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     

Time variation of the electromagnetic transfer function of the earth estimated by using wavelet transform

In order to accurately estimate the geomagnetic transfer functions in the area of the volcano Mt. Iwate (IWT), we applied the interstation transfer function (ISTF) method to the three-component geomagnetic field data observed at Mt. Iwate station (IWT), using the Kakioka Magnetic Observatory, JMA (KAK) as remote reference station. Instead of the conventional Fourier transform, in which temporary transient noises badly degrade the accuracy of long term properties, continuous wavelet transform has been used. The accuracy of the results was as high as that of robust estimations of transfer functions obtained by the Fourier transform method. This would provide us with possibilities for routinely monitoring the transfer functions, without sophisticated statistical procedures, to detect changes in the underground electrical conductivity structure.     

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.     

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.     

Synthesis and characterization of three novel perfluoro-oligothiophenes ranging in length from the trimer to the pentamer

In this Article, we report on the synthesis and full characterization of three perfluorinated oligothiophenes, ranging in length from the trimer to the pentamer (PF-nT, with n = 3, 4, or 5). The differential pulse voltammetry (DPV) analysis of the compounds showed that they can be both oxidized and reduced (i.e., they display a dual or amphoteric electrochemical behavior), with the reduction peaks positively shifted relative to those of the corresponding unsubstituted oligothiophenes. The electrochemically determined energy gaps are in agreement with those measured from the UV-vis-NIR absorption spectra in solution. The conjugational properties have been investigated by means of FT-Raman spectroscopy, both as pure solids and as dilute solutes in CH(2)Cl(2), revealing that: (i) pi-conjugation does not still reach saturation with chain length for the longest oligomer, and (ii) conformational distortions from a nearly coplanar arrangement of the successive thiophene units upon solution are not too large. DFT and TDDFT quantum chemical calculations have been performed, at the B3LYP/6-31G level, to assess information about the optimized molecular structure, equilibrium atomic charges distribution, energies and topologies of the frontier molecular orbitals (MO) around the gap, vibrational normal modes associated with the most outstanding Raman scatterings, and vertical one-electron excitations that give rise to the main optical absorptions.     

Stereoselective synthesis of cis- and trans-2,3-disubstituted eight-membered medium-ring ethers based on Ireland-Claisen rearrangement of 3-alkoxy-2-propenyl glycolate esters and ring-closing olefin metathesis

A simple stereoselective synthesis of cis- and trans-2,3-disubstituted medium-sized cyclic ethers has been developed based on geometry-selective synthesis of 3-alkoxy-2-propenyl glycolate esters, Ireland-Claisen rearrangement of the glycolate esters, and ring-closing olefin metathesis.     

Perfluoro-1,3,5-tris(p-oligophenyl)benzenes: Amorphous Electron-Transport Materials with High-Glass-Transition Temperature and High Electron Mobility

Perfluoro-1,3,5-tris(p-quaterphenyl)benzene (PF-13Y) and perfluoro-1,3,5-tris(p-quinquephenyl)benzene (PF-16Y) have been synthesized and characterized. They showed higher glass transition temperatures compared with perfluoro-1,3,5-tris(p-terphenyl)benzene (PF-10Y). Organic light-emitting diodes were fabricated using these materials as the electron-transport layers. PF-13Y and -16Y are better electron transporters than PF-10Y. The electron mobilities of PF-10Y and Alq₃ were measured by the time-of-flight technique. PF-10Y showed higher electron mobilities (10⁻⁴ cm²/V s) and weaker electric field dependence compared with Alq₃.     

Determination of trace elements in sea water by inductively-coupled plasma emission spectrometry

Pb, Zn, Cd, Ni, Mn, Fe, V and Cu in sea water are determined by extraction of their complexes with sodium diethyldithiocarbamate into chloroform, decomposition of the chelates and inductively-coupled plasma emission spectrometry. When 1-l water samples are used, the lowest determinable concentrations are: 0.063 μg Mn l^-1, 0.13 μg Zn l^-1, 0.25 μg Cd l^-1, 0.25 μg Fe l^-1, 0.38 μg V l^-1, 0.5 μg Ni l^-1, 0.5 μg Cu l^-1, and 2.5 μg Pb l^-1. Above these levels, the relative standard deviations are better than 12% for the complete procedure.     

Biodegradable Phosphorylcholine Polymer Hydrogels Cross‐Linked with Vinyl‐Functionalized Polyphosphate

A vinyl‐functionalized polyphosphate (PIOP) was synthesized by ring‐opening polymerization of 2‐isopropyl‐2‐oxo‐1,3,2‐dioxaphospholane and 2‐(2‐oxo‐1,3,2‐dioxaphosphoroyloxyethyl methacrylate) with triisobutylaluminum as an initiator. The number‐averaged molecular weight of the PIOP was 1.2 × 10⁴. The average number of vinyl groups in the PIOP is 2.20. Transparent hydrogels were prepared by the radical polymerization of 2‐methacryroyloxyethyl phosphorylcholine with PIOP as a cross‐linking reagent. These hydrogels may have many applications in the biomedical field because of their biodegradability and biocompatibility.

Synthetic route of PIOP.