共查询到20条相似文献,搜索用时 31 毫秒
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We present a new GCD algorithm for two integers that combines both the Euclidean and the binary gcd approaches. We give its worst case time analysis and we prove that its bit-time complexity is still for two n-bit integers in the worst case. Our preliminar experiments show a potential speedup for small integers. A parallel version matches the best presently known time complexity, namely time with processors, for any constant . 相似文献
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胡国恩 《数学物理学报(B辑英文版)》2005,25(3):545-554
Lp(Rn) (1<p<∞) boundedness and a weak type endpoint estimate are considered for the commutators of singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness of the singular integral operators implies the Lp(Rn) boundedness (1<p<∞) and the weak type (H1(Rn), L1(Rn))boundedness for the corresponding commutators. A new interpolation theorem is also established. 相似文献
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We show that there is a constant such that, for any set P of n⩾ 5 points in general position in the plane, a crossing-free geometric graph on P that is chosen uniformly at random contains, in expectation, at least edges, where M denotes the number of edges in any triangulation of P. From this we derive (to our knowledge) the first non-trivial upper bound of the form on the number of crossing-free geometric graphs on P; that is, at most a fixed exponential in n times the number of triangulations of P. (The trivial upper bound of , or , follows by taking subsets of edges of each triangulation.) If the convex hull of P is triangular, then , and we obtain .Upper bounds for the number of crossing-free geometric graphs on planar point sets have so far applied the trivial factor to the bound for triangulations; we slightly decrease this bound to . 相似文献
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Anton Alekseev Nariya Kawazumi Yusuke Kuno Florian Naef 《Comptes Rendus Mathematique》2017,355(2):123-127
We define a family of Kashiwara–Vergne problems associated with compact connected oriented 2-manifolds of genus g with boundary components. The problem is the classical Kashiwara–Vergne problem from Lie theory. We show the existence of solutions to for arbitrary g and n. The key point is the solution to based on the results by B. Enriquez on elliptic associators. Our construction is motivated by applications to the formality problem for the Goldman–Turaev Lie bialgebra . In more detail, we show that every solution to induces a Lie bialgebra isomorphism between and its associated graded . For , a similar result was obtained by G. Massuyeau using the Kontsevich integral. For , , our results imply that the obstruction to surjectivity of the Johnson homomorphism provided by the Turaev cobracket is equivalent to the Enomoto–Satoh obstruction. 相似文献
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《Computational Geometry》2014,47(1):42-51
Given a collection of n opaque unit disks in the plane, we want to find a stacking order for them that maximizes their visible perimeter, the total length of all pieces of their boundaries visible from above. We prove that if the centers of the disks form a dense point set, i.e., the ratio of their maximum to their minimum distance is , then there is a stacking order for which the visible perimeter is . We also show that this bound cannot be improved in the case of a sufficiently small uniform grid. On the other hand, if the set of centers is dense and the maximum distance between them is small, then the visible perimeter is with respect to any stacking order. This latter bound cannot be improved either.Finally, we address the case where no more than c disks can have a point in common.These results partially answer some questions of Cabello, Haverkort, van Kreveld, and Speckmann. 相似文献
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Bhama Srinivasan 《Journal of Algebra》2008,319(2):824-832
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