On the identification of degenerate indices in the nonlinear complementarity problem with the proximal point algorithm

In this paper we focus on the problem of identifying the index sets P(x):=i|x_i>0, N(x):={i|F_i(x)>0 and C(x):=i|x_i=F_i(x)=0} for a solution x of the monotone nonlinear complementarity problem NCP(F). The correct identification of these sets is important from both theoretical and practical points of view. Such an identification enables us to remove complementarity conditions from the NCP and locally reduce the NCP to a system which can be dealt with more easily. We present a new technique that utilizes a sequence generated by the proximal point algorithm (PPA). Using the superlinear convergence property of PPA, we show that the proposed technique can identify the correct index sets without assuming the nondegeneracy and the local uniqueness of the solution.This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan.Mathematics Subject Classification (2000): 90C33, 65K10     

Syntheses of fluorine-containing fused polycyclic compounds: photo-cycloaddition of indene to cyclic fluoro-olefins and some reactions concerning the adducts

Acetophenone photo-sensitized addition of indene to cyclic fluoro-olefins (1,2-dichlorohexafluorocyclopentene-1, 1,2-dichlorotetrafluorocyclobutene-1 and hexafluorocyclobutene) gave the corresponding cycloadducts in satisfactory yields. The cycloadducts obtained predominantly had exo configuration.Some reactions such as reduction, oxidation, dechlorination and halogenation, of the cycloadducts were also studied.     

Asymmetric synthesis of axially chiral benzamides and anilides by enantiotopic lithiation of prochiral arene chromium complexes

Axially chiral benzamides and anilides were prepared by enantiotopic lithiation at the distinguished benzylic methyl of prochiral tricarbonylchromium complexes of N,N-diethyl 2,6-dimethylbenzamide (1) and N-methyl-N-acyl 2,6-dimethylaniline (14 and 21) with a chiral lithium amide base followed by electrophilic substitution in good yields with high optical purity. The resulting axially chiral chromium-complexed benzamides and anilides were oxidized under air to give chromium-free axially chiral benzamides and anilides in an enantiomerically active form without axial bond rotation at room temperature.     

Application of non-thermal atmospheric pressure ac plasmas to the carbon dioxide reforming of methane

Methane conversions of 11.9%, yields of hydrogen as high as 23.3% and energy yields of 1.0 mol H₂/kWh have been achieved from CO₂ reforming of CH₄ in non-thermal, atmospheric pressure plasma reactors with Pt coated electrodes. Two reactors have been studied. A novel fan type reactor consisting of a movable rotor and immobile stator produced the highest yields in contrast to a tube type (silent discharge) reactor with a glass dielectric barrier. Conversions, yields of hydrogen and energy yields (expressed as mol H₂/kWh) were studied for CO₂/CH₄ concentrations of 1.1% and 5.0% in He as a function of flow rate and input voltage. Hydrogen yields are observed to increase as the input voltage is increased from 411 V to 911 V and the flow rate is decreased from 100 cc/min to 30 cc/min. Energy yields vary only slightly with input voltage and flow rate. Hydrogen yields show little dependence on CO₂/CH₄ concentrations, but energy yields are approximately five times greater for the 5.0% mixture than the 1.1% mixture. Selectivities to H₂, CO, coke, and low molecular weight hydrocarbons were also evaluated and compared to data obtained without CO₂ in the feed. Hydrogen selectivities of nearly 100% were obtained, with small amounts of ethane and propane as the only observed side products and the selectivites were approximately the same whether CO₂ was present or absent in the mixture. However, the reaction proceeds much more cleanly when CO₂ is present, producing CO. The syngas product has an H₂ : CO ratio of 1.5 with the fan type reactor and 0.67 with the tubular reactor. In the absence of CO₂, coke is the main carbonaceous product. Under all conditions studied the fan type reactor demonstrated higher methane conversions (up to 11.9%) and selectivities to hydrogen.     

Chemo-enzymatic Synthesis of Novel Oligo-N-acetyllactosamine Derivatives having a β(1-4)–β(1-6) Repeating Unit by Using Transition State Analogue Substrate

Chitinase-catalyzed hydrolytic and transglycosylating behavior of 1,2-oxazoline derivative of N-acetyllactosamine (LacNAc-oxa) 1 has been investigated. An extremely rapid hydrolysis (ring-opening of the oxazoline moiety) could be observed, suggesting that 1 behaves as a transition state analogue substrate for chitinase A1 (Bacillus circulans WL-12). This disaccharide monomer 1 was found to polymerize under basic conditions, giving rise to novel oligosaccharides having a β(1-4)–β(1-6) repeating unit in the main chain. The degree of polymerization of the resulting oligosaccharides was up to 5. This is the first example of enzymatic glycosylation reaction forming a β(1-6) bond catalyzed by chitinase.     

