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Based on the string duality Marifio and Vafa [MV] made a conjecture between Chem-Simons and string theory which generalizes the well-known Witten COnjecture/Kontsevich theorem([w],[Ko1],[CLL],[KarL],[KiL],[LX4],[Mil,Mi2],[S],[MS],[OP1],[LX4]).In 2003,C.-C.Liu,K.Liu,and J.Zhou [LLZ1]gave a proof of Mari(n)o-Vafa conjecture fanother proof see [OP1])using the localization technique on the moduli space of relative morphisms (M)g,0(P1,μ)constructed by J.Li [Li1,Li2].In this paper,we use the Mari(n)oVafa formula to give a simple proof ofλ9 conjecture([FabP3],[GJV2],[LiY],[LLZ2])and Witten con]ecture,also find a closed formula of a certain type of Hodge integrals [LiY].Now,we state our main results beginning with some notations and concepts.