ar X iv : m at h / 99 11 10 9 v 1 [ m at h . R A ] 1 5 N ov 1 99 9 – 1 – BIRKHOFF ’ S THEOREM FOR PANSTOCHASTIC MATRICES

m at h . R A ] 2 5 Fe b 20 00 – 1 – BIRKHOFF ’ S THEOREM FOR PANSTOCHASTIC MATRICES

The panstochastic analogue of Birkhoff's Theorem on doubly-stochastic matrices is proved in the case n = 5. It is shown that this analogue fails when n > 1, n = 5.

ar X iv : m at h / 99 11 14 3 v 1 [ m at h . D S ] 1 8 N ov 1 99 9 CANONICAL SYMBOLIC DYNAMICS FOR ONE - DIMENSIONAL GENERALIZED SOLENOIDS

We define canonical subshift of finite type cover for Williams' 1-dimensional generalized solenoids, and use resulting invariants to distinguish some closely related solenoids.

ar X iv : m at h / 99 11 07 4 v 1 [ m at h . Q A ] 1 1 N ov 1 99 9 CRYSTAL GRAPHS FOR BASIC REPRESENTATIONS OF THE QUANTUM AFFINE

We give a realization of crystal graphs for basic representations of the quantum affine algebra Uq(C (1) 2) in terms of new combinatorial objects called the Young walls.

ar X iv : h ep - p h / 99 11 40 8 v 1 19 N ov 1 99 9 Quark Matter 99 Summary : Hadronic Signals

ar X iv : m at h / 99 11 03 9 v 1 [ m at h . A T ] 7 N ov 1 99 9 A classification of S 3 - bundles over S 4

We classify the total spaces of S-bundles over S up to homotopy equivalence, homeomorphism and diffeomorphism. These total spaces have been of interest to both topologists and geometers. They play an important role in the recent work of Grove and Ziller [GZ], where it is shown that each of these total spaces admits metrics with non-negative sectional curvature.