  Pre-Novikov algebras and quasi-Frobenius Novikov algebras naturally appear in
the theory of Novikov bialgebras. In this paper, we show that there is a
natural pre-Novikov algebra structure associated to a quasi-Frobenius Novikov
algebra. Then we introduce the definition of double constructions of
quasi-Frobenius Novikov algebras associated to two pre-Novikov algebras and
show that it is characterized by a pre-Novikov bialgebra. We also introduce the
notion of pre-Novikov Yang-Baxter equation, whose symmetric solutions can
produce pre-Novikov bialgebras. Moreover, the operator forms of pre-Novikov
Yang-Baxter equation are also investigated.
