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The average number of distinct block sizes in a partition of a set of n elements is asymptotic to e log n as n → ∞. In addition, almost all partitions have approximately e log n distinct block sizes. This is in striking contrast to the fact that the average total number of blocks in a partition is ~n(log n)?1 as n → ∞. 相似文献
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We consider the class of stochastic matrices M generated in the following way from graphs: if G is an undirected connected graph on n vertices with adjacency matrix A, we form M from A by dividing the entries in each row of A by their row sum. Being stochastic, M has the eigenvalue λ=1 and possibly also an eigenvalue λ=-1. We prove that the remaining eigenvalues of M lie in the disk ¦λ¦?1–n-3, and show by examples that the order of magnitude of this estimate is best possible. In these examples, G has a bar-bell structure, in which n/3 of the vertices are arranged along a line, with n/3 vertices fully interconnected at each end. We also obtain better bounds when either the diameter of G or the maximal degree of a vertex is restricted. 相似文献
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CM Silva MF Duarte ML Mira MH Florêncio K Versluis AJ Heck 《Rapid communications in mass spectrometry : RCM》1999,13(12):1098-1103
Fast atom bombardment, combined with high-energy collision-induced tandem mass spectrometry, has been used to investigate gas-phase metal-ion interactions with captopril, enalaprilat and lisinopril, all angiotensin-converting enzyme inhibitors.Suggestions for the location of metal-binding sites are presented. For captopril, metal binding occurs most likely at both the sulphur and the nitrogen atom. For enalaprilat and lisinopril, binding preferably occurs at the amine nitrogen. Copyright 1999 John Wiley & Sons, Ltd. 相似文献
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Catarina IV Ramos Flávio Figueira Marcelo D Polêto Francisco ML Amado Hugo Verli João PC Tomé M Graça PMS Neves 《Journal of mass spectrometry : JMS》2016,51(5):342-349
Electrospray mass spectrometry/mass spectrometry was used to investigate the gas‐phase properties of protonated expanded porphyrins, in order to correlate those with their structure and conformation. We have selected five expanded meso‐pentafluorophenyl porphyrins, respectively, a pair of oxidized/reduced fused pentaphyrins (22 and 24 π electrons), a pair of oxidized/reduced regular hexaphyrins (26 and 28 π electrons) and a regular doubly N‐fused hexaphyrin (28 π electrons). The gas‐phase behavior of the protonated species of oxidized and reduced expanded porphyrins is different. The oxidized species (aromatic Hückel systems) fragment more extensively, mainly by the loss of two HF molecules. The reduced species (Möbius aromatic or Möbius‐like aromatic systems) fragment less than their oxidized counterparts because of their increased flexibility. The protonated regular doubly fused hexaphyrin (non‐aromatic Hückel system) shows the least fragmentation even at higher collision energies. In general, cyclization through losses of HF molecules decreases from the aromatic Hückel systems to Möbius aromatic or Möbius‐like aromatic systems to non‐aromatic Hückel systems and is related to an increase in conformational distortion. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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LetN(x, n, ) denote the number of integer lattice points inside then-dimensional sphere of radius (an)1/2 with center at x. This numberN(x,n, ) is studied for fixed,n , andx varying. The average value (asx varies) ofN(x,n, ) is just the volume of the sphere, which is roughly of the form (2 e, )
n/2. it is shown that the maximal and minimal values ofN (x,n, ) differ from the everage by factors exponential inn, which is in contrast to the usual lattice point problems in bounded dimensions. This lattice point problem arose separately in universal quantization and in low density subset sum problems. 相似文献
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Discrete Logarithms: The Past and the Future 总被引:5,自引:0,他引:5
Andrew Odlyzko 《Designs, Codes and Cryptography》2000,19(2-3):129-145
The first practical public key cryptosystem to be published, the Diffie–Hellman key exchange algorithm, was based on the assumption that discrete logarithms are hard to compute. This intractability hypothesis is also the foundation for the presumed security of a variety of other public key schemes. While there have been substantial advances in discrete log algorithms in the last two decades, in general the discrete log still appears to be hard, especially for some groups, such as those from elliptic curves. Unfortunately no proofs of hardness are available in this area, so it is necessary to rely on experience and intuition in judging what parameters to use for cryptosystems. This paper presents a brief survey of the current state of the art in discrete logs. 相似文献
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A.M Odlyzko 《Advances in Mathematics》1982,44(2):180-205
It is shown that the coefficients an of the power series f(z) = ∑∞n=1anzn which satisfies the functional equation display periodic oscillations; as n → ∞, where and u(x) is a positive, nonconstant, continuous function which is periodic with period log(4 ? ø). Similar results are obtained for a wide class of power series that satisfy similar functional equations. Power series of these types are of interest in combinatorics and computer science since they often represent generating functions. For example, the nth coefficient of the power series satisfying (1) enumerates 2, 3-trees with n leaves. 相似文献