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.     

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.     

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.     

萜品油烯的DeMayo光环加成产物的反应研究

通过萜品油烯和2，6-二氧代戊酸甲酯的de Mayo反应，使[2 + 2]环加成产物 3-6经retro-aldol重排，开环生成取代环己烯7和12。在不同反应介质中对开环产 物进行再环合，并对其反应机理进行研究。在碱性条件下，经分子内Claisen缩合 反应形成螺环化合物；以对甲本碘酸为催化剂的环合，除生成正常的Claisen缩合 产物以外，7和12均发生烯键亲核加成反应，生成具有二环[3.3.1]结构的桥环化合 物9-11和二环[3.2.1]结构的桥环化合物16-18。所得新化合物的化学结构均经IR, ~1H NMR，~(13)C NMR及元素分析予以确定。