水在密度测量中的妙用

在一些测量密度的实验题目中,在所给的器材中常会出现水.实际上这类题目能否顺利解决的关键,就是能否将水巧妙地用到实验中来,帮助我们解决遇到的困难.下面介绍几个用水帮助完成密度测量的实验题.     

R￣d中Hausdorff维数和packing维数的确定

本文目的在于建立确定Ｒ￣ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ和ｐａｃｋｉｎｇ维数Ｄｉｍ的两个命题（定理１和定理２），进而寻求Ｒ￣ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ与ｐａｃｋｉｎｇ维数Ｄｉｍ相等的条件；这使得我们能够引入分形测度的测度论定义。     

由一道考研题引起的对随机变量独立性的探讨

通过对2022年一道全国研究生入学考试数学试题中条件分布的研究,得到随机变量独立性的有关结论,具有一定的理论价值和应用价值.     

Numerical Simulation on the Production Mechanism of Surface-Wave Plasmas Sustained along a Metal Rod

For interpreting the production mechanism of surface-wave plasmas sustained along a metal rod, electromagnetic simulation on the electromagnetic field distributions and particle-in-cell/Monte Carlo collision （PIC/MCC） simulation of the ionization process are present. The results show that the enhanced electric field of surface plasmon polaritons （SPPs） can be excited in the ion sheath layer between the negative-voltage metal rod and the surface-wave plasmas, which is responsible for maintaining the plasma discharge. Moreover, the spatio-temporal evolutions of plasma density and electric fields are simulated by the PIC/MCC model. It is further suggested that the expanded ion sheath layer can extend the length of plasma domain by increasing the plasma absorbed energy from SPPs.     

表面润湿法合成β沸石体系中晶种作用的研究

系统研究了表面润湿法合成β沸石的体系中,干晶种、润湿态晶种、异晶晶种(Y沸石、ZSM 5沸石)以及碱处理β沸石晶种在此晶化体系中的作用.采用β沸石产品及异晶作晶种时,可使产品的相对结晶度稍有提高,但对沸石微晶核的结构导向作用不明显.经浓碱液处理20min后的β沸石产品(碱处理晶种)作晶种引入晶化体系后,可以显著提高产品的相对结晶度,降低模板剂的用量,缩短晶化诱导期,成为表面润湿法合成β沸石体系的有效晶种形式.     

开尔文电桥电路测量材料杨氏模量系统的实验设计与开发

本实验主要是应用开尔文电桥电路测微小电阻的原理,根据钢丝材料在受力的作用下,钢丝长度发生微小变化时其电阻也随之变化的关系,由相关理论推导出测量钢丝材料杨氏模量的计算公式,并提出了一种测量材料杨氏模量的方法。     

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.     

NH3(H2O)4稳定结构的理论研究

先构建氨水团簇的模型势,并计算得到NH3(H2O)4的模型势异构体,从中选取稳定性较好的异构体作为初始结构,分别利用密度泛函方法和二级微扰理论在6-31G(d)和6-311++G(d,p)基组水平上逐级进行结构优化、频率和单点能计算.发现包括第2和第3稳定结构等12种新异构体;NH3(H2O)4的五边形环状结构的稳定性最好;这种极性混合分子簇的偶极矩大小和包含的氢键数都与结构的稳定性无必然联系.     

Spin Polarization Properties of Na Doped Meridianal Tris（8-Hydroxyquinoline） Aluminum Studied by First Principles Calculations

We theoretically investigate the electronic structure and spin polarization properties of Na-doped meridianal tris（S-hydroxyquinoline） aluminum （Alq3） by first principles calculations. It is found that the spin density is distributed mainly in the Alq3 part in the Alq3：Na complex. Electron charge transfer takes place from the Na atom to the Alq3 molecule, which induces asymmetric changing of the molecule bond lengths, thus the spin density distribution becomes asymmetric. Spin polarization of the complex originates from the preferable filling of the spin-split nitrogen and carbon p-orbitals because of the different bond length changes of the Aiq3 molecule upon Na doping.