Conjugacy relationship between M-convex and L-convex functions in continuous variables

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions in continuous variables. In this paper, we consider a further extension to more general convex functions defined over the real space, and provide a proof for the conjugacy relationship between general M-convex and L-convex functions.Mathematics Subject Classification (1991): 90C10, 90C25, 90C27, 90C35This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan     

Synthesis of Bioactive and Porous Organic-Inorganic Hybrids for Biomedical Applications

Bioactivity has been exhibited by a limited range of ceramics since the invention of Bioglass®. Recently, some bioactive polymeric organic-inorganic hybrids were introduced, including not only organically modified silicates (Ormosils) synthesized from polydimethylsiloxane (PDMS) and tetraethoxysilane but also those with gelatin and 3-glycidoxypropyl-tremethoxysilane. Preparation of the bulk and porous hybrids and their polymeric structures analyzed by Si NMR spectroscopy were presented. In vitro bioactivity or apatite deposition in a simulated body fluid of the Kokubo recipe were also described for those hybrids. Freeze-drying techniques introduced porosity (up to 90%) and pores extending in a preferred direction.     

VISUAL PIGMENTS—10. SPECTROSCOPY AND PHOTOPHYSICAL DYNAMICS OF RETINOL AND RETINYL ETHER

Abstract— The absorption and emission spectra, lifetimes and quantum yields of all-trans retinol have been examined as a function of solvent and temperature. In addition, the spectroscopy of retinyl ether and 2 other polyene alcohols have been determined. Based on the results obtained, we conclude that the singlet excited state of retinol and retinyl cther is of a forbidden character and of the type loosely called ¹A^-_g. Retinol forms a dimer in an alkane solvent when cooling from 298 to 77 K. A general structure for the dimer is proposed.     

Radiation-induced polymerization of cyclohexene sulfide in the solid state

Radiation-induced solid-state polymerization of cyclohexene sulfide has been investigated. Differential thermal analysis shows that this compound has a phase transition point at ?74°C and behaves as a plastic crystal in the temperature range from ?74 to ?20°C (melting point). By rapid cooling, this plastic crystal was easily supercooled, and below ?166°C a glassy crystal, i.e., a supercooled nonequilibrium state of plastic crystal, was obtained. In-source polymerization proceeded in the plastic crystalline state. Postpolymerization of glassy crystalline monomer irradiated at ?196°C occurred above ?166°C (glass transition point) during subsequent heating.     

A study of novel heat-resistant polymers: Preparation of photosensitive fluorinated polybenzoxazole precursors and physical properties of polybenzoxazoles derived from the precursors

A series of novel photosensitive polybenzoxazole precursors were prepared from polycondensation of 2,2-bis(3,3′-amino-4,4′-hydroxyphenyl)hexafluoropropane with photosensitive dicarboxylic acid chlorides such as p-phenylenediacryloyl chloride and benzophenone-4,4′-dicarboxylic chloride. The precursors are soluble in common organic solvents owing to the presence of perfluoromethyl groups in the chain structure, and insolubilized in the solvents on irradiation with the light. Polybenzoxazole patterns with high resolution as well as high aspect ratio were reproduced by baking the precursor patterns at 300°C. The pattern shrinkage on the conversion to polybenzoxazole was slight. The polybenzoxazole films offered good heat-resistance up to 400°C in addition to good electrical properties.     

Regioselectivity in palladium-indium iodide-mediated allylation reaction of glyoxylic oxime ether and N-sulfonylimine

Allylation reaction of electron-deficient imines with allylic alcohol derivatives in the presence of a catalytic amount of palladium(0) complex and indium(I) iodide was studied. The reversibility of allylation was observed in the reaction of glyoxylic oxime ether having camphorsultam. As the important effect of water on regioselectivity, the gamma-adducts were kinetically formed from monosubstituted allylic reagents in the presence of water. The selective formation of thermodynamically stable alpha-adducts was observed in anhydrous THF. In contrast, the allylation of N-sulfonylimine gave the gamma-adducts with high regioselectivities even under anhydrous reaction conditions.     

The participation of the anion and alkyl substituent of diaryliodonium salts in photo‐initiated cationic polymerization reactions

The photo‐initiated cationic polymerization (PCP) of epoxides using diaryliodonium salt photoacid generators (PAGs) bearing alkyl groups and anions was investigated. The properties and reactivities of a series of iodonium salts containing various cations and anions were compared in the context of a PCP reaction. The products from the decomposition of the cations of these salts were analyzed using gas chromatography‐mass spectrometry (GC‐MS) spectra. The relationship between the molecular structure of the salts and their reaction mechanism in the PCP reaction was investigated. Based on the results of the investigation, it was concluded that the structures of the cations and anions of theiodonium salts affect the PCP reaction rate, which was controlled by the products from the diaryliodonium salts. As part of an additional investigation, the diaryliodonium salts‐epoxide materials were applied to 254 nm‐photo‐patterning. Copyright © 2006 John Wiley & Sons, Ltd.     

Destabilization of whole skin lipid bio-liposomes induced by skin penetration enhancers and FT-IR/ATR (Fourier transform infrared/attenuated total reflection) analysis of stratum corneum lipids.

Whole skin lipid bio-liposomes (skin bio-liposomes), in size ranging from 2 to 8 microns, were prepared by a reverse phase evaporation technique using rat full thickness skin. Leakage of an encapsulated fluorescence probe, ANTS (delta-amino-1,3,6-naphthalene-trisulfonate), was measured by adding transdermal penetration enhancers (penetrants) into the medium where the skin bio-liposomes were present. Oleylamine induced a fast release of ANTS from the liposomes compared to lauryl-amine which showed a weak action. With these penetrants, the degree of ANTS release from the prepared bio-liposomes was found to correlate well with the results of frequency changes in the CH-asymmetric stretching band near 2920 cm-1 in the rat stratum corneum. The penetrant which caused relatively strong leakage of ANTS induced the significantly large shift of the peak toward the higher wave-numbers due to the perturbation in the structure of lipids of the stratum corneum. The skin bio-liposomes prepared from the rat full thickness skin could be useful in evaluating the penetrants.     

Dynamic covalent approach to [2]- and [3]roxtanes by utilizing a reversible thiol-disulfide interchange reaction

A dynamic covalent approach to disulfide-containing [2]- and [3]rotaxanes is described. Symmetrical dumbbell-shaped compounds with two secondary ammonium centers and a central located disulfide bond were synthesized as components of rotaxanes. The rotaxanes were synthesized from the dumbbell-shaped compounds and dibenzo-[24]crown-8 (DB24C8) with catalysis by benzenethiol. The yields of isolated rotaxanes reached about 90 % under optimized conditions. A kinetic study on the reaction forming [2]rotaxane 2 a and [3]rotaxane 3 a suggested a plausible reaction mechanism comprising several steps, including 1) initiation, 2) [2]rotaxane formation, and 3) [3]rotaxane formation. The whole reaction was found to be reversible in the presence of thiols, and thermodynamic control over product distribution was thus possible by varying the temperature, solvent, initial ratio of substrates, and concentration. The steric bulk of the end-capping groups had almost no influence on rotaxane yields, but the structure of the thiol was crucial for reaction rates. Amines and phosphines were also effective as catalysts. The structural characterization of the rotaxanes included an X-ray crystallographic study on [3]rotaxane 3 a.