How to Test Scaling in Asymptotically Free Theories

It is shown how, in asymptotically free gauge theories, one can, given the deep-inelastic structure functions for values of $q^2$ in the asymptotic region, calculate explicitly the structure functions for all larger $q^2$. The ratio of structure functions for $q^2=50\mathrm{} \mathrm{and} 5$ ${\mathrm{GeV}}^2$ is estimated. Substantial deviations from scaling are found, as well as a dramatic $\omega$ dependence, for values of $1<~\omega <~4$.