Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

化学位移各向导性对半整数自旋四极核的2D NMR章动的影响

考察了化学位移各向异性对半整数自旋四极核2D NMR章动的影响.用数值方法对2D NMR章动实验的演化期的Hamiltonian矩阵进行对角化,然后用帐篷法进行粉末平均,获得了自旋为I=3/2、5/2、7/2和9/2的四极核在不同化学位移各向异性下的2D NMR章动谱.实验结果与理论计算符合较好.     

玻色—爱因斯坦凝聚和兰姆位移

扼要地介绍了ＢＥＣ研究的近况和研究方向，同时报道了我们在ＢＥＣ的光散射和兰姆位移方面的研究工作     

大非线性相移下光学非线性Z扫描特性的研究

采用高斯分解法(GD)对大非线性相移下的Z扫描特性进行了分析，通过对数值算法的优化，将GD推广到对脉冲入射激光下大非线性相移下的Z扫描理论分析.对不同条件下大非线性相移Z扫描曲线峰谷结构的比较，发现在大非线性相移的情况下，Z扫描曲线的峰和谷随透过光阑或入射光强变化表现出某些新的特性.随着透过光阑孔径的增加，Z扫描曲线峰的变化要明显快于谷的变化，而且在谷明显存在的情况下，峰很快消失.采用皮秒脉冲激光下的纯二硫化碳实验对理论结果加以验证，实验结果和理论分析相一致.我们的分析结果对大非线性相移下Z扫描测量有一定的指导性意义，避免在大非线性相移下对Z扫描结果产生错误的分析. 关键词： 大非线性相移 高斯分解法 Z扫描     

Pulsed pump: Thermal effects in solid state lasers under super-Gaussian pulses

Solid state laser (SSL) powers can be realistically scaled when pumped by a real, efficient and multimode pulse. In this work, a fourth-order super-Gaussian pulse was assumed as a pump for SSL’s and a complete analytical expression for the thermal phase shift is given. Moreover, the focal length of thermal lens in paraxial ray approximation regime was studied. The results when applied to a Ti: sapphire crystal show an appreciable correction for abberation compared to a top-hat pulse.     

对称双吡咯甲烷的合成与分子内氢键的研究

５－甲基吡咯－２－羧酸酯在磺酰氢，溴或四乙酸铅作用下，生成相应的在５－甲基上含取代基的产物，后者不经分离不便可自缩合得标题化合物，核磁共振氢谱研究和分子构象木匠，当３，３位的取代基为甲酸（酯）基或乙酸（酯）基时，可形成３，３位酯基与另一吡咯环上的氮氢之间的分子内氢键，而３，３位是其它取代基，如乙酰基，丙酸（酯）基，丁酸（酯）基时不能形成类似的分子内氢键。     

New Chiral Kemp's Acid Diamides for Chiral Amine Recognition by 1 H NMR

Two Kemp's acid diamides were synthesized and applied to chiral amine recognition using ¹H NMR analysis. One derivative based on 1-(1-naphthyl)ethylamine had good chiral recognition of six amines and was useful to determine the optical purity for three amines, i.e., methylbenzylamine, 1-(1-naphthyl)ethylamine and 1- henylpropylamine,however, the cyclohexylethylamine derivative showed little discrimination for the amines studied. Together with the results for alkylamines, it was shown that aromatic structure was important for aromatic shielding anisotropy and –– interactions between host and guest. The structure of the 1-(1-naphthyl)ethylamine derivative in solution was also considered based on ¹H NMR data and computer simulation.     

Manifestation of diamagnetic chemical shifts of proton NMR signals by an anisotropic shielding effect of nitrate anions

A remarkable upfield shift of the py_α protons of complexed 2,2′-bipyridine in [cis-Pd(bpy)(NO₃)₂] is observed which is considered to originate from the anisotropic influence of suitably positioned coordinated nitrate anions around the Pd(II) centre of the molecule. A typical complexation-induced downfield shift is observed for the NH₂ protons in [cis-Pd(en)(NO₃)₂] where ‘en’ stands for ethylenediamine.