THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

A Repeated Matching Heuristic for the Vehicle Routeing Problem

A new heuristic for the vehicle routeing problem which makes use of repeated matching is described. The numerical results are comparable to or better than the best published for most of the 14 benchmark problems commonly used to evaluate VRP heuristics.     

Crystal and molecular structure of crenatine carbonate

The crystal and molecular structure of 1-ethyl-4-methoxy-9H-pyrido[3,4b]indole (crenatine) carbonate C₁₄H₁₄N₂O·H₂CO₃, (MS, m/z 226)M _R 288.3, a-carboline alkaloid, has been determined from X-ray diffraction data. The compound crystallizes in the space group Pbca with cell parameters:a=11.616(4),b=18.450(8),c=12.992(5)Å,V=2784(2)ų,Z=8,D _calc=1.375 g cm^–3, (MoK)=0.71069Å,(Mo K)=0.94 cm^–1,F(000)=1216,R/R _w =8.2/10.3% for 1099 reflections. The ring system of the-carboline nucleus is planar. The title compound shows a two center hydrogen bond between the indole N-H group and the oxygen atom of a carbonate group. The structure does not display hydrogen bonding between-carboline groups but rather a bonding network involving the carbonate group.     

High-performance liquid chromatographic determination of lipids in vesicles

Accurate quantitation of the four lipid components in a vesicle formulation has been accomplished by selectively changing the high-performance liquid chromatographic mobile phase composition to arrive at an optimal separation requiring less than 10 min. A systematic approach to selection of the mobile phase conditions has minimized the number of experiments required to achieve the necessary separation. Relative standard deviations between one and four percent are obtained for the four lipid components. Accuracy, as measured by recovery experiments for spiked vesicle formulations, varies between one and two percent of target levels at the nominal lipid concentrations investigated.     

Stereoselective reductase-catalysed deoxygenation of sulfoxides in aerobic and anaerobic bacteria

Direct and indirect evidence, of unexpected stereoselective reductase-catalysed deoxygenations of sulfoxides, was found. The deoxygenations proceeded simultaneously, with the expected dioxygenase-catalysed asymmetric sulfoxidation of sulfides, during some biotransformations with the aerobic bacterium Pseudomonas putida UV4. Stereoselective reductase-catalysed asymmetric deoxygenation of racemic alkylaryl, dialkyl and phenolic sulfoxides was observed, without evidence of the reverse sulfoxidation reaction, using anaerobic bacterial strains. A purified dimethyl sulfoxide reductase, obtained from the intact cells of the anaerobic bacterium Citrobacter braakii DMSO 11, yielded, from the corresponding racemates, enantiopure alkylaryl sulfoxide and thiosulfinate samples.     

Multifunctional redox catalysts as selective enhancers of oxidative stress

Certain cancer cells proliferate under conditions of oxidative stress (OS) and might therefore be selectively targeted by redox catalysts. Among these catalysts, compounds containing a chalcogen and a quinone redox centre are particularly well suited to respond to the presence of OS. These catalysts combine the specific electrochemical features of quinones and chalcogens. They exhibit high selectivity and efficiency against oxidatively stressed rat PC12, human Jurkat and human Daudi cells in cell culture, where their mode of action most likely involves the catalytic activation of existent and the generation of new reactive oxygen species. The high efficiency and selectivity shown by these catalysts makes them interesting for the development of anti-cancer drugs.     

Complex coordinates and the Stark effect

The theories of the dilatation, r → r e^iθ, and translation, x → x + iq, transformations as related to the Stark problem are reviewed, and new results obtained. Results for the hydrogen atom n = 1 and n = 2 levels and the ¹P⁰, 2s2p H^? shape resonance in dc fields are presented, and the extension to the ac Stark effect made. Spectral estimates are made using the technique of the numerical range and via discussion of several model problems, using both coordinate rotation and coordinate translation.