ar X iv : m at h / 99 05 02 6 v 1 [ m at h . A G ] 5 M ay 1 99 9 DIFFERENTIAL EQUATIONS CHARACTERISING QUASI - PERIODIC SOLUTIONS OF THE KP HIERARCHY

ar X iv : m at h / 99 05 00 1 v 1 [ m at h . A G ] 1 M ay 1 99 9 Tacnodes and cusps

ar X iv : m at h / 99 05 15 4 v 1 [ m at h . G T ] 2 5 M ay 1 99 9 SUBSPACES OF KNOT SPACES

The inclusion of the space of all knots of a prescribed writhe in a particular isotopy class into the space of all knots in that isotopy class is a weak homotopy equivalence.

ar X iv : h ep - p h / 99 05 46 9 v 1 2 5 M ay 1 99 9 DESY 99 – 060 hep - ph / 9905469 May 1999 W Boson Production at NLO ∗

We discuss W boson production at HERA including NLO QCD corrections. A detailed comparison with previous work is presented.

ar X iv : s ol v - in t / 9 90 50 05 v 2 1 7 M ay 1 99 9 The KP Hierarchy in Miwa coordinates ∗

A systematic reformulation of the KP hierarchy by using continuous Miwa variables is presented. Basic quantities and relations are defined and determinantal expressions for Fay’s identities are obtained. It is shown that in terms of these variables the KP hierarchy gives rise to a Darboux system describing an infinite-dimensional conjugate net.

ar X iv : m at h / 99 05 12 2 v 1 [ m at h . L O ] 1 9 M ay 1 99 9 THE CICHOŃ DIAGRAM

We conclude the discussion of additivity, Baire number, uniformity and covering for measure and category by constructing the remaining 5 models. Thus we complete the analysis of Cicho´n's diagram.