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The conventional ways to calculate the perturbative component of the DIS singlet structure function F 1 involve approaches based on BFKL which account for the single-logarithmic contributions accompanying the Born factor 1/x. In contrast, we account for the double-logarithmic (DL) contributions unrelated to 1/x and because of that they were disregarded as negligibly small. We calculate the singlet F 1 in the double-logarithmic approximation (DLA) and account at the same time for the running α sdoi:10.1140/epjc/s10052-018-5675-6 fatcat:xtoi5v7gbrcfneaw22lseth6e4