Newton-Leibniz integration for ket-bra operators in quantum mechanics and derivation of entangled state representations

Newton-Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac’s symbols (ket versus bra, e.g., |q〉〈q| of continuous parameter q) in quantum mechanics are usually not commutative. Therefore, integrations over the operators of type |〉〈| cannot be directly performed by Newton-Leibniz rule. We invented an innovative technique of integration within an ordered product (IWOP) of operators that made the integration of non-commutative operators possible. The IWOP technique thus bridges this mathematical gap between classical mechanics and quantum mechanics, and further reveals the beauty and elegance of Dirac’s symbolic method and transformation theory. Various applications of the IWOP technique, including constructing the entangled state representations and their applications, are presented.     

4一致反超图的最小边数问题

混合超图是在超图的基础上添加一个反超边得到的图．超边和反超边的区别主要体现在着色要求上．在着色中,要求每一超边至少要有两个点着不同的颜色,而每一反超边至少有两个点着相同的颜色．最大最小颜色数分别称为混合超图的上色数和下色数。本文主要研究反超图,即只含反超边的超图。讨论了上色数为3的4一致超图的最小边数问题．给出了上色数为3的4一致反超图的最小边数的一个上界和一个下界．     

物理实验考核初探

在以素质教育为目标的今天，各类学校对实验的认识越来越重视，一般都建立了专门的物理实验室和配备专职的实验员．但对物理实验教学的效果学生实验能力的考查却不够重视．如，考核没有新的实验内容，仍停留在让学生死记一些实验现象或步骤，或者重复做某个实验操作等．随着物理教学改革的深入，物理实验的考核问题必须给予充分的重视，下面对实验考核中的几个问题作初步的探讨．     

Generation of UV laser light by stimulated Raman scattering in D2, D2/Ar and D2/He using a pulsed Nd:YAG laser at 355nm

A pulsed Nd:YAG laser at 355nm is used to pump Raman cell filled with D_2, D_2/Ar and D_2/He. With adequately adjusted parameters, the maximum photon conversion efficiency of the first-order Stokes light (S_1, 396.796nm) reaches 33.33% in D_2/Ar and the stability of S_1 in pure D_2 is fairly high, the energy drift being less than 10% when the pump energy drifts in the range of 5%. The conversion efficiency and stability, which are functions of the composition and pressure of the Raman medium and the energy of pump laser, are investigated. The result has been used to optimize the laser transmitter system for a differential absorption lidar system to measure NO_2 concentration profiles.     

The algebraic Bethe ansatz for the Izergin–Korepin model with open boundary conditions

We present the procedure of exactly solving the Izergin–Korepin model with open boundary conditions by using the algebraic Bethe ansatz, which include constructing the multi-particle state and achieving the eigenvalue of the transfer matrix and corresponding Bethe equations. We give a proof about our conclusions on the multi-particle state based on an assumption. When the model is U_q(su(2)) quantum invariant, our results agree with that obtained by analytic Bethe ansatz method.     

3-正则图的分割问题是NP-完全问题

证明了3-正则图的最小平分问题和最小α-分割问题都是NP-完全问题.     

NASICON型化合物结构的NMR研究

在水热晶化合成一系列NASICON型化合物的基础上,应用固体高分辨³¹P和²⁹Si MAS NMR,研究了几种NASICON化合物的结构,观察其骨架原子P和Si在结构中的状态及分布,并解释了由于在结构中发生取代作用而引起,Si或P的化学位移的变化.     

一类Narcissistic反应过渡态的优化

我们对一类narcissistic 反应XCH_2-CH_2Y→[过渡态TS]→YCH_2—CH_2X (1)进行了研究,结果表明其过渡态能在对称性限制下由能量极小化方法较容易地给出. 采用IMSPAK分子轨道从头算程序,在IBM VM/370计算机系统上用STO—3G极小基组以平衡几何构型的能量梯度优化方法,在对称性限制下对反应(1)的几种反应体系的过渡态构型进行了优化,其结果列于表1.     

The perturbation bounds for the solution of weighted kronecker product linear systems using thew-weighted drazin inverse

The classical perturbation theory is extended to the weighted Kronecker product linear systems W(A? B)Wx =h. Upper bounds are derived for the normwise condition number.