Limit cycles and Lie symmetries

Given a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem proposed by A.T. Winfree in the seventies about the existence of isochrons of limit cycles (the question suggested by the study of biological clocks), already answered by Guckenheimer using a different terminology. We apply our criterion to give upper bounds of the number of limit cycles for some families of vector fields as well as to provide a class of vector fields with a prescribed number of hyperbolic limit cycles. Finally we show how this procedure solves the problem of the hyperbolicity of periodic orbits in problems where other criteria, like the classical one of the divergence, fail.     

Abelian Ward identity from the background field dependence of the effective action

The dependence of the effective action for gauge theories on the background field obeys an exact identity. We show that for Abelian theories the Ward identity follows from the more general background field identity. This observation is relevant for the formulation of effective actions with an infrared cutoff since the solution of exact flow equations must obey an anomalous Ward identity.     

Organic–inorganic nanocomposites prepared from fluoro-aramid and silica

Fluoro-aramid-based sol/gel-derived nanocomposites were synthesized by condensing a mixture of 4,4′-(hexafluoro-isopropylidene)dianiline and 1,3-phenylenediamine with terephthaloylchloride (TPC) in dimethylacetamide. TPC was added in slight excess to produce amide chains with carbonyl chloride end groups and then replaced with alkoxy groups using aminophenyltrimethoxysilane to develop bonding with the silica network. Mechanical, dynamic mechanical thermal, water absorption and morphological measurements were carried out on the thin hybrid films. Increase in the tensile strength and modulus was observed as compared to pristine polyamide. The thermal decomposition temperature was found in the range of 400–500 °C. The water absorption was found to be reduced with higher silica content. The glass transition temperature and the storage moduli increased with increasing silica concentration. The maximum increase in the T _g value (345 °C) was observed with 20 wt% silica. Scanning electron microscopy revealed the uniform distribution of silica in the matrix with an average particle size ranging from 8 to 50 nm.     

Enhancement of distillate selectivity in Fischer-Tropsch synthesis by using iron and cobalt catalysts in a novel dual-bed reactor ?

Summary An integrated process for producing liquid fuels from synthesis gas via a two-stage Fischer-Tropsch (FT) reaction is disclosed. An iron catalyst was used in the first bed of a fixed-bed reactor followed by a ruthenium promoted cobalt catalyst in the second bed. The activity and selectivity of the dual-bed system were assessed and compared with those using catalysts in a single bed system, separately. The methane selectivity in the dual-bed reactor was about 11% less compared to that of the single-bed system. The C₅⁺ selectivity for the dual-bed reactor was 19.7% higher than that of the single-bed system.     

A closed-shell coupled-cluster treatment of the Breit-Pauli first-order relativistic energy correction

First-order relativistic corrections to the energy of closed-shell molecular systems are calculated, using all terms in the two-component Breit-Pauli Hamiltonian. In particular, we present the first implementation of the two-electron Breit orbit-orbit integrals, thus completing the first-order relativistic corrections within the two-component Pauli approximation. Calculations of these corrections are presented for a series of small and light molecules, at the Hartree-Fock and coupled-cluster levels of theory. Comparisons with four-component Dirac-Coulomb-Breit calculations demonstrate that the full Breit-Pauli energy corrections represent an accurate approximation to a fully relativistic treatment of such systems. The Breit interaction is dominated by the spin-spin interaction, the orbit-orbit interaction contributing only about 10% to the total two-electron relativistic correction in molecules consisting of light atoms. However, the relative importance of the orbit-orbit interaction increases with increasing nuclear charge, contributing more than 20% in H(2)S.     

Solvent and substituent effects on the conformational equilibria and intramolecular hydrogen bonding of 4-substituted-2-hydroxybenzaldehydes

By applying the B3LYP/6-31G(d) method with the SCIPCM model on seven 4X substituted 2-hydroxybenzaldehydes, some structural characteristics related with their conformational equilibria and intramolecular hydrogen bonds have been clarified. The compounds are almost completely under the planar conformation characterized by a strong intramolecular hydrogen bond, which decreases in those solvents that possess a higher hydrogen bond donating capability and polarity. The substituents exert a marked influence on the conformational equilibrium constants and the strength of the IHB. Moreover, the excellent Hammett-type equations obtained support the proposed conformational reactions to quantify the IHB in the o-hydroxybenzaldehydes studied.     

New [Mo(eta3-allyl)(CO)2L3]+ complexes with monodentate or tridentate nitrogen-donor ligands

Cationic complexes [Mo(eta(3)-allyl)(CO)2L3]+ (L3 = either nitrogen-donor tridentate ligand or three monodentate ligands) were prepared in high yield and under mild conditions using as precursors either the triflato complex [Mo(eta(3)-allyl)(OTf)(CO)2(NCMe)2] or the combination of the chloro complex [Mo(eta(3)-allyl)Cl(CO)2(NCMe)2] and the salt NaBAr'(4)(Ar'= 3,5-bis(trifluoromethyl)phenyl). The tridentate ligands employed were 2,2':6',2'-terpyridine (terpy) and cis,cis-1,3,5-cyclohexanetriamine (CHTA), whereas the monodentate ligands imidazole (im) and 3,5-dimethylpyrazole (dmpz) were chosen. In order to stabilize the labile intermediates, an excess of acetonitrile was used in most of the syntheses. However, the pyrazole complex was prepared through a nitrile-free route to avoid reactions at the coordinated nitrile. The solid state structures of [Mo(eta(3)-methallyl)(CO)2(terpy)]OTf (2), [Mo(eta(3)-methallyl)(CO)2(CHTA)]BAr'4 (3), [Mo(eta(3)-methallyl)(CO)2(NCMe)3]BAr'4 (4), [Mo(eta(3)-allyl)(CO)2(im)3]OTf (5) and [Mo(eta(3)-allyl)(CO)2(dmpz)3]BAr'4 (6) were determined by means of single-crystal X-ray diffraction.