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.     

De-mixing dynamics of a binary liquid system in a controlled-pore glass

The European Physical Journal E - The temperature-induced microphase separation of the binary liquid system iso-butyric acid+heavy water (iBA + D2O) in a mesoporous silica glass (CPG-10-75) of...     

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     

Bifurcation for a semilinear elliptic equation on ℛN with radially symmetric coefficients

We consider the semilinear eigenvalue problem on ^N (N 2) (N2) and investigate the question under which conditions on the radially symmetric function q, =0 is a bifurcation point for this equation in H¹, In H² and in L^p for 2p+.     

Goodisman's correction of the Thomas-Fermi-von Weizsäcker theory of atoms

Summary Following a suggestion of J. Goodisman, we substitute the therm by in the Thomas-Fermi-von Weizsäcker energy functional for atoms.f _z³ [0,1] is a function depending on the nuclear chargez.We establish conditions for the functionsf _z such that the ratio of this modified TFW-energyE _kz ^/TFWG (z) (kz is the total number of electrons) and the exact quantum mechanical energy converges to 1 asz. Moreover, we prove thatE _kz ^/TFWG (z)=E _kz ^/TFW (z)+Dz ²+o(z ²) (z) and determineD. Here,E _kz ^/TFW (z) is the unmodified TFW energy.

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Zusammenfassung Einem Vorschlag J. Goodismans folgend, ersetzen wir in dem Thomas-Fermi-von Weizsäcker Energiefunktional für Atome den Term durch .f _z³ [0,1] ist hierbei eine Funktion, die von der Kernladungszahlz abhängt.Wir geben dann Bedingungen für die Funktionenf _z an, unter denen der Quotient der so modifizierten TFW-energieE _kz ^/TFWG (z) (kz=Anzahl der Elektronen) und der exakten quantenmechanischen Energie fürz gegen 1 konvergiert. Darüber hinaus beweisen wir, daßE _kz ^/TFWG (z)=E _kz ^/TFW (z)+D·o(itz) ² (z) gilt und bestimmmenD. E _kz ^/TFW (z) ist hierbei die nicht-modifizierte TFW-Energie.