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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.     

Protein surface area and retention in hydrophobic interaction chromatography

Summary Molecular surface areas accessible to a 4 ? diameter spherical probe were calculated from crystallographic data for five proteins: α-chymotrypsinogen A, lysozyme, trypsinogen, ribonuclease A and ribonuclease S. The retention factors of various proteins were measured on stationary phases having polyether- and phenylligates and with aqueous eluents containing (NH₄)₂SO₄, Na₂SO₄ or NaCl at pH 7.0. The logarithmic retention factors were plotted against the salt molality and the hydrophobic interaction parameters evaluated from the limiting slopes of the plots at high salt concentrations for the proteins in the chromatographic systems investigated. The hydrophobic interaction parameters thus obtained were linear in both the molecular surface areas of the proteins and the molal surface tension increments of the salts. The experimental results obtained with these relatively simple proteins of known molecular structure, which were available in high purity, support earlier theoretical predictions for the dependence of the hydrophobic interaction parameter on the surface area of the protein and the surface tension raising effect of the salt.     

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.     

An unusual substitution reaction of an aromatic sulfonic group based on 3-carbonyl-4-phenolsulfonic acid

An unusual substitution reaction of an aromatic sulfonic group based on 3-carbonyl-4-phenolsulfonic acid was discovered in a diazo-coupling process.The reaction occurred under mild reaction conditions (pH 8.0-9.0.0-5 C,solvent:water) within a short reaction time(1h).A plausible substitution reaction mechanism by phenol-ketone resonance was proposed.