Bracket models for weight systems and the universal Vassiliev invariants

A bracket weight system is constructed. Three of its applications are given. The first is an observation of some special properties of HOMFLY and Kauffman polynomials. The second is an observation of an infinite set of nontrivial combinatorial identities. The third is a dimension formula and the computation of the universal invariant up to h5 for all prime knots with crossing number less than 10.