Abstract
A study is made of charm and bottom flavor matching conditions on parton densities. Starting from an $\overline{\mathrm{MS}}$ three-flavor density set, where the scale $\ensuremath{\mu}<{m}_{c},$ and using the recently derived two-loop matching conditions, we provide a new set of four-flavor parton densities where ${m}_{c}<~\ensuremath{\mu}<{m}_{b}$ and five-flavor densities where $\ensuremath{\mu}>~{m}_{b}.$ The effect of the next-to-next-to-leading order matching conditions on the evolution equations is important for scales just above the transition regions. This includes the small x and small ${Q}^{2}$ domain studied by the H1 and ZEUS experiments at DESY HERA. At small x the effects of the matching conditions never die away even for large ${\ensuremath{\mu}}^{2}.$
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