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.     

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.     

Projective structures with discrete holonomy representations

Let denote the set of projective structures on a compact Riemann surface whose holonomy representations are discrete. We will show that each component of the interior of is holomorphically equivalent to a complex submanifold of the product of Teichmüller spaces and the holonomy representation of every projective structure in the interior of is a quasifuchsian group.

     

Convex hull of set in thick part of Teichmller space

Let X be a non-elementary Riemann surface of type(g,n),where g is the number of genus and n is the number of punctures with 3g-3+n1.Let T(X)be the Teichmller space of X.By constructing a certain subset E of T(X),we show that the convex hull of E with respect to the Teichmller metric,the Carathodory metric and the Weil-Petersson metric is not in any thick part of the Teichmler space,respectively.This implies that convex hulls of thick part of Teichmller space with respect to these metrics are not always in thick part of Teichmller space,as well as the facts that thick part of Teichmller space is not always convex with respect to these metrics.