  Influence of uniaxial small-scale anisotropy and compressibility on the
stability of scaling regime and on the anomalous scaling of structure functions
of a scalar field is investigated in the model of a passive scalar field
advected by the compressible Gaussian strongly anisotropic velocity field with
the covariance $\propto \delta(t-t^{\prime})|{\bf x}-{\bf
x^{\prime}}|^{2\epsilon}$ by using the field theoretic renormalization group
and the operator product expansion. The inertial-range stability of the
corresponding scaling regime is established. The anomalous scaling of the
single-time structure functions is studied and the corresponding anomalous
exponents are calculated. Their dependence on the compressibility parameter and
anisotropy parameters is analyzed. It is shown that the presence of
compressibility leads to the decreasing of the critical dimensions of the
important composite operators, i.e., the anomalous scaling is more pronounced
in the compressible systems. This result is demonstrated for the structure
function of the third order. All calculations are done to the first order in
$\epsilon$.
