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.     

An anion-dependent switch in selectivity results from a change of C-H activation mechanism in the reaction of an imidazolium salt with IrH5(PPh3)2

Changing the counteranion along the series Br, BF4, PF6, SbF6 in their ion-paired 2-pyridylmethyl imidazolium salts causes the kinetic reaction products with IrH5(PPh3)2 to switch from chelating N-heterocyclic carbenes (NHCs) having normal C2 (N path) to abnormal C5 binding (AN path). Computational work (DFT) suggests that the AN path involves C-H oxidative addition to Ir(III) to give Ir(V) with little anion dependence. The N path, in contrast, goes by heterolytic C-H activation with proton transfer to the adjacent hydride. The proton that is transferred is accompanied by the counteranion in an anion-coupled proton transfer, leading to an anion dependence of the N path, and therefore of the N/AN selectivity. The N path goes via Ir(III), not Ir(V), because the normal NHC is a much less strong donor ligand than the abnormal NHC. PGSE NMR experiments support the formation of ion-pair in both the reactants and the products. 19F,1H-HOESY NMR experiments indicate an ion-pair structure for the products that is consistent with the computational prediction (ONIOM(B3PW91/UFF)).     

Protective properties of redox polymer film deposited on stainless steel

We propose a novel composite organic-inorganic coating in the form of a redox polymer film for protection of stainless steel against general corrosion in strong acid medium (2 M H₂SO₄). We utilize an anion exchange polymer, protonated poly(4-vinylpyridine), into which hexacyanoferrate anions have been introduced. Owing to the presence of Fe(CN)₆^3–/4– at the interface formed by the film and the steel, a sparingly soluble metal hexacyanoferrate (mostly Prussian blue, PB) is formed as an overcoating on the steels surface, presumably on the passive (metal oxide) layer. The redox polymer film on the steel seems to act as a composite three-dimensional bilayer-type coating in which hexacyanoferrate(III,II) anions (that are capable of effective charge storage) exist in the outer portions of the film, whereas the inner PB layer improves the systems overall adherence and stability. By analogy to a conducting polymer (e.g. polyaniline, polypyrrole), introduction of the redox polymer composite film leads to stabilization of the steel substrates potential within the passive range.Contribution to the 3rd Baltic Conference on Electrochemistry, Gdansk-Sobieszewo, Poland, 23–26 April 2003Dedicated to the memory of Harry B. Mark, Jr. (28 February 1934–3 March 2003)     

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.