  The low-energy physics of a spin-1/2 Kondo impurity in a gapless host, where
a density of band states $\rho_0(\epsilon)=|\epsilon|^r/(|\epsilon|^r+\beta^r)$
vanishes at the Fermi level $\epsilon=0$, is studied by the Bethe ansatz. The
growth of the parameter $\Gamma_r=\beta{\rm g}^{-1/r}$ (where ${\rm g}$ is an
exchange constant) is shown to drive the system ground state from the Kondo
regime with the screened impurity spin to the Anderson regime, where the
impurity spin is unscreened, however, in a weak magnetic field $H$, it exceeds
its free value, $S_i(H)>{1/2}$, due to a strong coupling to a band. It is shown
also that a sufficiently strong potential scattering at the impurity site
destroys the Anderson regime.
