  We present an unquenched lattice calculation for the SU(3) flavor breaking
ratios of the heavy-light decay constants and the $\Delta B = 2$ matrix
elements. The calculation was performed on $16^3 \times 32$ lattices with two
dynamical flavors of domain-wall quarks and inverse lattice spacing $1/a =
1.69(5)$ GeV. Heavy quarks were implemented using an improved lattice
formulation of the static approximation. In the infinite heavy-quark mass limit
we obtain $f_{B_s}/f_{B_d} = 1.29(4)(6)$, $B_{B_s}/B_{B_d} = 1.06(6)(4)$, $\xi
= 1.33(8)(8)$ where the first error is statistical and the second systematic.
