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.     

High-p T αα andαp interactions

Properties of secondaries associated with a high-p _T charged trigger particle (3<p _T <5 GeV/c) were studied for αp and αα interactions at c.m. energies \(\sqrt s = 88\) GeV and 125 GeV, respectively. Thep _T distributions of secondaries in the away-jet and trigger-jet regions were compared with those for high-p _{T pp} interactions. No statistically significant differences were seen, except at lowp _T . Momentum and angular distributions of spectator and leading protons were studied as a function of charge and rapidity of the trigger hadron. The observed correlations between trigger charge and number of spectator protons provide evidence of valence quark contributions to the trigger jet.     

R?ntgenspektrometrische Elementbestimmung in Abwasser: Probenvorbereitung und Matrixkorrekturverfahren

Zusammenfassung Für Elementbestimmungen in Abwasser wird ein Röntgenfluorescenzverfahren beschrieben. Zur Probenvorbereitung werden die Elemente durch Gefriertrocknung auf einem inerten Träger angereichert. Diese Anreicherung ist nicht selektiv und erfaßt praktisch alle in Abwasser gelösten und suspendierten Verunreinigungen. Für die Berechnung der Elementkonzentrationen aus den gemessenen Fluorescenzintensitäten wird ein Matrixkorrekturverfahren angegeben, welches dem unterschiedlichen Absorptionsverhalten der Probenmatrix Rechnung trägt. Die Massenabsorptionskoeffizienten werden durch Messung der diffus gestreuten Bremsstrahlung bzw. der Comptonstreustrahlung ermittelt. Die Selbstabsorption des zu bestimmenden Elementes wird rechnerisch berücksichtigt. Das Korrekturverfahren kann auf alle mit Röntgenfluorescenzanalyse bestimmbaren Elemente angewendet werden.

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Determination of elements in waste water by x-ray fluorescence analysis: Sample preparation and matrix correction method

Summary For sample preparation the elements are enriched upon an inert carrier by freeze-drying. This enriching procedure is not selective and collects all dissolved and suspended contaminations from the waste water. In order to calculate the element concentrations from the measured fluorescence intensities a matrix correction method is given which considers the different absorption behaviour of the matrix. The mass absorption coefficients are obtained by measuring the scattered X-ray tube spectrum or a Compton scattered X-ray tube line, respectively. The self-absorption of the element to be determined is taken into account. The correction method is applicable to all elements detectable by X-ray fluorescence.

Herrn Dr. H. Wagner danken wir für das stete Interesse, die zahlreichen konstruktiven Diskussionen und die Hilfe beim Abfassen des Manuskripts.     

Negatively charged hyperbranched polyether-based polyelectrolytes

The preparation of carboxylated hyperbranched polyglycerols of narrow polydispersity was achieved by modification (78–90%) of the hydroxyl end groups via Michael addition of acrylonitrile, followed by hydrolysis. High conversion could only be achieved for low molecular weight starting materials (520 and 1,030 g mol⁻¹). The solution properties of the resulting materials were investigated by dynamic light scattering (DLS), showing the formation of large aggregates with size depending on the pH value. After deposition on a negatively charged mica surface, the structures observed by atomic force microscope (AFM) show the coexistence of aggregates and single macromolecules. Most interesting, in the case of the lower molecular weight sample (PG 520 g mol⁻¹), extended and ordered terrace structures were formed, which are unprecedented for hyperbranched polymers and are of interest for surface modification in general.     

Electron-transfer reduction of selected alcohols with alkalide K, K(15-crown-5)2 via organometallic intermediates

The course of the reaction of alkalide K⁻, K⁺(15-crown-5)₂1 with selected alcohols depends on the kind of alcohol and the mode of substrate delivery. In the case of methanol, potassium methoxide formed initially undergoes destruction at the excess of 1. It results in potassium oxide and methylpotassium. The latter opens the crown ether ring giving potassium tetraethylene glycoxide vinyl ether and methane. A similar course of the process is observed for propanol. Potassium glycidoxide is the main product formed in the reaction of 1 with glycidol. Its oxirane ring is opened at the excess of 1. Organopotassium alkoxides, i.e., potassium potassiomethoxide and dipotassium potassiopropane-1,2-dioxide are intermediate products of this reaction. They react then with the crown ether. Potassium methoxide, potassium enolate of acetaldehyde, dipotassium propane-1,2-dioxide and potassium tetraethylene glycoxide vinyl ether are the final products of this process.