  Using the recent Gauss diagram formulas for Vassiliev invariants of
Polyak-Viro-Fiedler and combining these formulas with the Bennequin inequality,
we prove several inequalities for positive knots relating their Vassiliev
invariants, genus and degrees of the Jones polynomial. As a consequence, we
prove that for any of the polynomials of Alexander/Conway, Jones, HOMFLY,
Brandt-Lickorish-Millett-Ho and Kauffman there are only finitely many positive
knots with the same polynomial and no positive knot with trivial polynomial.
  We also discuss an extension of the Bennequin inequality, showing that the
unknotting number of a positive knot not less than its genus, which recovers
some recent unknotting number results of A'Campo, Kawamura and Tanaka, and give
applications to the Jones polynomial of a positive knot.
