Expected Reflection Distance in G(r, 1, n) after a Fixed Number of Reflections

Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G(r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G(r, 1, n)-characters and on the eigenvalues of certain adjacency matrices.Received December 8, 2003     

Whirling frequencies and amplitudes due to deviations of generator shape

Earlier measurements in large synchronous generators indicate the existence of backward whirling motion, and also relatively large deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The target of this paper is to analyse the whirling frequencies and amplitude of the response for large synchronous generators with a high number of poles, due to deviations of shape in the rotor and stator. A mathematical model is developed to describe the shapes of the rotor and stator, and the corresponding UMP is obtained by using the law of energy conservation. The UMP is analysed due to different deviations of shape. The result gives the average angular frequency and the magnitude of the UMP for certain deviations of shape. From this result, the whirling frequency and the amplitude of the corresponding response can be approximated. Simulations of the response of a Jeffcott rotor model show good agreement with the theoretical results of the UMP for some generator geometries. The conclusion is that different whirling frequencies, both backward and forward whirling, can occur in these machines due to deviations in shape of the generator. Therefore, the shape of the generator can excite resonance vibrations on several other frequencies than the rotation frequency. During maintenance of hydropower generators the shapes of the rotor and stator are frequently measured. The results from this paper can be used to evaluate such measurements and to explain the existence of complicated whirling motion.     

Magnetic resonance study on lamellar phases of ammonium perfluorooctanoate

The aggregation properties of ammonium perfluorooctanoate (NH₄-PFO) in concentrated aqueous phases have been investigated by magnetic resonance techniques and have been compared with the aggregation properties in dilute solutions. Magnetic resonance methods indicated that NH₄-PFO—water systems with surfactant concentrations below 45% (w/w) behaved as isotropic purely micellar solutions in the temperature range 285–340 K. For higher concentrations the system exhibited a rather complex structure, having both isotropic and anisotropic components. The nematic nature of the anisotropic fraction was demonstrated by ¹⁹F NMR studies. The ¹⁹F NMR and EPR of nitroxides (TempTMA⁺, 5- and 16-DXSA) inserted as paramagnetic probes into the concentrated NH₄-PFO—water systems allowed us to establish that the lamellar phase could be mechanically oriented between quartz slides. The EPR investigation also gave details concerning the dynamics of both the oriented and non-oriented structures.     

Charge recombination fluorescence in photosystem I reaction centers from Chlamydomonas reinhardtii

The fluorescence kinetics of photosystem I core particles from Chlamydomonas reinhardtii have been measured with picosecond resolution in order to test a previous hypothesis suggesting a charge recombination mechanism for the early electron-transfer steps and the fluorescence kinetics (Müller et al. Biophys. J. 2003, 85, 3899-3922). Performing global target analyses for various kinetic models on the original fluorescence data confirms the "charge recombination" model as the only acceptable one of the models tested while all of the other models can be excluded. The analysis allowed a precise determination of (i) the effective charge separation rate constant from the equilibrated reaction center excited state (438 ns(-1)) confirming our previous assignment based on transient absorption data (Müller et al. Biophys. J. 2003, 85, 3899-3922), (ii) the effective charge recombination rate constant back to the excited state (52 ns(-1)), and (iii) the intrinsic secondary electron-transfer rate constant (80 ns(-1)). The average energy equilibration lifetime core antenna/RC is about 1 ps in the "charge recombination" model, in agreement with previous transient absorption data, vs the 18-20 ps energy transfer lifetime from antenna to RC within "transfer-to-the-trap-limited" models. The apparent charge separation lifetime in the recombination model is about three times faster than in the "transfer-to-the-trap-limited" model. We conclude that the charge separation kinetics is trap-limited in PS I cores devoid of red antenna states such as in C. reinhardtii.     

Generation and capture of methyl(vinyl)silanone

Methyl(vinyl)dichlorosilane reacts with DMSO in the presence of hexamethyldisiloxane to give the corresponding linear oligosiloxanes of the general formula Me₃Si(OSiMeVin) _n OSiMe₃ (n=1–6) as well as MeSi(OSiMe₃)₃ and Me₃Si(MeOSiVin) _m OSi(OSiMe₃)(Me)OSiMe₃ (m=1–2). The same reaction in the presence of chlorotrimethylsilane results in oligomers of the general formula Me₃Si(OSiMeVin) _n Cl (n=1–3). A possible scheme of their formation is discussed. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 8, pp. 1614–1616, August, 1998.     

Oxidative Addition of Haloheteroarenes to Palladium(0): Concerted versus SNAr‐Type Mechanism

The kinetics of the oxidative additions of haloheteroarenes HetX (X=I, Br, Cl) to [Pd⁰(PPh₃)₂] (generated from [Pd⁰(PPh₃)₄]) have been investigated in THF and DMF and the rate constants have been determined. In contrast to the generally accepted concerted mechanism, Hammett plots obtained for substituted 2‐halopyridines and solvent effects reveal a reaction mechanism dependent on the halide X of HetX: an unprecedented S_NAr‐type mechanism for X=Br or Cl and a classical concerted mechanism for X=I. These results are supported by DFT studies.