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The relativistic quark model of nucleon and the quark-exchange formalism is
used to calculate the spin structure functions (SSF) of $^3$He, $^3$H, neutrons
and protons. We consider the quarks to be exchanged at most between two
nucleons. The up and down quarks treated separately and a well behaved
polarized distribution is found by considering energy-momentum conservation
properly. The SSF of $^3$He and $^3$H and convolution approximation are used to
find the SSF of protons and neutrons and the validity of
the Bjorken sum rule was tested. Finally it is shown that the result of our
calculation agrees qualitatively well with the available experimental data.
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