Hölder estimates of p-harmonic extension operators

It is now a well-known fact that for 1<p<∞ the p-harmonic functions on domains in metric measure spaces equipped with a doubling measure supporting a (1,p)-Poincaré inequality are locally Hölder continuous. In this note we provide a characterization of domains in such metric spaces for which p-harmonic extensions of Hölder continuous boundary data are globally Hölder continuous. We also provide a link between this regularity property of the domain and the uniform p-fatness of the complement of the domain.     

Local energy decay for a class of hyperbolic equations with constant coefficients near infinity

A uniform local energy decay result is derived to a compactly perturbed hyperbolic equation with spatial vari¬able coefficients. We shall deal with this equation in an N ‐dimensional exterior domain with a star‐shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data and the equation includes anisotropic variable coefficients {a_i(x): i = 1, 2, …, N }, which are not necessarily equal to each other (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gold-catalyzed substitution reaction with ortho-alkynylbenzoic acid alkyl ester as an efficient alkylating agent

ortho-Alkynylbenzoic acid alkyl esters behave as alkylating agents in combination with gold catalysts. The reaction with alcohols occurs smoothly in the presence of catalytic amounts of Ph₃PAuCl and AgOTf under mild conditions to produce the corresponding ether products in high yields. The protocol is also useful for Friedel-Crafts alkylation and N-alkylation of sulfonamides. The reaction likely proceeds through the gold-induced in situ construction of leaving groups and subsequent nucleophilic attack of nucleophiles, such as alcohols, aromatic compounds, and sulfonamides.     

Tribo-Excited Chemical Reaction Using an EuIII Complex with a Stacked Anthracene Framework

A spin-selective tribo-chemical reaction using a dinuclear lanthanide complex is demonstrated for the first time. The dinuclear complex is composed of two Eu^III ions, hexafluoroacetylacetonato ligands, and anthracene-based phosphine oxide bridges. Single-crystal analysis revealed a face-to-face-type anthracene dimer structure in the dinuclear Eu^III complex. Mechanical stimulus on the dinuclear Eu^III complex induced selective formation of oxidized anthracene. The tribo-chemical reaction is based on a characteristic energy-transfer pathway for the selective formation of an excited triplet state.     

Synthesis of 2‐Arylquinazolin‐4(3H)‐ones by N‐Aryl Benzamidines with Aromatic Carbonates

The reaction of N‐aryl benzamidines 1a , 1b , 1c , 1d , 1e , 1f , 1g , 1h , 1i , 1j , 1k , 1l , 1m , 1n with diphenyl carbonate 2a or ethyl phenyl carbonate 2b synthesized 2‐arylquinazolin‐4(3H)‐ones 3a , 3b , 3c , 3d , 3e , 3f , 3g , 3h , 3i , 3j , 3k , 3l , 3m , 3n in simple and safe process with good yields (71–90%). It was suggested that different electron‐donating substituent in N‐aryl benzamidines 1a , 1b , 1c , 1d , 1e , 1f , 1g , 1h , 1i , 1j , 1k , 1l , 1m , 1n afforded similar effect to the yields of 2‐arylquinazolin‐4(3H)‐ones 3a , 3b , 3c , 3d , 3e , 3f , 3g , 3h , 3i , 3j , 3k , 3l , 3m , 3n . In these reactions, N‐aryl benzamidines 1a , 1b , 1c , 1d , 1e , 1f , 1g , 1h , 1i , 1j , 1k , 1l , 1m , 1n built up intermediate compounds by nucleophilic addition to carbonates 2 to give annulation products 3a , 3b , 3c , 3d , 3e , 3f , 3g , 3h , 3i , 3j , 3k , 3l , 3m , 3n , following to cyclization involving the elimination of ethanol/phenol.     

Positive harmonic functions of finite order in a Denjoy type domain

We introduce a Denjoy type domain and prove that the dimension of the cone of positive harmonic functions of finite order in the domain with vanishing boundary values is one or two, whenever the boundary is included in a certain set.

