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.     

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.