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.     

Two-color laser desorption mass spectrometry using a single laser

A Nd: YAG laser has been used to perform IR desorption of analytes followed by UV ionization, all within the same laser pulse. At moderate laser powers, mass spectra recorded using this method are dominated by molecular ions.     

Reversible subsets of certain linear transformations

Summary Suppose U is a set,F is a field of subsets of U, p_AB is the set of all real-valued bounded finitely additive functions defined onF, and for each in p_AB, A()={: in p_AB, absolutely continuous with respect to }. SupposeM is a linear subspace of p_AB such that . A generalisation of a previously discussed collection of linear transformations (see J. London Math. Soc., vol. 44 (1969), pp. 385–396) is treated by letting C_M denote the set to which T belongs iff T is a linear transformation from M into p_AB such that for some K inR and all in M and V inF, . Certain theorems of the aforementioned reference are generalized, as well as one of Trans. Amer. Math. Soc., vol. 199, (1974), pp. 131–140. The principal result of the present paper is the following generalisation of a reversibility characterisation in the first mentioned reference: Theorem: If T is in C_M, then (, T()): in M A(T()) is the only reversible subset T⁰ if T such that: i) the domain M⁰ of T⁰ is a linear subspace of M and , and ii) the range of T⁰ is the range of T.     

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.