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乙函数和导函数的比较
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作者 马建萍 《青海师范大学民族师范学院学报》 2010年第1期72-74,共3页
不用极限定义导数已有两种不同方式的实现:差商有界的函数的乙函数和强可导函数的导函数。本文利用这两种方法对一些导数公式的验证过程进行了比较。
关键词 差商有界 乙函数 强可导 函数
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第三代微积分的研究
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作者 李子研 《数学学习与研究》 2016年第24期161-161,共1页
第三代微积分是以初等数学为基础,通过对导数与积分的定义研究,所发展起来的一代微积分.与前两代微积分相比第三代微积分所提供的理论通俗易懂,可以大大降低学习难度,提升微积分学习效果.由此,本文以第三代微积分为研究对象,在... 第三代微积分是以初等数学为基础,通过对导数与积分的定义研究,所发展起来的一代微积分.与前两代微积分相比第三代微积分所提供的理论通俗易懂,可以大大降低学习难度,提升微积分学习效果.由此,本文以第三代微积分为研究对象,在简要分析微积分发展历程之后,对甲、乙函数及其与导数之间的关系进行重点探究. 展开更多
关键词 第三代微积分 导数 初等数学 乙函数
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浅析第三代微积分
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作者 夏云青 夏云龙 《数学学习与研究》 2020年第4期5-6,共2页
本文首先回顾了微积分的发展史,重点介绍第三代微积分的内容及应用价值,最后提出希望广大数学教育工作者热心研究数学教育,随着新思想和新方法的普及,能将微积分变成多数学生都容易理解的一门数学课程.
关键词 极限 不等式 微分中值定理 乙函数 差商有界 强导数 广义差商有界 赫德尔导数 连续 数学教育
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DFT Calculation of Room Temperature Ionic Liquid 1-Ethyl-3-Methyl-Imidazolium Chlorocuprate (Ⅰ)
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作者 Lü Renqing Cao Zuogang (College of Chemistry and Chemical Engineering, China University of Petroleum (East China), Dongying 257061) 《China Petroleum Processing & Petrochemical Technology》 SCIE CAS 2008年第1期55-62,共8页
The density functional theory (DFT) has been employed to investigate the electronic structures ofEMIM^+(1-ethyl-3-methylimidazolium+), CuCl2^-, Cu2Cl3^- and EMIM^+-CuCl2^-, EMIM^+-Cu2Cl3^- pairs. Full optimiza... The density functional theory (DFT) has been employed to investigate the electronic structures ofEMIM^+(1-ethyl-3-methylimidazolium+), CuCl2^-, Cu2Cl3^- and EMIM^+-CuCl2^-, EMIM^+-Cu2Cl3^- pairs. Full optimization and frequency analyses of EMIM^+, CuCl2^-, Cu2Cl3^-, eight initial EMIM^+-CuCl2^-, and six initial EMIM^+-Cu2Cl3^- geometries have been carried out using Gaussian-94 software-package at 6-3 I+G (d, p) basis set level for hydrogen, carbon, nitrogen, chlorine atoms and the Hay-Wadt effective core potential for copper atoms. The electronic structures of the lowest energy of EMIM^+-CuCl2^-, EMIM^+-Cu2Cl3^- pairs, single EMIM^+, CuCl2^-, and Cu2Cl3^- have been comparatively studied. The calculated results showed that the optimized EMIM^+-CuCl2^- pair conformer of the lowest energy was five ring moiety parallel to CuCl2^- plane with a distance of around 3.5,A, while EMIM^+-Cu2Cl3^- pair conformer of the lowest energy was five ring moiety of EMIM^+ perpendicular to Cu2Cl3^- plane with a distance of around 3.0 ,A between terminal chlorine atoms and 5-ring plane of EMIM^+. The cohesion between cation and anion is electrostatic interaction and C-H---Cl hydrogen bonds are reinforced by charge assistance. The frequency analyses suggested that all stationary points are minimum points because of absence of imaginary frequency. The low energy of interaction caused by bulky asymmetry of EMIM^+, and charge dispersion of cation and anion give rise to low melting point of ionic liquids EMIM^+-CuCl2^-, and EMIM^+-Cu2Cl3^- . The interaction energy caused by the distance between cations and anions was investigated by single point energy scan. 展开更多
关键词 ionic liquid density functional theory 1-ethyl-3-methylimidazolium chlorocuprate (I)
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Understanding the interactions between tris(pentafluoroethyl)-trifluorophosphate-based ionic liquid and small molecules from molecular dynamics simulation 被引量:2
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作者 ZHANG XiaoChun LIU ZhiPing LIU XiaoMin 《Science China Chemistry》 SCIE EI CAS 2012年第8期1557-1565,共9页
Tris(pentafluoroethyl)trifluorophosphate ([FEP])-based ionic liquids have been widely applied in many fields. For better understanding the properties of [FEP]-based ionic liquids, the interactions between 1-hexyl-3-me... Tris(pentafluoroethyl)trifluorophosphate ([FEP])-based ionic liquids have been widely applied in many fields. For better understanding the properties of [FEP]-based ionic liquids, the interactions between 1-hexyl-3-methylimidazolium ([hmim])[FEP] and small molecules were investigated by molecular dynamics simulations in this work. The small molecules are water, methanol and dimethyl ether. The united-atom (UA) force fields were proposed for methanol and dimethyl ether based on AMBER force field. The densities, enthalpies of vaporization, excess molar properties, and diffusion coefficients of the mixtures were calculated, as well as the microscopic structures characterized by radial distribution functions. Both of the results of the excess energies and microscopic properties show that the strongest interaction is between [hmim][FEP] and dimethyl ether, whereas the interaction between [hmim][FEP] and water is the weakest. Moreover, [hmim][FEP] is more hydrophobic than [hmim] hexafluorophosphate ([PF6]), and the three solutes are mainly distributed around [FEP] anion. 展开更多
关键词 ionic liquid tris(pentafluoroethyl)trifluorophosphate small molecule interaction molecular dynamics simulations
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