  Relativistic mean-field theory with $\delta$ meson, nonlinear isoscalar
self-interactions and isoscalar-isovector cross interaction terms with
parametrizations obtained to reproduce Dirac-Brueckner-Hartree-Fock
calculations for nuclear matter is used to study asymmetric nuclear matter
properties in $\beta$-equilibrium, including hyperon degrees of freedom and
(hidden) strange mesons. Influence of cross interaction on composition of
hyperon matter and electron chemical potential is examined. Softening of
nuclear equation of state by the cross interactions results in lowering of
hyperonization, although simultaneously enhancing a hyperon-induced decrease of
the electron chemical potential, thus indicating further shift of a kaon
condensate occurence to higher densities.
