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数学中,有一些概念、定义、定理在结构上、性质上、用途上颇为相似,存在紧密联系.它们就像数学大家庭中的一对对“伴侣”一样,相互融合、相互渗透又相互作用、相互对比,共同诠释着数学的奥妙.笔者以高中数学几个经典知识为例,从分析数学的角度,让这一对对数学伴侣“双剑合璧”,以彰显数学别样之美.一、正、余弦定理“双剑合璧”,彰显数学“证明”之美 相似文献
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Several key problems involved in the analyses of spectra of asymmetric top molecules, i.e., the effective Hamiltonian, the representation and basis vector, identification of energy levels, the selection rules, the relative intensity, and Zeeman tuning rate, were elucidated systematically. Introducing the high-order centrifugal distortion terms into the effective Hamiltonian, the precision for calculation has been improved substantially, which allows us to analyze the high-lying rotational transitions. A global analysis of all available spectra of 14N16O2 in the ground vibronic state has been made to obtain a set of molecular constants of 14N16O2 in the ground vibronic state which is the most precise and extensive so far. Using the improved parameters, some FIR LMR lines left unassigned hitherto have been identified successfully. 相似文献
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本文报道国内建成的远红外激光磁共振 (FIRLMR)光谱仪的技术特点和工作原理。该谱仪采用CO2 激光横向泵浦远红外激光 ,样品吸收池置于远红外激光谐振腔内 ,由聚丙烯薄膜与远红外激光增益池隔开以获得很高的灵敏度 ,从而对寿命很短的自由基分子进行研究。利用该光谱仪在远红外波段测量得到了多个瞬态自由基分子CCH ,CF和CH2 的光谱 ,这些自由基分子由微波放电产生的氟原子与甲烷CH4 反应生成。 相似文献
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A simple model has been developed to describe the Zeeman patterns of far-infrared laser magnetic resonance spectra of the monobromomethyl radical CH2Br observed at 447.3 and 671.1μm. A satisfactory agreement between the experimental spectra of the radical and their simulation with this simple model has been achieved. This approach can be used to gain further information about the structure and the spectrum of this interesting radical. 相似文献
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COHERENT POPULATION TRAPPING IN MULTILEVEL LASER-INDUCED CONTINUUM STRUCTURE SYSTEM INCLUDING CASCADE TWO-PHOTON PROCESSES 下载免费PDF全文
We have investigated the atomic coherent population trapping in a mul tilevel laser-induced continuum structure system including cascade two-photon processes, in which two sets of quasicontinua of excited levels to be modeled as the Bixon-Jortner quasicontinuum are laser-embedded into a previously structu reless atomic continuum.The condition leading to the atomic coherent population trapping and the coherent population trapping state are given explicitly. And th e effects of the Fano factors, the laser intensities and the detunings on the am ount of population trapped in the atomic bound states and the populations distri buted in the two sets of quasicontinua are also examined. 相似文献
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Extended Measurement of the v2 (1- ←0+) Band of H3O+ by Mid-Infrared Diode Laser Spectroscopy 下载免费PDF全文
Twenty-five new R-branch lines of the v2(1^-← 0^+) band of H3O^+ are measured using diode laser velocity modulation spectroscopy between 1070 and 1230 cm^-1. The H3O^+ ions are produced in a high voltage ac discharge with water diluted in helium. The observed lines together with all the previously published measurements are fit to the standard vibration-rotational Hamiltonian of an oblate symmetric top, yielding a set of improved molecular constants. All the sextic centrifugal distortion constants for both 0^+ and 1^- states are determined precisely. The observed R(13, 0) transition is shifted about -0.129 cm^-1 from its calculated value, indicating that a near degeneracy exists between the (13, 0)^+ and (13, 3)^- ground-state rotation-inversion levels. 相似文献
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根据塞曼效应理论和激光磁共振光谱技术(LMR)的基本原理,讨论了双原子分子2П态的塞曼效应特性并导出了解释分子塞曼跃迁的简明代数拟合方程,用这些方程对14N16O(X2Π1/2,3/2)及15N16O(X2Π3/2) (υ=1←0)的LMR谱线进行数据拟合,得到塞曼跃迁上、下子能级的gJ因子值和二级塞曼效应因子k2.将按Hund耦合情形(a)及过渡情形(ab)的理论和拟合方程计算出的磁场位置分别与实验结果相比较,结果表明对NO分子而言,过渡情形(ab)能较真实反映它的耦合情况,且在较高强度磁场下,必须计及二级塞曼修正.验证了采用上述代数拟合方程实现新分子LMR谱线标识和指认的可靠性,并提供了系统的处理方法. 相似文献