     

Dynamic Chirality Control of tropos DPCB‐digold Skeleton by Chiral Binaphthyldicarboxylate

The planar 3,4‐diphosphinidenecyclobutene (DPCB) can be remarkably twisted into a C₂‐type helical structure by dual coordination of a AuCl moiety. A prompt chirality control of the twisted DPCB skeleton ligated by the digold units affords the enantiopure structure by exchanging the chloride ligands for chiral [1,1′‐binaphthalene]‐2,2′‐dicarboxylate. The chirality of the diaurated 2,2′‐bis(diphenylphosphanyl)‐1,1′‐biphenyl (BIPHEP) system can be controlled prior to that of DPCB. Mixing of a DPCB‐bis(chlorogold) complex with the chiral silver salt dynamically leads to a single diastereomer, which was characterized by the ³¹P NMR spectrum and the CD couplet patterns in the visible (DPCB) area. The absolute configuration of the singly induced helical structure was assigned by the theoretical CD spectra determined by TD‐DFT calculations. Intramolecular alkoxycyclization of hexa‐4,5‐dien‐1‐ol catalyzed by the asymmetric DPCB‐digold structure were also attempted.     

Effect of Poly(amine)s on the Redox Properties of Carboxymethylcellulose and Ferrocene‐modified Poly(amine) Layer‐by‐Layer Films

Multilayer films consisting of carboxymethylcellulose (CMC) and ferrocene‐modified poly(ethyleneimine) (Fc‐PEI) or poly(allylamine hydrochloride) (Fc‐PAH) were successfully prepared on a gold electrode to examine their redox properties. The redox current of (Fc‐PEI/CMC)_n film‐coated electrodes increased with the number of layers, while the (Fc‐PAH/CMC)_n film‐coated electrodes exhibited increased response only for the first eight bilayers. The (Fc‐PEI/CMC)_n and (Fc‐PAH/CMC)_n films deposited on the surface of Fc‐free multilayer film‐coated electrodes also showed a redox response. The (PEI/CMC)₅ film‐coated electrode showed redox responses in Fc‐PEI and Fc‐PAH solutions, confirming the uptake of the Fc‐polymers in the inner film. In contrast, the uptake of the Fc‐polymers in the (PAH/CMC)₅ film was severely suppressed, suggesting that different permeability of (PEI/CMC)₅ and (PAH/CMC)₅ films.     

Stereoselective formation of trisubstituted (z)-chloroalkenes adjacent to a tertiary carbon stereogenic center by organocuprate-mediated reduction/alkylation

A robust and efficient method for the synthesis of trisubstituted (Z)-chloroalkenes is described. A one-pot reaction of γ,γ-dichloro-α,β-enoyl sultams involving organocuprate-mediated reduction/asymmetric alkylation affords α-chiral (Z)-chloroalkene derivatives in moderate to high yields with excellent diastereoselectivity, and allylic alkylation of internal allylic gem-dichlorides is also demonstrated. This study provides the first examples of the use of allylic gem-dichlorides adjacent to the chiral center for novel 1,4-asymmetric induction.     

Significance of cell electrokinetic properties determined by soft-particle analysis in bacterial adhesion onto a solid surface

The influence of extracellular polymeric substances (EPSs) on bacterial cell electrokinetic properties and on cell adhesion onto glass beads in connection with bacterial cell electrokinetic properties was investigated using 12 heterotrophic bacterial strains. Bacterial cell surface properties such as the softness 1/lambda and charge density ZN were determined by Ohshima's soft-particle analysis using the measured electrophoretic mobility as a function of ionic strength. In 10 of 12 strains, when EPSs covering the cell surface were removed, the softness of the cell decreased, indicating that EPS adsorption enhanced the ease of liquid fluid in the ion-penetrable layer on the cell surface. On the other hand, the negative charge density of the cell surface increased for 9 of 12 strains, suggesting that EPSs covering the cell surface decreased the negative charge density of the cell surface layer. In addition, the characteristics of bacterial cell adhesion onto glass beads were evaluated by the packed-bed method and the data were interpreted to indicate cell adhesiveness. As a result, the efficiency of cell adhesion onto glass beads increased as negative cell surface potential psi0 decreased, whereas there seemed to be no correlation between zeta potential and cell adhesiveness. Cell surface potential psi0, which was derived by taking the bacterial polymer layer with EPSs into consideration, provided a more detailed understanding of the electrokinetic properties of bacterial cells.