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     

Laser systems specialized for laser spectroscopy at storage rings

Laser spectroscopy at storage rings often suffers from a limited resolution due to Doppler-broadened resonances. Broadening is caused by the velocity spread of the ions stored in the beam. In the following, the present status of our work on laser systems specialized on the specific needs of laser spectroscopy at storage rings is reported. Two pulsed laser systems were developed. One is a dye laser whose spectral bandwidth can be switched by inserting different Littrow-prisms into the resonator. An increase in bandwidth up to a factor of 45 was achieved. This laser was used for fast qualitative scans and high resolution measurements. The other laser system is a Nd : YAG laser pumped optical parametric oscillator. It is a tunable laser system covering the spectral range from 410 to 4000 nm. Furthermore, a continuous wave laser with a frequency shifted feedback cavity is described. It shows broadband emission with an adjustable bandwidth of up to 4.5 GHz. This laser can be advantageous for laser cooling of ion beams. This revised version was published online in August 2006 with corrections to the Cover Date.     

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 new high-spin isomer in 39 97 Y58

An isomeric state at 3,523 keV excitation energy in⁹⁷Y with a half-life of 144(10) ms has been discovered with the fission-product separator JOSEF. This isomer is depopulated through aγ transition of 162 keV. AnE3 multipolarity for this transition is consistent with the measured conversion coefficients ofα _K =0.98(20) andα _T =1.00(19). Subsequent electromagnetic transitions populate several new⁹⁷Y levels which have high spins. For the isomer the three-quasiparticle configuration [πg _9/2?ν(h _11/2,g _7/2)]27/2^? is proposed. TheE3 transition with a strength about 2 single-particle units is supposed to be of the typeh ₁₁ ^2/+1 →d ₅ ^2/?1 . These findings provide evidence for the rapid shape transition atA?100 since they indicate shell-model character of ₃₉ ⁹⁷ Y₅₈ even at high excitation energies while the immediate neighbour ₃₉ ⁹⁸ Y₅₉ contains a rotational band based on a level at 495 keV.     

Rapid determination of ethylene glycol at toxic levels in serum and urine

The rapid gas chromatographic detection and determination of ethylene glycol in biological fluids is described. Phenylboronic acid in acetone was used for the esterification of glycol. The phenylboronates of ethylene glycol and 1,2-propylene glycol are not separated on a packed column of medium polarity (OV-17), but they can be separated on a non-polar column (OV-101). In both instances, 1,3-propylene glycol can be used as an internal standard. The method requires only 100 microliters of serum or urine and is suitable for trace analysis in an emergency toxicological laboratory. The utility of the method is demonstrated on two cases of human intoxication with ethylene glycol.     

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.     

Study of perrhenate reduction by capillary electrophoresis

The influence of perrhenate concentration, the concentration of the reducing agent and pH of the reaction mixture on the yield of perrhenate reduction were studied to find a possibility to decrease the stannous chloride concentration in the reaction mixture without negative changes on the yield of perrhenate reduction. Britton-Robinson buffer solutions were selected as the background electrolytes because of their buffering capacity in a wide pH interval. The highest degree of perrhenate reduction was obtained at pH 2 at perrhenate concentrations ranging from 10(-4) to 10(-3) mol/L. The stability of reduced rhenium against pH change from 2 to 5.5 and against dilution of rhenium in the reaction mixture to the concentration suitable for the application in radiotherapy were studied as well. The results obtained by capillary electrophoresis and by thin-layer chromatography with radiometric detection were compared.     

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).