ar X iv : c on d - m at / 0 30 90 08 v 2 2 7 Ja n 20 05 Periodic diffraction patterns for 1 D quasicrystals

ar X iv : c on d - m at / 0 30 90 08 v 1 3 0 A ug 2 00 3 Periodic diffraction patterns for 1 D quasicrystals

A simple model of 1D structure based on a Fibonacci sequence with variable atomic spacings is proposed. The model allows for observation of the continuous transition between periodic and non-periodic diffraction patterns. The diffraction patterns are calculated analytically both using “cut and project” and “average unit cell” methods, taking advantage of the physical space properties of the str...

ar X iv : m at h / 05 01 14 5 v 1 [ m at h . D S ] 1 0 Ja n 20 05 WAVELET CONSTRUCTIONS IN NON - LINEAR DYNAMICS

We construct certain Hilbert spaces associated with a class of non-linear dynamical systems X. These are systems which arise from a generalized self-similarity, and an iterated substitution. We show that when a weight function W on X is given, then we may construct associated Hilbert spaces H(W) of L 2-martingales which have wavelet bases.

ar X iv : c on d - m at / 9 40 10 05 v 2 1 0 Ja n 19 94 Composite operators for BCS Superconductor

The new form of the composite operator generalizing the Cooper pairs for a BCS superconductor is introduced. The approach is similar to the derivation of the composite operator of the odd-frequency superconductors. The examples of the d x 2 −y 2 −, d xy − and p− wave composite operators for a 2D t − J model are given.

ar X iv : m at h - ph / 0 50 10 33 v 1 1 2 Ja n 20 05 Indefinite metric

ar X iv : 0 80 1 . 08 75 v 2 [ m at h . D S ] 2 6 Ja n 20 08 GROUPS NOT ACTING ON MANIFOLDS

In this article we collect a series of observations that constrain actions of many groups on compact manifolds. In particular, we show that “generic” finitely generated groups have no smooth volume preserving actions on compact manifolds while also producing many finitely presented, torsion free groups with the same property.