“容球旋转体的共性”再探

文[1]、文[2]、文[3]分别给出以下3个定理： 定理1 在存在内切球的前提下，多面体的体积均等于其表面积与相应内切球半径乘积的三分之一．     

“先重后单”法用于求空间曲面所围立体的体积

学生在用三重积分求体积时，当体积由比较复杂的空间曲面所围成，同学们由于对这样的空间曲面缺乏了解，作图也比较困难，所以通常做起来会感到束手无策，但是如果曲面为绕某一轴的旋转曲面，通过使用“先重后单”的方法，并且充分利用初等数学的公式，可使问题得到大量的简化。下面我们举几个具体例子。例1求曲面（x2＋y2＋z2）2＝a2（x2＋y2－z2）所界体积。分析与解：实际上这个曲面是WZ平面上双纽线（y2＋z2）2＝a2（y2－z2）绕z轴旋转一周而成。过X轴一点D作平行于Xoy平面的平面截旋转体得一圆环，如图1所示，内半径DA，外半径DB，…     

一类多面体体积公式的探求

在立体几何学习中，我遇到例1这样一个题目．     

争鸣

问题114对台体的体积公式可按下面类比引出．     

Bulk Modulus and Electronic Band Structure of ZnGa2Xa （X=S,Se）： a First-Principles Study

First-principles local density functional calculations are presented for the compounds ZnGa2X4 （X = S, Se）. We investigate the bulk moduli and electronic band structures in a defect chalcopyrite structure. The lattice constants and internal parameters are optimized. The electronic structures are analysed with the help of total and partial density of states. The relation between the cohesive energy and the unit cell volume is obtained by fully relaxed structures. We derive the bulk modulus of ZnGa2Xa by fitting the Birch-Murnaghan＇s equation of state. The extended Cohen＇s empirical formula agrees well with our ab initio results.     

Ultralite系列DPSS激光器

镭宝光电技术有限公司的Ultralite系列DPSS激光器，具有高性能、小体积、长寿命的特点，它按照输出波长的不同分为6种机型，有1064nm，1053nm，1319nm，660nm，527nm，355nm等输出波长，适用于各种科研、精细工业加工领域的应用。     

理想斯特林热机循环原理及其效率的计算和实际工作效率的简单讨论

本文首先从热机效率的基本公式出发,阐述理想斯特林热机的工作原理,从中看到斯特林热机独特的工程设计对效率计算的影响,使其效率达到理想卡诺循环效率;其次给出实际斯特林热机工作时的热损耗的来源分析;最后结合有关论文的结论,给出工质为范德瓦耳斯气体时的效率与体积比的关联.     

研测动态问题的旋转孔径散斑照相法Ⅱ:矩位、平四位、直三位孔径

本文提出了旋转孔径散斑照相法中三种新颖的基本孔径:矩位孔、平四位孔和直三位孔,进行了理论分析和实验证明。采用新孔径拍摄散斑照相,散斑信息利用率高,衍射晕能量分布合理,信噪比提高,因而散斑条纹清晰度得到改善,相应的实验误差减小。     

液-固色谱流动相体积分数层次结构模型与保留值的关系

用液-固色谱流动相"假定"的体积分数层次结构模型,可得到质点团溶解溶质时的体积分数,进而得到共溶剂中溶质的溶解度、固定相上的溶质吸附量,从而推导出多元流动相组成与溶质保留值的关系.如三元流动相与溶质保留值的关联式为:lnk'=φB3lnk'B3 φB2lnk'B2 φB1lnk'B1 φB1(φB20.5 φB30.5)ln(q)(外Ⅱ) φB30.5φB21.0φB11.5ln(q)(外Ⅰ),经实验数据拟合,本式较其他关联式略胜一筹.     

Structural, electronic, and optical properties of ZnOl_xSex alloys using first-principles calculations

The structural, electronic, and optical properties of binary ZnO, ZnSe compounds, and their ternary ZnOl_xSex alloys are computed using the accurate full potential linearized augmented plane wave plus local orbital （FP-LAPW ＋ lo） method in the rocksalt （B 1） and zincblende （B3） crystallographic phases. The electronic band structures, fundamental energy band gaps, and densities of states for ZnO1_xSex are evaluated in the range 0 〈 x 〈 1 using Wu-Cohen （WC） generalized gradient approximation （GGA） for the exchange-correlation potential. Our calculated results of lattice parameters and bulk modulus reveal a nonlinear variation for pseudo-binary and their ternary alloys in both phases and show a considerable deviation from Vegard＇s law. It is observed that the predicted lattice parameter and bulk modulus are in good agreement with the available experimental and theoretical data. We establish that the composition dependence of band gap is semi-metallic in B1 phase, while a direct band gap is observed in B3 phase. The calculated density of states is described by taking into account the contribution of Zn 3d, O 2p, and Se 4s, and the optical properties are studied in terms of dielectric functions, refractive index, reflectivity, and energy loss function for the B3 phase and are compared with the available experimental data.