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.     

Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

How do we understand mathematical practices in non-mathematical fields? Reflections inspired by cases from 12th and 13th century China

Recent studies of the history of mathematics have shed light on the diversity of mathematical practices in the ancient world. In this article, I address this issue from two perspectives. First, I analyze different mathematical instruments used in different domains in 12^th and 13^th century China. Second, by analyzing how the text is related to the problems written down in the same period, I argue that there existed two categories of mathematical problems. As a result, I suggest that problems, textual procedures, and material operations should be considered together when regarding various mathematical practices in mathematical and non-mathematical fields.     

具任意次非线性项的Camassa-Holm方程的双孤子新解

给出辅助方程、函数变换与变量分离解相结合的方法,构造了具任意次非线性项的Camassa-Holm方程的双孤子和双周期新解.首先,通过两个辅助方程、函数变换与变量分离解,将具任意次非线性项的Camassa-Holm方程的求解问题转化为非线性代数方程的求解问题.然后,借助符号计算系统Mathematica求出该方程组的解,并用辅助方程的相关结论,构造了双周期解和双孤子新解.     

Degasperis-Procesi方程的类孤子新解

利用辅助方程与函数变换相结合的方法,构造了Degasperis-Procesi(D-P)方程的无穷序列类孤子新解.首先,通过两种函数变换,把D-P方程化为常微分方程组.然后,利用常微分方程组的首次积分,把D-P方程的求解问题化为几种常微分方程的求解问题.最后,利用几种常微分方程的Bcklund变换等相关结论,构造了D-P方程的无穷序列类孤子新解.这里包括由Riemannθ函数、Jacobi椭圆函数、双曲函数、三角函数和有理函数组成的无穷序列光滑孤立子解、尖峰孤立子解和紧孤立子解.     

Solitons and other solutions to a new coupled nonlinear Schrodinger type equation

In this paper, the first integral method combined with Liu's theorem is applied to integrate a new coupled nonlinear Schrodinger type equation. Using this combination, more new exact traveling wave solutions are obtained for the considered equation using ideas from the theory of commutative algebra. In addition, more solutions are also obtained via the application of semi-inverse variational principle due to Ji-Huan He. The used approaches with the help of symbolic computations via Mathematica 9, may provide a straightforward effective and powerful mathematical tools for solving nonlinear partial differential equations in mathematical physics.     

氢键概念的形成和发展

1902年,瑞士化学家维尔纳对氯化铵结构的解释为氢键概念的形成奠定了基础。1920年,美国化学家拉提麦尔和罗德布什首先认识了水中的氢键：2个八隅体所持的氢核构成的“弱键(weak bond)”。1928年,美国化学家鲍林在解释[FHF]^-的结构时首次使用“氢键(hydrogen bond)”一词,但并未对氢键的概念进行明确定义。1939年,鲍林在《化学键的本质》中明确提出了氢键的概念,并解释了氢键的性质,自此,氢键的概念正式形成。近年来,科学家经过深入研究发现了氢键的新类型：π型氢键、双氢键、金属氢键和单电子氢键。随着科学思想和科学技术的发展,关于氢键的认识也会越来越深入。     

Electronic and optical properties of quaternary selenides for optoelectronic applications: Insights from DFT+U-computations

The optical properties, electronic charge density, electronic structure of the new layered selenides materials, BaGdCuSe₃, CsUCuSe₃, CsZrCuSe₃, and CsGdZnSe₃ compounds have been calculated by using the full potential and linear augmented plane wave (FP-LAPW) methods as applied in the WIEN2k package, which is based on the density functional theory. The ALnMSe3 compound's structure of these was (A = Cs, Ba; Ln = Zr, Gd, U; M = Cu, Zn) is composed of (n = 1, 2) layers, which might be separated by A atoms. It is to be observed that there is strong hybridization between the s, p, and d states of Zr, Gd, and Cu atoms. Around the gadolinium atom, the charge density contours are completely circular, but the Gadolinium “Gd” atom shows an ionic nature. To calculate the refractive index, we used Kramer's Kronig correlations with the imaginary part dielectric function. The decrease in the refractive index is due to the lack of probability for direct excitation of the electrons, resulting in a loss of energy. The value of the static refractive index for all reference compounds is about 1.75–2.25, which is indication that the material used in optoelectronic devices.     

毒品与化学*

毒品与化学的种种纠葛在2018年中国毒品形势报告中得到了淋漓尽致的体现,因此为做好禁毒工作,必须厘清化学与毒品的关系。从为什么毒品是化学品(毒品的本质),毒品检验和识别,毒品成瘾的本质,由传统毒品到新型毒品的转变等4个方面系统阐述毒品与化学的关系。     

化学学科核心素养在高中教材习题中的表现—以人教版教材为例

教材习题是落实新课标倡导的基于化学学科核心素养进行评价的重要载体。以化学学科核心素养的水平划分和学业质量水平为依据,分析人教版高中必修化学教材课后习题考查的核心素养及其水平。结果表明,2007年版和2019年版教材均注重全面考查核心素养和对基础性的考查,突出考查宏观辨识与微观探析素养,突出化学本质;但2019年版教材习题在数量上有所减少,加强了科学思维和科学实践的考查,合理拓展了核心素养考查的广度和深度。最后,依据习题特征获得相应的教学启示,以促进学生核心素养的发展。