矩阵方程A^TXB＋B^TX^TA=D的极小范数最小二乘解的迭代解法

1 引言 设R^m×n表示m×n实矩阵的全体，A^T表示矩阵A的转置，R（A）和N（A）分别表示矩阵A的值域和零空间，A^＋表示矩阵A的Moore—Penrose广义逆，A×B表示矩阵A与B的Kronecker乘积，     

温梯法生长的Ti:Al2O3晶体的光谱分析

本文研究了不同掺Ti^3＋浓度对温梯法生长的Ti：Al2O3晶体吸收光谱、荧光光谱和X射线衍射光谱的影响。根据吸收光谱提出了一个色心模型。对比了样品各处420nm荧光谱，发现掺Ti^3＋浓度越大，该处荧光强度越弱，同时解释了420肿处荧光峰的起源。对比了样品各处720nm处的荧光谱，发现掺Ti^3＋浓度越大，该处荧光强度越强。X射线衍射谱（XRD）表明，衍射峰强度随掺Ti^3＋浓度的增大而逐渐增强。     

广义Bott-Duffin逆及加权Drazin逆的若干性质

本文给出了L-零矩阵的广义Bott-Duffin逆及矩阵的加权Drazin逆的若干性质及表达形式．     

钾分子2~3Π_g→a~3Σ_u~＋辐射跃迁的荧光寿命测量

本文介绍了用Ｂｏｘｃａｒ测量分子激发态荧光寿命的方法，测量了钾分子２３ΠΣ→ａ３Σｕ＋辐射跃迁的寿命，计算机模拟的结果与实验基本符合。     

Quantum coherent control of two-photon transitions by square phase-modulation

A femtosecond laser pulse can be tailored to control the two-photon transitions using the ultra-fast pulse-shaping technique. This paper theoretically and experimentally demonstrates that two-photon transitions in molecular system with broad absorption line can be effectively controlled by square phase-modulation in frequency domain, and the influence of all parameters characterizing the square phase-modulation on two-photon transitions is systemically investigated and discussed. The obtained results have potential application in nonlinear spectroscopy and molecular physics.     

POPULATION TRAPPING IN MULTI-LEVEL SYSTEM VIA QUANTUM INTERFERENCE

Population trapping via quantum interference in a multi-level system driven by a coherent field is investigated. The influences of the alignment of the transition dipole moments and the energy-level separation of the upper levels are taken into account. Detailed trapping population profiles under the different conditions are given. The research result is helpful for simplifying the theoretical model and selection rational energy level system.     

一种新的亚酞菁的共振三阶非线性光学性质

用简并四波混频技术研究了一种新的亚酞菁(三新戊氧基溴硼亚酞菁)的三阶非线性光学性质.测得纯固体三新戊氧基溴硼亚酞菁的三阶非线性极化率χ(3)pure和分子二阶超极化率〈γ〉分别为69×10-10esu和30×10-31esu.χ(3)pure的响应时间为20ps.并对这些结果进行了讨论 关键词：     

加权总体最小二乘问题的分析

总体最小二乘问题由Golub和Van Loan首先进行数学的分析,随后人们对于总体最小二乘问题的算法、解的各种形式、总体最小二乘解和最小二乘解的关系、总体最小二乘解的扰动理论以及数值试验作了大量的研究工作。近来,[10]中给出了总体最小二乘问题(TLS)较一般地讨论。另一方面,Golub和Van Loan研究了总体最小二乘问题的特殊均加权形式。本文试图在[10,11]的基础上讨论最一般的总体最小二     

关于A+,A+MN的表达式及其应用

For A ∈ Cm×nr, let M and N be Hermitian positive definite matrices oforder m and n respectively. We derived the representation of the Moore-PenroseA+MN in terms of maximal nonsin-inverse A+ and weighted Moore-Penrose inverse +gular submatrices of A. In our notation,A+ = | detA[plq]|2A+pq1/vol2(A) (p,q)∈N(A)AM+N = 1/vol2(A)(p,q)∈N(A) |detA[p|q]|2N-1/2A+pqM1/2where A=M1/2 AN -1/2. From this, we propose a new method to calculate A+A+MN. The results generalize that of Moore-Penrose inverse in [2][3].     

Na-Na碰撞引起的钠共振荧光线型变异

在钠原子气体中,观察到了由激光诱导的光抽运和Na－Na碰撞效应引起的钠原子共振荧光的线型变化。运用计及“速度改变碰撞”效应的速率方程计算和讨论了共振荧光的线型变窄现象。