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In this paper,we give an explicit and systematic study on the double constructions of Frobenius Hom-algebras and introduce the close relations between O-operators and Homdendriform algebras.Furthermore,we study the double constructions of Connes cocycles in terms of Hom-dendriform algebras.Finally,we give a clear analogy between antisymmetric infinitesimal Hom-bialgebras and Hom-dendriform D-bialgebras.