We obtain an approximate solution of Altarelli-Parisi equations yielding a sample of quantum chromodynamic structure function. The SLAC-MIT data are analysed with it. Possible effects of intrinsic charm and higher twist are also included. Agreement is found to be good forx⩾0.25.

We have presented here an improved solution to Altarelli-Parisi equations, and it is found to be in good agreement with SLAC-MIT data up tox⩾0.1.

We show that the assumptions of factorizability of the structure functionF(x, t) inx andt and the equality oft evolution of the singlet and gluon distributions are not necessary to obtain the approximate solutions of Altarelli-Parisi equations derived by us recently.

We obtain approximate solutions of Altarelli-Parisi equations beyond leading logarithmic approximation. Our results suggest quantitative utility of higher order terms in the structure function analysis of deep inelastic scattering.

We analytically examine the asymptotic solution of gluon evolution equation in terms of the ‘double scaling variables’ρ andσ of perturbative QCD and find the approximate lower bounds on these, above which the solution is considered to be valid. Comparison of this asymptotic solution is made with the fit obtained from data and the estimated lower bound onρ is nearly equal to our analytical finding. To analyze the data below the lower bound onρ, other analytical solutions of gluon evolution equation are to be used which depend highly on the inputx-distributions of gluon to study the physics at low-x of HERA range.

A simple method has been applied to solve the approximate gluon evolution equation for small-x at fixedρ(≡√ln(x₀/x)/ln[ln(Q²/Λ²)/ln(Q₀²/Λ²)]. Numerical comparison is made with the predictions from ‘double asymptotic scaling’ and fit. Better agreement is found between our solution and fit nearρ=1. The solution gives approximate double scaling in this region having ‘hard’ pomeron with small contamination.

We found an approximate simple solution of sea-quark evolution equation in terms ofρ(=√ln(x₀/x)/ln[ln(Q²/Λ²)/(Q₀²/Λ²)]) andζ(≡ln[ln(Q²Λ²)/ln(Q₀²/Λ²)]) in the small-x region whenρ is fixed and compared with HERA data. Agreement with data is found for largeQ² and smallρ. Comparison with double asymptotic scaling prediction is made. We found a critical value ofρ. More data are needed to confirm this point.

We obtain a relation between the longitudinal structure function F_L(x, Q²), F₂(x, Q²) and G(x, Q²) at small x, using the formalism recently reported by one of the authors [2]. We also obtain a relation between F_L(x, Q²), F₂(x, Q²) and its slope (dF₂(x, Q²))/(dlnQ²). This provides us with the determination of the longitudinal structure function F_L(x, Q²) from F₂(x, Q²) data and hence extract the gluon distribution G(x, Q²).