Lax Pair and Darboux Transformation for a Variable-Coefficient Fifth-Order Korteweg-de Vries Equation with Symbolic Computation

In this paper, we put our focus on a variable-coe~cient fifth-order Korteweg-de Vries （fKdV） equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.     

狭义相对论的数学问题（三）—洛伦兹协变量

在郭硕鸿《电动力学》教材中狭义相对论部分的基础上对洛伦兹协变量作了较详细的讨论．     

A New Route to the Interpretation of Hopf Invariant

We discuss an object from algebraic topology, Hopf invariant, and reinterpret it in terms of the Ф-mapping topological current theory. The main purpose of this paper is to present a new theoretical framework, which can directly give the relationship between Hopf invariant and the linking numbers of the higher dimensional submanifolds of Euclidean space R^2n-1. For the sake of this purpose we introduce a topological tensor current, which can naturally deduce the （n- 1）-dimensional topological defect in R^2n-1 space. If these （n- 1）-dimensional topological defects are closed oriented submanifolds of R^2n-1, they are just the （n - 1）-dimensional knots. The linking number of these knots is well defined. Using the inner structure of the topological tensor current, the relationship between Hopf invariant and the linking numbers of the higher-dimensional knots can be constructed.     

QSAR Studies on the COX-2 Inhibition by 3,4-Diarylcycloxazolones Based on MEDV Descriptor

Selective inhibition of cyclooxygenase-2 (COX-2) might avoid the side effects of current available nonsteroidal antiinflammatory drugs while retaining their therapeutic efficacy. A novel variable selection and modeling method based on prediction is developed to construct the quantitative structure-activity relationships (QSAR) between the molecular electronegativity distance vector (MEDV) based on 13 atomic types and the biological activities of a set of selective cyclooxygenase-2 inhibitory molecules, 3,4-diarylcycloxazolones (DAA) plus indomethacin,naproxen, and celecoxib. Using multiple linear regression, a 5-variable linear model is developed with the calibrated correlation coefficient of 0.9271 and root mean square error of 0.17 in modeling stage and the validated correlation coefficient of 0.9030 and root mean square error of 0.20 in leave-one-out validation step, respectively. To further test the predictive ability of the model, 20 DAA compounds are picked up to construct a training set which is used to build a QSAR model and then the model is employed to predict the biological activities of the balance compounds. The predicted correlation coefficient and root mean square error are 0.9332 and 0.19, respectively.     

混合物和溶液的组成标度和组成变量

组成标度按５类逐一给出了名称，符号，定义和ＳＩ单位，并指出了一些常见的错误，按混合物和溶液讨论了组成变量的选择。量纳一的量的ＳＩ单位１的字母符号问题也作了讨论。     

电拓扑状态预测有机磷酸酯类化合物的气相色谱保留指数

以原子类型电拓扑状态指数(ETSI)有效表征35个有机磷酸酯类化合物(OP)的分子结构, 应用基于预测的变量选择与模型化(VSMP)方法建立OP化合物在3种不同固定相上的气相色谱保留指数(RI)与分子结构(ETSI)的定量相关模型. 结果表明, 影响不同固定相上OP色谱保留的主要结构因素都是由7个ETSI描述子对应的子结构碎片, 即: ＝CH₂,≡C—, aaC—, ＝O, —O—, Cl和Br. 其中子结构aaC—, ＝O和—O与OP化合物母体骨架密切相关, 而＝CH₂,≡C—, —Cl和—Br反映支链或取代基的变化. 通过多元线性回归法建立OP化合物在三个固定相上的定量结构-保留相关模型(QSRR)发现, 各QSAR模型的估计相关系数均在0.99以上, LOO检验相关系数在0.98以上, 表明模型具有良好估计能力与稳定性. 应用28个OP训练集样本构建的QSRR模型预测外部7个检验集RI结果表明训练集模型具有良好预测能力.     

探究实验教学中“控制单一变量”思想的培养——以“浓度对化学反应速率的影响”为例

控制单一变量思想是化学学科的本质之一,是探究实验中不可或缺的认知成分。针对人教版高中《化学反应原理》"浓度对化学反应速率的影响"一节,充分挖掘实验的定量价值,以3种不同层次浓度方案的设计和评价,生成控制单一变量思想的具体内涵。教学过程中以任务驱动的形式,充分激发学习兴趣,培养实验探究能力、深化思维水平。     

食品中合成色素快速检测仪器的研制

基于人工合成色素在可见光区的光吸收及偏最小二乘变量筛选法,研制出合成色素速测仪器,并应用于饮料、糖果、果冻、调色酒等食品中合成色素的快速检测.速测仪具有便携、功耗低、操作简便、检测时间短并可同时对多种人工合成色素进行实时现场快速检测、检测结果准确等优点.对样品中5种食用合成色素柠檬黄、日落黄、胭脂红、苋菜红和亮蓝的检测...     

基于近红外光谱的维生素C片无损鉴别分析

基于近红外光谱技术与化学计量学方法,建立了一种国内外不同品牌维生素C片的无损鉴别方法。采集了国内外8个品牌的维生素C片共计40个样本的近红外光谱数据,比较了完整样品以及粉末样品的近红外光谱,采用连续小波变换技术消除背景干扰和基线漂移,基于标准偏差与相对标准偏差的变量筛选方法筛选出具有代表性的波数点,结合主成分分析方法对国内外不同品牌维生素C片进行鉴别分析。结果表明:原始光谱存在着明显的背景干扰和基线漂移现象,且粉末样品的重现性要优于完整样品;单纯使用原始光谱无法辨别来自不同品牌的维生素C片;连续小波变换可以有效消除背景干扰,提高模型鉴别能力;完整样品的鉴别准确率优于粉末样品,说明国内外不同品牌维生素C片主要成分基本一致,可能是辅剂和工艺上存在细微差异。通过结合近红外光谱分析技术与化学计量学方法,可实现对国产以及进口不同品牌维生素C片的鉴别分析。