ar X iv : m at h / 99 11 13 3 v 2 [ m at h . O A ] 1 8 N ov 1 99 9 GEOMETRY OF OBLIQUE PROJECTIONS ∗ †

ar X iv : m at h / 99 11 13 3 v 1 [ m at h . O A ] 1 7 N ov 1 99 9 GEOMETRY OF OBLIQUE PROJECTIONS ∗ †

Let A be a unital C∗-algebra. Denote by P the space of selfadjoint projections ofA. We study the relationship between P and the spaces of projections Pa determined by the different involutions #a induced by positive invertible elements a ∈ A. The maps φp : P → Pa sending p to the unique q ∈ Pa with the same range as p and Ωa : Pa → P sending q to the unitary part of the polar decomposition of t...

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 06 09 7 v 2 [ m at h . C O ] 3 1 A ug 1 99 9 BOUNDS ON ARITHMETIC PROJECTIONS , AND APPLICATIONS TO THE KAKEYA CONJECTURE

Let A, B, be finite subsets of an abelian group, and let G ⊂ A × B be such that #A, #B, #{a + b : (a, b) ∈ G} ≤ N. We consider the question of estimating the quantity #{a − b : (a, b) ∈ G}. In [2] Bourgain obtained the bound of N 2− 1 13 , and applied this to the Kakeya conjecture. We improve Bourgain's estimate to N

ar X iv : h ep - t h / 94 10 11 8 v 2 2 2 N ov 1 99 4 WILSON LOOPS , qq̄ and 3 q POTENTIALS , BETHE – SALPETER EQUATION

ar X iv : h ep - p h / 98 11 43 9 v 1 2 3 N ov 1 99 8 Pomeron Flux Factor and Diffractive W and Jet Rates ∗

Experimental rates of W and dijets diffractively produced at the Tevatron Collider have recently become available. We use parametrizations of the pomeron structure function obtained from HERA data by two different schemes to compare theoretical expectations with the measured rates.