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.     

Valuations dominating regular local rings and proximity relations

We study zero-dimensional valuations dominating a regular local ring of dimension n≥2. For this we introduce the proximity matrix and the multiplicity sequence (extending classical definitions of the case n=2) that are associated with the sequence of the successive quadratic transforms of the ring along the valuation. We describe the precise relations between these invariants and study their properties.     

Self-assembled peptide tubelets with 7 A pores

Here we report the preparation and structural characteristics of self-assembling peptide tubelets composed of 32-membered rings formed of alternating alpha-amino acids and cis-3-aminocyclohexanecarboxylic acids. The tubelets possess a partial hydrophobic core environment, provided by the projection of the cyclohexane C2 methylene moiety into the lumen, and a Van der Waals pore diameter of about 7 A.     

The spatial distribution of poly(methyloctylsiloxane) deposited by solvent evaporation in the pores of HPLC silica particles

Summary Poly(methyloctylsiloxane) (PMOS), sorbed into the pores of HPLC silica particles by solvent evaporation, can function as a useful stationary phase for reversed-phase chromatography. The present work addresses the question of how the PMOS is distributed in the pores. Measurements of the surface area (BET, N₂) of a series of partially loaded samples (0–40% PMOS, m/m) using a typical batch of HPLC silica (10 μm irregular particles with 6 nm pores) show that the specific surface area of the samples decreases linearly with the specific loading (mass of PMOS per gram of silica). This result is not consistent with a “film” model in which the PMOS is deposited uniformly on the pore walls, but is consistent with a model in which long segmented “plugs” of PMOS are deposited within the pore system. Presented at the 21^st ISC held in Stuttgart, Germany, 15^th–20^th September, 1996     

Access to [6.4.0]carbocyclic systems by tandem metathesis of dienynes. A step toward the synthesis of a PreD3-D3 transition state analogue

[reaction: see text] A new approach to the synthesis of linearly fused 6-8-6 tricarbocyclic systems, tandem ring-closing metathesis of dienynes, allows access to compounds with a carbon framework analogous to the proposed transition state of the isomerization of previtamin D(3) to vitamin D(3).     

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.