On the q=1/2 non-extensive maximum entropy distribution
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A detailed mathematical analysis on the q = 1/2 non-extensive maximum entropy distribution of Tsallis' is undertaken. The analysis is based upon the splitting of such a distribution into two orthogonal components. One of the components corresponds to the minimum norm solution of the problem posed by the fulfillment of the a priori conditions on the given expectation values. The remaining component takes care of the normalization constraint and is the projection of a constant onto the Null space of the "expectation-values-transformation"