Rapid syntheses of oligo(p-phenyleneethynylene)s via iterative convergent approach

A general and controlled bidirectional growth strategy enable a very rapid and efficient construction of oligo(phenyleneethynylene)s possessing functional groups such as methylthio and thioacetate groups at both ends. The strategy employs only one reaction type with good to moderate yields to grow the conjugated chains. The synthesis is efficient and can give 23 benzene rings and 22 carbon-carbon triple bonds in the conjugated chains. The compounds are fully characterized by ¹H and ¹³C NMR and UV/vis and fluorescence spectroscopy.     

Covering group and graph of discretized volumes

We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L _V the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γ _v associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering groups are Sunada pairs.     

液态金属流的表面张力问题中的两点边值问题解的存在性

本文讨论了在区域提纯过程中，研究液态金属流的表面张力时提出的一个带有非负参数Ｑ的两点边值问题．利用上、下解方法和Ｓｃｈａｕｄｅｒ不动点定理，证明了当０Ｑ８５１时，该问题至少有一个解，对已有结果０Ｑ＜１进行了重要的改进．     

A laser micro-chopper approach for molecular beam probe

A laser micro-chopper has been designed to respond fast to a molecular beam. A method of spectral structure measurement is established to analyse the responding signals. In experiments, the minimum detectable signals correspond to an air molecular-beam intensity of 5 × 10⁸/s     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

Synthesis and characterization of poly(higher‐α‐olefin)s with a nickel(α‐diimine)/methylaluminoxane catalyst system: Effect of chain running on the polymer properties

Homopolymerization of octadecene‐1 at different reaction conditions has been studied. Significant chain running can be seen at higher polymerization temperatures. Interestingly, insertion of octadecene‐1 into a sterically hindered nickel‐cation/carbon (secondary) bond is observed. The microstructure of the polymer was established using NMR spectroscopy. The effects of chain running on polymer melting, crystallization behavior, and dynamic mechanical thermal properties were studied using DSC and DMTA. The extent of chain running (i.e., 2,ω‐, 1,ω‐enchainments) decreases with an increase in the carbon number of α‐olefins. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 191–210, 2007     

Alternating copolyfluorenevinyles with polynuclear aromatic moieties: Synthesis,photophysics, and electroluminescence

Three new copolymers, namely poly(fluorenevinylene‐alt‐naphthalenevinylene) ( N ), poly(fluorenevinylene‐alt‐anthracenevinylene) ( A ) and poly(fluorenevinylene‐alt‐pyrenevinylene) ( P ), were synthesized by Heck coupling of 9,9‐dihexyl‐2, 7‐divinylfluorene with a polynuclear aromatic dibromide. The 9,10‐disubstituted anthracene was obtained exclusively for A while N and P were obtained as a mixture of two isomers with predominant the 1,4‐disubstituted naphthalene and 1,8‐disubstituted pyrene, respectively. The polymers were soluble in common organic solvents and decomposed above 370 °C. Their glass transition temperature increased from 58 to 110 °C by increasing the number of the phenyl rings of the polynuclear aromatic moiety. Rather high‐efficiency blue and blue‐greenish photoluminescence (PL) of these copolymers in solution was largely decreased in their films, indicating the presence of concentration quenching in the solid state. The OLED using these polymers demonstrated green EL in the case of copolymers N and A , and red EL in the P derivative with η_EL = 0.26–0.31%. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4661–4670, 2007     

LIPSCHITZ STABILITY OF GENERAL CONTROL SYSTEMS Ⅱ.IN TERMS OF TWO MEASURES

1IntroductionStabilityintermsoftwomeasures,thisconceptenableustounifyava-rietyofstabilityconceptsandtoofferageneralandunifiedframeworkforinvestigationofstabilitytheory.AndtheoriginalLiapunovtheoremshavebeenextended,generalizedandweakenedinvariousaspects[3…     

One-pot synthesis of an ionic half-sandwich complex of neodymium. Application to isoprene polymerisation catalysis

The reaction of one equivalent of Nd(BH₄)₃(THF)₃ with an half equivalent of dialkylmagnesium in the presence of a stoichiometric amount of pentamethylcyclopentadiene cleanly affords a new kind of half-sandwich of neodymium that is stable toward comproportionation. This strategy can be advantageously applied to generate in situ catalysts allowing the controlled polymerisation of isoprene.