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     

Magnetic properties of the Cr(0 0 1) surface studied by spin-polarized scanning tunneling spectroscopy

The magnetic properties of the Cr(0 0 1) surface have been studied by spin-polarized scanning tunneling spectroscopy (SP-STS). Spatially resolved mapping of the spectroscopic dI/dU signal at an energy close to the spin-polarized Cr(0 0 1) surface state allows the confirmation of the topological antiferromagnetic order of the Cr(0 0 1) surface. It is shown that the presence of screw dislocations leads to the formation of domain walls which exhibit a width of 120–170 nm. A long-period modulation of the SP-STS signal was not observed indicating that the bulk spin-density wave is modified at the surface due to symmetry breaking.     

Confinement by polynomial potentials

It is shown that the Dirac equation with attractive monomial vector potential cannot confine a particle. General polynomial type vector potential cannot confine a particle, either. This condition is not changed by a scalar potential smaller than the vector one.     

Preparation and properties of molybdenum and tungsten dinitrogen complexes : `XVI. Electrochemical properties of tungsten and molybdenum diazoalkane complexes

Diazoalkane complexes of type [MF(NNCRR′)(dpe)₂][BF₄] (M = Mo or W; dpe = Ph₂PCH₂CH₂PPh₂), which are easily derived from bis(dinitrogen) complexes [M(N₂)₂(dpe)₂], undergo consecutive one- and two-electron oxidations and reductions under voltammetric conditions at a platinum electrode. The ESR spectra of the species generated by the controlled potential electrolysis show that primary oxidation occurred on the metal atom (M = Mo) and reduction on the two nitrogen atoms in the diazoalkane ligands (M = Mo or W).     

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.     

Isolation of novel lignans, heteroclitins F and G, from the stems of Kadsura heteroclita, and anti-lipid peroxidative actions of heteroclitins A-G and related compounds in the in vitro rat liver homogenate system.

From the stems of Kadsura heteroclita, two new lignans named heteroclitins F and G were isolated and their structures were determined by various spectroscopic means including an X-ray diffraction method. Dibenzocyclooctadiene type lignans and related compounds isolated from the stems of K. heteroclita, potently inhibited the lipid peroxidation in the rat liver homogenate stimulated by Fe(2+)-ascorbic acid, CCl4-reduced form of nicotinamide adenine dinucleotide phosphate (NADPH) and adenosine 5'-diphosphate-NADPH.     

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.