Pseudo‐spherical normal Darboux images of curves on a lightlike surface

We introduce the notions of the pseudospherical normal Darboux images for the curve on a lightlike surface in Minkowski 3‐space and study these Darboux images by using technics of the singularity theory. Furthermore, we give a relation between these Darboux images and Darboux frame from the viewpoint of Legendrian dualities.     

Evolution of highly symmetric curves under the shrinking curvature flow

Under the shrinking curvature flow with inner normal velocity V = k^α(α > 1), it is shown that highly symmetric, locally convex initial curves evolve into a point asymptotically like an multi‐circles. The proof relies on a crucial use of Bonnensen inequality for highly symmetric, locally convex curves. Copyright © 2016 John Wiley & Sons, Ltd.     

Chemometrics‐assisted chromatographic fingerprinting: An illicit methamphetamine case study

The volatile chemical constituents in complex mixtures can be analyzed using gas chromatography with mass spectrometry. This analysis allows the tentative identification of diverse impurities of an illicit methamphetamine sample. The acquired two‐dimensional data of liquid–liquid extraction was resolved by multivariate curve resolution alternating curve resolution to elucidate the embedded peaks effectively. This is the first report on the application of a curve resolution approach for chromatogram fingerprinting to identify particularly the embedded impurities of a drug of abuse. Indeed, the strong and broad peak of methamphetamine makes identifying the underlying peaks problematic and even impossible. Mathematical separation instead of conventional chromatographic approaches was performed in a way that trace components embedded in methamphetamine peak were successfully resolved. Comprehensive analysis of the chromatogram, using multivariate curve resolution, resulted in elution profiles and mass spectra for each pure compound. Impurities such as benzaldehyde, benzyl alcohol, benzene, propenyl methyl ketone, benzyl methyl ketone, amphetamine, N‐benzyl‐2‐methylaziridine, phenethylamine, N ,N ,α‐trimethylamine, phenethylamine, N ,α,α‐trimethylmethamphetamine, N‐acetylmethamphetamine, N‐formylmethamphetamine, and other chemicals were identified. A route‐specific impurity, N‐benzyl‐2‐methylaziridine, indicating a synthesis route based on ephedrine/pseudoephedrine was identified. Moreover, this is the first report on the detection of impurities such as phenethylamine, N ,α,α‐trimethylamine (a structurally related impurity), and clonitazene (as an adulterant) in an illicit methamphetamine sample.     

Bounds on partial derivatives of NURBS surfaces

In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.     

用硝酸银溶液沉淀及分步沉淀卤素离子的数字化实验研究*

卤化银难溶电解质的沉淀溶解平衡是中学化学教学的重要知识点。应用本项目组研制的MXLab21先进数字化实验系统,结合银硫离子电极,测定AgNO₃溶液沉淀Cl^-,Br^-,I^-及其混合离子的沉淀曲线,即电动势(E)随AgNO₃溶液体积(V)变化的关系曲线。3种单一离子的沉淀曲线可以直观体现出滴定的电动势突跃范围与相应沉淀的溶度积大小的关系及其规律性变化。通过混合离子的沉淀曲线分析3种离子两两混合或3者混合时分步沉淀的可行性。Cl^-,Br^-,I^-的沉淀及分步沉淀的动态E-V曲线的建立,对中学化学教学具有重要作用,对化学学科核心素养的发展和培养具有重要价值。     

基于曲线问题情境的信息化教学尝试*——以“沉淀溶解平衡”为例

基于高中生对实验曲线理解困难的现状,为挖掘实验曲线的教学价值,以沉淀溶解平衡为例,结合课堂演示实验和教学软件,设计了“宏观微观符号曲线”多重表征教学为一体的实验探究课。根据沉淀溶解平衡实验证据,绘制实验曲线,构建微观模型和图像,从而培养学生的证据收集与应用意识,提高学生对曲线的分析和理解能力,领会各种变化曲线的来源。在曲线理解的基础上建立“溶解平衡转化”思维模型,以此为开展“曲线融入式”的问题引导型实验教学提供参考案例。     

植物油中脂肪酸不同定量方法的比较分析

比较峰面积归一化法与标准曲线法两种方法分析植物油中脂肪酸百分比含量的差异。利用气相色谱-质谱联用仪(GC-MS)检测10种市售食用植物油中的8种主要脂肪酸,峰面积归一化法和标准曲线法计算脂肪酸的百分比含量。结果表明,标准曲线法与峰面积归一化法相比,肉豆蔻酸、棕榈酸、十七烷酸、硬脂酸和棕榈油酸所占的百分比升高,而油酸、亚油酸和亚麻酸比例降低;饱和脂肪酸比例升高,不饱和脂肪酸百分比降低。利用峰面积归一化法计算植物油中脂肪酸百分比时,降低了饱和脂肪酸比例,升高了不饱和脂肪酸比例,可能对健康有潜在的不利影响。建议使用标准曲线法计算不同植物油中脂肪酸的百分比。