ar X iv : m at h - ph / 0 50 10 26 v 1 1 1 Ja n 20 05 Projective dynamics and classical gravitation

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 / 05 01 28 1 v 1 [ m at h . A G ] 1 9 Ja n 20 05 Multivariate Subresultants in Roots

We give a rational expression for the subresultants of n+ 1 generic polynomials f1, . . . , fn+1 in n variables as a function of the coordinates of the common roots of f1, . . . , fn and their evaluation in fn+1. We present a simple technique to prove our results, giving new proofs and generalizing the classical Poisson product formula for the projective resultant, as well as the expressions of...

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 / 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 : m at h - ph / 0 50 10 26 v 2 3 M ay 2 00 5 Projective dynamics and classical gravitation

Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a field of projective forces, we define a law of dynamics such that the position of the particle is a ray i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is a 2-plane containing the ray. Throwing the particle with a given initial impulsio...