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.     

The Adsorption and Thermal Decomposition of CH2CO (CD2CO) on Si(111)-7 × 7

The adsorption and thermal decomposition of ketene on Si(l 11)-7 × 7 were investigated using various surface analysis techniques. When the surface was exposed to ketene at 120 K, two CO stretching modes at 220 and 273 meV appeared in HREELS, corresponding to two adsorbed ketene states. After the sample was annealed at ?250 K, the 273 and the 80 meV peaks vanished, indicating the disappearance of one of the adsorption states by partial desorption of the adsorbate. In a corresponding TPD measurement, a desorption peak for ketene species was noted at 220 K. Annealing the sample at 450 K caused the decomposition of the adsorbate, producing CH_x and O adspecies. Further annealing of the surface at higher temperatures resulted in the breaking of the CH bond, the desorption of H and O species and the formation of Si carbide. The desorption of H at 800 K was confirmed by the appearance of the D₂ (m/e = 4) TPD peak at that temperature when CD₂CO was used instead of CH₂CO.     

CF3CO和CF3C（O）O自由基分解反应理论研究

利用文献结果，用统计热力学和过渡态理论计算了ＣＦ３ＣＯ和ＣＦ３Ｃ（Ｏ）Ｏ自由基分解反应的热力学和动力学数据。计算结果表明，计算值与最新实验数据甚相符合，并据此判断，ＣＦ３ＣＯ和ＣＦ３Ｃ（Ｏ）Ｏ均很不稳定，不可能参加Ｏ３分解的循环催化反应。     

On the Proper Normalization Constraint

In the variational optimization of a trial function the proper functional to be varied is the Rayleigh quotient with the normalization constraint explicitly imposed. It will be shown that only under certain very rigorous conditions can one use the energy functional to replace the Rayleigh quotient and that, therefore, the normalization constraint is by no means a matter of no consequence.     

Direct transformation of variational problems into Cauchy systems. I. Scalar-quadratic case

This series of papers addresses three interrelated problems: the solution of a variational minimization problem, the solution of integral equations, and the solution of an initial-valued system of integro-differential equations. It will be shown that a large class of minimization problems requires the solution of linear Fredholm integral equations. It has also been shown that the solution of a linear Fredholm integral equation is identical to the solution of a Cauchy system. In this paper, we bypass the Fredholm integral equations and show that the minimization problem directly implies a solution of a Cauchy system. This first paper in the series looks only at quadratic functionals and scalar functions.This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-77-3383.     

Preparation of nanometer FeCuP alloy and its application in decomposition of PH3

A new ternary Fe-based alloy catalyst FeCuP applied to decompose PH_3 was prepared with low-cost material by chemical reduction deposition method.The properties of it were characterized by XRD,ICP and SEM.Its catalytic activity on the decomposition of PH_3 and the decomposition conditions were studied.FeCuP alloy exhibits high thermal stabilities and high catalytic activity.Using it as catalyst,the decomposition temperature of phosphine decreases from over 800℃to 400-500℃.The decomposition rate of phosphine achieved 100%.     

Test of variational transition state theory with multidimensional tunneling contributions against experimental kinetic isotope effects for the CHnD4−n + OH→P (n=0, 4) reactions

 Variational transition state theory including tunneling corrections (as implemented in Polyrate 8.7) and using multilevel energy calculations at the MCCM-CCSD(T)-1sc level for the CH₄ + OH reaction and at the MCCM-CCSD(T)-2m level for the CD₄ + OH process, reproduces very well the experimental rate constants. However, no single methodology was found that reproduces equally well the experimental rate constants for both title reactions. Received: 24 March 2002 / Accepted: 11 April 2002 / Published online: 4 July 2002     

氟化钾负载改性法制备碱性NaY沸石

氟化钾（ＫＦ）可以高度分散于八面沸石表面，通过与ＮａＹ沸石表面发生相互作用产生ＫＯＨ类碱物种，使ＫＦ／ＮａＹ具有类似于ＫＯＨ／ＮａＹ的碱性，在异丙醇探针反应的碱性催化活性也与ＫＯＨ／ＮａＹ相似，由于沸石中的Ｓｉ组分容易与ＫＯＨ生成强度低的碱性化合物，妨碍ＫＦ或ＫＯＨ负载过程中强碱位的生成，因此ＫＦ／ＮａＹ的碱强度介于ＫＦ／ＳｉＯ２和ＫＦ／γ－Ａｌ２Ｏ３之间。     

SiO2—Al2O3和MgO催化剂上吸附CH3NO2的TPD和IR研究

用TPD和IR方法研究了CH_3NO_2在典型固体酸SiO_2-Al_2O_3和固体碱MgO催化剂上的吸附分解。结果表明,在SiO_2-Al_2O_3表面CH_3NO_2吸附转化为表面甲酰胺物种,后者在高温下分解为CO_2和NH_3。在MgO表面CH_3NO_2吸附形成多种表面化学物种,它们在升温过程中脱附,并通过表面亚硝基甲烷物种分解为NO、C_2H_4、C_2H_6和N_2O.讨论了CH_3NO_2分解过程中表面酸、碱中心的作用。     

Kinetics study of thermal decomposition of epoxy resins containing flame retardant components

Hyperbranched polyphosphate ester (HPPE) and phenolic melamine (PM) were blended in different ratios with a commercial epoxy resin to obtain a series of flame retardant resins. The thermal decomposition mechanism of their cured products in air was studied by thermogravimetric analysis and in situ Fourier-transform infrared spectroscopy. The degradation behaviours of epoxy resins containing various flame retardant components were found to be greatly changed. The incorporation of phosphorus and nitrogen compounds improved the thermal stability at elevated temperature. The kinetics of thermal decomposition was evaluated by Kissinger method, Flynn-Wall-Ozawa method and Horowitz-Metzger method. The results showed that the activation energy at lower degree of the degradation decreased by the incorporation of flame retardant components, while increased at higher degree of the degradation.