ar X iv : m at h / 04 06 21 2 v 1 [ m at h . D G ] 1 0 Ju n 20 04 REFLECTION OF A WAVE OFF A SURFACE

ar X iv : a st ro - p h / 04 06 56 7 v 1 2 4 Ju n 20 04 1

ar X iv : m at h / 04 06 08 3 v 3 [ m at h . PR ] 1 7 Ju n 20 05 Large deviations for empirical entropies of g - measures

The entropy of an ergodic finite-alphabet process can be computed from a single typical sample path x1 using the entropy of the k-block empirical probability and letting k grow with n roughly like logn. We further assume that the distribution of the process is a g-measure. We prove large deviation principles for conditional, non-conditional and relative k(n)-block empirical entropies.

ar X iv : m at h / 04 06 31 1 v 3 [ m at h . A C ] 2 0 Ju n 20 06 MODULE STRUCTURE OF AN INJECTIVE RESOLUTION

Let A be the ring obtained by localizing the polynomial ring κ[X, Y, Z, W ] over a field κ at the maximal ideal (X, Y, Z, W) and modulo the ideal (XW − Y Z). Let p be the ideal of A generated by X and Y. We study the module structure of a minimal injective resolution of A/p in details using local cohomology. Applications include the description of Ext i A (M, A/p), where M is a module construct...

ar X iv : m at h / 04 05 17 6 v 4 [ m at h . R T ] 1 6 Ju n 20 06 QUANTIZED SYMPLECTIC OSCILLATOR ALGEBRAS OF RANK ONE

A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with Uq(sl2). We study its representation theory, and in particular, its category O.

ar X iv : m at h - ph / 0 40 60 24 v 1 1 3 Ju n 20 04 p - Adic wavelet transform and quantum physics ∗

p-Adic wavelet transform is considered as a possible tool for the description of hierarchic quantum systems.