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Shift Harnack and integration by part formula are establish for semilinearspde with delay and a class of stochastic semilinear evolution equation whichcover the hyperdissipative Naiver-Stokes/Burges equation. For the case ofstochastic equation with delay, an extension to path space is given.

Shift Harnack Inequality and Integration by Part Formula for Semilinear SPDE