Phases of Dense Matter in Supernovae and Neutron Stars

We study the properties of dense matter at finite temperature with various proton fractions for use in supernova simulations.The relativistic mean-field theory is used to describe homogeneous nuclear matter,while the Thomas-Fermi approximation is adopted to describe inho-mogeneous matter.We also discuss the equation of state of neutron star matter at zero tempera-ture in a wide density range.The equation of state at high densities can be significantly softened by the inclusion of hyperons.