Abstract
A partial proof of the Nambu-Sugawara-Miyazawa hypothesis is given. On the basis of unitarity and analyticity it is shown that if alpha 'p (0) = 0 then the vacuum pole trajectory in the Regge-Pomeranchuk hypothesis alpha p(t) = 1. It is also proved that the unitarity and analyticity are not sufficient conditions to bound the total cross sections in the high energy limit. If alpha p(t) = 1 the non-shrinkage diffraction scattering in the high energy limit is obtained. (C.E.S.)
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