数学建模对高中生构建数学底层思维的作用及其教学实施建议

数学底层思维即用数学的眼光观察世界、用数学的思维分析世界以及用数学的语言表达世界,是人们面对自然和社会中纷繁多样的现象和问题时,所展现的自发的、不依赖监督的、融汇数学学科核心素养的思维方式.作为国家高中新课程标准中数学六大核心素养之一的数学建模,是培养学生数学底层思维的良好载体,对人才培养和社会发展均起到良好的促进作用.本文主要阐述了数学建模对高中生构建数学底层思维的作用,并结合教学实例给出教学实施建议.     

Comprehensive characterization and quantification of multiple components in Dan‐Huang‐Qu‐Yu capsule using a multivariate data processing approach based on microwave‐assisted extraction with UHPLC and Q Exactive quadrupole‐orbitrap high‐resolution mass spectrometry

Dan‐Huang‐Qu‐Yu capsule, a Chinese herbal medicine compound preparation, is widely used for chronic pelvic inflammatory disease. In this study, a rapid, selective, and sensitive microwave‐assisted extraction ultra‐high‐performance liquid chromatography‐Q Exactive quadrupole‐orbitrap high‐resolution mass spectrometry method was developed for analyzing its chemical compositions. A total of 85 compounds, including 22 flavonoids, 8 terpenoids, 5 quinones, 5 phthaleolactone, 23 organic acids, and 22 other compounds were identified from Dan‐Huang‐Qu‐Yu capsule. Among them, 35 major compounds were unambiguously detected by comparing them with reference standards and selected as quality control markers, which were simultaneously determined in Dan‐Huang‐Qu‐Yu capsule. The established method was successfully validated and applied for simultaneous determination of 35 bioactive compounds in Dan‐Huang‐Qu‐Yu capsule from ten sample batches. The quantitative data of the analytes were analyzed by principal component analysis for quality assessment of Dan‐Huang‐Qu‐Yu capsule. Six compounds (e.g., astragaloside IV, salvianolic acid B, ellagic acid, chlorogenic acid, N‐butylidenephthalide, and luteolin) were screened out and regarded as chemical markers for quality control of Dan‐Huang‐Qu‐Yu capsule. The established method has been proved to be a novel and useful tool for rapid research of Dan‐Huang‐Qu‐Yu capsule. This research will provide reference for the scientific research of traditional Chinese medicines.     

Establishing the chromatographic fingerprint of traditional Chinese medicine standard decoction based on quality by design approach: A case study of Licorice

A novel analytical quality by design approach for developing a chromatographic fingerprint was established for analyzing complex traditional Chinese medicine, using a licorice standard decoction as an example. Considering the characteristics of integrity and ambiguity, the resolution of eight common peaks, total peak number, capacity factor distributions, and peak purity were selected as potential critical method attributes for assessing the quality of the chromatographic fingerprint. A central composite design was used to evaluate the relationship between critical method attributes and critical method parameters, including column temperature, wavelength, flow rate, formic‐acid concentration, and gradient parameters. A standard probability method was employed to calculate the design space of the fingerprint analysis parameters and evaluate the robustness of the methodology. The optimized high‐performance liquid chromatography fingerprint conditions were acetonitrile and 0.1% formic acid water gradient elution (0‐5 min, 5–19% A; 5–10 min, 19% A; 10–50 min, 19–42% A; 50–54 min, 42–100% A; 54–60 min, 100% A), column temperature 25±5°C, detection wavelength 265 nm. The design space of fingerprint analytical method based on the analytical quality by design approach not only met the requirements of the fingerprint analysis, but also improved the robustness and applicability of the fingerprint method.     

Simultaneous quantitation of 23 bioactive compounds in Tanreqing capsule by high‐performance liquid chromatography electrospray ionization tandem mass spectrometry

