Liouville theorem and coupling on negatively curved Riemannian manifolds

By using probabilistic approaches, Liouville theorems are proved for a class of Riemannian manifolds with Ricci curvatures bounded below by a negative function. Indeed, for these manifolds we prove that all harmonic functions (maps) with certain growth are constant. In particular, the well-known Liouville theorem due to Cheng for sublinear harmonic functions (maps) is generalized. Moreover, our results imply the Brownian coupling property for a class of negatively curved Riemannian manifolds. This leads to a negative answer to a question of Kendall concerning the Brownian coupling property.     

Facile preparation of organozinc bromides using electrogenerated highly reactive zinc and its use in cross-coupling reaction

Highly reactive zinc was readily prepared by electrolysis of a DMF solution containing pyrene as a mediator with a platinum cathode and a zinc anode. Preferential reduction of pyrene occurred to generate the corresponding radical anion, which reduced zinc ions generated from anodic dissolution to give zero valent zinc with high reactivity. The reactive zinc was successfully used for an efficient transformation of bromoalkanes into the corresponding organozinc bromides. Organozinc bromides obtained were further used successfully in Pd-catalyzed cross-coupling reaction with various aryl iodides and bromides.     

Synthesis of new axially dissymmetric ligand with large perfluoroalkyl groups

A new axially dissymmetric ligand with large perfluoroalkyl groups, 2,2′-bis(1-hydroxy-1H-perfluorooctyl)biphenyl (1c), which could not be obtained by the coupling reaction of the aryl bromide using copper powder, was synthesized successfully by the coupling reaction using Ni(COD)₂. This ligand showed much higher asymmetric induction in the reaction of diethylzinc with benzaldehyde than the trifluoromethyl (1a) or pentafluoroethyl (1b) analogues.     

Synthesis and structural characterization of [(C5H4)SiMe2(N-t-Bu)]Ti[(o-C6H4)C(Ph)C(Ph)], generated via an alkyne-Ti benzyne coupling reaction

The thermolysis of [(C₅H₄)SiMe₂(N-t-Bu)]TiPh₂ in the presence of diphenylacetylene proceeds at 80 °C in cyclohexane solution with the sole formation of the titanacyclic complex [(C₅H₄)SiMe₂(N-t-Bu)]Ti[(o-C₆H₄)C(Ph)C(Ph)], which has been characterized by solution NMR measurements and X-ray crystallographic analysis. This reaction is accompanied by the elimination of benzene and presumably occurs via coupling of a titanium benzyne intermediate with diphenylacetylene. The two chemically inequivalent Ti-C bonds of 2.081(7) and 2.103(6) Å in [(C₅H₄)SiMe₂(N-t-Bu)]Ti[(o-C₆H₄)C(Ph)C(Ph)] reflect the increased electrophilicity of the d⁰ Ti(IV) center arising from the presence of the bifunctional ansa-cyclopentadienyldimethylsilylamido ligand.     

CaCO3/PEEK复合体系的力学行为和热行为研究

以聚醚醚酮和碳酸钙复合体系为研究对象,考察了偶联剂和填料添加量对复合材料力学行为和热行为的影响.发现磺化聚醚醚酮作为偶联剂能有效地改善材料的力学性能,提高基体树脂的玻璃化转变温度,降低基体树脂的熔点,有助于改善聚醚醚酮的加工条件     

EFFECTS OF COUPLING AGENTS ON THE CRYSTALLIZATION BEHAVIOR OF PP/T-ZnOw COMPOSITES

The objectives of this paper are to understand the crystallization behavior of polypropylene(PP)composites with surface modified tetra-needle-shaped zinc oxide whisker(T-ZnOw).T-ZnOw was surface modified with different coupling agents,such as silane coupling agents(KH-550,KH-560)and titanate coupling agent(NDZ-105),in order to improve the compatibility between PP and T-ZnOw.DSC and POM were used to characterize the melt and crystallization behavior and the crystalline structures of the composites,respectively.The results show that the surface modified T-ZnOw acts as a nucleating agent of PP crystallization,depending on the coupling agent used for modification.KH-550 and KH-560 have more apparent role in improving the interfacial interaction than NDZ-105 and induce PP crystallization at higher temperature and with smaller spherulites size.The results also suggest that the crystallization behavior depends on not only the content of coupling agent,but also the content of the surface modified T-ZnOw used in the composites.     

An iterative acetylene-epoxide coupling strategy for the total synthesis of longimicin C

Longimicin C, a naturally occurring annonaceous acetogenin possessing a C₂-symmetrical bis-THF moiety and a short hydrocarbon chain between its THF-containing region and a terminal γ-lactone, was synthesized for the first time. The total synthesis was successfully achieved by an iterative acetylene-epoxide coupling strategy. d-Mannitol was used to establish the bis-THF-containing segment, in which the additional stereochemistries were introduced by Sharpless dihydroxylations and intramolecular Williamson etherifications. Regioselective epoxide-openings by the appropriate terminal acetylenes allowed coupling and elaboration of all four fragments including the introduction of three essential hydroxyls into the proper sites of the target skeleton.     

Stereoselective total synthesis of (S)-Virol C and (S)-1-dehydroxyvirol A

A stereoselective total synthesis of (S)-Virol C and (S)-1-dehydroxyvirol A has been developed, based upon the selective and sequential substitution of the two trimethylsilyl groups of readily available 1,4-bis(trimethylsilyl)-1,3-butadiyne.     

Rhodium and iridium complexes of N-heterocyclic carbenes: Structural investigations and their catalytic properties in the borylation reaction

Bridged and unbridged N-heterocyclic carbene (NHC) ligands are metalated with [Ir/Rh(COD)₂Cl]₂ to give rhodium(I/III) and iridium(I) mono- and biscarbene substituted complexes. All complexes were characterized by spectroscopy, in addition [Ir(COD)(NHC)₂][Cl,I] [COD = 1,5-cyclooctadiene, NHC =  1,3-dimethyl- or 1,3-dicyclohexylimidazolin-2-ylidene] (1, 4), and the biscarbene chelate complexes 12 [(η⁴-1,5-cyclooctadiene)(1,1′-di-n-butyl-3,3′-ethylene-diimidazolin-2,2′-diylidene)iridium(I) bromide] and 14 [(η⁴-1,5-cyclooctadiene)(1,1′-dimethyl-3,3′-o-xylylene-diimidazolin-2,2′-diylidene)iridium(I) bromide] were characterized by single crystal X-ray analysis. The relative σ-donor/π-acceptor qualities of various NHC ligands were examined and classified in monosubstituted NHC-Rh and NHC-Ir dicarbonyl complexes by means of IR spectroscopy. For the first time, bis(carbene) substituted iridium complexes were used as catalysts in the synthesis of arylboronic acids starting from pinacolborane and arene derivatives.     

A new approach to the synthesis of oligomers. Application to the synthesis of p-phenylene thioether wires

Oligothioethers 4-RC₆H₄(SC₆H₄-4)_nX (n = 1-3; X = Br, I; R = NO₂; X = Br; R = MeO. n = 1 and 2; X = I; R = MeO. n = 4; X = Br; R = NO₂) have been prepared through a process involving (i) palladium-catalyzed C-S coupling between 4-RC₆H₄(SC₆H₄-4)_n−1I and 4-BrC₆H₄SH to give 4-RC₆H₄(SC₆H₄-4)_nBr and (ii) copper-catalyzed replacement of Br by I.