ar X iv : m at h / 03 10 01 7 v 1 [ m at h . C A ] 1 O ct 2 00 3 Change of Variable for Multi - dimensional Integral 4 March 2003

ar X iv : m at h / 03 10 27 4 v 1 [ m at h . A P ] 1 7 O ct 2 00 3 THE RADIATION FIELD IS A FOURIER INTEGRAL OPERATOR

ar X iv : m at h / 03 08 02 3 v 2 [ m at h . Q A ] 1 3 O ct 2 00 3 MONOMIAL HOPF ALGEBRAS

Let K be a field of characteristic 0 containing all roots of unity. We classified all the Hopf structures on monomial K-coalgebras, or, in dual version, on monomial K-algebras.

ar X iv : a st ro - p h / 01 03 44 4 v 1 2 7 M ar 2 00 1 From Centimeter to Millimeter Wavelengths : A High Angular Resolution Study of 3 C 273

We monitored 3C 273 with VLBI at 15–86 GHz since 1990. We discuss component trajectories, opacity effects, a rotating jet, and outburst-ejection relations from Gamma-ray to radio bands.

ar X iv : m at h / 03 10 11 1 v 1 [ m at h . G T ] 8 O ct 2 00 3 On Kontsevich Integral of torus knots ∗

We study the unwheeled rational Kontsevich integral of torus knots. We give a precise formula for these invariants up to loop degree 3 and show that they appear as a coloring of simple diagrams. We show that they behave under cyclic branched coverings in a very simple way. Our proof is combinatorial: it uses the results of Wheels and Wheelings and new decorations of diagrams.

ar X iv : h ep - p h / 01 10 03 9 v 1 3 O ct 2 00 1 On spectroscopy of ρ ′ , ρ ′ ′ and ω ′ , ω ′ ′ resonances