  We report RBC and RBC/UKQCD lattice QCD numerical calculations of nucleon
electroweak matrix elements with dynamical domain-wall fermions (DWF) quarks.
The first, RBC, set of dynamical DWF ensembles employs two degenerate flavors
of DWF quarks and the DBW2 gauge action. Three sea quark mass values of 0.04,
0.03 and 0.02 in lattice units are used with about 200 gauge configurations
each. The lattice cutoff is about 1.7 GeV and the spatial volume is about (1.9
fm)^3. Despite the small volume, the ratio of the isovector vector and axial
charges g_A/g_V and that of structure function moments <x>_{u-d}/<x>_{Delta u -
Delta d} are in agreement with experiment, and show only very mild quark mass
dependence. The second, RBC/UK, set of ensembles employs one strange and two
degenerate (up and down) dynamical DWF quarks and Iwasaki gauge action. The
strange quark mass is set at 0.04, and three up/down mass values of 0.03, 0.02
and 0.01 in lattice units are used. The lattice cutoff is about 1.6 GeV and the
spatial volume is about (3.0 fm)^3. Even with preliminary statistics of 25-30
gauge configurations, the ratios g_A/g_V and <x>_{u-d}/<x>_{Delta u - Delta d}
are consistent with experiment and show only very mild quark mass dependence.
Another structure function moment, d_1, though yet to be renormalized, appears
small in both sets.
