I would like to change the argument of the UnitStep function as follows:
maintaining the usual properties at the same time. There was some time ago an answer which suggested a combination of Unprotect and Protect commands but unfortunately does not work for version 4.
Another question has to do with the Simplification command. Assuming that we know how to deal the previous problem how can one simplify expressions that contain products of DeltaDirac and UnitStep functions using the rule DiracDelta[t-s]UnitStep[t-s]=1/2?