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.     

高脂饮食对小鼠脂肪代谢和矿物元素代谢的影响

为探讨高脂饮食对小鼠脂肪代谢和矿物元素代谢的影响,用昆明(KM)小鼠24只,出生28 d后随机分成2组,各12只,分别给予高脂饲料与普通饲料,饲养至第9周眼球取血处死,取皮下、腹腔、肠系膜脂肪,毛,肝,血,计算体质量脂肪质量比,测定毛、肝、血中Zn、Ca、Cu、Mn、Mg、Fe含量。结果表明,高脂饮食小鼠体质量增加(P<0.05),单位腹腔脂肪及血Ch显著性增加(P<0.01)。肝Zn、Cu、Mg、Fe、Mn显著降低(P<0.01),血凝块Zn升高(P<0.05),Cu降低(P<0.05),毛Mg降低(P<0.05)。提示高脂饮食引起体质量与血脂增加,脂肪堆积,矿物元素代谢紊乱;不同器官矿物元素的代谢紊乱有差异,以肝脏最显著。     

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.     

On-line enzymatic reaction,extraction, and chromatography of fatty acids and triglycerides with supercritical carbon dioxide

Supercritical carbon dioxide can be utilized both as an introduction solvent in capillary SFC and as a reaction medium; both possibilities are illustrated in this study. An off-line SFE unit was modified for on-line SFE-SFC. To facilitate rapid depressurization of the extraction cell and to prevent memory effects, a 6-port valve was installed at the outlet line of the extraction unit. An increased background signal was obtained when PEEK polymer was used in the construction of the extraction vessel; when stainless steel was used, the blanks improved. The synthesis of methyl esters and butyl esters of fatty acids from triglycerides in edible fat was examined using an immobilized lipase as a catalyst in on-line SFE-SFC. As a result of 30 minutes reaction – extraction time, high yields of fatty acid esters were obtained at a pressure of 150 bar and a temperature of 50°C.     

Thermal transitions and fat droplet stability in ice-cream mixmodel systems

We studied thermal transitions and physical stability of oil-in-water emulsions containing different milk fat compositions, arising from anhydrous milk fat alone (AMF) or in mixture (2:1 mass ratio) with a high melting temperature (AMF–HMT) or a low melting temperature (AMF–LMT) fraction. Changes in thermal transitions in bulk fat and emulsion samples were monitored by differential scanning calorimetry (DSC) under controlled cooling and reheating cycles performed between 50 and –45°C (5°C min^–1). Comparison between bulk fat samples and emulsions indicated similar values of melting completion temperature, whereas initial temperature of fat crystallization (T_onset) seemed to be differently affected by storage temperature depending on triacylglycerols (TAG) composition. After storage at 4°C, T_onset values were very similar for emulsified and non-emulsified AMF–HMT blend, whereas they were lower (by approx. 6°C) for emulsions containing AMF or mixture of AMF–LMT fraction. After storage at –30°C, T_onset values of re-crystallization were higher in emulsion samples than in bulk fat blends, whatever the TAG fat composition. Light scattering measurements and fluorescence microscopic observations indicated differences in fat droplet aggregation-coalescence under freeze-thaw procedure, depending on emulsion fat composition. It appeared that under quiescent freezing, emulsion containing AMF–LMT fraction was much less resistant to fat droplet aggregation-coalescence than emulsions containing AMF or AMF–HMT fraction. Our results indicated the role of fat droplet liquid-solid content on emulsion stability.     

Partially concurrent eluent evaporation with an early vapor exit; detection of food irradiation through coupled LC-GC analysis of the fat

This paper reports two subjects. It describes LC-GC transfer by partially concurrent eluent evaporation at a greatly accelerated rate, as required for optimal compatibility with 2–3 mm i.d. LC columns and LC flow rates up to some 500 μl/min. Evaporation rates around 200 μl/min were obtained using a 0.53 mm. i.d. uncoated pre-column and an early vapor exit. A stationary-phasecoated “retaining” pre-column was used for preventing escape of volatile solutes through the vapor exit. The technique was used for the detection of food irradiation by analyzing selected radiolysis products of triglycerides, namely alkanes/alkanes and aldehydes. Extracted fat of chicken, hazel-nuts, and soup mixes was injected in LO and the relevant fractions were transferred on-line to GC. For chicken and nuts, detection of irradiation was possible down to doses below 0.5 kGy. Detection limits were higher for soup mixes due to interfering peaks.