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We introduce and study Hopf monads on autonomous categories (i.e., monoidal categories with duals). Hopf monads generalize Hopf algebras to a non-braided (and non-linear) setting. In particular, any monoidal adjunction between autonomous categories gives rise to a Hopf monad. We extend many fundamental results of the theory of Hopf algebras (such as the decomposition of Hopf modules, the existence of integrals, Maschke's criterium of semisimplicity, etc.) to Hopf monads. We also introduce and study quasitriangular and ribbon Hopf monads (again defined in a non-braided setting). 相似文献
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Luc Hillairet 《Annales Henri Poincare》2006,7(4):689-710
We consider Riemannian surfaces in which there are many embedded Euclidean cylinders. We show that quantitative assumptions
on the number of such cylinders provide estimates for the counting function of eigenvalues. These results in particular apply
to translation surfaces.
Communicated by Jens Marklof
Submitted: 3/03/ 2005 Accepted: 18/11/2005 相似文献
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Alexis C. Kaporis Lefteris M. Kirousis Yannis C. Stamatiou Malvina Vamvakari Michele Zito 《Discrete Applied Mathematics》2007,155(12):1525-1538
The problem of determining the unsatisfiability threshold for random 3-SAT formulas consists in determining the clause to variable ratio that marks the experimentally observed abrupt change from almost surely satisfiable formulas to almost surely unsatisfiable. Up to now, there have been rigorously established increasingly better lower and upper bounds to the actual threshold value. In this paper, we consider the problem of bounding the threshold value from above using methods that, we believe, are of interest on their own right. More specifically, we show how the method of local maximum satisfying truth assignments can be combined with results for the occupancy problem in schemes of random allocation of balls into bins in order to achieve an upper bound for the unsatisfiability threshold less than 4.571. In order to obtain this value, we establish a bound on the q-binomial coefficients (a generalization of the binomial coefficients). No such bound was previously known, despite the extensive literature on q-binomial coefficients. Finally, to prove our result we had to establish certain relations among the conditional probabilities of an event in various probabilistic models for random formulas. It turned out that these relations were considerably harder to prove than the corresponding ones for unconditional probabilities, which were previously known. 相似文献
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Numerous versions of the Lanczos τ-methods have been extensively used to produce polynomial approximations for functions verifying
a linear differential equation with polynomial coefficients. In the case of an initial-value problem, an adapted τ-method
based on Chebyshev series and the use of symbolic computation lead to a rational approximation of the solution on a region
of the complex plane. Numerical examples show that the simplicity of the method does not prevent a high accuracy of results.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Joël J. E. Moreau Luc Vellutini Catherine Bied Michel Wong Chi Man 《Journal of Sol-Gel Science and Technology》2004,32(1-3):63-67
The acid-hydrolysis of an organo-bridged bisdiethoxysilylated molecular precursor bearing urea groups, (EtO)2MeSi(CH2)3NHCONH(CH2)12NHCONH(CH2)3SiMe(OEt)2, has been performed in pure aqueous medium. Scanning electron microscopy (SEM) analysis of the resulting insoluble solid revealed plate-like forms with a lamellar structure as determined by powder X-ray diffraction (PXRD) studies with a sharp peak at 28.5 Å. The solid state 29Si MAS-NMR spectrum of this bridged siloxane hybrid is consistent with a moderately condensed material with complete preservation of the Si–C bonds throughout the hybrid network. In comparison, the classical sol–gel hydrolysis-condensation of the molecular precursor in ethanol with stoichiometric amount of water and fluoride anion as catalyst produced an amorphous featureless solid. 相似文献