Abstract
We calculate stellar oscillations including the hadron-quark mixed phase considering the finite size effects. We find that it is possible to distinguish whether the density discontinuity exists or not in the stars, even if one will observe the gravitational waves of the fundamental mode. Additionally, the normalized eigenfrequencies of pressure modes depend strongly on the stellar mass and on the adopted equation of state. Especially, in spite of the fact that the radius of the neutron star with $1.4M_\odot$, which is standard mass, is almost independent from the equation of state with quark matter, the frequencies of pressure modes depend on the adopted equation of state. Thus, via observing the many kinds of gravitational waves, it will be possible to make a restriction on the equation of state.
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