探秘数学问题1888

1 问题与解答《数学通报》2010年12月第1888号数学问题如下:设A(非顶点)为双曲线上任一点,则过A点切线作法如下:在双曲线实轴上找一点B,使B与A在虚轴同侧,B到虚轴距离是A到虚轴距离的2倍,以B为圆心,以A到虚轴距离平方2倍,减去实半轴长平方的算术平方根为半径作圆,与过A的实轴的垂线交于点C,过C作圆的切线交实轴于D,则直线AD就是该双曲线的切线,给予证明.     

三角板中的向量问题

2009年高考湖南卷第15题：如图1,两块斜边长相等的直角三角板拼在一起,若→AD=x→AB＋y→AC,则x=________,y=_________.     

Improved Active Vibration Isolation Systems

The control force, feedback gain, and actuator stroke of several active vibration isolation systems were analyzed based on a single-layer active vibration isolation system. The analysis shows that the feedback gain and actuator stroke cannot be selected independently and the active isolation system design must make a compromise between the feedback gain and actuator stroke. The performance of active isolation systems can be improved by the joint vibration reduction using an active vibration isolation system with an adaptive dynamic vibration absorber. The results show that the joint vibration reduction method can successfully avoid the compromise between the feedback gain and actuator stroke. The control force and the object vibration amplitude are also greatly reduced.     

超细金属铁颗粒的高分子修饰及其悬浮液的磁流变性能

报道了γ射线辐照方法合成具有良好分散性的高分子复合金属铁粒子，分别选择十二烷基硫酸钠、溴化十六锘三甲基胺、Ｔｗｅｅｎ－８０、ＴｒｉｔｏｎＸ－２００和ＯＰ－１０表面活必睡有机单体、无机铁颗粒一起制备乳状液，通过对这种含有超细金属铁颗粒乳状液稳定性的比较，以寻求合适的乳化剂，并对以ＴｒｉｔｏｎＸ－２００为乳化剂时合成出的高聚物复合铁颗进行了ＸＲＤ、ＴＥＭ和ＩＲ表征，还将实验中所获得的高聚物复合铁粒子与