Study of the nucleon spin-dependent structure function $g_1$. A comparison with recent HERMES and COMPASS data

Predictions for the spin dependent structure function $g_1$ of the nucleon are presented. We use an unified approach incorporating the LO DGLAP evolution and the resummation of double logarithmic terms $ln^2(x)$. We show, that the singular input parametrisation as $x\to 0$ can be a substitute of the $ln^2(x)$ resummation. An impact of the `more running' coupling is discussed. We determine the contribution to the Bjorken sum rule solving the evolution equation for the truncated moment of $g_1^{NS}$. A comparison with the re-analysed HERMES and COMPASS data is given.