改进的PNC方法及其在非线性偏微分方程多解问题中的应用

2017年，李昭祥等提出了一种偏牛顿-校正法（Partial Newton-Correction Method，简记为PNC方法），并利用它成功地计算出了三类非线性偏微分方程的多重不稳定解.本文在PNC方法的基础上，提出并发展了一种改进的PNC方法.首先，利用Nehari流形$\mathcal{N}$与零平凡解的可分离性，建立并证明了$\mathcal{N}$的某特殊子流形$\mathcal{M}$上的全局分离定理及其推广（即局部分离定理）.全局分离定理只跟非线性偏微分算子或相应的非线性泛函本身有关，而与具体的计算方法无关.对一些典型的非线性偏微分方程多解问题（比如，Henon方程问题），该全局分离定理的分离条件，经验证是成立的.另一个方面，通过修改或补充原辅助变换的定义，去掉了原辅助变换的奇异性；接着建立并证明了某些非线性偏微分方程问题的新未知解与该非线性偏微分算子零核空间的密切关系；在证明中，去掉了在原奇异变换下所需的标准收敛（standard convergence）假设.最后，计算实例与数值结果验证了改进的PNC方法的可行性和有效性；同时表明子流形$\mathcal{M}$与已知解的可分离性是PNC方法和本文新方法能成功找到多解的关键.     

基于2,5-二溴对苯二甲酸配体的锌/钴配合物合成、晶体结构及性质

将有机物2,5-二溴对苯二甲酸(H₂L₁)和2,2′-联吡啶(L₂)作为双配体,使用溶剂热法和七水合硫酸锌(ZnSO₄·7H₂O)、六水合硝酸钴(Co(NO₃)₂·6H₂O)分别反应,得到配合物[Zn(L₁)(L₂)(H₂O)]_n(1)和配合物[Co(L₁)(L₂)(H₂O)]_n(2)。采用单晶X射线衍射、元素分析、红外光谱、紫外光谱、荧光光谱、热重分析等测试方法对这两种物质进行分析研究。单晶测试结果表明配合物1是单斜晶系,以Zn²⁺配位连接L^2-₁与L₂形成一维链状结构,各条链在分子间氢键和π…π共轭作用下有规律地堆叠形成三维网络结构。配合物2是三斜晶系,Co1离子和Co1ⁱ离子由H₂L₁上的羧酸氧原子O4和O4ⁱ连接,形成双齿螯合的配位结构单元,以Co²⁺配位连接 L^2-₁和L₂形成二维网格结构,各层在O—H…O分子间氢键和范德瓦耳斯力作用下有规律的堆叠形成三维网络结构。配合物1和2均含有芳香杂环、羧基杂环和氮杂环,具有良好的荧光性质和热稳定性,最大发射波长分别为345 nm和333 nm。     

移动加热器法生长碲锌镉晶体的组分输运与界面形貌研究

移动加热器法(THM)生长碲锌镉晶体时,界面稳定性对晶体生长的质量有很大影响。本文基于多物理场有限元仿真软件Comsol建立了THM生长碲锌镉晶体的数值模拟模型,讨论了Te边界层与组分过冷区之间的关系,对不同生长阶段的物理场、Te边界层与组分过冷区进行仿真研究,最后讨论了微重力对物理场分布的影响,并对比了微重力与正常重力下的生长界面形貌。模拟结果表明,Te边界层与组分过冷区的分布趋势是一致的,在不同生长阶段,流场中次生涡旋的位置会发生移动,从而导致生长界面的形貌随着生长的进行发生变化,同时微重力条件下形成的生长界面形貌最有利于单晶生长。因此,在晶体生长的中前期,对次生涡旋位置的控制和对组分过冷的削弱,是THM生长高质量晶体的有效方案。     

Microfunnel‐filter‐based emulsification microextraction followed by gas chromatography for simple determination of organophosphorus pesticides in environmental water samples

A simple and fast method named microfunnel‐filter‐based emulsification microextraction is introduced for an efficient determination of some organophosphorus pesticides including diazinon, malathion, and chlorpyrifos in the environmental samples including the river, sea, and well water. This method is based upon the dispersion of a low‐toxicity organic solvent (dihexyl ether), as the extractant, in a high volume of an aqueous sample solution (45 mL). It is implemented without a centrifugation step, and using a syringe filter and a micro‐funnel, the phase separation and transfer of the enriched analytes to the gas chromatograph are simply achieved. By filtration of the extractant phase, a suitable sample clean‐up is obtained, and the total extraction time is just a few minutes. The factors influencing the extraction efficiency are optimized, and under the optimal conditions, the proposed method provides a good linearity (in the range of 15–1500 ng/mL (R² > 0.996). A high enrichment factor is obtained (in the range of 306–342), and the method provides low limits of detection and quantification (in the ranges of 4–8 and 15–25 ng/mL, respectively).     

