Majorana Neutrino Masses and Neutrino Oscillations

We examine some patterns of Majorana neutrino mass matrix which is compatible with the phenomenological lepton flavor mixing matrix and non-observation of neutrinoless double beta decay. Imposing $(M_{\nu})_{ee}=0$ for the Majorana neutrino mass matrix in the leading order, we obtain a relationship between the solar mixing angle and the neutrino masses $m_1$ and $m_2$. Additional possible texture zeros are assigned to the mass matrix so as for the nonvanishing $\theta_{13}$ to be predictable in terms of neutrino masses. We also show how three neutrino masses can be predicted from the solar mixing angle and the experimental results of $\Delta m^2_{sol}$ and $\Delta m^2_{atm}$ in this framework, and we discuss naturality of the forms of the mass matrix found in our work.