Conductive characteristics of radical‐bearing polythiophenes using a microcomb‐shaped electrode

The electric conductivity of π‐conjugated and radical‐bearing polymers, i.e., polythiophenes bearing pendant galvinoxyl and phenoxyl radical groups, was measured using a microcomb‐shaped electrode. The electric conductivity was found to be enhanced by the radical content in the polymer. The infrared (IR) and Raman spectroscopies suggested a structural change from an aromatic form to a quinoid one in the polythiophene backbone by the phenoxyl radical generation. The effect of the pendant galvinoxyl radical's unpaired electron on the electric conductivity of the polythiophene was discussed by comparing the conductivity of a radical‐bearing polystyrene and a polythiophene mixed with low‐molecular radical molecules. Copyright © 2007 John Wiley & Sons, Ltd.     

Salt effects in the base-catalyzed polymerization of unsaturated amide compounds. II. Polymerization of p-vinylbenzamide and acrylamide

In the presence of a variety of inorganic salts, p-vinylbenzamide underwent vinyl-type polymerization by anionic initiators to form the polystyrene derivative, whereas in dimethyl sulfoxide as solvent the aromatic polyamide was always obtained through a proton-transfer mechanism regardless of the presence of the salts. In the presence of of the salts, acrylamide is generally polymerized to the polyamide through a proton transfer reaction.     

Synthesis of 4,6-disubstituted 2-methylpyridines and their 3-carboxamides

A new one-pot synthesis of title compounds by the reactions of α,β-unsaturated carbonyl compounds with β-aminocrotononitrile in the presence of sodium hydroxide is described.     

Generation of functionalized asymmetric benzynes with TMP-zincates. Effects of ligands on selectivity and reactivity of zincates

We have developed new methods for preparing functionalized benzynes through deprotonative zincation as a key reaction using R2Zn(TMP)Li, and we also describes dramatic ligand effects on the benzyne formation. Deprotonative zincation of various meta-substituted bromobenzenes with Me2Zn(TMP)Li proved effective for the one-pot generation of various 3-functionalized benzynes, particularly those electrophilic substituents such as ester, amide, and cyano. On the other hand, zincation with tBu2Zn(TMP)Li, followed by electrophilic trapping (with I2) proved a powerful tool for the preparation of 1,2,3-trisubstituted aromatic compounds.8 The resultant 1,2,3-trisubstituted benzenes are available as precursors for generation of 3-substituted benzynes by halogen-zinc exchange reactions with Me3ZnLi. These methods offer far greater generality than previous methods for the synthesis of functionalized asymmetric benzynes, and should be of value in new syntheses of various natural products and functional materials. In addition, these results underline the utility of spectator ligands on the central metal of ate complexes as a tunable functionality in the development of new ate complex-promoted reactions.     

Simultaneous liquid chromatographic determination of 39 polycyclic aromatic hydrocarbons in indoor and outdoor air and application to a survey on indoor air pollution in Fuji, Japan

An analytical method was established for the simultaneous determination of 39 polycyclic aromatic hydrocarbons (PAHs) in air. The method was applied to a survey of gaseous and particulate PAHs in household indoor air. The survey was performed in 21 houses in the summer of 1999 and in 20 houses in the winter of 1999-2000 in Fuji, Japan. Thirty-eight PAHs were determined in indoor and outdoor air in the summer, and 39 PAHs were determined in indoor and outdoor air in the winter. The concentrations of gaseous PAHs in indoor air tended to be higher than those in outdoor air in the summer and winter. The concentrations of particulate PAHs in indoor air were the same as or lower than those in outdoor air in the summer and winter. PAH profiles, correlations between PAH concentrations, and multiple regression analysis were used to determine the factors affecting the indoor PAH concentrations. These results showed that gaseous PAHs in indoor air were primarily from indoor emission sources, especially during the summer, and that indoor particulate PAH concentrations were significantly influenced by outdoor air pollution.