Graph consists of a set of vertices V={Xj: j I}, a set of finite edges L={Ljn:(Xj, Xn) IL I I} and a set of infinite edges L={Lj: Xj IC} attached to them. We regard it as a configuration space of a quantum system with the Hilbert space
We combine the method of searching for an invariant subspace of the unbalanced Oil and Vinegar signature scheme and the Minrank method to defeat the new TTS signature scheme, which was suggested for low-cost smart card applications at CHES 2004. We show that the attack complexity is less than 2^{50}.
We consider the Laplacian in curved tubes of arbitrary crosssection rotating together with the Frenet frame along curves in Euclidean spaces of arbitrary dimension, subject to Dirichlet boundary conditions on the cylindrical surface and Neumann conditions at the ends of the tube. We prove that the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Dirichlet Laplacian in a torus determined by the geometry of the tube.
Dawei ChenDepartment of Mathematics, Boston College, Chestnut Hill, MA, USAMartin MöllerInstitut für Mathematik, Goethe–Universität Frankfurt, Frankfurt am Main, GermanyAdrien SauvagetLaboratoire de Mathématiques AGM, UMR 8088 du CNRS, Université de Cergy-Pontoise, Cergy-Pontoise Cedex, FranceDon ZagierMPIM Bonn, Bonn, Germany
We show that the Masur–Veech volumes and area Siegel–Veech constants can be obtained using intersection theory on strata of Abelian differ- entials with prescribed orders of zeros. As applications, we evaluate their large genus limits and compute the saddle connection Siegel–Veech constants for all strata. We also show that the same results hold for the spin and hyperelliptic components of the strata.