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.     

In vitro determination of the release kinetics of peptides and free amino acids during the digestion of food proteins

The kinetics of peptide release during in vitro digestion of 4 protein sources (casein, cod protein, soy protein, and gluten) were investigated. Samples were sequentially hydrolyzed with pepsin (30 min) and pancreatin (2, 4, or 6 h) in a dialysis cell with continuous removal of digestion products. Nondialyzed digests were fractionated by ion-exchange chromatography and ultrafiltration. Animal proteins were digested at a greater rate than plant proteins. Target amino acids of specific enzymes appeared more rapidly in the dialyzed fractions when compared to other amino acids. Throughout the hydrolysis, nondialyzed digests contained a higher proportion of peptide mixtures with basic-neutral properties. Except for gluten, peptide fractions with molecular weights that exceeded 10 kDa (basic-neutral, BN > 10) were rapidly hydrolyzed during the first 2 h of pancreatin digestion. The kinetics of release and the composition of peptide fractions were different when the protein sources were compared. The analysis of amino acids revealed that threonine and proline proportions were relatively high in BN > 10 and in peptide fractions with molecular weight between 10-1 kDa (BN 10-1), while tyrosine, phenylalanine, lysine, and arginine predominated in the low molecular weight (<1 kDa) fractions. More resistant peptides were generally rich in proline and glutamic acid. The role of in vitro digestion assays in dietary protein quality evaluation is discussed.     

Fractionation of casein hydrolysates using polysulfone ultrafiltration hollow fiber membranes

The objective of this study was to characterize the fractionation profile of casein hydrolysates obtained with polysulfone hollow fiber ultrafiltration membranes. The two-step ultrafiltration process developed by Turgeon and Gauthier [J. Food Sci., 55 (1990) 106] was used: a caseinate solution was submitted to proteolysis with chymotrypsin or trypsin, and the reaction mixture (RM) was subsequently ultrafiltered using a 30 kDa (MWCO) hollow-fiber polysulfone membrane. The total hydrolysate permeating from this first step was further fractionated using a 1 kDa (MWCO) membrane, producing the mixture of polypeptides (retentate) and the amino acid fraction (permeate). The effect of enzyme specificity and of membrane retentivitiy on the total composition (total nitrogen, fat, lactose, minerals) and amino acid profile of the fractions was studied. The overall composition of the fractions was not significantly affected by the nature of the enzyme but the degree of hydrolysis and the molecular weight distribution profile analyses showed a marked effect of the enzyme specificity, with trypsin giving a larger proportion of small peptides (< 200 Da) in the mixture of polypeptides. Amino acid profile analyses provided useful information on the phenomena governing the fractionation of amino acids with a polysulfone membrane: (1) the target amino acids of the enzyme are concentrated in the permeate as a result of their presence in all peptides produced by hydrolysis, (2) polar amino acids are retained by the membrane, (3) non-polar amino acids are not selectively rejected by the membrane. Our results suggest that the charge/hydrophobicity balance of the peptides produced is the predominant factor determining the fractionation of casein hydrolysates.     

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.