2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209980We give an upper bound for the dealternating number of a closed 3-braid. As applications, we determine the dealternating numbers, the alternation numbers and the Turaev genera of some closed positive 3-braids. We also show that there exist infinitely many positive knots with any dealternating number (or any alternation number) and any braid index.We corrected Section 6Geometric Topology57M25text