On the advantage over a random assignment

We initiate the study of a new measure of approximation. This measure compares the performance of an approximation algorithm to the random assignment algorithm. This is a useful measure for optimization problems where the random assignment algorithm is known to give essentially the best possible polynomial time approximation. In this paper, we focus on this measure for the optimization problems Max‐Lin‐2 in which we need to maximize the number of satisfied linear equations in a system of linear equations modulo 2, and Max‐k‐Lin‐2, a special case of the above problem in which each equation has at most k variables. The main techniques we use, in our approximation algorithms and inapproximability results for this measure, are from Fourier analysis and derandomization. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Determination of Pentachlorophenol and 1-Naphthol by Peroxyoxalate Chemiluminescence

Abstract

Peroxyoxalate chemiluminescence is used for the determination of pentachlorophenol and 1-naphthol in soil. 1-Naphthol is brominated to make it amenable to the procedure. Calibration curves are linear over concentration ranges spanning four orders of magnitude and limits of detection are at the micromolar level. the processes can be carried out in the soil without prior extraction of the analytes.     

C−N,C−S and S−S Bond Cleavage by Rhodium PCcarbeneP Pincer Complexes

Rhodium PC_carbeneP complexes 1‐L {L=PPh₃, PPh₂(C₆F₅)} react with isothiocyanate, carbodiimide and disulphide to enable C?S, C?N and S?S bond cleavage. The cleaved molecules are sequestered by the metal center and the pincer alkylidene linkage, forming η²‐coordinated sulfide or imide centered pincer complexes. When a C?S or S?S bond is cleaved, the resulting complexes can bridge two rhodium centers through sulphur forming dimeric complexes and eliminating a monodentate phosphine ligand.     

Characteristics of strontium isotopes and their implications in the Qixing Cave of Guizhou,China

The strontium isotopic compositions (87Sr/86Sr) of samples including soils, bedrock, soil waters, drip waters and their corresponding speleothems in the Qixing Cave (QXC), Guizhou Province, China, were systemically measured and analyzed. The results indicate that there are significant Sr isotopic differences among samples. The mean 87Sr/86Sr ratios in drip water for the samples 1#, 4# and 9# were 0.709568, 0.709139 and 0.708761, respectively, which possibly result from different flow paths, residence times, and other hydrogeological processes in the unsaturated zone overlying QXC. Meanwhile, levels of 40.8%, 57.6% and 72.4% of Sr in drip waters for 1#, 4# and 9#, respectively, were derived from bedrock dissolution, which was calculated by the mixture model of the two end-members (soil and bedrock). There is, however, no positive correlation between the relative proportion from bedrock dissolution (δ13C value is 1.8‰) and drip water δ13CDIC values. The mean drip water δ13CDIC value in 1# is the heaviest (–4.5‰) with the lowest contribution rate of bedrock dissolution, whereas the value in 9# is the lightest (–9.3‰) with the highest contribution rate of bedrock dissolution. The proportion from host rock dissolution in 4# is higher than that in 1# and lower than that in 9#, while its mean drip water δ13CDIC value (–8.6‰) is higher than that of 9# and lower than that for 1#. This suggests that the prior calcite precipitation (PCP) processes in the unsaturated zone overlying the cave are responsible for the δ13CDIC value differences between different drip waters, and not bedrock dissolution. Furthermore, this study also demonstrates that the 87Sr/86Sr ratios of speleothems in the 1# and 4# mainly reflect the variation in the relative proportions from the soil system (soil water) and bedrock dissolution overlying the cave. It is, therefore, feasible to use the strontium isotopic signals of speleothems as an indicator for soil chemical weathering intensity, and consequently as a monsoon proxy in the study area.     

超高效液相色谱-高分辨质谱确证分析泥鳅体内五氯酚代谢物

建立了超高效液相色谱-高分辨质谱(UPLC-HRMS)鉴定泥鳅体内五氯酚代谢物五氯酚磺酸酯的方法。将在低浓度五氯酚下暴露的泥鳅样品粉碎,采用含8%(体积分数)三乙胺的70%(体积分数)乙腈水溶液提取,经混合阴离子交换小柱萃取净化,在ACQUITY BEH C18色谱柱(100 mm×2.1 mm,1.7μm)上分离,采用电喷雾负离子(ESI-)一级质谱全扫描加数据依赖的二级质谱扫描(full mass-ddMS2)模式测定,获得代谢物的准分子离子、同位素离子和二级质谱碎片离子的精确质量数。结果表明,五氯酚在泥鳅体内的代谢以磺化为主,没有发现羟基化和葡萄糖醛酸化。代谢物主要为五氯酚磺酸酯,其含量随着暴露时间(t)的延长逐渐增加,当暴露时间为36 h时达到峰值,随后逐渐减小,当t≥120 h时,五氯酚磺酸酯含量基本维持不变。该方法可用于生物体内五氯酚的代谢研究。     

