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.     

Kinetics of thermal oxidation of titanium carbide and its carbon nano-composites in dry air atmosphere

Results of research work on oxidation of TiC/C nano-composites in air and under non-isothermal conditions are presented. The oxidation of nano-crystalline titanium carbide as well as its carbon composites were studied using TG-DSC method in dry air atmosphere. The investigated samples were as follows: commercial TiC nano-powders from Alfa Aesar (80 nm) and carbon composites including nano-crystalline TiC (30 nm and 50, 10, 3 mass% of carbon in matrix). The measurements were executed in the Setaram thermoanalyser TG-DSC 92-15 in non-isothermal conditions, with mass samples of 30±0.2 mg and constant heating rate in the range 2–10 K min⁻¹.     

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.     

The least element property of center location on tree networks with applications to distance and precedence constrained problems

In the classicalp-center location model on a network there is a set of customers, and the primary objective is to selectp service centers that will minimize the maximum distance of a customer to a closest center. Suppose that thep centers receive their supplies from an existing central depot on the network, e.g. a warehouse. Thus, a secondary objective is to locate the centers that optimize the primary objective as close as possible to the central depot. We consider tree networks and twop-center models. We show that the set of optimal solutions to the primary objective has a semilattice structure with respect to some natural ordering. Using this property we prove that there is ap-center solution to the primary objective that simultaneously minimizes every secondary objective function which is monotone nondecreasing in the distances of thep centers from the existing central depot.Restricting the location models to a rooted path network (real line) we prove that the above results hold for the respective classicalp-median problems as well.     

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.     

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.