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The explicit expressions for the non-singlet DIS structure function g_1 atsmall $x$ are obtained by resumming the leading logarithmic contributions. Therole played by the fits for the initial parton densities currently used in theDGLAP on the small-x behavior of the non-singlet g_1 is discussed. Explicitexpressions combining DGLAP with our results are presented.Comment: Talk given at XIII International Workshop on Deep Inelastic  Scattering, April,27 - May,1, 2005, Madison, Wisconsin, USA, 3 pages, no  figure

Synthesis of DGLAP and total resummation of leading logarithms for the non-singlet spin structure function g1