(P-Bis(pentafluorophenyl) substituted) PCP-pincer Ru(II) complexes: A theoretical study of the molecular structure and electronic properties

The differences between the molecular structures of the PCP-pincer complex [RuCl{C₆H₃(CH₂P(C₆H₅)₂)₂-2,6}(PPh₃)] ([RuCl(PCP^H)(PPh₃)], 1) and its tetrakis-pentafluorophenyl substituted analogue [RuCl{C₆H₃(CH₂P(C₆F₅)₂)₂-2,6}(PPh₃)] ([RuCl(PCP^F20)(PPh₃)], 2) have been rationalised by performing calculations on the cations [Ru(PCP^H)(PPh₃)]⁺ (1cat) and [Ru(PCP^F20)(PPh₃)]⁺ (2cat). The molecular interactions between the chloride ligand and the axial rings, as found in 1 and 2, respectively, have been studied computationally in the model systems [(C₆X₅PH₂)₂Cl⁻] (X = H, F). The calculations on 2cat show that in 2 it is most likely the attractive electrostatic interaction between the chloride ligand and the fluorinated phenyl rings that forces the C_ipso atom to occupy an axial position rather than an equatorial one in the observed (X-ray of 2) square pyramidal arrangement. In 1, however, repulsive steric hindrance forces the PPh₃ ligand to take the apical position. The applicability of the TD-DFT method for the calculation of the electronic spectra of the PCP-pincer compounds 1 and 2 has been tested. The results indicate that the excitation energies calculated for both complexes are in a reasonable agreement with the experimental absorption maxima. However, for 1, all the calculated transition energies are underestimated.     

W^＊—PCP与（W^＊—W）PCP的关系

本文证明了下面２个结果：（１）Ｗ＾＊－紧集Ｋ具有Ｗ＾＊－ＰＣＰ当且仅当Ｋ具有ＰＣＰ和Ｗ＾＊－稠密（Ｗ＾＊－Ｗ）ＰＣ点集；（２）Ｗ＾＊－紧集Ｋ具有Ｗ＾＊－ＰＣＰ当且仅当９Ｗ＾＊－Ｗ）ＰＣ（Ｋ）含有Ｋ的一个Ｗ＾＊－稠密Ｇδ子集。     

离子液体超声辅助萃取/LC-MS法测定环境水中痕量五氯酚

建立了离子液体超声辅助萃取/液相色谱-质谱联用测定环境水中痕量五氯酚(PCP)的方法。采用离子液体1-丁基-3-甲基咪唑六氟磷酸盐[C4mim][PF6]为萃取剂,考察了试样体积、p H值、温度、超声萃取时间和无机盐含量等因素对PCP萃取效率的影响,试样在XDB C18(150 mm×2.1 mm,5μm)色谱柱上,以甲醇-2 mmol/L醋酸铵溶液(70∶30)为流动相,电喷雾(ESI)电离负离子选择离子监测模式(SIM)进行测定。在优化的萃取条件下,PCP在0.005~1.0μg·L-1范围内具有良好线性,相关系数(r)为0.999 2,回收率为91.0%~97.0%,日内相对标准偏差(RSD)为1.1%~5.4%,日间RSD为3.8%~8.3%,定量下限为0.005μg·L-1。建立的方法简便、干扰少、特异性强,可用于环境水样中痕量PCP的测定。     

线性双层规划的改进PCP全局求解算法

本文采用K-T条件将线性双层规划模型改写为单层规划后,将参数引入上层目标函数,构造了含参线性互补问题(PLCP)并给出它的一些性质。进而通过改进Lemke算法的进基规则,在保持互补旋转算法原有优势的基础上,引入充分小正数ε,设计了改进参数互补旋转(PCP)算法求取全局最优解,最后通过两个算例说明了其有效性。     

Simple protocol for the synthesis of the asymmetric PCP pincer ligand [C6H4-1-(CH2PPh2)-3-(CH(CH3)PPh2)] and its Pd(II) derivative [PdCl{C6H3-2-(CH2PPh2)-6-(CH(CH3)PPh2)}]

The asymmetric PCP pincer ligand [C₆H₄-1-(CH₂PPh₂)-3-(CH(CH₃)PPh₂)] (4) has been synthesized in a facile manner in three simple steps in high yield. Metallation of PCP pincer ligand (4) with [Pd(COD)Cl₂] affords complex [PdCl{C₆H₃-2-(CH₂PPh₂)-6-(CH(CH₃)PPh₂)}] (7) in good yield.