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.     

Collection of iron(III) from homogeneous aqueous solutions on membrane filters using Chromazurol B with Triton X-100.

A membrane filtration method was examined concerning the effective collection of iron(III) from a homogeneous aqueous solution with Chromazurol B (CAB), one of the triphenylmethane dyes, as a precipitating reagent in the presence of a non-ionic surfactant, polyethylene glycol mono[4-(1,1,3,3-tetramethylbutyl)phenyl]ether (Triton X-100). A formed blue Fe(III)-CAB complex was collected as a precipitate on a membrane filter by filtration under suction from a homogeneous aqueous solution in the pH range over about 2. The original solution was prepared at a concentration ratio of CAB to Fe(III) of to 10, and that of Triton X-100 to CAB of 10 to 100. It was then adjusted to a pH value of between 1.0 and 6.5. A linear relationship (r = 0.999) was obtained between the initial concentration and the found one of Fe(III) in the range of 2.0 x 10(-5) to 4.0 x 10(-4) mol dm(-3) at a fixed concentration ratio of CAB to Fe(III) of 3 and that of Triton X-100 to CAB of 20. This membrane filtration with CAB and Triton X-100 may be utilized for the separation of Fe(III) as a background species.     

Primal-dual proximal point algorithm for linearly constrained convex programming problems

A primal-dual version of the proximal point algorithm is developed for linearly constrained convex programming problems. The algorithm is an iterative method to find a saddle point of the Lagrangian of the problem. At each iteration of the algorithm, we compute an approximate saddle point of the Lagrangian function augmented by quadratic proximal terms of both primal and dual variables. Specifically, we first minimize the function with respect to the primal variables and then approximately maximize the resulting function of the dual variables. The merit of this approach exists in the fact that the latter function is differentiable and the maximization of this function is subject to no constraints. We discuss convergence properties of the algorithm and report some numerical results for network flow problems with separable quadratic costs.     

Catalytic property of Europium supported on alumina from its ammoniacal solution

Europium supported on alumina (Eu/Al₂O₃) was prepared by impregnation from an ammoniacal solution of the metal. The catalytic activity of Eu/Al₂O₃ for the isomerization of 2,3-dimethylbut-1-ene to 2,3-dimethylbut-2-ene was examined. Eu/Al₂O₃ showed the highest catalytic activity for the isomerization when heated under a vacuum at 523 K, the yield of 2,3-dimethylbut-2-ene in 20 min being 81.6% at 314 K. IR spectrum shows the presence of two kinds of Eu amides. The change of the IR spectra and the catalytic activities with evacuation temperature suggest that only one of the two Eu amides is catalytically active for this base-catalyzed isomerization.     

Asymmetric interaction of optically active polymers with asymmetric small molecules. IV. Effect of hydrophobic groups on asymmetric interaction

In order to investigate the mechanism of the asymmetric interaction between optically active polymers and small molecules, optically active copolymers of N-acrylyl L-amino acids(N-acrylyl-L -phenylalanine, N-acrylyl-L -tryptophan, and N-acrylyl-L -leucine, respectively) and N,N′-hexamethylene diacrylylamide were synthesized, and interaction of these polymers with the optical isomers of phenylalanine and tryptophan was investigated. In the interaction of these acidic polymers with amino acids performed at pH 5.0, significant difference in amount of adsorption between the D and L isomers of amino acids were observed, and the L form of amino acids was adsorbed preferentially. The interaction between optically active small molecules was also investigated: these results showed a similarity to the results for interaction between optically active polymers and amino acids. In some instances of asymmetric interaction the influence of hydrophobic interaction between a polymer and substrate was clearly perceived. The stereoselective effects on the asymmetric interaction are discussed.     

XPS study of one-dimensional compounds: TiS3

X-Ray photoelectron spectra of TiS₃ with a one-dimensional structure were measured. TiS₃ may be regarded as Ti⁴⁺(S₂)^2?S^2? with pairs of S atoms (S₂) and isolated S atoms. The spectra of the sulfur core-levels are assigned by comparison with those of TiS₂, where all S atoms are largely separated. The binding energy of the S₂ pairs is found to be 1.4 eV higher than that of the isolated S atoms, which is consistent with the larger negative charge of the isolated atoms. The structures of the valence band of TiS₃ are discussed in terms of a molecular orbital scheme for the S₂ pairs.     

An intramolecular diels-alder approach to quassinoids—a stereoselective construction of a-aromatic klaineanone

Thermolysis of a benzocyclobutene derivative ($\text{20}$) prepared from norcamphor produced stereoselectively a tetracyclic compound ($\text{2}$), which was converted to a lactone ($\text{21}$) having correct stereochemistry at C₇, C₈, C₉, C₁₁, C₁₃, and C₁₄ positions of (±)-klaineanone.     

Stability and vibrational spectra of toroidal isomers of C 240

To study the thermodynamic and mechanical stability of toroidal isomers of C ₂₄₀, we use a semi-empirical tight-binding theory and calculate their electronic structure, cohesive energy and vibrational spectra within the harmonic approximation. From these, we deduce their free energy at temperatures up to 1500K. The results are also compared to the isomer with icosahedral symmetry. Finally, we discuss within this approach, their stability and abundance.     

Isolation and characterization of thermophilic benzothiophene-degrading Mycobacterium sp.

A bacterial strain, SWU-4, capable of using benzothiophene (BT) as a sole carbon and energy source was isolated from a petroleum-contaminated site in Thailand and identified by 16S rRNA gene sequence analysis to be in the genus of Mycobacterium. The strain was Gram-positive, nonspore former, and grew at 50° C. Colonies of the strain on nutrient agar were rod-shaped, smooth with a convex surface, slightly mucoid, and yellow pigmented. The thermophilic Mycobacterium sp. strain SWU-4 rapidly degraded 2% (w/v) BT at 50°C. Interestingly, this strain was able to degrade a wide variety of organosulfur compounds including thiophene, bromo(α)thiophene, and 3-methylthiophene in liquid minimum medium at 50°C, which will be beneficial for industrial applications.     

Studies on the syntheses of heterocylic compounds—762: Synthesis of 3-benzyl-6-methyl-2-oxo-3,6-diazabicyclo[3.1.0]hexane as a synthetic intermediate of mitomycins

(±)-1-Benzyl-3α-hydroxy-4β-methylamino-2-oxopyrrolidine (15) and its cis-isomer (16) were synthesised from 1-benzyl-4-ethoxycarbonyl-2,3-dioxopyrrolidine (2) in several steps. The former (15) was converted to 3-benzyl-6-methyl-2-oxo-3,6-diazabicyclo[3.1.0]hexane (17) with a mixture of triphenylphosphine, carbon tetrachloride and triethylamine.