The Newton modified barrier method for QP problems

The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues, to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a hot start. Starting at such a hot start, at mostO(In In ^-1) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, >0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that onlyO(In ^-1)O(In In ^-1) Newton steps are required to reach an -approximation to the solution from any hot start. In order to reach the hot start, one has to perform Newton steps, wherem characterizes the size of the problem andC>0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.Partially supported by NASA Grant NAG3-1397 and National Science Foundation Grant DMS-9403218.     

HPLC study of the binding of sulfinpyrazone to serum albumin

Summary A thin layer chromatographic method for a qualitative screening-test and a quantitative analysis of 2,4,6-TNT, biodegradation products, octogen and hexogen in ammunition wastes was developed using both polar and non-polar modified sorbents. For enrichment a solidphase extraction on LiChrolut® EN followed by removal with methanol/acetonitrile (11 v/v) was chosen. To imitate real samples, spiked tap water samples of known composition were used.     

A new symmetrically modified α-cyclodextrin tripode: selective metal complexation and fluorescence properties

A new tripodal α-cyclodextrin having three ureido-bipyridyl tethers symmetrically distributed on its upper rim was prepared in one step by the polymer supported ‘phosphine imide’ reaction in a medium yield. As expected, the highly selective complexation properties towards ‘hard’ and ‘soft’ cations were maintained with regards to the URFT-Cd (upper rim fully tethered) family previously investigated. Its Eu^III and Tb^III lanthanide complex fluorescence behaviour clearly indicates that a limited number of tethers allow a better bis-heterocyclic antenna self-organisation around the cation leading to enhanced fluorescence properties.     

Amperometric detection of nitrite and nitrate at tetraruthenated porphyrin-modified electrodes in a continuous-flow assembly

The modification of a glassy carbon surface by coating with an electrostatically assembled film of tetraruthenated cobalt porphyrin/(meso-tetra(4-sulphonatephenyl)porphyrinate zinc(II) yields an indicator electrode that allows the determination of nitrite to be performed with a limit of detection of 0.1 μM in a flow injection configuration. The dynamic range extends up to 1000 μM and the repeatability of the measurements was evaluated to be 1.5% with a throughput of 50 samples per hour. The efficiency of the bilayered film to mediate the electron transfer allows the determinations to be performed at a less positive potential (+0.75 V) with enhanced sensitivity. The coating also prevents the surface poisoning and its stability is maintained over several weeks. The same detector was used for determination of nitrate after reduction to nitrite in a reductor column containing copperised cadmium. This method was used for the determination of nitrate and nitrite in mineral water, saliva and cured meats, the results being in agreement with certified values and those obtained by using recommended procedures.     

双波长分光光度法同时测定浆料中的聚乙烯醇和淀粉

本文报道了用双波长分光光度法同时测定变性聚乙烯醇和淀粉醋酸酯的一种新方法。分别选择670.0～540.0nm以及590.0～730.0nm波长对测定变性聚乙烯醇和淀粉醋酸酯。变性聚乙烯醇)～32μg/ml,淀粉醋酸酯0～130μg/ml浓度范围内,吸光度差值△A遵循比耳定律。当淀粉醋酸酯与变性聚乙烯醇的浓度比在1.3～16范围内,变性聚乙烯醇和淀粉醋酸酯的样品回收率分别为99.5～105%和97～108%。所拟定的方法可测定浆料中变性聚乙烯醇和淀粉醋酸酯。本法与盐酸水解淀粉法测定的聚乙烯醇含量相吻合。本法简便快速。     

辅酶Ⅰ在Co／CFUE上的电化学行为及应用

辅酶I(NAD+)在0.005moL/LTris 0.01moL/LNaCl溶液(pH7.0)中,于钴离子注入修饰碳纤维电极上出现一个S形的还原波,半波电位为-1.45V(vs.SCE)。峰电流与NAD+的浓度在2.38×10-5～4.76×10-4mol/L(r=0 9992)和4.76×10-4～1.78×10-3mol/L(r=0.9982)之间成线性关系,检出限为1.19×10-5mol/L,回收率在96.7%～103.4%之间。用线性扫描、循环伏安法研究了钴离子注入修饰碳纤维电极上NAD+的电化学行为。电极反应机理为:NAD++e NAD·;NAD·+e+H+ NADH;2NAD·→NAD2。另外,钴离子注入修饰碳纤维电极对NAD+具有电催化作用。     

