从数学解题看数学美

本论述了“教学好玩”(陈省身语)的五个方面；教学语言精确；教学发现(类比发现；归纳发现和直党发现)；教学解题思路；教学思想方法和数学应用都体现了教学关。     

负反馈放大电路的网络参数分析法

利用双口网络参数分析负反馈放大电路的方法．通过对典型电流串联负反馈电路的z参数分析，得到了与其它分析方法相同的结果．分析过程简洁，物理概念清晰．     

The completely positive and doubly nonnegative completion problems

We prove the following. Let G be an undirected graph. Every partially specified symmetric matrix, the graph of whose specified entries is G and each of whose fully specified submatrices is completely positive (equal to BB^T for some entrywise nonnegative matrix B), may be completed to a completely positive matrix if and only if G is a block-clique graph (a chordal graph in which distinct maximal cliques overlap in at most one vertex). The same result holds for matrices that are doubly nonnegative (entrywise nonnegative and positive semidefinite).     

In search of new resonance structures in dissociative photoionization of H2

We present a theoretical study of dissociative photoionization of H₂ via the ¹Π_u symmetry in the photon energy range 30–43 eV. Our results explain the various peaks observed in the experiments below 40 eV and illustrate, in particular, the important role of the ²Π_u(2pπ_u) ionization threshold. At higher photon energies, they suggest the existence of new resonance structures that may be associated with doubly excited states of H₂ lying above the third and fourth ionization thresholds (the Q₃ and Q₄ resonance series). From the calculated resonance parameters, we conclude that the dominant mechanism at high photon energies should involve the Q₄ (and probably higher) doubly excited states of H₂. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

Synthesis of the new chiral tridentate ligand bis(pyrid-2-ylethyl) menthylphosphine and its use in the palladium-catalyzed allylic alkylations

We describe the synthesis of a new asymmetric P,N,N′-tridentate ligand (bis(pyrid-2-ylethyl) menthylphosphine, BPEMP), containing two pyridyl rings and (1S,2R,5S)-menthylphosphino group. The ligand is obtained in five steps from natural abundant l-menthol. The coordination behavior of the ligand toward cationic (allylic)Pd(II) moiety and its first application in palladium-catalyzed asymmetric allylic alkylation are presented. Crystallographic and spectroscopic analyses reveal that [(η³-allylic)Pd(BPEMP)]⁺ complex forms only one isomer in the solid state as well as in solution.     

Asymmetric Diels-Alder Reactions of Chiral Menthyl α-Sulfinylacrylates

Introducing two chiral auxiliaries, sulfoxide and menthol, into an acrylate would have either matched or mismatched pair systems. The presence of chiral menthol in α-sulfinylacrylates can change the diastereoselectivity from 24% d.e. to a single diastereomer by manipulation of the double asymmetric strategy.     

Particle velocity measurements in induction plasma spraying

Laser Dopple anemometry (LDA) measurements of the particle velocity are carried out during an induction plasma spraying operation. The velocity of nickel alloy particles, or molten droplets, at the exit of an induction plasma torch prior to impact on the substrate is shown to vary with the plasma and powder injection conditions. Plasma spraying under soft vacuum (150–450 Torr) gives rise to substantially higher particle velocities (40–60 m/sec) compared to those attained at atmospheric pressure (10–20 m/sec).     

Remote substituent effect favoring the formation of syn-adducts in the chelation controlled radical reactions of γ-benzyloxy-α-methylenecarboxylic acid esters

The chelation controlled radical reactions of ethyl γ-benzyloxy-α-methylenecarboxylates bearing a bulky γ-substituent, such as CHMe₂, CHPh₂, c-C₆H₁₁ and CH(Ph)OTBDMS, with alkyl iodides gave the syn-adducts with high diastereoselectivities. However, the diastereoselectivity for the substrates bearing a γ-substituent CH(i-Pr)OTBDMS depended critically on the configuration of the substituent; the substrate bearing the OTBDMS group anti to the γ-benzyloxy group showed poor diastereoselectivity, but its diastereomer gave syn-adduct exclusively. The high syn-selectivitiy is referred to the H-atom transfer to the outside face of radical center in the sharply folded seven-membered chelate intermediate bearing the ethoxy group with Z-geometry. The corner flapping of the radical center atom of the global minimum energy conformer generates a local minimum conformer and the H-atom transfer to the outside face of the radical center of the newly formed structure gives the anti-adduct. The poor diastereoselectivity is due to the very small energy difference between the two conformers and consequently both the syn- and anti-adducts are yielded in nearly equal amounts.     

地面突风对通航飞行器的影响及数值模拟研究

突风一直以来都是危及飞行安全的重要气象要素之一,造成国民经济和人民生命财产的损失。利用常规观测资料、ADWR-X多普勒气象雷达资料和ERA5逐小时再分析资料,对四川盆地西部一次爆发性大风过程中风场的精细化特征、成因及对飞行的影响进行诊断和模拟研究,结果表明：此次大风过程风速增长快,爆发性强。地面风速自午后开始出现4次波动,且每一次波动期间风速峰值呈增加趋势,时间呈缩短趋势。由于第4次波动风速呈爆发性增加,最大瞬时风达到了16.1 m/s,地面风速脉动值超过5 m/s,致使跑道区域内流场的不稳定性增加,起降跑道侧风值超过了中小型飞行器的起降标准。高空动量下传对本次大风过程中风速的爆发性增加起主导作用。中层强偏南气流与低层偏北急流配和,中层辐合以及低层辐散下沉的垂直结构使得低层下沉气流异常强劲,将900～850 hPa的大风核快速向地面传导。通过天气研究与预报(weather research and forecasting, WRF)模式四重嵌套对本次过程进行模拟,表明WRF对盆地西部冷空气补充南下引起的在风速演变趋势、风速最大值和大风影响时段的风向有较好的模拟能力,对飞行起飞和着陆有一...     

高层建筑外附雨篷的表面风压和气动力系数

采用风洞试验方法研究高层建筑外附雨篷的风压特征,分析风压系数、风压相关性、非高斯性和整体升力系数随风向角的变化,给出围护结构的设计风压,最后研究倾角和出挑长度对整体力系数的影响. 研究发现,高层建筑外附雨篷上表面风压系数在正迎风时最大值接近1.4,系气流受到后方高层建筑的阻挡下翻导致;上、下表面的最大整体压力系数出现正迎风情况,最大值分别为1.24和0.76;上、下表面的最大整体升力系数出现侧风面,最大值分别为1.13和1.01;上下叠加后测点风压的非高斯性比单表面增强;上表面和下表面的升力系数在0°~70°风向呈现高斯分布,在80°~180°风向呈现较强的非高斯分布;高层建筑外附雨篷上表面的极值正压大于下表面;雨篷整体升力系数按照倾角-10°、0°、10°依次递增.