  Here we obtain explicit formulae for bounds on the complex electrical
polarizability at a given frequency of an inclusion with known volume that
follow directly from the quasistatic bounds of Bergman and Milton on the
effective complex dielectric constant of a two-phase medium. We also describe
how analogous bounds on the orientationally averaged bulk and shear
polarizabilities at a given frequency can be obtained from bounds on the
effective complex bulk and shear moduli of a two-phase medium obtained by
Milton, Gibiansky and Berryman, using the quasistatic variational principles of
Cherkaev and Gibiansky. We also show how the polarizability problem and the
acoustic scattering problem can both be reformulated in an abstract setting as
"Y -problems". In the acoustic scattering context, to avoid explicit
introduction of the Sommerfeld radiation condition, we introduce auxilliary
fields at infinity and an appropriate "constitutive law" there, which forces
the Sommerfeld radiation condition to hold. As a consequence we obtain
minimization variational principles for acoustic scattering that can be used to
obtain bounds on the complex backwards scattering amplitude. Some explicit
elementary bounds are given.
