A globally convergent Newton method for solving strongly monotone variational inequalities

Variational inequality problems have been used to formulate and study equilibrium problems, which arise in many fields including economics, operations research and regional sciences. For solving variational inequality problems, various iterative methods such as projection methods and the nonlinear Jacobi method have been developed. These methods are convergent to a solution under certain conditions, but their rates of convergence are typically linear. In this paper we propose to modify the Newton method for variational inequality problems by using a certain differentiable merit function to determine a suitable step length. The purpose of introducing this merit function is to provide some measure of the discrepancy between the solution and the current iterate. It is then shown that, under the strong monotonicity assumption, the method is globally convergent and, under some additional assumptions, the rate of convergence is quadratic. Limited computational experience indicates the high efficiency of the proposed method.     

Synthesis of large macrocyclic tetraaza compounds with a methylene backbone: Cyclo[-NH- (CH2)n-]4, (n = 6, 7, 8, 9 and 10). The formation of 28-, 32-, 36-, 40- and 44-membered rings

A series of macrocyclic tetraamines with 28-, 32-, 36-, 40- and 44-membered rings have been efficiently prepared from the corresponding ditosylamide and monobromoalcohol derivatives in 6 steps via a double condensation reaction. Overall yields were: 41, 41, 46, 29, and 33%, respectively, for 1,8,15,22-tetraazacyclooctacontane ( 11a ), 1,9,17,25-tetraazacyclodotriacontane ( 11b ), 1,10,19,28-tetraazacyclohexatriacontane ( 11c ), 1,11,21,31-tetraazacyclotetracontane ( 11d ) and 1,12,23,34-tetraazacyclotetratetracontane ( 11e ).     

In Situ Processing of Nano Crystalline Oxide Particles/Polymer Hybrid

Nano sized crystalline particles/polymer hybrids were synthesized form designed metal-organic precursors. The newly developed method is composed of the synthesis of organic matrix by polymerization and the in situ nucleation and growth of crystalline oxide particles in the organic matrix below 100°C. The design of metal-organic precursor modified with polymerizable ligand and the selection of reaction conditions does influence the size and crystallinity of ceramic particles in organic matrix. The nano-sized magnetic particle/polymer hybrid exhibits the interesting feature of superparamagnetism and quantum size effect. The crystalline particles of BaTiO₃/, PbTiO₃/, and KNbO₃/polymer hybrids behave to be dielectric and show the typical electro-rheological behavior.     

Perturbation analysis for the rotational spectrum of the NiBr radical in the X2Pi3/2 and A2Delta5/2 states

The millimeter- and submillimeter-wave spectra of the NiBr radical in the X (2)Pi(3/2) and A (2)Delta(5/2) states were observed by a source-modulated microwave spectrometer. The NiBr radical was generated in a dc glow discharge through the mixture of Br(2) vapor and Ar gas by the sputtering reaction with a Ni cathode. Observed transition frequencies were independently analyzed for both electronic states using a standard polynomial expression of a Hund's case (c) approximation. Anomalous behavior of the effective molecular constants in the X (2)Pi(3/2) state was interpreted as the result of the perturbation between the X (2)Pi(3/2) and A (2)Delta(5/2) states. The deperturbed molecular constants were derived using a simplified supermultiplet Hamiltonian including the interaction terms between the two electronic states.     

Preparation and characterization of novel branched beta-cyclodextrins having beta-D-galactose residues on the non-reducing terminal of the side chains and their specific interactions with peanut (Arachis hypogaea) agglutinin

Six novel branched beta-cyclodextrins (betaCDs) having beta-D-galactose residues on the non-reducing terminal of the sugar side chains, namely 6(1),6(4)-di-O-(beta-D-galactosyl)-betaCD (10), 6-O-(beta-D-galactosyl)-betaCD (11), 6(1),6(4)-di-O-(beta-lactosyl)-betaCD (14), 6-O-(beta-lactosyl)-betaCD (15), 6(1),6(4)-di-O-(4'-O-beta-D-galactosyl-beta-lactosyl)-betaCD (18), and 6-O-(4'-O-beta-D-galactosyl-beta-lactosyl)-betaCD (19), were chemically synthesized using the trichloroacetimidate method. The reaction products were separated by HPLC on an amino column into dibranched and monobranched betaCDs. Their structures were confirmed by mass spectrometry (MS) and two-dimensional (2D) NMR spectroscopic analysis. To study the length of the sugar side chains attached to the CD ring, which leads to differences in the functions of the branched CDs, interactions of these compounds with peanut (Arachis hypogaea) agglutinin (PNA) were investigated using an optical biosensor and an inhibition assay based on hemagglutination. The results showed that all branched betaCDs interacted with PNA, and the binding affinity was 18>14>10 and 19>15>11 when the derivatives were compared on the basis of side chain length.     

Alkane Oxidation with Molecular Oxygen Using a New Efficient Catalytic System: N-Hydroxyphthalimide (NHPI) Combined with Co(acac)(n)() (n = 2 or 3)

A novel class of catalysts for alkane oxidation with molecular oxygen was examined. N-Hydroxyphthalimide (NHPI) combined with Co(acac)(n)() (n = 2 or 3) was found to be an efficient catalytic system for the aerobic oxidation of cycloalkanes and alkylbenzenes under mild conditions. Cycloalkanes were successfully oxidized with molecular oxygen in the presence of a catalytic amount of NHPI and Co(acac)(2) in acetic acid at 100 degrees C to give the corresponding cycloalkanones and dicarboxylic acids. Alkylbenzenes were also oxidized with dioxygen using this catalytic system. For example, toluene was converted into benzoic acid in excellent yield under these conditions. Ethyl- and butylbenzenes were selectively oxidized at their alpha-positions to form the corresponding ketones, acetophenone, and 1-phenyl-1-butanone, respectively, in good yields. A key intermediate in this oxidation is believed to be the phthalimide N-oxyl radical generated from NHPI and molecular oxygen using a Co(II) species. The isotope effect (k(H)/k(D)) in the oxidation of ethylbenzene and ethylbenzene-d(10) with dioxygen using NHPI/Co(acac)(2) was 3.8.     

Chromium- and tungsten-triggered valence isomerism of cis-1-acyl-2-ethynylcyclopropanes via [3,3]sigmatropy of (2-acylcyclopropyl)vinylidene-metal intermediates.

The reaction of cis vicinal acetylethynylcyclopropanes 1 with a catalytic amount of M(CO)5(THF) (M = Cr or W) in the presence of Et3N at room temperature gave ortho-substituted phenols 7 in good yields as valence isomerized products. In the absence of Et3N the reactions did not work at all. The reaction of a cyclopropane having an ester or an amide instead of an acetyl moiety with M(CO)5(THF) did not take place, whereas an ethynylvinylcyclopropane gave a mixture of 1- and 2-substituted 1,3,5-cycloheptatrienes. These valence isomerization reactions are assumed to proceed via the formation of vinylidene-metal intermediates 2 from terminal alkynyl moieties followed by [3,3]sigmatropy of 2 to give seven-membered carbene complexes 3.