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In order to explain the recently reported result on the double beta decay experiment, together with the earlier established data on LMA MSW solar and atmospheric neutrino oscillations, we generate the textures of the nearly degenerate as well as the inverted hierarchical models of the left-handed Majorana neutrino mass matrices within the framework of the see-saw mechanism in a model independent way. The leptonic mixings are generated from the texture of the right- handed Majorana mass matrices while keeping the Dirac neutrino mass matrices in diagonal forms.

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