  We present a calculation of the perturbative matching coefficients including
mixing with higher dimensional operators for the temporal component of the
heavy-light axial current, $A_{4}$, and the $\Delta B=2$ operator, $O_S$. For
$A_{4}^{\scriptsize static, NRQCD}$, calculations with various RG-improved
gauge actions are peformed. Matching coefficients with NRQCD and heavy-clover
actions are also compared.
