2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68511We give necessary conditions of a surface-knot to be ribbon concordant to another, by introducing a new variant of the cocycle invariant of surface-knots in addition to using the invariant already known. We demonstrate that twist-spins of some torus knots are not ribbon concordant to their orientation reversed images.14 pages, eight figures, interesting applicationsGeometric TopologyQuantum Algebra57Q45,57Q60,57M25,55N99text