The behavior of the gluon distribution function and the reduced cross section considered from the proton structure function and its derivatives at low values of x. These behaviors studied and compared with the experimental data. These results are augmented by including an additional higher-twist term in the description of the nonlinear correction. This additional term, modified nonlinear correction, improves the description of the reduced cross sections significantly at low values of $Q^2$. We discuss, furthermore, how this behavior can be determine the reduced cross section with respect to the proton parameterization at high-y values. The resulting predictions for ${\sigma }_r$ suggest that further corrections are required for $Q^2$ less than about $3{\text{GeV}}^2$.

从质子结构函数及其导数在低x值下考虑的胶子分布函数和缩减截面的行为。这些行为进行了研究，并与实验数据进行了比较。通过在非线性校正的描述中包括附加的较高扭转项，可以增强这些结果。这个附加项，即修改后的非线性校正，可显着改善在低值时减小的横截面的描述。${问}^2$。此外，我们讨论了如何确定高y值下相对于质子参数化的截面减小的行为。由此产生的预测${\sigma }_{\mathrm{[R}}$ 建议需要进一步更正 ${问}^2$ 少于大约 $3{\text{GeV}}^2$。