Steenrod-Operationen in Kobordismen-Theorien

Ohne Zusammenfassung     

Every Finite Topology is Generated by a Partial Pseudometric

Given any preorder on a finite set , we present an algorithm to construct a partial pseudometric on which generates in the sense that if and only if . The specialization topology generated by agrees with the topology generated by the partial pseudometric -balls, and consequently any topology on is generated by a partial pseudometric.     

Metallorganische Chemie mit P/N-Chelatliganden. I. Molybdän- und Eisen(0)-Verbindungen des 2-Diphenylphosphinomethylpyridins

Organometallic Chemistry with P/N-Chelating Ligands. I. Molybdenum and Iron(0) Compounds of 2-Diphenylphosphinomethylpyridine The reaction of 2-diphenylphosphinomethylpyridine 1 (PN) with norbornadiene-tetracarbonylmolybdenum gives (PN)Mo(CO)₄ 2 in good yield. The acetonitrile ligands in (π-C₃H₅)Mo(CO)₂(CH₃CN)₂Br 3 are easily exchanged by 1 . The thus formed complex (π-C₃H₅)(PN)Mo(CO)₂Br 4 undergoes a reductive deallylation with further 1 to afford cis-(PN)₂Mo(CO)₂ 6 . Deallylation of 3 by triphenylphosphine and subsequent reaction with 1 yields the complex cis-(CO)₂-trans-(PPh₃)₂Mo(PN) 7 . Ligand 1 displays a chelating function in all of the molybdenum complexes. The structures of the (PN)-complexes are deduced mainly from the nmr data. The initial product of the photochemical reaction of 1 with ironpentacarbonyl is (PN)Fe(CO)₄ 8 , followed by trans-(PN)₂Fe(CO)₃ 9 . In both cases 1 is bonded via the phosphorus atom only. Prolonged irradiation affords the chelated tricarbonyl (PN)Fe(CO)₃ 10 . The thermal reaction of 1 with Fe₂(CO)₉ is different in that the first product is a sensitive red compound 11 , which still contains bridging carbonyl groups and has to be formulated as (PN)Fe₂(CO) 7 . Longer reaction times, but also the reaction of 8 with Fe₂(CO)₉ finally give a new type of complex, (PN)Fe₂(CO)₆ 12 , without bridging carbonyls.     

Synthesis and characterization of polyaryloxyphosphazene copolymers

A series of polyaryloxyphosphazene copolymers with the general formulas [NP(OC₆H₅)(OR)]_n and [NP(OC₆H₄–4–OCH₃)(OR)]_n, where R = C₆H₄–4–CH₃, C₆H₄–4–C₂H₅, C₆H₄–4–isoC₃H₇, C₆H₄–4–sec-C₄H₉, C₆H₄–4–tert–C₄H₉, C₆H₄–4–OCH₃ or C₆H₄–4–OC₄H₉, have been prepared under anhydrous conditions. Copolymers as well as selected homopolymers were prepared by the reaction of polydichlorophosphazene with appropriate sodium aryloxides. Each of the polymers was characterized by elemental analysis, infrared spectroscopy, gel–permeation chromatography, and differential scanning calorimetry. Elemental analysis established the empirical formula for the polymers and showed that there were no residual P? Cl bonds left on the polymer backbone. Infrared spectroscopy indicated the presence of a phosphorus–nitrogen backbone with two aryloxy groups bonded to each phosphorus atom. The copolymers examined exhibited molecular weights of above 1 × 10⁶. Polyaryloxyphosphazene copolymers were examined by differential scanning calorimetry and compared to several of the corresponding homopolymers. Glass transition temperatures ranged between ?34 and +44°C for the polymers. The Kelley-Bueche equation was used to predict the glass transition temperatures of the copolymers. Close agreement was found between calculated and experimental values for most of the systems examined.