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.

     

Biradicals/zwitterions from thermolysis of enyne-isocyanates. Application to the synthesis of 2(1H)-pyridones, benzofuro[3,2-c]pyridin-1(2H)-ones, 2,5-dihydro-1H-pyrido[4,3-b]indol-1-ones, and related compounds

Thermolysis of benzannulated enyne-isocyanates 13 and enyne-isocyanates 36 and 37 promoted the cycloaromatization reactions to generate in situ O,4-didehydro-2-hydroxyquinolines and O,4-didehydro-2-hydroxypyridines, respectively, as reactive intermediates. These cycloaromatized intermediates could be captured either as biradicals and/or as zwitterions depending on the nature of the substituent at the alkynyl terminus. The intermediate derived from cycloaromatization of 13a bearing a phenyl substituent could be regarded as biradical 14, which then abstracts hydrogen atoms from gamma-terpinene leading to 2(1H)-quinolinone 15. Alternatively, the same intermediate could also be regarded as zwitterion 14', which then undergoes an initial hydride abstraction from gamma-terpinene followed by protonation to produce 15. The presence of a 2-phenylethyl substituent in 13b and 37a or a 2-methylphenyl substituent in 37b also allowed the resulting intermediates to be captured intramolecularly either as biradicals or as zwitterions, producing 2(1H)-quinolinone 19, 2(1H)-pyridone 39, and benzopyranopyridine 43, respectively. On the other hand, with a 2-methoxyphenyl, a 2-(dimethylamino)phenyl, or a 3-methoxypropyl substituent, the chemical behavior of the cycloaromatized adduct could be best accounted for in terms of a zwitterionic intermediate leading to benzofuro[3,2-c]quinolin-6(5H)-one (20), 5,11-dihydro-11-methyl-6H-indolo[3,2-c]quinolin-6-one (25), benzofuro[3,2-c]pyridin-1(2H)-one 44, 2,5-dihydro-2,5-dimethyl-1H-pyrido[4,3-b]indol-1-one 46, and related compounds. Interestingly, thermolysis of 37f bearing a 2-(methoxymethyl)phenyl substituent at the alkynyl terminus produced the unexpected benzopyranopyridine 56 as the major product in a process involving the cleavage of the bond between the methoxyl oxygen and the adjacent methylene carbon. The efficiency and selectivity of the cycloaromatization reaction could also be enhanced by the introduction of 1.1 to 10 equiv of dimethylphenylsilyl chloride to the reaction mixture to capture the resulting zwitterion.