Left versus right canonical Wiener-Hopf factorization and realization

For an arbitrary rational matrix function, not necessarily analytic at infinity, the existence of a right canonical Wiener-Hopf factorization is characterized in terms of a left canonical Wiener-Hopf factorization. Formulas for the factors in a right factorization are given in terms of the formulas for the factors in a given left factorization. All formulas are based on a special representation of a rational matrix function involving a quintet of matrices.     

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.     

Ein Beitrag über Oxide vom Typ AMO4 (A = Ti3+, Cr3+; M = Nb5+, Ta5+)

A Contribution on Ternary Oxides of the AMO₄-Type (A = Ti³⁺, Cr³⁺; M = Nb⁵⁺, Ta⁵⁺ ) CrNbO₄, CrTaO₄, TiNbO₄, and TiTaO₄ were prepared by CO₂-laser technique. X-ray single crystal investigations show a random distribution of the metal ions in Rutil type structure, space group D–P4₂/mnm. Calculations of the free energy of reaction between Ti₂O₃ and Nb₂O₅ show higher stability of TiO₂ beside NbO₂. In TiNbO₄ both metals exhibit the oxidation state +4.     

Bacterial Reduction of Chromium

A mixed culture was enriched from surface soil obtained from an eastern United States site highly contaminated with chromate. Growth of the culture was inhibited by a chromium concentration of 12 mg/L. Another mixed culture was enriched from subsurface soil obtained from the Hanford reservation, at the fringe of a chromate plume. The enrichment medium was minimal salts solution augmented with acetate as the carbon source, nitrate as the terminal electron acceptor, and various levels of chromate. This mixed culture exhibited chromate tolerance, but not chromate reduction capability, when growing anaerobically on this medium. However, this culture did exhibit chromate reduction capability when growing anaerobically on TSB. Growth of this culture was not inhibited by a chromium concentration of 12 mg/L. Mixed cultures exhibited decreasing diversity with increasing levels of chromate in the enrichment medium. An in situ bioremediation strategy is suggested for chromate contaminated soil and groundwater.