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Average-Case Polynomial-Time Computability of Hamiltonian Dynamics

. Math., 44 : 61 - 71 , 1957 . Akitoshi Kawamura. Lipschitz Continuous Ordinary Differential Equations are PolynomialSpace Complete . Computational Complexity , 19 ( 2 ): 305 - 332 , 2010 . Akitoshi ... Kawamura and Stephen Cook . Complexity theory for operators in analysis . ACM Transactions on Computation Theory , 4 ( 2 ):Article 5, 2012 . Ker-I Ko . On the computational complexity of ordinary

A Lower Bound on Opaque Sets

It is proved that the total length of any set of countably many rectifiable curves, whose union meets all straight lines that intersect the unit square U, is at least 2.00002. This is the first improvement on the lower bound of 2 by Jones in 1964. A similar bound is proved for all convex sets U other than a triangle.