Permutation graphs, fast forward permutations, and sampling the cycle structure of a permutation

PS_N is a fast forward permutation if for each m the computational complexity of evaluating P^m(x) is small independently of m and x. Naor and Reingold constructed fast forward pseudorandom cycluses and involutions. By studying the evolution of permutation graphs, we prove that the number of queries needed to distinguish a random cyclus from a random permutation in S_N is Θ(N) if one does not use queries of the form P^m(x), but is only Θ(1) if one is allowed to make such queries. We construct fast forward permutations which are indistinguishable from random permutations even when queries of the form P^m(x) are allowed. This is done by introducing an efficient method to sample the cycle structure of a random permutation, which in turn solves an open problem of Naor and Reingold.     

High-precision measurements of 17O/16O and 18O/16O of O2 and O2/Ar ratio in air

A method for high-precision and high-accuracy mass spectrometric measurements of the ratios among the three oxygen isotopes, and of the O(2)/Ar ratio, is presented. It involves separation of the O(2)-Ar mixture from air and includes a fully automated system that ensures highly reliable sample processing. Repeated measurements of atmospheric oxygen yield the repeatability (+/-SE x t, standard error of the mean (n = 12) multiplied by Student's t-factor for a 95% confidence limit) of 0.004, 0.003 and 0.2 per thousand for delta(18)O, delta(17)O and delta O(2)/Ar, respectively.     

d-orbital stereoelectronic control of the stereochemistry of SN2′ displacements by organocuprate reagents

The $\text{anti}$ stereochemistry observed in organocuprate S_N2′ displacements can be rationalized as a stereoelectronic effect arising from “bidentate” binding involving a d orbital of nueleophilic copper and π* and σ* orbitals of the substrate. The extension of this idea to other reactions of organocuprates including additions to acetylenes and enones is discussed.