Formulae of proton and neutron boson structure functions (BSF's) are deduce
d in terms of a microscopic approach of sdgIBM (namely, microscopic sdgIBM)
. For the nucleus Os-190, the value of BSF's is worked out. Due to the high
similarity, the maximum F-spin truncation is made under the full-symmetry
approximation. Thereafter, calculations of E2 and E4 transition charge dens
ities (TCD's) are performed in the sdgIBM-1. It is found that the E2 and E4
TCD's can be reproduced quite satisfactorily in the uniform frame of micro
scopic sdgIBM-1.