Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions

We prove Polya's conjecture of 1943: For a real entire function of order greater than 2, with finitely many non-real zeros, the number of non-real zeros of the n-th derivative tends to infinity with n. We use the saddle point method and potential theory, combined with the theory of analytic functions with positive imaginary part in the upper half-plane.Comment: 26 page

Dynamic light scattering from solutions of microtubules.

Calf brain microtubule protein was assembled in vitro to form dilute solutions of microtubules (240 A diameter) having lengths greater than 1 micrometer. The microtubule solutions were examined by dynamic laser light scattering techniques. The angular dependence of the correlation function leads to the conclusion that the correlation function is measuring the translational diffusion constant of the particles. The length dependence of the correlation function, however, shows that the translational diffusion constant is not being measured and that the diffusion constant for the microtubules cannot be straightforwardly determined. These results suggest that a collective property of the rods is being measured by the laser light scattering. Although specific microtubule-microtubule interactions are a possible explanation for the observed results, we present arguments that suggest that the solution can be adequately modeled as a network of entangled polymers