Asymptotic Solutions of Hamilton-Jacobi Equations with State Constraints

We study Hamilton-Jacobi equations in a bounded domain with the state constraint boundary condition. We establish a general convergence result for viscosity solutions of the Cauchy problem for Hamilton-Jacobi equations with the state constraint boundary condition to asymptotic solutions as time goes to infinity.     

Fabrication of well‐aligned electrospun nanofibrous membrane based on fluorinated polyimide

We have fabricated novel nanofibrous fluorinated polyimide membranes on a specially designed collector, which is composed of conductive aluminum plates and glass insulator materials and can be removed from the apparatus, using an electrospinning method. We describe the structure and water flux properties of the nanofibrous fluorinated polyimide membranes. The electrospun nanofibers were deposited across the plates and uniaxially aligned to the collector. In addition, the multi‐layer stacked nanofibrous membranes, consisting of three‐dimensionally ordered nanopores, were produced. The pure water fluxes for the stacked membranes were measured, using a stirred dead‐end filtration cell, and were linearly decreased with an increasing deposition time, indicating that the nanopores formed in the nanofibrous membrane were further narrowed due to the regularly accumulated nanofibers. Copyright © 2009 John Wiley & Sons, Ltd.     

The order of a group of even order

We will give an estimation of the order of a group of even order by the order of the centralizer of an involution using the classification of finite simple groups.

     

A new method for the stereoselective construction of angular methyl group of fuzed cyclic ethers

A convenient method for the stereoselective construction of angular methyl group of fuzed cyclic ethers is described. Reactions of mixed thioacetals with Me₂Zn/Zn(OTf)₂ afforded the corresponding methylated products in good yields. Various protective groups such as MOM ether, benzylidene acetal, TBS ether, and pivaloyl group were stable under the reaction conditions.     

Function of vinyl copolymers with pendant porphyrin or metalloporphyrin dimers as photoredox catalyst

Photoredox catalytic functions of water-soluble vinyl copolymers with pendant porphyrin or metalloporphyrin dimers were investigated. With FRA-L-ascorbic acid in aqueous solution, a vinyl copolymer bearing Mg-porphyrin dimer linked with the shortest N,N′-methylenebisamide bridge was found to have a remarkable accelerating effect under illumination of visible light as compared with that bearing Mg-porphyrin monomer and other copolymers with longer dimer bridges as well as vinyl copolymers bearing porphyrin dimers and monomer. A copolymer bearing Zn-porphyrin dimer was much inferior to that bearing monomer. Copolymers with other metals such as Co(II), Ni(II), and Cu(II) were almost inert.     

Rational development of caged-biotin protein-labeling agents and some applications in live cells

Biotin-(strept)avidin complex is widely used in biotechnology because of its extremely high binding constant, but there is no report describing spatiotemporally controlled formation of the complex in live cells. Here, based on X-ray crystal structure analysis and calorimetric data, we designed and synthesized photoreleasable biotins, which show greatly reduced affinity for (strept)avidin, but recover native affinity after UV irradiation. For application at the cell surface, we introduced an amine-reactive moiety into these "caged" biotin molecules. Specific fluorescence imaging of live cells that had been labeled with these agents and then UV-irradiated, was accomplished by addition of streptavidin conjugated with a fluorophore. We also demonstrated the applicability of these compounds for UV-irradiated-cell-specific drug delivery by using caged-biotin-labeled cells, a prodrug, and streptavidin conjugated with a prodrug-activating enzyme.     

Convergent synthesis of the HIJKLM ring system of ciguatoxin CTX3C

The HIJKLM ring system of ciguatoxin CTX3C was synthesized in a convergent manner. The key steps were a conjugate addition/alkylation sequence, spiroacetalization, intramolecular allylation, ring-closing metathesis, and hydrogenation to form the 36-α-methyl substituent.     

Octaalkyl tetracene-1,2,3,4,7,8,9,10-octacarboxylates: synthesis by twofold [2+2+2] cocyclization and crystallochromy

Tetracene octaesters, which were prepared by twofold [2+2+2] cocyclization, were isolated as red, orange, and orange-yellow solids for the methyl, ethyl, and propyl ester derivatives, respectively. X-Ray crystallographic analysis reveals that the difference in solid-state color arises owing to differences in molecular packing.     

SOLVENT EFFECTS ON TRIPLET-STATE BACTERIOCHLOROPHYLL a AS DETECTED BY TRANSIENT RAMAN SPECTROSCOPY AND THE ENVIRONMENT OF BACTERIOCHLOROPHYLL a IN THE LIGHT-HARVESTING COMPLEX OF Rhodobacter sphaeroides R26

The frequency of BChl that was bound to the light-harvesting complex (LHC) of Rhodobacter sphaeroides R26 was found to be 1598 cm^-1, a result which suggests that a pair of BChl molecules form a dimer in the LHC in the T₁ state.     

Syntheses of polymerizable hydroquinone derivatives

Several polymerizable hydroquinone derivatives were prepared by the Williamson synthesis. Thus, hydroquinone mono(p-vinylbenzyl) ether (III-1), hydroquinone methyl p-vinylbenzyl ether (III-4), and hydroquinone benzyl p-vinylbenzyl ether (III-5), tert-butylhydroquinone mono(p-vinylbenzyl) ether (III-2), and 2,5-di-tert-butylhydroquinone mono(p-vinylbenzyl) ether (III-3) were synthesized by the reactions of p-chloromethylstyrene with the corresponding hydroquinone derivatives in alcoholic potassium hydroxide or with their potassium salts in dipolar aprotic solvents. All monomers were found to polymerize by free-radical initiation except III-3, which required a cationic initiator.