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…     

High Power One- and Two-Order Cascaded Raman Lasers Based on Home-Made Phosphosilicate Fibre

One- and two-order cascaded Raman fibre lasers are demonstrated by using home-made P-doped Raman fibres.An output power of 2.8 W at 1245 nm with a slope efficiency of 33.4% and an output power of 2.0 W at 1495 nm with a slope efficiency of 23.5% are obtained with the pump source at 1069. 7nm.     

火花熔蚀-电感耦合等离子体光谱法分析地质矿物

火花熔蚀-电感耦合等离子体光谱法(SA-ICP)用于测量锆石中铪-锆比值和锰铁矿瘤中的铈、钴、铁、铅、镍和磷。用信背比和信嗓比的序贯单纯形优化法建立了用于高压火花和氩气ICP系统的六个操作参数。将磨细的样品与铜压成饼,从样品中熔蚀出的分析物和基体元素的原于发射信号的时间相关性给出一种用火花来作选择取样的方法。测量锆石中的铪、锆浓度比的精密度为4%(相对标准偏差)。对于锰铁矿瘤,根据分析线对锰(Ⅱ)257.610纳米线强度比的光谱测量结果达到分析精密度范围为7-14%(相对标准偏差)。分析的准确度用参比物USGS诺得(Nod)P-1的标准物加入法来决定,而与锰浓度的测量无关。     

不同羧酯化的聚马来酸十八醇酯齐聚物的镉盐LB膜成膜特…

由聚马来酸酐和十八醇合成了一系列不同羧酯比的聚马来酸十八醇酯，并以其为成膜材料，ＣｄＣｌ２水溶液为亚相制备了一系列聚马来酸十八醇酯镉盐ＬＢ膜，借助小角Ｘ射线衍射和红外吸收光谱表征了成膜条件及羧酯比对ＣｄＰＭＡ膜有序结构的影响。在较高膜压和快速提拉条件下，低羧酯比的ＣｄＰＭＡ可得到有序性很高的Ｙ－型ＬＢ多层膜；高羧酯比的ＣｄＰＭＡ得不到高有序性的ＬＢ多层膜。     

Multiband Terahertz Photonic Band Gaps of Subwavelength Planar Fractals

Optical transmission properties of subwavelength planar fractals in terahertz （THz） frequency regime are studied by means of time-domain spectroscopy. The transmission spectra with multiple pass bands and stop bands are observed. The tunable photonic band gaps are realized by changing the angle between the principle axis of planar fractal and the polarization of THz wave. The possible application of the subwavelength optical component is discussed. We attribute the detected transmittance from subwavelength fractals to localized resonances.     

低电阻测量设计实验中电位差计指针不稳的解决方法

本文分析了J33Q型电位差计在实验中指针不稳的原因,并提出了解决的办法。     

Design and Fabrication of 1.06 μm Resonant-Cavity Enhanced Reflective Modulator with GaInAs/GaAs Quantum Wells

A resonant-cavity enhanced reflective optical modulator is designed and fabricated, with three groups of three highly strained InGaAs/GaAs quantum wells in the cavity, for low voltage and high contrast ratio operation. The quantum wells are positioned in antinodes of the optical standing wave. The modulator is grown in a single growth step in an molecular beam epitaxy system, using GaAs/AlAs distributed Bragg reflectors as both the top and bottom mirrors. Results show that the reflection device has a modulation extinction of 3 dB at -4.5 V bias.     

N-(取代)对三氟甲基苯基-1,3,5-三取代吡唑-4-酰胺衍生物的合成与生物活性

设计合成10个未见文献报道的N-对三氟甲基苯基-1,3,5-三取代吡唑-4-酰胺类化合物, 其结构经元素分析, ¹H NMR, IR 确证. 初步生物活性测试结果表明, 部分化合物对水稻纹枯病、小麦赤霉病、辣椒枯萎病和马铃薯晚疫病有一定的杀菌活性.