Invariant Cocycles Have Abelian Ranges

 Let R be a discrete nonsingular equivalence relation on a standard probability space , and let V be an ergodic strongly asymptotically central automorphism of R. We prove that every V-invariant cocycle with values in a Polish group G takes values in an abelian subgroup of G. The hypotheses of this result are satisfied, for example, if A is a finite set, a closed, shift-invariant subset, V is the shift, μ a shift-invariant and ergodic probability measure on X, the two-sided tail-equivalence relation on X, a shift-invariant subrelation which is μ-nonsingular, and a shift-invariant cocycle.     

Validation of a thermal decomposition mechanism of formaldehyde by detection of CH2O and HCO behind shock waves

The thermal decomposition of formaldehyde was investigated behind shock waves at temperatures between 1675 and 2080 K. Quantitative concentration time profiles of formaldehyde and formyl radicals were measured by means of sensitive 174 nm VUV absorption (CH₂O) and 614 nm FM spectroscopy (HCO), respectively. The rate constant of the radical forming channel (1a), CH₂O + M → HCO + H + M, of the unimolecular decomposition of formaldehyde in argon was measured at temperatures from 1675 to 2080 K at an average total pressure of 1.2 bar, k_1a = 5.0 × 10¹⁵ exp(‐308 kJ mol^?1/RT) cm³ mol^?1 s^?1. The pressure dependence, the rate of the competing molecular channel (1b), CH₂O + M → H₂ + CO + M, and the branching fraction β = k_1a/(kA_1a + k_1b) was characterized by a two‐channel RRKM/master equation analysis. With channel (1b) being the main channel at low pressures, the branching fraction was found to switch from channel (1b) to channel (1a) at moderate pressures of 1–50 bar. Taking advantage of the results of two preceding publications, a decomposition mechanism with six reactions is recommended, which was validated by measured formyl radical profiles and numerous literature experimental observations. The mechanism is capable of a reliable prediction of almost all formaldehyde pyrolysis literature data, including CH₂O, CO, and H atom measurements at temperatures of 1200–3200 K, with mixtures of 7 ppm to 5% formaldehyde, and pressures up to 15 bar. Some evidence was found for a self‐reaction of two CH₂O molecules. At high initial CH₂O mole fractions the reverse of reaction (6), CH₂OH + HCO ? CH₂O + CH₂O becomes noticeable. The rate of the forward reaction was roughly measured to be k₆ = 1.5 × 10¹³ cm³ mol^?1 s^?1. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 157–169 2004     

Über Antimon-haltige Heterocyclen. I. Molekül- und KristallStruktur von 2-Chlor- 1,3,6-trithia-2-stibaocan

On Antimony Containing Heterocyclic Systems. I. Molecular and Crystal Structure of 2-Chloro-1,3,6-trithia-2-stibaocane 2-Chloro-1,3,6-trithia-2-stibaocane crystallizes in the orthorhombic space group P2₁2₁2₁ with cell dimensions a = 9.054, b = 22.610, c = 9.097 Å and Z = 8. The crystal structure has been determined from single crystal X-ray data and refined to a conventional R of 0.038. The eight-membered ring has deformated boat-conformation with 1,5-intraannular Sb? S-interaction. The coordination of the Sb-atom is ψ-trigonal-bipyramidal with axial distances Sb? Cl 2.51 Å, Sb? S 2.86 Å and equatorial distances Sb? S 2.44 and 2.45 Å. The Sb? S-bond is discussed. The structure consists of 14-coordinated molecules densest packed parallel to the x? y-plane and less densely packed perpendicular to this plane.     

Ab initio investigation of the potential energy surfaces of C2H2F2 and C2H2F2+

Ab initio MO calculations have been performed for neutral and cationic C₂H₂F₂ structures. Olefinic and carbene structures are investigated for the neutral isomers, while olefinic, carbene, and fluoronium-type cations are found. Stability orders and rotational barriers are discussed in terms of orbital and Coulomb interaction. Contrary to previous studies, the higher stability of the geminal isomers is interpreted to be caused by Coulomb attraction.