Rapid and easy quantification of elemental sulphur in aqueous samples from biological reactors: the turbidimetric method revisited

Recent developments in wastewater treatment have led to a renewed interest to obtain elemental sulphur (S°) as a by-product from bioreactors. However, practical studies are limited by the gap of adequate analytical techniques for its determination. This paper provides a statistical study and matrix effect evaluation of an adapted spectrophotometric method for routine S° analyses in aqueous samples, based on a methodology previously described by Hart (1961). Four complex matrices were tested: domestic sewage and effluent samples from three different bioreactors. Tested performance criteria included linearity, matrix effect, limit of detection and quantification and S° recovery. Results were linear (R² = 0.99994) in the studied range (5 to 100 mg S° L^?1) and no matrix effect was observed. The accuracy was based on recovery values that varied from 100% to 106%. The colloidal S° separation and extraction protocol was also considered suitable for aqueous samples, reaching more than 99.0% of S° recovery.     

A novel microwave assisted reverse micelle fabrication route for Th (IV)‐MOFs as highly efficient adsorbent nanostructures with controllable structural properties to CO and CH4 adsorption: Design,and a systematic study

Reducing gas contaminants by affordable and effective adsorbents is a major challenge in the 21^st century. In the present study, thorium metal organic framework (Th‐MOF) nanostructures are introduced as highly efficient adsorbents. These compounds were manufactured via a novel route resulting from the development of microwave assisted reverse micelle (MARM) and ultrasound assisted reverse micelle (UARM) methods. The products were characterized utilizing XRD, SEM, TGA/DSC, BET, and FT‐IR analyses. Based on the results, the samples synthesized by MARM had uniform size distribution, high thermal stability, and significant surface area. Calculations using DFT/B3LYP indicated that the compounds have a tendency to the polymeric form, which could theoretically confirm the formation of Th‐MOF. Results of analysis of variance (ANOVA) showed that synthesis parameters played a critical role in the manufacturing of products with distinctive properties. Response surface methodology (RSM) predicted the possibility of creating Th‐MOF adsorbents with the surface area of 2579 m²/g, which was a considerable value in comparison with the properties of other adsorbents. Adsorption studies showed that, in the optimum conditions, the Th‐MOF products had high adsorption capacity for CO and CH₄. It is believed that the synthesis protocol developed in the present study and the systematic studies conducted on the samples which lead to products with ideal adsorption properties.     

Data assimilation and pollution forecasting in Burgers' equation with model error function

This article presents a correction method for a better resolution of the problem of estimating and predicting pollution, governed by Burgers' equations. The originality of the method consists in the introduction of an error function into the system's equations of state to model uncertainty in the model. The initial conditions and diffusion coefficients, present in the equations for pollution and concentration, and also those in the model error equations, are estimated by solving a data assimilation problem. The efficiency of the correction method is compared with that produced by the traditional method without introduction of an error function.Three test cases are presented in this study in order to compare the performances of the proposed methods. In the first two tests, the reference is the analytical solution and the last test is formulated as part of the “twin experiment”.The numerical results obtained confirm the important role of the model error equation for improving the prediction capability of the system, in terms of both accuracy and speed of convergence.     

Validation of a HPLC/MS method for simultaneous quantification of clonidine,morphine and its metabolites in human plasma

A high‐performance liquid chromatography–tandem mass spectrometry method was developed and validated for the simultaneous quantification of morphine, morphine's major metabolites morphine‐3‐glucuronide and morphine‐6‐glucuronide, and clonidine, to support the pharmacokinetic analysis of an ongoing double‐blinded randomized clinical trial that compares the use of morphine and clonidine in infants diagnosed with neonatal abstinence syndrome. Plasma samples were processed by solid‐phase extraction and separated on an Inertsil ODS‐3 (4 μm) column using an 0.1% formic acid in water–0.1% formic acid in methanol gradient. Detection of the analytes was conducted in the positive multiple reaction monitoring mode. The range of quantitation was 1–1000 ng/mL for morphine, morphine‐3‐glucuronide and morphine‐6‐glucuronide, and 0.25–100 ng/mL for clonidine. Intra‐day and inter‐day accuracy and precision were ≤15% for all analytes across the quantitation range. Extraction recovery rates were ≥94% for morphine, ≥90% for M3G, ≥87% for M6G and ≥ 79% for clonidine. Matrix effect ranged from 85–94% for clonidine to 101–106% for M3G. The method fulfilled all predetermined acceptance criteria and required only 100 μL of starting plasma volume. Furthermore, it was successfully applied to 30 clinical trial plasma samples.