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.     

Chelation of carbocations by polyethers and polyamines

Chelates formed by carbocations and cyclic polyethers and polyamines are studied with semiempirical and ab initio MO methods.     

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.     

Comparative molecular orbital study of polynitromethanes and their anions

The performance of ab initio STO-3G and CNDO/2 molecular orbital methods in the calculation of properties of polynitromethanes is studied.     

Dynamic light-scattering analysis of the electrostatic interaction of hexahistidine-tagged cytochrome P450 enzyme with semiconductor quantum dots.

Currently, there is great interest in the development of methods suitable for determining the stoichiometry of biomolecules attached to nanoparticles. We describe the use of the dynamic light-scattering technique (DLS) to determine the stoichiometry of the protein cytochrome P450(BSbeta) attached to CdS and CdSe quantum dots (QDs). The enzyme-conjugated QDs have different diffusion characteristics compared to the QD and enzyme precursors, expressed in their size, scattering intensity as well as zeta-potential values. The significant enhancement of the scattering intensity of QDs observed upon conjugation with the P450(BSbeta) due to the refractive-index increment and the systematic variation in zeta potential resulting from charge neutralization of the anionic QDs by the cationic histidine-tagged P450(BSbeta) have been used for stoichiometry determination.     

Electrical and infrared dielectrical properties of silica aerogels and of silica-aerogel-based composites

In this contribution we have studied the key electrical parameters of silica aerogels and of silica-aerogel-based composites, namely the dielectric constants , the dielectric losses tan (at 1 kHz), and the breakdown fields E _b (at 50 Hz). For low-density bulk silica aerogels we find =1.25 and tan =0.0005. E _b is about 500 kV/cm in quasi-homogeneous fields, and of the order of MV/cm in strongly inhomogeneous fields. The dielectric constants of partially densified aerogels increase linearly with density; their dielectric losses are relatively large and their breakdown fields are comparativiely low. The same results are found for aerogels in the form of settled materials, i.e. aerogel granules and powders in air. Acrylate-based aerogel composites with volume fractions larger than 70% have low dielectric constants but their losses are at least 10 times higher than those of low-density aerogels. These materials sustain high local fields in the MV/cm region, while in quasihomogeneous fields, breakdown occurs at about 100 kV/cm. Based on the present results and the interplay with other physical properties (low mechanical resistance, low thermal conductivity, adsorption of water, etc.), silica aerogels and silica aerogel-acrylate-based composites are predicted to have a low potential for electrical insulation.     

Phase Transition and Crystal Structure of the Monomeric Europium(II) Thiolate Eu(SC36H49)2

Single crystal X‐ray diffraction of Eu(SC₃₆H₄₉)₂ has revealed a first order phase transition at a temperature of 119 K, that involves a reduction of the specific volume by 1 %. The transition corresponds to a doubling of the unit cell, as it is the result from reorientations of isopropyl groups that appear at peripheral sites of the organic ligands. It is argued that a denser packing is achieved at the expense of a less favourable conformation of one of the two crystallographically‐independent complexes in the low‐temperature phase. The Bond‐Valence method is used to show that interactions of equal strengths are present between europium and both sulphur atoms and both coordinating phenyl rings.