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.     

Mechanism for semiquinone formation in the oxygen negative chemical ionization mass spectrometry of 2,3,7,8-tetrachlorodibenzo-p-dioxin

The high toxicity of 2,3,7,8-tetrachlorodibenzo-p-dioxin (2,3,7,8-TCDD) has led to the development of selective and highly sensitive quantitative methods for mass spectral analysis. Analytical selectivity has been demonstrated for the oxygen negative chemical ionization (ONCI) reaction of TCDD in an oxygen-rich plasma. While the reaction product (4,5-dichloro-1,2-benzoquinone anion) of 2,3,7,8-TCDD and oxygen is well known, the mechanism of its formation has not been studied thoroughly. In this report the results of a study involving the reaction of ¹⁸O₂ with 2,3,7,8-TCDD under high pressure and low pressure ONCI conditions are reported. A mechanism is proposed which is compatible with the observation that one ¹⁸O atom is incorporated into the product anion.     

Quantification of beta-trace protein and detection of transferrin isoforms in mixtures of cerebrospinal fluid and blood serum as models of rhinorrhea and otorrhea diagnosis

Different mixtures from a serum pool and a cerebrospinal fluid (CSF) pool were used as models to study CSF contamination in secretions by determining two CSF specific proteins: beta-trace protein (beta-TP) and the asialo-transferrin (a-Tf) band which was detected by isoelectric focusing (IEF) with Tf specific immunofixation. Beta-TP and total Tf were measured immunonephelometrically. Secretion/serum ratios of beta-TP content > 2.0 indicated CSF contaminations with > or = 5% (v/v) CSF; this was confirmed by detecting the a-Tf band by IEF. Reliable a-Tf bands were only revealed with secretion/serum rations of Tf contents < 0.1, indicating an interference of major sialo-Tf fractions with the a-TF band detection in the sample. For CSF detection in rhinorrhea and otorrhea, complementary use of beta-TP assay and a-Tf assay is recommended. Preanalytically, dilution or concentration of the sample as well as denaturation of Tf and beta-TP should be prevented by optimizing sample collection.     

Gårding's Theory of Hyperbolic Polynomials

This paper presents a simple, self‐contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke‐Güler‐Lewis‐Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated “branches” are independent of the choice of hyperbolic direction. © 2013 Wiley Periodicals, Inc.