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.     

Chirality control in optically active polysilane aggregates

A novel strategy for controlling the higher order chirality of aggregates prepared from enantiopure polysilanes is experimentally probed and discussed. Structurally similar poly[n-alkyl(aryl)]silanes were synthesized in which one side chain comprised the chiral (S)-2-methylbutyl group and the other an achiral m- or p-alkyl-substituted phenyl ring. In solution the polymers adopt helical conformations with the same induced preferential screw sense chirality, as evidenced by circular dichroism (CD) spectroscopy. Aggregates, however, formed by addition of a nonsolvent to a polymer solution, show oppositely signed CD spectra. Consistent results were obtained for another series of poly[p-n-alkyl(aryl)]silanes where alkyl is butyl, propyl, and ethyl. The sense of the aggregate higher order chirality is dependent on the chemical composition and environment and is coarse-tunable by adjusting the length of the achiral side chain and fine-tunable by adjusting the good/poor solvent ratio. The origin of these effects is discussed with reference to a simple model.     

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.     

Synthesis,structure and catalytic properties of bis[2‐(trifluoromethyl)phenyl]silanediol

A novel trifluoromethylaryl‐substituted disilanol, bis[(2‐trifluoromethyl)phenyl] silanediol, was prepared by hydrolysis of the precursor dichloride and fully characterized. Single‐crystal X‐ray diffraction indicates doubly linked hydrogen bonded dimers and also hydrogen bonding to tetrahydrofuran solvent. The acidity of the silanol functions is enhanced by the presence of the trifluoromethyl groups and the compound is found to be active in promoting a standard Diels–Alder reaction, increasing yields by a factor of three.