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.     

Probing for electrical inclusions with complex spherical waves

Let a physical body Ω in ?² or ?³ be given. Assume that the electric conductivity distribution inside Ω consists of conductive inclusions in a known smooth background. Further, assume that a subset Γ ? ?Ω is available for boundary measurements. It is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on Γ. More precisely: given a ball B with center outside the convex hull of Ω and satisfying (B? ∩ ?Ω) ? Γ, boundary measurements on Γ with explicitly given Dirichlet data are enough to determine whether B intersects the inclusion. An approximate detection algorithm is introduced based on the theory. Numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion‐free domain near Γ and is robust against measurement noise. © 2007 Wiley Periodicals, Inc.     

Crystallographic report: Bis{µ‐[O‐cyclopentyl(4‐methoxyphenyl)dithiophosphonato]1κ:S,2κ:S‐[O‐cyclopentyl(4‐methoxyphenyl)dithiophosphonato]‐1κ2S,S′}dicadmium(II)

The centrosymmetric title compound, [Cd₂{CH₃OC₆H₄P(OC₅H₉)S₂}₄], features an eight‐membered [? Cd? S? P? S? ]₂ ring owing to the presence of bridging dithiolate ligands. Tetrahedral coordination geometries for cadmium are completed by chelating ligands. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Catalytic transformation of methane over in-loaded ZSM-5 zeolite in the presence of ethene

Methane is shown to react with ethene over In-loaded ZSM-5 to higher hydrocarbons such as propene and toluene at around 673 K. Such methane conversion is not catalyzed by proton-exchanged ZSM-5 (H-ZSM-5) under the same conditions, only C2H4 being converted to higher hydrocarbons. By using 13C-labeled methane (13CH4) as a reactant, the reaction paths for the formation of propene, benzene and toluene were examined. 13C-labeled propene (13CC2H6) is formed by the reaction of 13CH4 with C2H4. The lack of 13C-labeled benzene revealed that propene is not transformed to benzene, which instead originates entirely from C2H4. The 13C atom is inserted both into the methyl group and benzene ring in the toluene formed. This indicates that toluene is formed by two reaction paths; the reaction of 13CC2H6 with butenes formed by the dimerization of C2H4 and the reaction of benzene with 13CH4. The existence of the latter path was proved by the direct reaction of 13CH4 with benzene. The reaction of methane with benzene was also carried out in a continuous flow system over In-loaded ZSM-5. The reaction afforded 7.6% and 0.9% yields of toluene and xylenes, respectively, at 623 K.     

Dynamic covalent approach to [2]- and [3]roxtanes by utilizing a reversible thiol-disulfide interchange reaction

A dynamic covalent approach to disulfide-containing [2]- and [3]rotaxanes is described. Symmetrical dumbbell-shaped compounds with two secondary ammonium centers and a central located disulfide bond were synthesized as components of rotaxanes. The rotaxanes were synthesized from the dumbbell-shaped compounds and dibenzo-[24]crown-8 (DB24C8) with catalysis by benzenethiol. The yields of isolated rotaxanes reached about 90 % under optimized conditions. A kinetic study on the reaction forming [2]rotaxane 2 a and [3]rotaxane 3 a suggested a plausible reaction mechanism comprising several steps, including 1) initiation, 2) [2]rotaxane formation, and 3) [3]rotaxane formation. The whole reaction was found to be reversible in the presence of thiols, and thermodynamic control over product distribution was thus possible by varying the temperature, solvent, initial ratio of substrates, and concentration. The steric bulk of the end-capping groups had almost no influence on rotaxane yields, but the structure of the thiol was crucial for reaction rates. Amines and phosphines were also effective as catalysts. The structural characterization of the rotaxanes included an X-ray crystallographic study on [3]rotaxane 3 a.     

Practical enantioselective synthesis of endothelin antagonist S-1255 by dynamic resolution of 4-methoxychromene-3-carboxylic acid intermediate

A practical multikilogram-scale synthesis of enantiomerically pure S-1255 (1), a potent and orally active ET(A) receptor antagonist, is described. Utilizing readily available starting materials and reagents, the entire sequence of reactions starting from 2,5-dihydroxyacetophenone 8 proceeded under mild conditions to give 1 in an excellent chemical yield (8 steps, 41% overall yield) and in a high enantiopurity (98% ee). The crucial step of the synthesis is a dynamic resolution of key intermediate 16. (R)-Methoxy acid (R)-16 having 97-99% ee was obtained in 83-84% yield from racemic 16 as a crystalline (1S,2R)-(+)-norephedrine or (+)-cinchonine salt by the dynamic resolution comprising concurrent crystallization and in situ racemization. A mechanism of the dynamic resolution through a ring-opened zwitterionic intermediate is discussed. In the final synthetic step, an effective carbon-carbon bond formation between the C4 carbon and the p-anisyl group was accomplished by a conjugate addition-elimination reaction of Grignard reagent 3 to (R)-16 to give 1 having 98% ee. Owing to high efficiencies of functional group transformations, carbon-carbon bond formations, and the dynamic resolution, the synthesis required no chromatographic purification and was amenable to a multikilogram-scale preparation. Several kilograms of 1 for clinical trials were successfully prepared by this process.     

Effect of various halide salts on the incompatibility of cyanocobalamin and ascorbic acid in aqueous solution

Combination of cyanocobalamin (VB12) and ascorbic acid (VC) has been widely seen in pharmaceutical products and dietary supplements. However, VB12 has been reported that its behavior in stability in aqueous solution is quite different when VC is mixed. In the present study, we examined the stabilities of these vitamins in acetate buffer (pH 4.8) using high performance liquid chromatography. Degradation of VB12 was not observed in the absence of VC in the buffer. However, when VC was mixed in the VB12 solution, VB12 concentrations decreased in accordance with VC degradation. VB12 and VC degradations were inhibited by adding sodium halides to acetate buffer at pH 4.8. These stabilization effects were also observed in the range from pH 3.5 to 5.3 and by adding potassium, magnesium, and calcium halides. Furthermore, our data demonstrated that increases in the halide anion concentrations and atomic number (Cl-相似文献   

Studies on orally active cephalosporin esters. II. Chemical stability of pivaloyloxymethyl esters in phosphate buffer solution

The degradation kinetics of pivaloyloxymethyl (POM) esters of cephalosporins in phosphate buffer solution (pH 6-8) were investigated. The degradation of the starting delta 3 cephalosporin ester proceeded mainly via isomerization to the delta 2 ester and subsequent hydrolysis to the delta 2 acid. Hydrolysis to the delta 3 acid (the parent acid) was very slow. Analysis of the rate constants indicated that the isomerization rate k12 was approximately equal to the apparent degradation rate of the delta 3 ester kdeg, and slower than the hydrolysis rate of the delta 2 ester k24. The isomerization process to the delta 2 ester was found to be the rate-determining step in the degradation of cephalosporin esters. The substituent at the C-3 position of the cephalosporins affected the degradation kinetics. The degradation was accelerated by increase of pH, buffer concentration and added protein.