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We present a set of formula to extract exponents of the longitudinalstructure function and reduced cross section from the Regge-like behavior atsmall $x$. The exponents are found to be independent of $Q^{2}$ at NNLOanalysis. As a result, we show that the reduced cross section exponents do nothave the same behavior at some values of $x$. This difference predicts thenon-linear effects and some evidence for shadowing and antishadowing at LHeC.Also the ratio $\frac{F_{2}}{\sigma}$ is calculated and compared with thecorresponding HERA data. Our calculations show a very good agreement with theDIS experimental data throughout the small values of $x$.

The exponent of the longitudinal structure function $F_{L}$ at low $x$