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.     

New Classes of Toda Soliton Solutions

We provide a detailed investigation of limits of N–soliton solutions of the Toda lattice as N tends to infinity. Our principal results yield new classes of Toda solutions including, in particular, new kinds of soliton–like (i.e., reflectionless) solutions. As a byproduct we solve an inverse spectral problem for one–dimensional Jacobi operators and explicitly construct tri–diagonal matrices that yield a purely absolutely continuous spectrum in (-1,1) and give rise to an eigenvalue spectrum that includes any prescribed countable and bounded subset of . Received: 16 October 1995/Accepted: 23 July 1996     

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     

THE PHOTOSYNTHETIC APPARATUS OF Acetabularia mediterranea GROWN UNDER RED OR BLUE LIGHT. BIOPHYSICAL QUANTIFICATION and CHARACTERIZATION OF PHOTOSYSTEM II and ITS CORE COMPONENTS

Abstract— The photosynthetic activity of white light-grown Acetabularia mediterranea Lamouroux (= A. acetabulum (L.) Silva) decreases under continuous red light to less than 20% within 3 weeks. Subsequent blue light reactivates photosynthesis within a relatively short period of 3 days. In a former publication (Wennicke and Schmid, Plant Physiol. 84 ,1252–1256, 1987) we have shown that the regulated rate limiting step, which is an immediate light driven reaction, is part of photosystem II (PS II). The following biophysical properties of PS II were analyzed in thylakoids isolated from algae grown 3 weeks under either blue or red light with or without subsequent 3 days of blue light illumination: (a) fluorescence induction in the short time domain dominated by Q_A reduction, (b) the slow fluorescence decline reflecting pheophytin photoaccumulation, (c) absorption changes at 320 and 830 nm under repetitive flash excitation as indicator for the turnover of Q_A and P₆₈₀, respectively, (d) oscillation pattern of the oxygen yield by a flash train in dark adapted samples and (e) the binding capacity for atrazine. None of these PS II functions were severely affected, but a minor impairment of20–30% was observed in the thylakoids from algae grown for 3 weeks in red irradiation. The changes do not fully account for the drastic reduction of the electron transport through PS II which was 80% after red light treatment. Therefore, the regulated rate-limiting step appears to not be mainly located in the PS II core complex itself. It seems likely that the regulation process predominantly comprises the antenna system.     

PHOTOCHEMISTRY OF THE REACTION CENTERS OF SYSTEM II UNDER REPETITIVE FLASH GROUP EXCITATION IN ISOLATED CHLOROPLASTS

Abstract— Absorption changes induced in isolated chloroplasts by excitation with repetitive flash groups have been measured at 690 nm, indicating the photochemical turnover of chlorophyll-a_II (Chl-αn), and at 480 nm and 513 nm respectively, reflecting via electrochromic effect the formation of a transmembrane electric field. The data are compared with measurements of oxygen evolution. In chloroplasts with practically fully intact oxygen evolving capacity it was found: 1. The initial amplitude of the 690 nm absorption change induced by the second flash as a function of the time t_v between the first and second flash of a group increases with a half life of about 35 µs. On the other hand, the average oxygen yield due to the second flash as a function of the time t_v rises with a half life of about 600 µs (and a kinetics in the ms-range of minor extent), confirming the data of Vater et al. (1968). 2. Under far red background illumination, where contributions due to PS I in the µs-range can be excluded, the difference spectrum in the red of the absorption changes induced by the first flash corresponds with that of the absorption changes induced by the second flash fired 200 µ after the first flash. 3. The pattern of the absorption changes at 690 nm induced by repetitive double flash groups at t_v= 200 µs does not markedly change in normal chloroplasts by the presence of DBMIB?. Similar 690 nm absorption changes occur in trypsin treated chloroplasts, independent of the presence of DCMU. 4. The fast regeneration in the µs-range of Chl-a_n is also observed in the third flash of a triple flash group at a time t_v= 200 µs between the flashes of the group. 5. The initial amplitudes of the absorption changes with a decay kinetics slower than 100 µs induced by the second flash at 480 nm and 513 nm, respectively, as a function of the time t, between the first and second flash of a group, are characterized by a recovery half-time of about 600 µs, confirming earlier measurements at 520 nm (Witt and Zickler, 1974). On the basis of these results it is inferred that there does exist a photoreaction of Chl-α_n., with an electron acceptor, referred to as X_a, other than the ‘primary’ plastoquinone acceptor X320, if X320 persists in its reduced state. Under conditions of X320 being in the reduced state, this photochemical reaction was shown to be highly dissipative with respect to charging up the watersplitting enzyme system Y. Furthermore, this Chl-a_n-photoreaction with X_a does not lead to a vectorial transmembrane charge separation, which is stable for more than a few microseconds. Different models for the functional and structural organization of PS II are discussed.