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In this paper, we study the structure of the quantum cohomology ring of aprojective hypersurface with non-positive 1st Chern class. We prove a theoremwhich suggests that the mirror transformation of the quantum cohomology of aprojective Calabi-Yau hypersurface has a close relation with the ring ofsymmetric functions, or with Schur polynomials. With this result in mind, wepropose a generalized mirror transformation on the quantum cohomology of ahypersurface with negative first Chern class and construct an explicitprediction formula for three point Gromov-Witten invariants up to cubicrational curves. We also construct a projective space resolution of the modulispace of polynomial maps, which is in a good correspondence with the terms thatappear in the generalized mirror transformation.Comment: 32 pages, 3 figures, discussion in section 5 is refined, some minor  errors are correcte

ON THE QUANTUM COHOMOLOGY RINGS OF GENERAL TYPE PROJECTIVE HYPERSURFACES AND GENERALIZED MIRROR TRANSFORMATION