Quadratic Hom-leibniz Conformal Superalgebras And Quadratic Hom-Left-Symmetric Conformal Superalgebras

In this paper,we recall the definitions of Hom-Lie superalgebras,Hom-Leibniz superalgebras,Hom-Lie conformal superalgebras,Hom-Novikov superalgebras and super Hom-Gel'fand-Dorfman bialgebras.In Chapter 2,we give the definitions of Hom-Leibniz conformal superalgebras and quadratic Hom-Leibniz conformal superalgebras,show quadratic Hom-Leibniz conformal superalgebra is also equal to a super bialgebra structure,and construct Hom-Leibniz conformal superalgebras using this super bialgebra structure.We also study the center extension of quadratic Hom-Leibniz conformal superalgebra.In Chapter 3,we give the definitions of Hom-Left-symmetric conformal algebras and quadratic Hom-Left-symmetric conformal algebra,show that quadratic Hom-Left-symmetric conformal algebra is equal to a bialgebra structure,Finally,we give the definitions and constructions of Hom-ass-Nov-left-symmetric superalgebras,Hom-pre-Novikov-Poisson superalgebras,Hom-Left-symmetric-Poisson superalgebras and Hom-Novikov-Poisson superalgebras.