Let R = C[x1, x2, . . . , xn]/(f1, . . . , fm) be a positively graded Artinian
algebra. A long-standing conjecture in algebraic geometry, differential
geometry, and rational homotopy theory is the non-existence of negative weight
derivations on R. Alexsandrov conjectured that there are no negative weight
derivations when R is a complete intersection algebra, and Yau conjectured
there are no negative weight derivations on R when R is the moduli algebra
of a weighted homogeneous hypersurface singularity. This problem is also important
in rational homotopy theory and differential geometry. In this paper
we prove the non-existence of negative weight derivations on R when the degrees
of f1, . . . ,fm are bounded below by a constant C depending only on the
weights of x1, . . . , xn. Moreover this bound C is improved in several special
cases.