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…     

Unusual Transport Properties near the Insulator-Metal Transition in Colossal Magnetoresistive Manganites

It is argued that a combination of the Griffiths theory and the double-exchange mechanism predicts the random distribution of ferromagnetic metallic clusters above the Curie temperature TC in colossal magnetoresistive manganites. Along this line, we propose a model for the temperature dependence of resistivity that yields a quantitative agreement with experimental data obtained in a typical manganite La2/3Ca1/3MnO3. Our result indicates that the formation and growth of ferromagnetic metallic clusters are responsible for the observation of unusual transport properties near the insulator-metal transition.     

大焦深成像系统仿真实验研究

如何增大非相干光学成像系统的焦深是应用光学研究领域的热点问题.本文对采用高次非球面光学掩模板与图像处理相结合增大成像光学系统焦深的新方法进行了深入分析,建立了大焦深成像系统仿真实验模型,并进行了大焦深成像系统仿真实验.实验结果证明了该方法在维持原相对孔径的同时使光学系统在较大的离焦范围内有好的成像质量.实际应用中还要综合考虑模板参量、信噪比等关键因素.     

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.