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.     

Influence of perfluorinated carboxylic acids on ion-pair reversed-phase high-performance liquid chromatographic separation of betacyanins and 17-decarboxy-betacyanins

The ability of trifluoroacetic acid, pentafluoropropionic acid and heptafluorobutyric acid to act as ion-pairing agents for betacyanins and 17-decarboxy-betacyanins during HPLC analysis on a Luna C18(2) reversed-phase column is reported. While the perfluorinated carboxylic acids affect the retention of both groups of compounds by changing the pH of the mobile phase, the possibility of ion-pair chromatography for 17-decarboxy-betacyanins was noticed. In order to explain the accessibility of the positive charge for the counter-anion in decarboxy-betacyanins, the mesomeric structures of the polymethine system at low pH (around a value of 1.5), when the carboxylic group in the 2 position is protonated, should be taken into consideration.     

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.     

Tuning Chemical and Physical Properties of Phosphorus Corroles for Advanced Applications

Although the affinity of metallocorroles to axial ligands is quite low, this is not the case when the chelated element is phosphorus. This work is hence focused on the mechanism of ligand exchange of six-coordinate phosphorus corroles as a tool for affecting their chemical and physical properties. These fundamental investigations allowed for the development of facile methodologies for the synthesis of a large series of complexes and the establishment of several new structure/activity profiles that may be used to understand and predict spectroscopic features and for tailor-made modification of photophysical and electrochemical properties. This is exemplified by the facile access to complexes with terminal groups that are of large potential for practical applications based on click chemistry, optical imaging, and surface science.     

Frequency shifts and interaction strength of model hydrogen-bonded systems: new NBO and QTAIM characteristics

An innovative theoretical study of intermolecular properties of standard hydrogen-bonded complexes of H₂O···HCF₃, NH₃···HCF₃, H₂O···HF, and NH₃···HF is presented in this work. Several computational strategies were used, so initially the MP2/6-311++G(d,p) level of theory was applied to determine the optimized geometries by which the structural parameters, electronic properties, and the stretch vibration modes of these systems were examined. By taking into account the infrared spectrum analysis, the frequency shifted either to the red- or blue-region is the principal interpretation upon formation of intermolecular complexes. Due to this, the analysis of the interaction strengths corroborates with these vibration behaviors, and besides, the Natural Bond Orbital calculations revealed systematic changes in the percentage of the s and p orbitals, by which the stretch deformations on the proton donors (HF and HCF₃) could be understood. In advance, it was quoted the appearing of intermolecular covalence in these complexes, and this event could be theoretically discovered through the topological computations based on the Bader's Quantum Theory of Atoms in Molecules.     

Novel active noise-reducing headset using earshell vibration control

Active noise-reducing (ANR) headsets are available commercially in applications varying from aviation communication to consumer audio. Current ANR systems use passive attenuation at high frequencies and loudspeaker-based active noise control at low frequencies to achieve broadband noise reduction. This paper presents a novel ANR headset in which the external noise transmitted to the user's ear via earshell vibration is reduced by controlling the vibration of the earshell using force actuators acting against an inertial mass or the earshell headband. Model-based theoretical analysis using velocity feedback control showed that current piezoelectric actuators provide sufficient force but require lower stiffness for improved low-frequency performance. Control simulations based on experimental data from a laboratory headset showed that good performance can potentially be achieved in practice by a robust feedback controller, while a single-frequency real-time control experiment verified that noise reduction can be achieved using earshell vibration control.     

Phosphinoferrocenylaminophosphines as novel and practical ligands for asymmetric catalysis

[structure: see text] A new series of ligands with a novel phosphine-aminophosphine ligation design as depicted in structure 1 has been prepared on a ferrocenylethyl backbone. These BoPhoz ligands of structure 2 have afforded exceedingly high activity and enantioselectivity in the rhodium-catalyzed asymmetric hydrogenation of dehydro-alpha-amino acid derivatives, itaconic acids, and alpha-ketoesters. These air-stable ligands are readily prepared from cost-effective and non-pyrophoric intermediates.