; Published online before print September 26, 2012; Neurology Joshua M. Shulman and Julie A. Schneider disease Molecular mechanisms of cortical degeneration in Parkinson October 15, 2012 This information is current as of http://www.neurology.org/content/early/2012/09/26/WNL.0b013e31827040c6 located on the World Wide Web at: The online version of this article, along with updated information and ...

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Birkhäuser Verlag, Basel–Boston–Berlin, x + 202 pp., $49.95, ISBN 978-3-76437705-2 “If the area of a membrane be given, there must evidently be some form of boundary for which the pitch (of the principal tone) is the gravest possible, and this form can be no other than the circle,” wrote Lord Rayleigh in his book “The Theory of Sound” ([R], vol. 1, §210.) A membrane is a planar domain Ω, and it...

This paper gives a survey on recent results about the existence of knotted vortex structures in incompressible fluids. includes proof Lord Kelvin's conjecture tubes steady Euler flows and new probabilistic approach to address Arnold's speculation that typical Beltrami fields should exhibit lines arbitrary topological complexity. We review key tools establish these results: global approximation ...

The “balayage” method introduced by H. Poincaré in his proof of Theorem 1 relies heavily on tools of Potential theory: maximum principle, Harnack’s inequality, explicit representation formulas for the Dirichlet problem in a ball (Poisson integral), etc. In 1900, D. Hilbert [39], in a celebrated address, followed by a (slightly) more detailed paper in 1904, announced that he had solved the Diric...