We consider systems of partial differential equations of the first order in$t$and of order 2$s$in the$x$variables, which are uniformly parabolic in the sense of Petrovskii. We show that the classical maximum modulus principle is not valid in$R$^{n}×(0,$T$] for$s$≥2.

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A recent approach of D. S. Lubinsky yields universality in random matrix theory and fine zero spacing of orthogonal polynomials under very mild hypothesis on the weight function, provided the support of the generating measure μ is [-1,1]. This paper provides a method with which analogous results can be proven on general compact subsets of$R$. Both universality and fine zero spacing involves the equilibrium measure of the support of μ. The method is based on taking polynomial inverse images, by which results can be transferred from [-1,1] to a system of intervals, and then to general sets.