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We calculate high energy massive scattering amplitudes of closed bosonicstring compactified on the torus. We obtain infinite linear relations amonghigh energy scattering amplitudes. For some kinematic regimes, we discover thatsome linear relations break down and, simultaneously, the amplitudes enhance topower-law behavior due to the space-time T-duality symmetry in the compactdirection. This result is consistent with the coexistence of the linearrelations and the softer exponential fall-off behavior of high energy stringscattering amplitudes as we pointed out prevously. It is also reminiscent ofhard (power-law) string scatterings in warped spacetime proposed by Polchinskiand Strassler.

Power-law Behavior of High Energy String Scatterings in Compact Spaces