Global solvability for the Kirchhoff equations in exterior domains of dimension larger than three

We consider the unique global solvability of initial (boundary) value problem for the Kirchhoff equations in exterior domains or in the whole Euclidean space for dimension larger than three. The following sufficient condition is known: initial data is sufficiently small in some weighted Sobolev spaces for the whole space case; the generalized Fourier transform of the initial data is sufficiently small in some weighted Sobolev spaces for the exterior domain case. The purpose of this paper is to give sufficient conditions on the usual Sobolev norm of the initial data, by showing that the global solvability for this equation follows from a time decay estimate of the solution of the linear wave equation. Copyright © 2004 John Wiley & Sons, Ltd.     

Enzymatic resolution of 4-methyl-, 4-phenyl- and 6-phenyltetrahydro-2H-pyran-2-one using esterases

Enantioselective hydrolysis of racemic tetrahydro-2H-pyran-2-ones (δ-valerolactones) using esterase resulted in the formation of optically active (R)-4-methyl-, (R)-4-phenyl- or (R)-6-phenyltetrahydro-2H-pyran-2-ones and the corresponding (S)-8-hydroxypentanoic acid derivatives.     

Enzymatic resolution of trans-2,3-dihydro-3-hydroxy-2-phenyl-4H-1-benzopyran-4-one (trans-flavanon-3-ol) by lipase

trans-2,3-Dihydro-3-hydroxy-2-phenyl-4H-l-benzopyran-4-one (trans-flavanon-3-ol) was resolved to acetate of (2S,3S)-(-)-trans-flavanon-3-ol and (2R,3R)-(-)-trans-flavanon-3-ol by an enzymatic transesterification with vinyl acetate in the presence of Pseudomonas cepacia lipase.     

Effects of reaction temperature and acyl group for lipase-catalyzed chiral binaphthol synthesis

Candida antarctica lipase-catalyzed hydrolysis of O-butyryl-BINOL [(±)-3] or O-butyryl-6,6′-dibromo-BINOL [(±)-5] yielded optically active BINOL [(R)-1] or 6,6′-dibromo-BINOL [(R)-4] with high enantiomeric excess at 80 °C. Reaction temperature and acyl group of substrate had a great influence on the reactivity and enantioselectivity, respectively, of lipase-catalyzed hydrolysis for chiral binaphthol synthesis.     

Electron-transfer fluorescence quenching of aromatic hydrocarbons by europium and ytterbium ions in acetonitrile

To make the effects of molecular size on photoinduced electron-transfer (ET) reactions clear, the ET fluorescence quenching of aromatic hydrocarbons by trivalent lanthanide ions M3+ (europium ion Eu3+ and ytterbium ion Yb3+) and the following ET reactions such as the geminate and free radical recombination were studied in acetonitrile. The rate constant k(q) of fluorescence quenching, the yields of free radical (phi(R)) and fluorescer triplet (phi(T)) in fluorescence quenching, and the rate constant k(rec) of free radical recombination were measured. Upon analysis of the free energy dependence of k(q), phi(R), phi(T), and k(rec), it was found that the switchover of the fluorescence quenching mechanism occurs at deltaG(fet) = -1.4 to -1.6 eV: When deltaG(fet) < -1.6 eV, the fluorescence quenching by M3+ is induced by a long-distance ET yielding the geminate radical ion pairs. When deltaG(fet) > -1.4 eV, it is induced by an exciplex formation. The exciplex dissociates rapidly to yield either the fluorescer triplet or the geminate radical ion pairs. The large shift of switchover deltaG(fet) from -0.5 eV for aromatic quenchers to -1.4 to -1.6 eV for lanthanide ions is almost attributed to the difference in the molecular size of the quenchers. Furthermore, it was substantiated that the free energy dependence of ET rates for the geminate and free radical recombination is satisfactorily interpreted within the limits of the Marcus theory.     

Synthesis and structural characterization of mesitylphosphinidene-capped ruthenium and osmium clusters

Thermal reaction of [Ru₃(CO)₁₂] with PH₂Mes (Mes = mesityl) in refluxing toluene afforded mesitylphosphinidene-capped ruthenium carbonyl clusters, [Ru₃(CO)₉(μ-H)₂(μ₃-PMes)] (1), [Ru₃(CO)₈(PH₂Mes)(μ-H)₂(μ₃-PMes)] (2), [Ru₃(CO)₉(μ₃-PMes)₂] (3), [Ru₄(CO)₁₀(μ-CO)(μ₄-PMes)₂] (4), and [Ru₅(CO)₁₀H₂(μ₄-PMes)(μ₃-PMes)₂] (5). All products were fully characterized and structurally confirmed by X-ray crystal structure analysis. Complexes 2-4 were also obtained in high yields by stepwise reaction starting from 1. Fluxional behavior of carbonyl groups was observed in case of 4. Complex 5 reveals a new type of skeletal structure, bicapped-octahedron having μ₃- and μ₄-phosphinidene ligands at the capping positions. Similar reaction of [Os₃(CO)₁₂] with PH₂Mes yielded a phosphido-bridged osmium cluster [Os₃(CO)₁₀(μ-H)(μ-PHMes)] (6) and a phosphinidene-capped cluster [Os₃(CO)₉(μ-H)₂(μ₃-PMes)] (7).     

Rücktitelbild: C?H Activation Generates Period‐Shortening Molecules That Target Cryptochrome in the Mammalian Circadian Clock (Angew. Chem. 24/2015)

The synthesis and functional analysis of KL001 derivatives, which are modulators of the mammalian circadian clock, are described. By using cutting‐edge C H activation chemistry, a focused library of KL001 derivatives was rapidly constructed, which enabled the identification of the critical sites on KL001 derivatives that induce a rhythm‐changing activity along with the components that trigger opposite modes of action. The first period‐shortening molecules that target the cryptochrome (CRY) were thus discovered. Detailed studies on the effects of these compounds on CRY stability implicate the existence of an as yet undiscovered regulatory mechanism.     

Ruthenium-catalyzed carbon-carbon formation to synthesize tetraarylethanes and tetraarylxylylene through dechlorinative dimeric reaction

Dechlorinative coupling-dimerization reaction is studied to synthesize alkanes by using tris-triphenylphosphine ruthenium (II) in the presence of hydrogen atmosphere. Two types of halides (α-chlorodiarylmethanes 1a-d and bis(chlorophenylmethyl)-1,3-phenylene 6) are employed as substrates to form radical species and then dimerized to generate alkanes in high yields. To our knowledge, it is the first time that the formation of 1,1,2,2-tetraarylethanes and 1,2,9,10-tetraphenyl-di-m-xylylene over typical ruthenium-catalyzed dehalogenative coupling-dimerization conditions is reported.