数学问题解答

20 0 2年 8月号问题解答(解答由问题提供人给出 )1 3 86　试证明 :有两边及一个角的角平分线对应相等的两个三角形全等 .(湖北宜昌市十一中学　是海松　443 0 0 3 )证明　设△ＡＢＣ和△Ａ′Ｂ′Ｃ′的三边分别记为ａ、ｂ、ｃ和ａ′、ｂ′、ｃ′,三条角平分线分别记为ｔａ、ｔｂ、ｔｃ和ｔａ′、ｔｂ′、ｔｃ′,半周长分别记为ｐ和ｐ′.当有两边及它们的夹角的平分线对应相等时 ,不妨设ｂ=ｂ′,ｃ =ｃ′,ｔａ =ｔａ′.由ｔａ =2ｂ+ｃ ｂｃｐ(ｐ -ａ) ,ｔａ′ =2ｂ′+ｃ′ ｂ′ｃ′ｐ′(ｐ′ -ａ′)得 :2ｂ+ｃ ｂｃｐ(ｐ -ａ) =2ｂ+ｃ ｂｃｐ…     

《电子技术基础》课程教学的几点思考

《电子技术基础》是学好其他专业课程的基础,它研究电子元器件和电子电路在各种领域的应用,它的发展水平直接影响着各行各业的发展,因此,应帮助学生学好本课程．1联系实际激发学生学习的主动性兴趣是学习的动力,因此在学习之初就必须激发学生的学习兴趣,消除厌学畏难的心理．如在绪论课,给学生介绍日常生活息息相关的电子产品,如电视机、手机、DVD等,同时介绍电子技术在自动控制中的重要性,让学生了解其实用性,激发学习兴趣．再如,在     

Fast Optical Switching Using Oriented Cyanine Dye-Doped Nematic Liquid Crystal

A cyanine dye, 2-[7-（1,3-dihydro-1,3,3-trimethyl-2H-indol-2-ylidene）-1,3,5-heptatrienyl]-1,3,3-trimethyl-3H-indolium iodide （NK-125）, is doped in 4-cyano-4＇-pentylbiphenyl （5 CB）, and the mixture is sandwiched between two pieces of rubbed glass plates. The third-order nonlinear optical properties of the oriented NK-125-SCB layers are measured by the resonant femtosecond degenerate four-wave mixing （DFWM） technique at 760 nm. The third-order nonlinear optical susceptibility of one of the present samples is 5.5×10^-8 esu. The slow DFWM response of the NK-125-SCB layers due to a population grating is accelerated by the increasing laser power because of amplified spontaneous emission （ASE）. On the other hand, we do not observe a similar phenomenon for NK-125- polyethylene glycol （PEG-400）. Oriented NK-125 molecules in nematic liquid crystals must have very high ASE efficiency. Hence the population grating in a DFWM signal disappears within about 4 ps. It is expected that NK-125-SCB can be used as a material for very fast all-optical switching.     

Crystal-Orientation Dependent Evolution of Edge Dislocations from a Void in Single Crystal Cu

The micro-void growth by dislocation emission under tensile loading is explored with focus on the influence of crystal orientations. Based on the elastic theory, a dislocation emission criterion is formulated. It is predicted that the preferential location of dislocation nucleation and its threshold stress are dependent on the crystal orientation. Large-scale molecular dynamics （MD） simulations are also performed for single crystal copper to illustrate the dislocation evolution pattern associated with a nano-void growth. The results are in line with those given by the theoretical prediction. As revealed by MD simulations, the characteristics of void growth at micro-scale depend greatly on the crystal-orientation.     

祖国万岁

祖国万岁1 算式中“祖国万岁”代表4个小同的数字,相同的汉字代表相同的数字,你能很快写出这道有趣的“国庆”算式吗?提示:“庆”代表最小的质数.     

石英晶体微天平技术研究纳米TiO_2表面Cu(Ⅱ)吸附与光化学还原过程

环境中排放的重金属离子Cu!对水生和陆生生物有强的毒害性。饮用水中Cu!的浓度高于1.0mg·L-1时,将会导致人畜得血色沉着病和胃肠粘膜病[1]。Cu!无法进行生物降解,除去废水中Cu!的常见方法有离子交换、置换、化学沉淀等[2],然而这些方法需要消耗大量的化学试剂,成本高。近来,研     

新试剂10—（2—羧基苯偶氮）—9—菲酚的合成及与铈显色反应的研究

本文研究新试剂１０－（２－羧基苯偶氮）－９－菲酚（简称ＣＡＰ的合成，测定试剂的高解常数。研究了试剂ＣＡＰ与铈（Ⅳ）的显色反应。在表面活性剂ＯＰ存在下，光度法测定球墨铸铁中铈的含量，结果较满意。     

[Co(amp)2Cl2]2[ZnCl4]体系中两对称异构体的2D NMR研究

The two symmetrical isomers in [Co(amp)₂Cl₂]₂[ZnCl₄](amp=2-(Aminomethyl)pyridine) system were syn-thesized by general oxidation method and were separated by chromatography and recrystallization method. Their configurations were assigned by using 2D NMR techniques, particularly the NOESY NMR spectra. Solvent used was Me₂SO-d₆ with the central peak of the CD₃ septet as the reference ( ₁₃C,δ 39.37; ₁H,δ 2.49 relative to SiMe₄). Cation exchange media used was Dowex 50Wx 2(H⁺ form, 200～400mesh; Biorad).