“定因”与“算理”剖析一例

题1已知抛物线y2=4x及点P(2,2),斜率为1的直线l不过点P,且与抛物线交于点A和B,直线AP、BP分别交抛物线于另一点C和D.证明:AD与BC交于定点Q.文[1]分析了题1的"动源",并利用"动源"将上述问题演变成相关的三个问题,但未能彻底剖析"定因"与"动源"的关系,以致作者最后谈到,"由于运算量过大以及笔者自身的水平有限,未能完成:(1)能否将上述命题一般化;(2)能否将命题类比到椭圆、     

基于TDC-GP2的时间间隔测量系统设计

精确的时间间隔测量在时间同步系统有着至关重要的作用,为了满足大量程和高精度的需求,介绍了一种直接计数法和时间-数字装换法相结合的时间间隔测量系统;设计中采用两片TDC-GP2时间-数字转换芯片,结合FPGA和上位机,可以实现精度为1 ns时差测量;经过大量的实际测量,系统的分辨率为70 ps,精度为1 ns,最大可以测量1 s的时间间隔;该设计的系统具有可靠性高、功耗低、精度高、使用灵活等优点。     

Structure and Luminescent Properties of the First Cadmium Complex with Isophthalate and Di-pyrazole Ligands

The title complex [Cd(IPA)L(H2O)]n(1,H2IPA = isophthalic acid,L = 1,4-bis(pyra-zole-1-ylmethyl)benzene) has been hydrothermally synthesized,and characterized by elemental analyses,IR spectroscopy,TGA and X-ray single-crystal diffraction.It crystallizes in the triclinic system,space group P1 with a = 9.3060(6),b = 10.2374(7),c = 11.9706(8) ,α = 73.804(6),β = 77.883(5),γ = 85.942(5)°,V = 1070.7(1) 3,Z = 2,C22H20CdN4O5,Mr = 532.82,Dc = 1.653 g/cm3,μ = 1.062 mm-1,λ(MoKα) = 0.71073 ,F(000) = 536,R = 0.0392 and wR = 0.0640 for 3751 observed reflections with I > 2σ(I).Crystal structure analysis showed that complex 1 has a 1D double chain structure,which is assembled together through strong O-H...O hydrogen bonding interactions between coordinated water molecules and carboxylate groups of isophthalate to form a 2D supramolecular network.In addition,the solid-state fluorescent spectrum of 1 exhibits strong emission at 364 nm.     

带色散项的周期可积Hunter-Saxton方程的波的破裂

本文考虑一个带色散项的可积Hunter-Saxton方程的周期柯西问题.首先,我们得出该模型的强解的一个精确的爆破机制.其次,利用守恒量和特征方法,分别建立了有限时间内强解的爆破发生的充分条件.最后,给出了强解的爆破率.     

数学多选题的命题

2020年山东省高考数学模拟卷中出现了多选题,据可靠消息,教育部考试中心非常认同这种题型的考查.其实,《中国数学教育》杂志2019年第1-2期就已刊登教育部考试中心任子朝先生的文章《新高考数学多选题考查功能研究》(见文[1]),新高考数学多选题的考查应无悬念.     

电泳沉积法制备V2O5薄膜的结构和性能

将V2O5溶胶电泳沉积在ITO导电基片上制备V2O5薄膜.运用X射线衍射和扫描电镜对薄膜的结构进行分析,通过紫外-可见光透射光谱和循环伏安法分别测试其光学和电化学性能.实验结果表明,电泳沉积V2O5薄膜具有致密的显微结构,薄膜厚度均匀、与基片的粘附性很好;循环实验中,薄膜呈现黄色到绿色的可逆变化,最大的透射率变化达到30%左右;薄膜具有很好的注入/退出可逆性和循环稳定性,50次循环效率仍能达到88.02%,并且循环后的薄膜与ITO导电玻璃的粘附性仍然很好,没有溶解现象;应用交流阻抗法计算Li+在V2O5薄膜着色过程的扩散系数为5.10×10-12cm2/s,表明该薄膜可以作为电致变色材料得到应用.     

Ge BEAM TREATMENT OF Si SUBSTRATE FOR MOLECULAR BEAM EPITAXY

A new surface cleaning method for Si MBE is described in which a very weak Ge beam flux is deposited on the surface for removing the thin passivative layer of SiO₂ on the Si subetrate. It has proved that the SiO₂ will react with Ge at a relatively low temperature (620℃), and as a result, the oxide layer becomes volatile. Here the high temperature annealing in the conventional Shiraki method is no longer required, and since the oxide layer is removed in ultra high vacuum, only very little carbon contamination may occur. Furthermore, to reduce the excessive Ge on the substrate surface, Ge is deposited at 620℃ and then the sample is annealed at 700℃; the residual Ge atoms on Si substrate can be reduced to less than 0.1 monolay-er (ML). Ge beam treatment turns out to be an effective low-temperature Si surface-cleaning method, especially for the heteroepitaxial growth of Ge_xSi_1-x/Si.     

ELECTROLUMINESCENCE SPECTRA OF GexSi1-x/Si SINGLE QUANTUM WELL

The electroluminescence of Ge_xSi_1-x/Si single quantum well was measured at temper-atures above room temperature along the growth direction and the direction normal to it. TO and NP peaks were resolved.     

用乒乓球化解浮力教学中的两个难点

1 实验:浮力方向总是竖直向上的 在初中物理浮力的教学中,浮力的方向总是竖直向上的,教材中没有专门的实验直观显示,学生虽能理解浮力的方向是向上的.但理解浮力方向总是竖直向上的就有一定困难.     

葡萄糖粉末的近红外光谱

糖尿病患者的自我监测是减少由糖尿病引发并发症的重要手段。无创血糖监测的近红外光谱分析方法是最具有应用前景的一种，葡萄糖近红外光谱则是研究无损血糖检测基础。本文通过实验采集了葡萄糖粉末的近红外光谱，并对结果作了详细分析。