  The Bruggeman formalism provides an estimate of the effective permittivity of
a particulate composite medium comprising two component mediums. The Bruggeman
estimate is required to lie within the Wiener bounds and the Hashin-Shtrikman
bounds. Considering the homogenization of weakly dissipative component mediums
characterized by relative permittivities with real parts of opposite signs, we
show that the Bruggeman estimate may not be not physically reasonable when the
component mediums are weakly dissipative; furthermore, both the Wiener bounds
and the Hashin-Shtrikman bounds exhibit strong resonances.
