  Recent dispersive techniques developed by us are applied to discuss three
problems: 1. A long standing discrepan-cy between the measurements of $R(s)$
for $\sqrt{s} = (5\div 7.5)GeV$ by Crystal Ball and MARK I has been analyzed
and its consequences analyzed for the number of contributing quarks. 2. Noting
that the perturbative $\alpha_s$ has the wrong analyticity, analytic models
consistent with asymptotic freedom (AF) and confinement have been constructed
and applied to discuss $\tau$ decay. 3. It is shown that AF leads to a wrong
sign for $\im\big(\alpha(s)\big)$ which signals an instability of the
perturbative QCD vacuum.
