surface areas. The proof can be modified to cover the corresponding results about mixed volume

Fibre tilings

Generalizing an earlier notion of secondary polytopes, Billera and Sturmfels introduced the important concept of fibre polytopes, and showed how they were related to certain kinds of subdivision induced by the projection of one polytope onto another. There are two obvious ways in which this concept can be extended: first, to possibly unbounded polyhedra, and second, by making the definition a categorical one. In the course of these investigations, it became clear that the whole subject fitted even more naturally into the context of finite tilings which admit strong duals. In turn, this new approach provides more unified and perspicuous explanations of many previously known but apparently quite disparate results

NUMBER OF SIMPLICIAL NEIGHBORLY D-POLYTOPES WITH D+3 VERTICES

In this paper is proved a formula for the number of simplicial neighbourly d-polytopes with d + 3 vertices, when d is odd

Constructions for projectively unique polytopes

AbstractA convex polytope P is projectively unique if every polytope combinatorially isomorphic to P is projectively equivalent to P. In this paper are described certain geometric constructions, which are also discussed in terms of Gale diagrams. These constructions are applied to obtain projectively unique polytopes from ones of lower dimension; in particular, they lead to projectively unique polytopes with many vertices

Identifying a polytope by its fibre polytopes

It is shown that a full-dimensional polytope P is uniquely determined by its r-dimensional fibre polytopes when r≥2. Further, if r≥4 and the r-dimensional fibre polytopes are zonotopes, then P itself must be a zonotope

Flywheel energy storage system with homopolar electrodynamic magnetic bearing

The goal of this research was to evaluate the potential of homopolar electrodynamic magnetic bearings for flywheel energy storage systems (FESSs). The primary target was a FESS for Low Earth Orbit (LEO) satellites; however, the design can also be easily adapted for Earth-based applications. The main advantage of Homopolar Electrodynamic Bearings compared to more conventional Active Magnetic Bearings (AMB) is simplicity and very low power rating of its electronics, resulting in higher system reliability - a critical factor for space applications. For commercial applications this technologies may also be found very attractive due to a potentially lower cost compared to AMB.Center for Electromechanic

A comparison of the biodegradation of phenol and o-chlorophenol using a municipal mixed liquor and three commercial microbial preparations

The biodegradation of phenol and O-chlorophenol was studied in six-liter batch reactors, using a municipal mixed liquor (from the Livingston, NJ treatment plant) that had not previously been exposed to either of the substrates. In addition, three commercial microbial preparations: BI-CHEM (Sybron), Hydrobac (Polybac), and LLMO (General Environmental Science), were tested alone and in combination with the municipal mixed liquor. It was found that the municipal mixed liquor performed significantly better than any of the commercial preparations by themselves. When the commercial preparations were mixed with the municipal mixed liquor in a ratio of 1:10 it was found that the rate of degradation of each substrate increased over the rate of the municipal mixed liquor by itself. However, the increase in rate would not be great enough to justify the cost of using the commercial preparations

The isodiametric problem with lattice-point constraints

In this paper, the isodiametric problem for centrally symmetric convex bodies in the Euclidean d-space R^d containing no interior non-zero point of a lattice L is studied. It is shown that the intersection of a suitable ball with the Dirichlet-Voronoi cell of 2L is extremal, i.e., it has minimum diameter among all bodies with the same volume. It is conjectured that these sets are the only extremal bodies, which is proved for all three dimensional and several prominent lattices.Comment: 12 pages, 4 figures, (v2) referee comments and suggestions incorporated, accepted in Monatshefte fuer Mathemati