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.     

A microcomputer-based system for potentiometric measurements with ion-selective electrodes

A comparison, on completely equal terms, of a microcomputer-based system with manual measurements is described in detail. The main features compared are the precision and accuracy of the results and the number of determinations per time unit. The example used is a standard addition measurement of fluoride in toothpaste. The microcomputer system and its interfacing to the peripheral units are also described. The microcomputer system for control, supervision and evaluation of the measurements results in a significant gain in precision and speed. Accuracy requires the use of a non-theoretical value of the Nernstian slope. The memory effect of the ion-selective electrode is large when the type of sample is changed.     

Optimisation and robustness analysis of a hydrophobic interaction chromatography step

Process development, optimisation and robustness analysis for chromatography separations are often entirely based on experimental work and generic knowledge. The present study proposes a method of gaining process knowledge and assisting in the robustness analysis and optimisation of a hydrophobic interaction chromatography step using a model-based approach. Factorial experimental design is common practice in industry today for robustness analysis. The method presented in this study can be used to find the critical parameter variations and serve as a basis for reducing the experimental work. In addition, the calibrated model obtained with this approach is used to find the optimal operating conditions for the chromatography column. The methodology consists of three consecutive steps. Firstly, screening experiments are performed using a factorial design. Secondly, a kinetic-dispersive model is calibrated using gradient elution and column load experiments. Finally, the model is used to find optimal operating conditions and a robustness analysis is conducted at the optimal point. The process studied in this work is the separation of polyclonal IgG from BSA using hydrophobic interaction chromatography.     

Electrophoretic properties of complexes between DNA and the cationic surfactant cetyltrimethylammonium bromide

We use agarose gel electrophoresis to characterize how the monovalent catioinic surfactant cetyltrimethylammonium bromide (CTAB) compacts double-stranded DNA, which is detected as a reduction in electrophoretic DNA velocity. The velocity reaches a plateau at a ratio R = 1.8 of CTAB to DNA-phosphate charges, i.e., above the neutralization point, and the complexes retain a net negative charge at least up to R = 200. Condensation experiments on a mixture of two DNA sizes show that the complexes formed contain only one condensed DNA molecule each. These CTAB-DNA globules were further characterized by time-resolved measurements of their velocity inside the gel, which showed that CTAB does not dissociate during the migration but possibly upon entry into the gel. Using the Ogston-model for electrophoresis of spherical particles, the measured in-gel velocity of the globule is quantitatively consistent with CTAB having two opposite effects, reduction of both the electrophoretic charge and DNA coil size. In the case of CTAB the two effects nearly cancel, which can explain why opposite velocity shifts (globule faster than uncomplexed DNA) have been observed with some catioinic condensation agents. Dissociation of the complexes by addition of anionic surfactants was also studied. The DNA release from the globule was complete at a mixing ratio between anionic and cationic surfactants equal to 1, in agreement with equilibrium studies. Circular DNA retained its supercoiling, and this demonstrates a lack of DNA nicking in the compaction-release cycle which is important in DNA transfection and purification applications.     

Synthesis of Optically Active endo,endo Bicyclo[2.2.2]octane-2,5-diol, Bicyclo[2.2.2]octane-2,5-dione, and Related Compounds

Optically active C(2)-symmetric (1S,2S,4S,5S)-bicyclo[2.2.2]octane-2,5-diol ((+)-12; 98% ee) and several selectively protected optically active intermediates useful for synthetic transformations were synthesized via a 1,2-carbonyl transposition route starting from the easily available optically active (1R,4S,6S)-6-hydroxybicyclo[2.2.2]octan-2-one ((-)-2). The synthetic route also allowed the preparation of optically active (1S,4S)-bicyclo[2.2.2]octane-2,5-dione ((+)-14; 98% ee).     

Synthesis of 2,3′-biindolyls and indolo[3,2-a]carbazoles

Several highly activated 2,3′-biindolyls were prepared from methyl 5,6-dimethoxyindole-2-carboxylate and oxindoles. The 2,3′-biindolyls were further transformed into a hydroxy indolo[3,2-a]carbazole and a bisindole amide.     

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.     

Design and optimization of modified simplex methods

Four test functions are used to evaluate different modifications of the modified simplex method and to optimize the contraction, reflection and expansion parameters. The evaluation shows that some of the modifications and the optimization of the parameters result in a simplex method that has gained in convergence ability, with some improvement in speed.