ar X iv : m at h - ph / 0 70 10 45 v 1 1 5 Ja n 20 07 AN EXTENDED ABEL - JACOBI MAP

ar X iv : m at h - ph / 0 30 10 19 v 1 1 5 Ja n 20 03 Which distributions of matter diffract ? — Some answers

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

ar X iv : m at h - ph / 0 70 10 56 v 1 2 3 Ja n 20 07 ENTROPY ENCODING USING HILBERT SPACE AND KARHUNEN - LOÈVE TRANSFORMS PALLE

By introducing Hilbert space and operators, we show how probabilities, approximations and entropy encoding from signal and image processing allow precise formulas and quantitative estimates. Our main results yield orthogonal bases which optimize distinct measures of data encoding.

ar X iv : m at h - ph / 0 70 10 79 v 1 3 1 Ja n 20 07 CONTINUOUS SYMMETRIES OF THE LATTICE POTENTIAL KDV EQUATION

In this paper we present a set of results on the integration and on the symmetries of the lattice potential Korteweg-de Vries (lpKdV) equation. Using its associated spectral problem we construct the soliton solutions and the Lax technique enables us to provide infinite sequences of generalized symmetries. Finally, using a discrete symmetry of the lpKdV equation, we construct a large class of no...

ar X iv : m at h / 99 06 16 5 v 1 [ m at h . A G ] 2 4 Ju n 19 99 Albanese and Picard 1 - motives

LetX be an n-dimensional algebraic variety over a field of characteristic zero. We describe algebraically defined Deligne 1-motives Alb(X), Alb−(X), Pic(X) and Pic−(X) which generalize the classical Albanese and Picard varieties of a smooth projective variety. We compute Hodge, l-adic and De Rham realizations proving Deligne’s conjecture for H, H2n−1, H 1 and H1. We investigate functoriality, u...