The axial vector coupling constants of the beta decay processes of the
neutron and hyperon are calculated in SU(3) chiral color dielectric m
odel (CCDM). Using these axial coupling constants of the neutron and h
yperon, in the CCDM we calculate the integrals of the spin-dependent s
tructure functions for the proton and neutron. Our result is similar t
o the results obtained by MIT bag and cloudy bag models (CBM).