Tanreqing capsule (TRQC) is a formulation frequently used in traditional Chinese medicine to treat pyrexia, cough, expectoration and pharyngalgia. Since the pharmacological action of traditional Chinese medicines is closely related to their complex and diverse constituents, understanding the exact composition of TRQC is important to elucidate its clinical effectiveness and mechanism of action as well as to establish quality control methods and resolve safety issues. Herein, we employed high‐performance liquid chromatography coupled with electrospray ionization tandem mass spectrometry for the simultaneous quantitation of 23 bioactive compounds in five batches of TRQC; the analytes could be categorized into five types: organic acids (seven compounds), flavonoids (10 compounds), iridoids (two compounds), phenylethanoid glycosides (two compounds) and bile acids (two compounds). The calibration curves for all analytes showed good linearity (r > 0.9953), and the inter‐ and intra‐day precisions did not exceed 4.94 and 4.97%, respectively. The recoveries varied from 90.47% to 109.80%; the corresponding relative standard deviations (RSDs) did not exceed 4.94%; and the repeatability (RSD < 4.72%) and stability (RSD < 4.88%) were also within acceptable limits. Thus, this study can be viewed as a fundamental reference for setting comprehensive TRQC quality standards.     

Comparative analysis of the main active components and hypoglycemic effects after the compatibility of Scutellariae Radix and Coptidis Rhizoma

In this study, a rapid and highly sensitive ultra high performance liquid chromatography with triple quadrupole mass spectrometry method with the mobile phase of acetonitrile and 0.1% aqueous formic acid was established and successfully applied to comparatively analyze main active components after their compatibility. Besides, the effects of Scutellariae Radix, Coptidis Rhizoma and combined extracts on type 2 diabetic rats induced by high‐fat diet along with low dose of streptozocin were investigated. Under the optimized chromatographic conditions, good separation of seven target components was achieved within 12 min. All calibration curves exhibited good linearity (R² ≥ 0.999). The relative standard deviation of precision, repeatability and stability varied from 0.69 to 2.23, 0.98 to 2.56, and 0.92 to 2.57%, respectively. The recovery ranged from 91.11 to 105.35%. The contents of seven active components were notably reduced after compatibility; however, the hypoglycemic effect of combined extracts was stronger than single drug by decreasing the activities of fructose‐1,6‐bisphosphatase, glucose 6‐phosphatase, phosphoenolpyruvate carboxykinase and increasing the activities of glucokinase, phosphofructokinase, pyruvate kinase. Accordingly, the established analytical method was accurate and sensitive enough for quantitative evaluation of seven investigated compounds. Moreover, the combined extract had definite effects on type 2 diabetes through multiple components against multiple targets.     

融合形态学连通域和CV模型的民族服饰图案纹样元素分割方法

对民族服饰图案进行自动分割以提取图案纹样元素，是民族服饰图案素材库构建急需解决的难题。通过融合形态学连通域标记和CV模型（MCC-CV），提出了一种民族服饰图案自动分割方法，首先对民族服饰图案进行预处理，然后采用形态学连通域标记算法获得待分割目标的位置和大致轮廓信息，对CV模型进行初始化，最后通过CV模型对不同分割目标进行边缘追踪，以实现民族服饰图案纹样元素的自动分割。实验表明，融合形态学连通域和CV模型的民族服饰图案纹样元素自动分割方法在边界召回率（BR）为0.5时，分割准确率为60%，与其他自动分割算法相比，该算法更为有效，满足了民族服饰图案素材库建设对图案纹样元素分割的基本要求。     

近红外光谱的古筝面板用木材等级识别研究

目前民族乐器古筝面板用板材的等级主要依靠乐器技师凭借个人经验进行判断，此方法受限于有丰富经验的技师且容易受其主观判断影响。针对此现状，以用于制作古筝面板的泡桐木材为实验样本，提出了一种利用近红外光谱结合改进的BP神经网络方法，实现快速识别古筝面板用板材的不同等级。近红外光谱可以表征丰富的物质结构与组成信息，并且测量仪器成本较低，附件形式多样化，所以针对泡桐板材的近红外光谱实验分析有实用意义首先进行光谱去噪，消除系统误差等以提高光谱分辨率，根据均方根误差与信号平方和作为多种预处理方法评价指标，选取一阶导数为本实验最终预处理方式，15为合适的滤波去噪窗口大小，然后通过主成分分析法压缩数据以及马氏距离法剔除建模集异常样本，从而建立更具代表性的建模集。然后通过聚类分析无监督学习方法进行板材等级分析，证明板材分级的可行性。由于H₂O在近红外光谱区域具有较大吸收，根据实验光谱分析结果，不考虑其基频振动波段5 396.0～4 978.0 cm-1区域和第一泛音振动波段6 800～7 000 cm-1区域，仅考虑剩余近红外光谱波段信息，将不同光谱信息波段组合，共七种组合波段区域作为神经网络模型的输入，进行面板板材等级识别模型实验。对传统的BP神经网络模型作改进。BP神经网络中学习率的设置采用自适应学习率优化策略，弥补传统神经网络训练速率慢等劣势。同时采用交叉熵函数作为代价函数，从而加快权重的更新速度。选取Relu函数作为输入层与隐藏层之间的传递函数，提高了模型训练速度，有效防止过拟合的发生。选取Softmax函数作为最后一层的传递函数，以此减少复杂计算，构成该研究最终BP神经网络模型。选取不同数量的主成分变量所能提取的光谱信息量不同，通过不断增加主成分个数和调整参与模型的光谱波段区间，调整BP神经网络模型的输入，当主成分个数为11和光谱区间为10 000～7 000和4 976～4 000 cm-1时，未知样本识别率达到99.7%，所选光谱区间涵盖C-H等基团全部特征信息。研究结果表明，近红外光谱结合神经网络可以对不同等级的泡桐木材进行有效的识别，降低人工检测误差，缩短板材分级时间，更好地满足乐器市场需求。     

