空间几何体

1.本单元重、难点、热点分析重点:(1)理解平行投影与中心投影的区别;(2)掌握柱、锥、台、球及简单组合体的结构特征,会用斜二测画法画其直观图;(3)掌握空间几何体的三视图,会根据三视图构建空间几何体,由空间几何体画三视图;(4)掌握空间几何体的表面积和体积的计算公式及计算方法.     

常见客体分子对笼型水合物晶格常数的影响

Natural gas hydrates are considered as ideal alternative energy resources for the future, and the relevant basic and applied research has become more attractive in recent years. The influence of guest molecules on the hydrate crystal lattice parameters is of great significances to the understanding of hydrate structural characteristics, hydrate formation/decomposition mechanisms, and phase stability behaviors. In this study, we test a series of artificial hydrate samples containing different guest molecules (e.g. methane, ethane, propane, iso-butane, carbon dioxide, tetrahydrofuran, methane + 2, 2-dimethylbutane, and methane + methyl cyclohexane) by a low-temperature powder X-ray diffraction (PXRD). Results show that PXRD effectively elucidates structural characteristics of the natural gas hydrate samples, including crystal lattice parameters and structure types. The relationships between guest molecule sizes and crystal lattice parameters reveal that different guest molecules have different controlling behaviors on the hydrate types and crystal lattice constants. First, a positive correlation between the lattice constants and the van der Waals diameters of homologous hydrocarbon gases was observed in the single-guest-component hydrates. Small hydrocarbon homologous gases, such as methane and ethane, tended to form sI hydrates, whereas relatively larger molecules, such as propane and iso-butane, generated sⅡ hydrates. The hydrate crystal lattice constants increased with increasing guest molecule size. The types of hydrates composed of oxygen-containing guest molecules (such as CO₂ and THF) were also controlled by the van der Waals diameters. However, no positive correlation between the lattice constants and the van der Waals diameters of guest molecules in hydrocarbon hydrates was observed for CO₂ hydrate and THF hydrate, probably due to the special interactions between the guest oxygen atoms and hydrate "cages". Furthermore, the influences of the macromolecules and auxiliary small molecules on the lengths of the different crystal axes of the sH hydrates showed inverse trends. Compared to the methane + 2, 2-dimethylbutane hydrate sample, the length of the a-axis direction of the methane + methyl cyclohexane hydrate sample was slightly smaller, whereas the length of the c-axis direction was slightly longer. The crystal a-axis length of the sH hydrate sample formed with nitrogen molecules was slightly longer, whereas the c-axis was shorter than that of the methane + 2, 2-dimethylbutane hydrate sample at the same temperature.     

巧构造等差数列 妙解非数列问题

有些数学问题,乍看上去,与数列没有丝毫联系,但仔细研究其结构特征后,又可通过构造基本数列模型使问题巧妙获解,本文略谈构造等差数列解决几类常见的非数列问题,供参考.     

巧构造等差数列 妙解非数列问题

有些数学问题,乍看上去,与数列没有丝毫联系,但仔细研究其结构特征后,又可通过构造基本数列模型使问题巧妙获解,本文略谈构造等差数列解决几类常见的非数列问题,供参考．     

空间几何体

1．本单元重、难点及考试热点分析 本单元的重点是认识空间几何体的结构特征,画出空间几何体的三视图、直观图,培养空间想象能力、几何直观能力、运用图形语言进行交流的能力．由空间图形说出其结构特征,由结构特征想象出空间几何体,进行空间图形与其三视图的相互转化．     

利用独立事件巧证不等式

有些不等式,若能深入挖掘题目的内含与外延,根据其结构特征,大胆想象,构造独立事件,使不等式获得简证．请看下面两例：     

A New Coordination Polymer Containing 4-[（8-Hydroxy-5-quinolinyl）azo]-benzenesulfonic Acid： Synthesis,Structure and Fluorescent Property

A new coordination polymer, {[CdL（en）]＇DMF}n （1, H2L = 4-[（8-hydroxy-5- quinolinyl）azo]-benzenesulfonic acid, en = ethylenediamine, DMF = N,N-dimethylformamide）, has been solvothermally synthesized and structurally characterized by single-crystal X-ray diffrac- tion, infrared （IR） spectra, elemental analysis, powder X-ray diffractions （PXRD） and thermo- gravimetric analysis （TGA）. Compound 1 crystallizes in monoclinic, space group P2Jc with a = 14.6525（9）, b = 13.3917（9）, c = 11.8838（8） A, β = 101.2290（10）°, V = 2287.2（3） A3, Z = 4, C20H24CdN6OsS, Mr = 572.91, Dc. = 1.664 mg-mm-3, F（000） = 1160, p = 1.091 mm-1, R = 0.0232 and wR = 0.0587 for 3597 observed reflections （I 〉 2σ（I））. Compound 1 exhibits a one-dimensional （1D） double-chain structure which is further connected through hydrogen bonding and π-π interactions into a three-dimensional （3D） supramolecular network. In addition, it exhibits blue fluorescence at room temperature in the solid state.     

2011年重庆高考数学文科第15题解法探讨

考题1（2011年重庆文科15题）若实数a,b，c满足2^a＋2^b=2^a＋b，2^a＋2^b＋2^c=2^a＋b＋c，则C的的最大值是______． 考虑到题目的结构特征，不妨采用换元方法做变更处理．     

一个“特殊”不定方程的六种解法

毕达哥拉斯学派将抽象的数作为万物的本原,认为"万物皆数",试图通过揭示数的奥秘来探索宇宙的真理.因此,他们对数作了深入的研究.并获得了很多重要的结果,其中有很多发现是对后来影响深远的趣味数学问题.     

Structure and Semiconducting Character of a Polymeric Iodoplumbate Coordination Complex

A new polymeric iodoplumbate complex [Zn(DMF)6][Pb2I6] 1 has been prepared and characterized by elemental analysis and single-crystal X-ray analysis. Its structure contains infinite iodoplumbate chains constructed by the [PbI5] subunit. EHT crystal orbital calculation and the experimental results show that this material is an unconventional semiconductor and the electrical character is associated with its structural feature.