A Siloxane Homopolymer with Interacting Ferrocenes as a New Material for the Preparation of Sensors Based on the Detection of Hydrogen Peroxide

The electrochemical characterization of a hydrogen peroxide sensor based on a ferrocene‐containing polymer electrochemically deposited onto a platinum electrode is described. The redox polymer consists of a siloxane‐based homopolymer, with pendant electronically communicated ferrocenyl moieties. The electrodes were used as the transducer for glucose and lactate‐sensing enzyme sensors. Amperometric biosensors were prepared by immobilization of glucose oxidase (Gox) or lactate oxidase (Lox) onto these modified electrodes. The steady‐state amperometric response of the sensors is investigated as a function of the applied potential and substrate concentration. Interferences, sensitivity and stability of the sensors were also studied.     

离子注入修饰电极检测硝基苯

离子注入是一种新技术，可按人们的意愿和需要，将不同的离子注入不同的基本电极表面，制成具有催化活性强，稳定性高，重现性好等特点的修饰电极。作者研究了离子注入钴和注入镍的玻碳电极在０．１ｍｏｌ／ＬＨＡｃ－ＮａＡｃ缓冲溶液中硝基苯的行为及测定。     

溶胶-凝胶-钴-邻菲啰啉修饰电极对一氧化氮的电催化氧化及其测定

报道了溶胶 凝胶 钴 邻菲口罗啉膜修饰电极的制备方法及其在一氧化氮(NO)检测中的应用,采用循环伏安法(CV)研究修饰电极的电化学特性,差示脉冲伏安法(DPV)对NO进行检测。该修饰电极对NO的电化学氧化具有很好的催化作用,使其氧化电位负移了210mV,氧化峰电流与NO浓度在5.6×10-8～2.8×10-5mol/L范围内呈良好的线性关系,相关系数r=0.999,检测限为1.4×10-8mol/L,且生物体内常见的干扰物质如抗坏血酸、NO2-和儿茶酚胺类神经递质的代谢物等不干扰测定。     

High performance liquid chromatographic studies on lanthanides, uranium and thorium on amide modified reversed phase supports

The retention behavior of uranium, thorium and lanthanides has been investigated with amide modified reversed phase C₁₈ supports using α-hydroxy isobutyric acid (α-HIBA) as the mobile phase. Four structurally different amide moieties namely, 4-hydroxy-N,N-dihexyl butyramide (4HHBA), 4-hydroxy-N,N-di-2-ethylhexylhexanamide (4HEHHA), bis(N,N,N′,N′-2-ethylhexyl)malonamide (B2EHM) and N-methyl-tris(dihexylcarbamoyl-3-methoxy)pivolamide (MTDCMPA) have been synthesized and studied. Among the various amide coated columns, the supports modified with 4HHBA, B2EHM and MTDCMPA exhibit an interesting retention for uranium and thorium, which is different from 4HEHHA modified support. The retention time for uranium and thorium increases with increasing amide concentration for 4HHBA, B2EHM and MTDCMPA supports, while the same decreases with increasing 4HEHHA content. However, the separation factor for uranium and thorium is greater on a 4HEHHA support, compared to an unmodified C₁₈ column, reflecting the amide's preferential complexation of uranium over thorium.Columns modified with 4HHBA, B2EHM and MTDCMPA exhibit relatively higher retentions for lanthanides. However, MTDCMPA modified support shows a different elution profile for lanthanides compared to 4HHBA, and B2EHM modified columns. Individual separations of heavier lanthanides, i.e., from gadolinium to lutetium also have been achieved using 4HHBA and B2EHM modified supports.The influence of modifier content, mobile phase concentration and its pH on the retention of metal ions has also been studied. Based on these investigations, an efficient high performance liquid chromatographic method (HPLC) has been developed for the rapid separation of uranium from thorium as well as for the individual separation of heavier lanthanides.