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.     

Über das Alkaloid Lonicerin aus Callichilia barteri. 137. Mitteilung über Alkaloide

The alkaloid lonicerine was isolated from Callichilia barteri (Apocynaceae). By chemical and spectroscopic evidence it could be shown to be 16-epi-aspidodasycarpine ( 1 ).     

Determination of lead in the urine of exposed and unexposed adults by extraction and flow-injection/atomic absorption spectrometry

Lead is extracted from urine with ammonium pyrrolidien dithiocrbamate into methyl isobutyl ketone, and 20 μl of the extract is injected into a water carrier stream in a flow-injection/atomic absorption system. The procedure is simple, quick, accurate and reproducible. Recoveries are 96–105%. The mean urine lead contents of 20 unexposed and 20 printing-press lead exposed workers was found to be 39.0 ± 8.3 and 71.7 ± 26.3 μg Pb l^?1, respectively.     

A suite of algorithms for key distribution and authentication in centralized secure multicast environments

The Extended Euclidean algorithm provides a fast solution to the problem of finding the greatest common divisor of two numbers. In this paper, we present three applications of the algorithm to the security and privacy field. The first one allows one to privately distribute a secret to a set of recipients with only one multicast communication. It can be used for rekeying purposes in a Secure Multicast scenario. The second one is an authentication mechanism to be used in environments in which a public-key infrastructure is not available. Finally, the third application of the Extended Euclidean algorithm is a zero-knowledge proof that reduces the number of messages between the two parts involved, with the aid of a central server.     

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.     

Thermal Characterizations of Inorganic and Organometallic Polymers

This review emphasizes the breadth of metallic and metallic-like polymers evaluated as to thermal properties. Techniques usefully applied to particular systems are noted with the aim of suggesting their application to other systems.