  When the initial state evolution of a parton shower is organized according to
the standard "backward evolution'' prescription, ratios of parton distribution
functions appear in the splitting probabilities. The shower thus organized
evolves from a hard scale to a soft cutoff scale. At the end of the shower, one
expects that only the parton distributions at the soft scale should affect the
results. The other effects of the parton distributions should have cancelled.
This means that the kernels for parton evolution should be related to the
shower splitting functions. If the initial state partons can have non-zero
masses, this requires that the evolution kernels cannot be the usual MSbar
kernels. We work out what the parton evolution kernels should be to match the
shower evolution contained in the parton shower event generator Deductor, in
which the b and c quarks have non-zero masses.
