  The nucleon-quark mixed matter is defined in the Brueckner-Hartree-Fock
framework, in which quark densities are determined by equilibrium conditions
between nucleon and quark chemical potentials, and nucleon-quark interactions
play critical roles for resulting EoSs (equation of state). The two models of
EoSs are derived from the nucleon-quark mixed matter (NQMM): The NQMM-A EoSs
are based on the simple assumption that nucleons and free quarks occupy their
respective Fermi levels and their Fermi spheres overlap from each other. In
NQMM-B EoSs, the quark Fermi repulsion effect is incorporated on the basis of
quakyonic matter, meaning that the nucleon Fermi levels are pushed up from the
quark Fermi sphere by the Pauli exclusion principle. For the NQMM-A EoSs, the
neutron-star mass-radius ($MR$) curves are pushed up above the region of $M
\sim 2.1M_\odot$ and $R_{2.1M_\odot}\sim$ 12.5 km indicated by the recent
observations, as the $qN$ repulsions increase. For the NQMM-B EoSs, the similar
results are obtained by the combined contributions from the $qN$ repulsion and
the quark Fermi repulsion. In both models of EoSs, the important roles of the
$qN$ di-quark exchange repulsions are demonstrated to reproduce reasonable
values of $M_{max}$ and $R_{2.1M_\odot}$.
