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

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

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

Non-uniqueness of ergodic measures with full Hausdorff dimension on a Gatzouras-Lalley carpet

In this note, we show that on certain Gatzouras-Lalley carpet, there exist more than one ergodic measures with full Hausdorff dimension. This gives a negative answer to a conjecture of Gatzouras and Peres

Regular Incidence Complexes, Polytopes, and C-Groups

Regular incidence complexes are combinatorial incidence structures generalizing regular convex polytopes, regular complex polytopes, various types of incidence geometries, and many other highly symmetric objects. The special case of abstract regular polytopes has been well-studied. The paper describes the combinatorial structure of a regular incidence complex in terms of a system of distinguished generating subgroups of its automorphism group or a flag-transitive subgroup. Then the groups admitting a flag-transitive action on an incidence complex are characterized as generalized string C-groups. Further, extensions of regular incidence complexes are studied, and certain incidence complexes particularly close to abstract polytopes, called abstract polytope complexes, are investigated.Comment: 24 pages; to appear in "Discrete Geometry and Symmetry", M. Conder, A. Deza, and A. Ivic Weiss (eds), Springe

Zero field muon spin lattice relaxation rate in a Heisenberg ferromagnet at low temperature

We provide a theoretical framework to compute the zero field muon spin relaxation rate of a Heisenberg ferromagnet at low temperature. We use the linear spin wave approximation. The rate, which is a measure of the spin lattice relaxation induced by the magnetic fluctuations along the easy axis, allows one to estimate the magnon stiffness constant.Comment: REVTeX 3.0 manuscript, 5 pages, no figure. Published in Phys. Rev. B 52, 9155 (1995

A series of coverings of the regular n-gon

We define an infinite series of translation coverings of Veech's double-n-gon for odd n greater or equal to 5 which share the same Veech group. Additionally we give an infinite series of translation coverings with constant Veech group of a regular n-gon for even n greater or equal to 8. These families give rise to explicit examples of infinite translation surfaces with lattice Veech group.Comment: A missing case in step 1 in the proof of Thm. 1 b was added. (To appear in Geometriae Dedicata.