Are deviation from bi-maximal mixing and non-zero Ue3 related to non-degeneracy of heavy Majorana neutrinos?

We propose a scenario that the mass splitting between the first generation of the heavy Majorana neutrino and the other two generations of degenerate heavy neutrinos in the seesaw framework is responsible for the deviation of the solar mixing angle from the maximal mixing, while keeping the maximal mixing between the tau and muon neutrinos as it is. On top of the scenario, we show that the tiny breaking of the degeneracy of the two heavy Majorana neutrinos leads to the non-zero small mixing angle Ue3 in the PMNS matrix and the little deviation of the atmospheric neutrino mixing angle from the maximal mixing.