A generalized Dantzig—Wolfe decomposition principle for a class of nonconvex programming problems

Since Dantzig—Wolfe's pioneering contribution, the decomposition approach using a pricing mechanism has been developed for a wide class of mathematical programs. For convex programs a linear space of Lagrangean multipliers is enough to define price functions. For general mathematical programs the price functions could be defined by using a subclass of nondecreasing functions. However the space of nondecreasing functions is no longer finite dimensional. In this paper we consider a specific nonconvex optimization problem min {f(x):h _j (x)g(x),j=1, ,m, xX}, wheref(·),h _j (·) andg(·) are finite convex functions andX is a closed convex set. We generalize optimal price functions for this problem in such a way that the parameters of generalized price functions are defined in a finite dimensional space. Combining convex duality and a nonconvex duality we can develop a decomposition method to find a globally optimal solution.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.     

On the nature of the transition state in catechol O-methyltransferase. A complementary study based on molecular dynamics and potential energy surface explorations

The way in which enzymes influence the rate of chemical processes is still a question of debate. The protein promotes the catalysis of biochemical processes by lowering the free energy barrier in comparison with the reference uncatalyzed reaction in solution. In this article we are reporting static and dynamic aspects of the enzyme catalysis in a bimolecular reaction, namely a methyl transfer from S-adenosylmethionine to the hydroxylate oxygen of a substituted catechol catalyzed by catechol O-methyltransferase. From QM/MM optimizations, we will first analyze the participation of the environment on the transition vector. The study of molecular dynamics trajectories will allow us to estimate the transmission coefficient from a previously localized transition state as the maximum in the potential of mean force profile. The analysis of the reactive and nonreactive trajectories in the enzyme environment and in solution will also allow studying the geometrical and electronic changes, with special attention to the chemical system movements and the coupling with the environment. The main result, coming from both analyses, is the approximation of the magnesium cation to the nucleophilic and the hydroxyl group of the catecholate as a result of a general movement of the protein, stabilizing in this way the transition state. Consequently, the free energy barrier of the enzyme reaction is dramatically decreased with respect to the reaction in solution.     

酰胺型萃取剂N-503的合成

酰胺型萃取剂N-503[N,N-二-(1-甲基庚基)乙酰胺]可以用甲庚醇或2-氯代辛烷为原料来合成。它的重要中间体二-(1-甲基庚基)胺的制备方法有二:一是从甲庚醇制备的方法,将甲庚醇用阮来镍催化,常压氨解,得率95～99％左右;二是从2-氯代辛烷制备,此法需要高压设备,得率35％左右。第一个方法在扩大试验中,产率和产品质量都比较好,是一个较好的制备长碳链仲胺的方法。     

Visual recognition of melamine in milk via selective metallo-hydrogel formation

A novel protocol allowing convenient and highly selective visual recognition of melamine in raw milk via selective metallo-hydrogel formation at a concentration as low as 10 ppm without any tedious pretreatment has been developed.     

Determination of sulfur dioxide in vitriol plant wastewater by using a polyNiMe4TAA electrochemically modified Pt microelectrode

A Pt microelectrode modified with nickel(II) polytetramethyldibenzo[b,i]tetraaza[14]annulene was prepared by electropolymerization of nickel(II) tetramethyldibenzo[b,i]tetraaza[14]annulene monomers and applied to determine sulfur dioxide in vitriol plant wastewater. For determination of SO2 with this electrochemically modified Pt microelectrode, the linear range was from 9.6 x 10(-6) to 2.4 x 10(-4) mol L-1, the sensitivity was 1.8 x 10(-4) A L mol-1, the detection limit was calculated to be 4.8 x 10(-6) mol L-1 (S/N = 3), the response time was less than 20 s and the relative standard deviation was found to be 2.1% on analyzing 4.8 x 10(-5) mol L-1 SO2 solution repeatedly (n = 7). These results demonstrated good accuracy compared with those obtained by the conventional iodimetric method.