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.     

Socket with built-in valves for the interconnection of microfluidic chips to macro constituents

This paper reports a prototype for a standard connector between a microfluidic chip and the macro world. This prototype demonstrate a fully functioning socket for a microchip to access the outside world by means of fluids, data signals and energy supply. It supports up to 10 channels for the input and output of liquids or gases, as well as compressed air or vacuum lines for pneumatic power lines. The socket has built-in valves for each flow channel. It also contains 28 pins for the connection of electrical signals and power. Built-in valves make it possible to control the flow in each channel independently. A chip ( 11.0 x 11.0 x 0.9 mm) can be mounted into or dismounted from the socket with one touch. The fluidic connectors of the socket are designed to contact vertically on the top of chip. And the electrical connectors (the spring array) of that physically support the chip and contact lead pads at the bottom of chip. No adhesives or solders are used at any contact points. The pressure limit for the connection of working fluids was 0.2 MPa and the current limit for the electrical connections was 1 A. This socket supports both serial and parallel processing applications. It exhibits great potential for developing microfluidic systems efficiently.     

Preparation,stability, reactivity and synthetic utility of a cadmium stabilized complex of difluoromethylene phosphonic acid ester

Diethyl bromodifluoromethyl phosphonate reacts readily with cadmium metal to form a stable cadmium complex. Depending on solvent, this functionalized organocadmium reagent exhibits stability for days to months. It reacts with a variety of electrophiles and serves as a synthetically useful source for the introduction of the difluoromethylene phosphonate group into organic compounds.The synthetic utility of a wide variety of fluoromethylene phosphonium ylides has been a major effort in our laboratory over the past several years [1]. The generation and capture of difluoromethylene ylides ($\text{1}$) as a general route to difluoromethylene olefins has been of especial interest to us [2]. In an effort to increase the nucleophilicity of the ylide, we have attempted to prepare the analogous phosphonate ylide ($\text{2}$). Although we have achieved modest success [3] by $\text{insitu}$ capture of ($\text{2}$) in the reaction of

sodium dialkyl phosphites with diethyl bromodifluoromethylphosphonate ($\text{3}$), attempts to pregenerate ($\text{2}$), either from diethyl difluoromethylphosphonate ($\text{4}$) or ($\text{3}$), have met with little success. ($\text{2}$) appears to have minimal stability even at low temperatures, and scale up processes of synthetic value would seem to be difficult.     

Probing surface properties and glass-liquid transition of amorphous solid water: temperature-programmed TOF-SIMS and TPD studies of adsorption/desorption of hexane

The interaction of hexane with amorphous solid water has been investigated in terms of the surface diffusion, hydrogen bond imperfections, hydrophobic hydration, crystallization, and glass-liquid transition. The hexane exhibits two main peaks in temperature-programmed desorption: one is ascribed to a complex formed at the surface or subsurface sites (135 K) and the other is caused by a bulk complex (165 K). The latter is associated with the presence of frozen-in imperfections in hydrogen bonds and formed provided that the annealing temperature of the film is below 130 K, whereas the former is created even when the film is annealed up to 150 K. Thus, the hexane-water interaction is hardly characterized by simple physisorption. The hexane is incorporated in the bulk during reorganization of hydrogen bonds due to rotational and translational diffusions of water molecules above 120-140 K, whereas the surface complex is formed even below 120 K due to the surface diffusion of molecules. The film undergoes abrupt dewetting at 165 K as a consequence of the glass-liquid transition. The slow evolution of the fluidity in the supercooled liquid phase may be responsible for the delay of the structural relaxation (165 K) relative to the onset of the translational molecular diffusion (135-140 K).     

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.     

Radical cyclization by ipso substitution of the methoxy group: considerable effect of HMPA on samarium-mediated cyclization

Alkyl radicals generated by treatment of thiocarbamates of conformationally favorable 3-alkyl-3-arylpropan-1-ols with tris(trimethylsilyl)silane and AIBN efficiently undergo intramolecular ipso substitution of the methoxy group, yielding the corresponding cyclized products. In contrast, either conformationally favorable or flexible 1-arylalkan-3- or 4-ones easily cyclize into five- or six-membered condensed rings by treatment with SmI(2) via ketyl radical intermediates. The addition of HMPA as cosolvent dramatically changes the cyclization mode of the SmI(2)-induced reaction, and the para-cyclization products are exclusively formed. This "HMPA effect" can be rationalized by the strong chelating ability of HMPA with the samarium atom.     

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.     

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.