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.     

Unusual ligand coordination for cesium

When complexed by tetrabenzo-24-crown-8, the cesium ion can accommodate unprecedented ligation. The structures of the following complexes are presented. [Cs(tetrabenzo-24-crown-8)(eta 1-NCMe)2(eta 2-NCMe)][NO3] (1): triclinic P1, a = 12.0119(14) A, b = 13.3680(15) A, c = 13.7859(12) A, alpha = 89.124(8) degrees, beta = 66.928(9) degrees, gamma = 71.536(10) degrees, V = 1916.7(4) A3, Z = 2. [Cs(tetrabenzo-24-crown-8)(eta 1-NCMe)2(eta 2-CH2Cl2)][NO3] (2): triclinic, P1, a = 12.295(3) A, b = 13.295(3) A, c = 13.782(3) A, alpha = 89.105(17) degrees, beta = 66.096(18) degrees, gamma = 71.980(19) degrees, V = 1929.5(8) A3, Z = 2. These structures are the first reported examples of linear eta 2-acetonitrile coordination to any metal ion and the first structures illustrating eta 2-acetonitrile and dichloromethane ligation to an alkali metal ion. Possible steric and electronic origins of these unusual metal-ligand interactions are discussed.     

Prediction of Complexation Properties of Crown Ethers Using Computational Neural Networks

A computational neural network method was used for the prediction of stability constants of simple crown ether complexes. The essence of the method lies in the ability of a computer neural network to recognize the structure-property relationships in these host-guest systems. Testing of the computational method has demonstrated that stability constants of alkali metal cation (Na+, K+, Cs+)-crown ether complexes in methanol at 25 °C can be predicted with an average error of ±0.3 log K units based on the chemical structure of the crown ethers alone. The computer model was then used for the preliminary analysis of trends in the stabilities of the above complexes.     

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.     

Low-lying energy levels of the FeH molecule

Multireference configuration interaction (MRCI) and complete active space second-order perturbation theory (CASPT2) calculations are performed on Fe₂ and Fe^? ₂. Although it is not possible to definitively identify the ground states of Fe₂ and Fe^? ₂, the calculations suggest that the ground state of Fe^? ₂ in ⁸Σ^? _u derived from 3d¹³4σ² _g4σ² _u and that the states observed in photodetachment are the ⁹Σ^? _g and ⁷Σ^? _g states with a 3d¹³4σ² _g4σ¹ _u occupation, but that the ground state of Fe₂ is ⁷Δ_u(3d¹⁴4σ² _g) and is not observed in the photo-detachment spectra.