Analysis of Chuanxiong Rhizoma substrate on production of ligustrazine in endophytic Bacillus subtilis by ultra high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry

Ligustrazine was the active ingredient of the traditional Chinese medicine Chuanxiong Rhizoma. However, the content of ligustrazine is very low. We proposed a hypothesis that ligustrazine was produced by the mutual effects between endophytic Bacillus subtilis and the Ligusticum chuanxiong Hort. This study aimed to explore whether the endophytic B. subtilis LB5 could make use of Chuanxiong Rhizoma fermentation matrix to produce ligustrazine and clarify the mechanisms of action preliminarily. Ultra high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry analysis showed the content of ligustrazine in Chuanxiong Rhizoma was below the detection limit (0.1 ng/mL), while B. subtilis LB5 produced ligustrazine at the yield of 1.0268 mg/mL in the Chuanxiong Rhizoma‐ammonium sulfate fermentation medium. In the fermented matrix, the reducing sugar had a significant reduction from 12.034 to 2.424 mg/mL, and rough protein content increased from 2.239 to 4.361 mg/mL. Acetoin, the biosynthetic precursor of ligustrazine, was generated in the Chuanxiong Rhizoma‐Ammonium sulfate (151.2 mg/mL) fermentation medium. This result showed that the endophytic bacteria B. subtilis LB5 metabolized Chuanxiong Rhizoma via secreted protein to consume the sugar in Chuanxiong Rhizoma to produce a considerable amount of ligustrazine. Collectively, our preliminary research suggested that ligustrazine was the interaction product of endophyte, but not the secondary metabolite of Chuanxiong Rhizoma itself.     

Probing the degradation mechanism of forsythiaside A and simultaneous determination of three forsythiasides in Forsythia preparations by a single marker

Forsythiaside A is the major component of Forsythia suspensa. This study investigated the degradation mechanism of forsythiaside A. Eight degraded components including forsythiaside I, forsythiaside H, forsythiaside E, caffeic acid, suspensaside A, β‐hydroxy forsythiaside I, β‐hydroxy forsythiaside H, and β‐hydroxy forsythiaside A were identified by using ultra‐high performance liquid chromatography quadrupole time‐of‐flight mass spectrometry. Then, the quantitative analysis of multi‐components by a single‐marker was performed with ultra‐high performance liquid chromatography to simultaneously determine forsythiaside A, forsythiaside H, and forsythiaside I in Forsythia suspensa preparations. The result showed good linear relationships within 2.871–287.1, 0.231–23.1, and 0.983–98.3 μg/mL (r > 0.9998), with average recoveries of 97.7, 95.7, and 95.8% and relative standard deviations of 1.4, 2.4, and 1.8%, respectively. Using forsythiaside A as an internal reference, the relative retention values of forsythiaside H and forsythiaside I to forsythiaside A were calculated to be 0.89 and 0.61, respectively, and the relative correction factors were 0.816 and 0.799, respectively. The method for quantitative analysis of multi‐components by a single‐marker was applied to evaluate the overall quality of forsythia preparations. There was no significant difference in the measurement results of the method developed and the method of external standard.