第23届希望杯邀请赛部分试题的向量解法

本文利用向量基底思想与回路法结合的方法给出第23届希望杯全国数学邀请赛培训和竞赛试题中的向量问题的优美解答,供大家参考.例1(高一培训题41题)△ABC中,已知AB     

Temperature dependence of line parameters of ~(12)C~(16)O_2 near 2.004 μm studied by tunable diode laser spectroscopy

The absorption spectrum of carbon dioxide at 2.004 μm has been recorded at sample temperatures between 218.0 K and room temperature, by using a high-resolution tunable diode laser absorption spectrometer(TDLAS) combined with a temperature controlled cryogenically cooled absorption cell. The self-, N~(2-), and air-broadening coefficients for nine transitions of ~(12)C~(16)O_2 belonging to the 20012←00001 band in the 4987 cm~(-1)–4998 cm~(-1) region have been measured at different temperatures. From these measurements, we have further determined the temperature dependence exponents of the pressure-broadening coefficients. To the best of our knowledge, the temperature dependence parameters of the collisional broadening coefficients are reported experimentally for the first time for these nine transitions. The measured halfwidth coefficients and the air temperature dependence exponents of these transitions are compared with the available values reported in the literature and HITRAN 2012 database. Agreements and discrepancies are also discussed.     

基于灰色BP神经网络的陀螺电机状态预测

陀螺电机状态直接影响惯导系统的精度和可靠性,对其进行预测是惯导系统性能评估和寿命预测的重要途径。利用灰色理论的建模预测方法对随机性较大的数据预测精度不高;BP神经网络模型的预测方法具有良好的非线性和自学习能力,但训练效率不高且训练效果受样本数影响较大,网络容易限于局部最小值。针对陀螺电机状态特征参数的特点,本文提出一种基于灰色BP神经网络的混合模型。该模型利用BP神经网络对灰色模型误差进行建模,模型输出返回灰色模型进行输入修正。利用灰色理论、BP神经网络以及混合模型对状态特征参数进行建模和预测,结果表明,混合模型的预测误差比灰色模型减小了约2／3,比神经网络减小了约1／3,证明了该模型的有效性。     

基于光纤输出光斑旋转的位移传感器

实验设计了两个光纤环,减小光纤环1的半径使光纤发生宏弯损耗,获得两光斑。此时再压缩光纤环2,发现两光斑整体随光纤环2的受压位移在一定受压范围内表现出了很好的旋转性。通过两光斑旋转角度随光纤环2受压位移的一一对应关系,经实验数据处理获得了光斑角度与线圈受压位移存在一定范围的线性关系。同时实验分析了光纤环2的直径和光纤环2的紧绕圈数对压缩位移灵敏度的影响。     

Demonstration of a Shock-Timing Experiment in a CH Layer at the Shen Guang Ⅲ Laser Facility

Shock-timing experiments are indispensable to inertial confinement fusion mainly because the timing of multiple shock waves is crucial to understanding the processes of laser irradiation of targets. Investigations into shock waves driven by a two-step radiation pulse in polystyrene(CH) capsule targets are experimentally conducted at the Shen Guang Ⅱ laser facility. Differing from the traditional shock-timing implementation in which one shock wave could catch up with another one in solid CH, in this experiment, the second shock front in a rarefaction CH layer is observed through velocity interferometry. This second shock could also be made to converge with rarefaction waves within only a few micrometers of the CH capsule by designing the two-shock coalescence time. A shock-timing diagnostic technique to tune the multi-shock convergence in the CH capsule can thereby be achieved.The experimental results in the CH layer are quasi-quantitatively interpreted using streamlines simulated with the Multi-1 D program. The experimental results are expected to offer important information for target structure and laser pulse design, both of which are important for realizing inertial confinement fusion.     

Amberlyst-15催化丁酮氧化制备过氧化甲乙酮

作为一种新型绿色催化剂,离子交换树脂能够代替某些有机反应中的传统催化剂。本文以离子交换树脂Amberlyst-15为催化剂,由30%的双氧水、丁酮和稀释剂邻苯二甲酸二丁酯合成过氧化甲乙酮。在双氧水与丁酮的摩尔比为1.0,离子交换树脂与丁酮的质量比为0.06,反应温度为27℃,反应时间55 min的条件下,过氧化甲乙酮的产率接近86%,活性氧含量为12.9%。Amberlyst-15在循环使用8次后,依然保持良好的稳定性。研究表明:Amberlyst-15用于过氧化甲乙酮的制备具有催化活性高、可重复使用、清洁无腐蚀等优点,为工业环保生产有机过氧化物提供了新途径。