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In this paper, we mainly present some new solutions of the Hom-Yang-Baxterequation from Hom-algebras,  Hom-coalgebras and Hom-Lie algebras, respectively.  Also, we prove that these solutions are all self-inverse and give someexamples.  Finally, we introduce the notion of Hom-Yang-Baxter systems and obtain twokinds of Hom-Yang-Baxter systems.

Hom-Yang-Baxter equations and Hom-Yang-Baxter systems