Majorana neutrino masses and neutrino oscillations

We examine some patterns of the Majorana neutrino mass matrix which are compatible with the phenomenological lepton flavor mixing matrix and non-observation of neutrinoless double beta decay. Imposing ${(M}_{\nu }{)}_{\mathrm{ee}}=0\mathrm{}$ 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 $\Delta m_{\mathrm{sol}}^2$ and $\Delta m_{\mathrm{atm}}^2$ in this framework, and we discuss the naturality of the forms of the mass matrix found in our work.