On Constraint Qualifications in Nonsmooth Optimization

We introduce extensions of the Mangasarian-Fromovitz and Abadie constraint qualifications to nonsmooth optimization problems with feasibility given by means of lower-level sets. We do not assume directional differentiability, but only upper semicontinuity of the defining functions. By deriving and reviewing primal first-order optimality conditions for nonsmooth problems, we motivate the formulations of the constraint qualifications. Then, we study their interrelation, and we show how they are related to the Slater condition for nonsmooth convex problems, to nonsmooth reverse-convex problems, to the stability of parametric feasible set mappings, and to alternative theorems for the derivation of dual first-order optimality conditions.In the literature on general semi-infinite programming problems, a number of formally different extensions of the Mangasarian-Fromovitz constraint qualification have been introduced recently under different structural assumptions. We show that all these extensions are unified by the constraint qualification presented here.     

多目标半定规划的互补弱鞍点和G-鞍点最优性条件

对于含矩阵函数半定约束和多个目标函数的多目标半定规划问题，给出Lagrange函数在弱有效意义下的互补弱鞍点和Geofrrion恰当有效意义下的G-鞍点的定义及其等价定义．然后，在较弱的凸性条件下，利用含矩阵和向量约束的择一性定理，建立多目标半定规划的互补弱鞍点和G-鞍点充分必要条件．     

An Alternative Approach to the Extraction of Structure Functions in Deep Inelastic e-p Scattering at 5 to 20 GeV

Two structure functions W1(x,Q2) and W2(x,Q2) are determined by using the cross sections measured in the deep inelastic electron-proton scattering experiments at Stanford Linac in the energy range of 5 to 20 GeV. In this paper an alternative mathematical approach have been used in such determination, resulting in a larger number of points in the graphs of the structure functions.     

Energy Recovery from Municipal Solid Waste in Small Communities

The heating values of municipal solid waste generated in three towns with a population of less than 50 000, situated in Galicia (Spain), were measured with a static bomb calorimeter. Samples of raw refuse were burnt either as received or after sorting of the different combustible components. A study was made of samples from controlled and uncontrolled landfills. The calorific values were compared with those corresponding to a commercial residual derived fuel in order to study the possibility of using municipal solid waste as a source of recovered energy. This revised version was published online in July 2006 with corrections to the Cover Date.     

旋转铂盘电极上Cu(phen)_2~(2 )与6-巯基嘌呤的相互作用

在Tris-NaC1*(pH=7.2)缓冲溶液中,应用循环伏安法,微分脉冲伏安法、旋转圆盘电极实验、交流阻抗法及其数据模拟等技术研究了Cu(phen)2 25(phcn=1.10-邻菲咯啉)与6-巯基嘌呤(6-MP)的相互作用.结果显示.Cu(phen)2 2MP与6-MP无论在扩散控制过程或电化学控制过程都发生了相互作用.Cu(phen)2 2及其与6-MP的作用产物于铂电极上均呈现一对氧化还原峰,但后者呈现的氧化还原峰负移.峰电流减小.交流阻抗结果显示,无论6-MP存在与否,Cu(phen)2 2在交流阻抗谱上均呈现两个清晰的电容弧,但当6-MP存在时,电化学反应电阻和电化学吸脱附电阻均增大.Cu(phen)2 2在不同转速下的阻抗拟合结果显示.随转速增大.电化学反应电阻和电化学吸脱附电阻均减小.双电层电容呈增大趋势,而吸脱附电容呈减小趋势:当6-MP存在时.仍然呈现此变化规律.     

Asymptotic expansions of the distributions of some test statistics

Summary A modified Wald statistic for testing simple hypothesis against fixed as well as local alternatives is proposed. The asymptotic expansions of the distributions of the proposed statistic as well as the Wald and Rao statistics under both the null and alternative hypotheses are obtained. The powers of these statistics are compared and its is shown that for special structures of parameters some statistics have same power in the sence of order . The results obtained are applied for testing the hypothesis about the covariance matrix of the multivariate normal distribution and it is shown that none of the tests based on the above statistics is uniformly superior. Research supported by the National Science Foundation Grant MCS 830149.     

共聚物配体交替结构与其催化活性关系的理论研究

本文采用以ASED-MO(含原子对排斥的EHMO法)为基础的结构自动优化的EHTOPT法及Monte-Carlo法, 对甲醇羰基化制乙酸催化剂的共聚物配体交替结构进行了理论研究。计算了AA, AB, BB, BA二聚反应的反应途径, 找出了过渡态, 并确定了反应活化势垒。在假设两反应频率因子相同的前提下, 求出竞聚率, 采用Monte-Carlo法模拟共聚物结构, 计算出共聚物配体中起催化活性的AB交替结构所占比率。比较不同共聚物配体的活性, 并研究了温度及单体配比对共聚物配体交替结构的影响。     

Convexlike and concavelike conditions in alternative,minimax, and minimization theorems

Convexlike and concavelike conditions are of interest for extensions of the Von Neumann minimax theorem. Since the beginning of the 80's, these conditions also play a certain role in deriving generalized alternative theorems of the Gordan, Motzkin, and Farkas type and Lagrange multiplier results for constrained minimization problems.In this paper, we study various known convexlike conditions for vector-valued functions on a set and investigate convexlike and concavelike conditions for real-valued functions on a product setC×D, where we are mainly interested in the relationships between these conditions. At the end of the paper, we point out several conclusions from our results for the above-mentioned mathematical fields.The author is indebted to Dr. R. Reemtsen and Dr. V. Jeyakumar for their helpful comments during the preparations of this paper.     

Contribution à l'étude Électrochimique de Dérivés de l'Acide Mercapto-2 Pyridinecarboxylique-5. II

Abstract

Electrochemical caracteristics of 2-mercaptopyridine-5-carboxylic acid and its methylic ester have been determined using recent polarographic techniques. Measurements have been carried out as a function of parameters such as frequency, others surimposed signals and as a function of concentration and pH. Results are compared to those obtained for selectively methylated on sulfur or nitrogen atoms derivatives. Interpretations of the data are given. The optimal conditions for a quantitative determination by D.C. and differential pulse polarography are fixed.     

Application of topological degree theory to semi-definite complementarity problem

The topological degree theory is applied to study the problem of existence of solutions to the semi-definite complementarity problem (SDCP). A notion of an exceptional family of matrices is introduced, and assertions of a non-strict alternative type are obtained. Namely, for a continuous mapping, there exists at least one of the following two items: either a solution to the SDCP, or an exceptional family of matrices. Hence, if there is no exceptional family, then at least one solution exists