Approximate first-order and second-order directional derivatives of a marginal function in convex optimization

Given a convex functionf: ^p × ^q (–, +], the marginal function is defined on ^p by (x)=inf{f(x, y)|y ^q }. Our purpose in this paper is to express the approximate first-order and second-order directional derivatives of atx ₀ in terms of those off at (x ₀,y ₀), wherey ₀ is any element for which (x ₀)=f(x ₀,y ₀).The author is indebted to one referee for pointing out an inaccuracy in an earlier version of Theorem 4.1.     

Theoretical and Experimental Studies on a Metallorganic Complex of (Isopropylxanthato)(Phenyl)Mercury(I) [Hg(I)(C<Subscript>6</Subscript>H<Subscript>5</Subscript>)(C<Subscript>4</Subscript>H<Subscript>7</Subscript>OS<Subscript>2</Subscript>)]

The title compound, (isopropylxanthato)(phenyl)mercury(I), was synthesized and characterized by elemental analysis, IR and thermogravimetric analysis. Density functional theory (DFT) method calculations were performed at B3LYP/CEP-121G and B3LYP/CEP-31G levels of theory, respectively. Vibrational frequencies were predicted, assigned, compared with the experimental values, and they are supported each other. The calculated results show that the strength of bond Hg—C is stronger than that of Hg—S, which is good agreement with the experimental data. The calculations of the second order optical nonlinearity and electronic absorption spectra are also performed.     

A comparison of double-focusing sector field ICP-MS, ICP-OES and octopole collision cell ICP-MS for the high-accuracy determination of calcium in human serum

Human serum is routinely measured for total calcium content in clinical studies. A definitive high-accuracy and low-uncertainty method is required for reference measurements to underpin medical diagnoses. This study presents a novel octopole collision cell ICP-MS, high-accuracy, methodology and comparison of that technique with double-focusing sector field ICP-MS and an ICP-OES method. Double-matched isotope dilution mass spectrometry (IDMS) was employed for ICP-MS techniques and an exact matching bracketing technique using scandium as an internal standard was used for ICP-OES analysis. Medium resolution mode was utilised for double-focusing sector field ICP-MS analysis to resolve the dominant interferences on the ⁴⁴Ca/⁴²Ca isotope pair. Hydrogen reaction gas was employed to chemically resolve a number of polyatomic interferences predominantly through charge transfer reactions in the octopole collision cell. Comparison data presented for NIST CRM 909b human serum analysis from all three techniques demonstrates highest accuracy (99.6%) and lowest uncertainty (1.1%) for octopole collision cell ICP-MS. Data from ICP-OES using a non-IDMS technique produces comparably accurate data and low-uncertainties. The much higher total expanded uncertainties for double-focusing sector field ICP-MS compared with octopole collision cell data are explained by lower precision on the measurement of the ⁴⁴Ca/⁴²Ca isotope ratio. Data for octopole collision cell ICP-MS submitted for an international blind trial comparison (CCQM K-14) demonstrated excellent agreement with the mean of all participants with a low expanded uncertainty.     

Identification of micro-scale calorimetric devices

Micro-calorimetric devices using Si-based sensors are very useful for the study of gas–solid reactions, in which very low mass of reactants are necessary. But in fact the consequence of using flat detectors is an increase of the uncertainty in the measured energy. In this work a calorimetric gas sensor based on Xensor chip is analysed studying the local x–y contributions of dissipation to the sensitivity related to the value in the centre. We study also the effects of the gas-flow on the sensitivity, comparing the results obtained with two Xensor type chips. Finally we carry out a deeper analysis of the x–y effects on the calorimetric detector for dissipations in the reactant shell extremely close to the detector surface to visualize the link between the power density distribution and the output signal.     

2-苯基苯并咪唑衍生物非线性光学性质的从头算研究

采用HF／6-31G^*方法优化分子构型，在此基础上用CPHF方法系统地研究了多种基团取代的2-苯基苯并咪唑衍生物的二阶非线性光学系数βvec，并对βvdc的影响因素进行了探讨，为进一步设计综合性能优良的有机非线性光学材料提供理论指导．     

The predictive accuracy for estimating infinite dilution activity coefficients by γ∞-based UNIFAC

The predictive accuracy for estimating infinite dilution activity coefficients by a modification of the UNIFAC method wherein the group interaction parameters were based on only data (referred to as -based UNIFAC) has been studied. Estimates and measured values were compared for six prototypical solutes in a series of homologous n-alkanes, l-alcohols and alkanenitrile solvents. Despite the fact that the interaction parameters were derived using only data, this approach still gave serious errors due to several inherent problems in the original UNIFAC model. Its performance is sometimes even poorer than that of the original UNIFAC method. For example for nitromethane in alcohols and p-dioxane in nitriles values predicted by the -based UNIFAC are essentially zero. The large errors for these systems are most likely due to inaccurate interaction parameters in the -based UNIFAC method.     

亚烷基卡宾与甲醛环加成反应机理的理论研究

用二阶微扰理论研究了单重态亚烷基卡宾与甲醛发生的三种环加成反应的机理 ，采用MP2/6－31G~*方法计算了势能面上各驻点的构型参数、振动频率和能量。根 据能量数据可以预言环加成反应（1）的a途径将是单重态亚烷基卡宾与甲醛环加成 反应的主要反应通道，该反应由两步组成：（I）亚烷基卡宾与甲醛生成了一富能 中间体（INT1a），是一无势垒的放热反应，（II）中间体异构化为产物亚烷基环 乙烷，其势垒为24.1 kJ·mol~(-1)(MP2/6-31G~*)。     

Accurate Gaussian basis sets for the H2O molecule generated with the molecular improved generator coordinate Hartree–Fock method

The molecular improved generator coordinate Hartree–Fock (MIGCHF) method is used to generate accurate basis sets of primitive Gaussian-type functions for the H₂O molecule. Sequences of increasing size atom centered basis sets are employed to explore the accuracy that can be achieved with this method. Using the O(24s14p8d5f2g1h);H(22s9p5d2f1g) basis set, the HF and second-order electron correlation energies of the H₂O ground state at the experimental geometry are computed as −76.0674680 and −0.3491935 hartree, respectively. The HF energy is in error by 20 μhartree and the second-order correlation energy corresponds to 96.5% of an estimate of the limiting value. The relevance of the present calculations is to show the accuracy that can be achieved in studies of small polyatomic molecules with the MIGCHF method.     

Effects of Lead on Temporal Response Properties of Retinal Ganglion Cells in Developing Rats

Neonatal rats have taken in lead, during the period from their parturition to their weaning, from the milk of dams fed with water containing 0.2% lead acetate solutions. The alterations in the temporal response properties of retinal ganglion cells in adult rats (90 days) following the lead exposure at their developing stage have been studied. The results of this investigation demonstrate that the lead exposure in neonatal rats causes decreases in the optimal temporal frequency, bandwidth at half amplitude, temporal resolution and response phase of the retinal ganglion cells in adult rats. Compared with the sustained cells, the transient cells have a much greater alteration in temporal response properties.     

水中溶解氧的微量滴定

将微量滴定技术应用于常规的碘量法测定水中溶解氧。在实验中采用了WD-CO3型微量滴定装置，并使用自行设计制成的高精度微量移液管（移液的体积可准确至0．001mL），作为转移标准溶液及试样溶液的工具。对微量滴定及微量移液与常量滴定和常量移液作了对比试验，结果表明两者的分析结果完全吻合，微量滴定（其中包括微量移液）所得结果的精密度也在定量分析允许范围之内。由此，微量滴定技术应用于水中溶解氧的日常分析的可行性得到了验证。