A highly ordered m-phenylenediimino-bridged ladder polyhydrosiloxane （abbr. OLPHS） with Mn = 1.24 × 10^4 was synthesized stoichiometric hydrolysis and dehydrochlorination condensation reaction between Si-Cl and...A highly ordered m-phenylenediimino-bridged ladder polyhydrosiloxane （abbr. OLPHS） with Mn = 1.24 × 10^4 was synthesized stoichiometric hydrolysis and dehydrochlorination condensation reaction between Si-Cl and Si-OH bonds. The complete ladder structure of OLPHS has been confirmed by the following three data. Two characteristic Bragg＇s peaks representing the ladder width （w = 0.94 nm） and ladder thickness （t = 0.42 nm） were observed in XRD analysis, which are consistent with those calculated by molecular simulation. The very sharp absorption with a small half-peak width （w1/2 = 0.5 ppm） for [（-HN）HSiO2/2]n moiety of OLPHS in ^29Si NMR spectrum indicated presence of the complete ladder structure. As collateral evidence, a higher glass transition temperature （Tg = 105 ℃） is also recorded in the DSC measurement, implying the high stiffness of ladder chain of OLPHS.展开更多
By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show ...By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality.展开更多
文摘A highly ordered m-phenylenediimino-bridged ladder polyhydrosiloxane （abbr. OLPHS） with Mn = 1.24 × 10^4 was synthesized stoichiometric hydrolysis and dehydrochlorination condensation reaction between Si-Cl and Si-OH bonds. The complete ladder structure of OLPHS has been confirmed by the following three data. Two characteristic Bragg＇s peaks representing the ladder width （w = 0.94 nm） and ladder thickness （t = 0.42 nm） were observed in XRD analysis, which are consistent with those calculated by molecular simulation. The very sharp absorption with a small half-peak width （w1/2 = 0.5 ppm） for [（-HN）HSiO2/2]n moiety of OLPHS in ^29Si NMR spectrum indicated presence of the complete ladder structure. As collateral evidence, a higher glass transition temperature （Tg = 105 ℃） is also recorded in the DSC measurement, implying the high stiffness of ladder chain of OLPHS.
文摘By virtue of Cauchy’s integral formula in the theory of complex functions,the authors establish an integral representation for the weighted geometric mean,apply this newly established integral representation to show that the weighted geometric mean is a complete Bernstein function,and find a new proof of the well-known weighted arithmetic-geometric mean inequality.
