特殊矩阵反问题的最小二乘解及最佳逼近

1引言近年来,关于矩阵的反问题国内外有诸多学者都做了研究工作.如,双对称(反对称)矩阵反问题、中心对称(反中心对称)矩阵反问题、对称次反对称(反对称次对称)矩阵反问题.这些矩阵在信息论、线性系统理论及数值分析等领域中有其广泛应用.研究反问题的工具大多是奇异值分解(SVD)[6,8,9,5]、广义奇异值分解(GSVD)[4],且部分学者利用广义逆的方法[7]讨论上述的问题.本文的主要思想是找出这些矩阵的共同特点,利用矩     

利用干涉探测技术对相干声子的研究

利用带有环形回路的干涉探测装置,研究了光程差精确为零时参考光和探测光的相干振荡信号,对数据的拟合给出了相干声子诱导的折射率相关变化.由信噪比较高的反射率相位变化信号,不仅清楚地辨别出铝膜中的四种相干声子模式,还分辨出声子回波信号.     

Optimal Control of Population Transfer in Three-Level A System with Genetic Algorithms

Population transfer in a three-level A system is simulated numerically and optimized. Almost complete population transfer from |1) to |3) is achieved by a genetic algorithm while the population in state |2) reached minimum over the entire evolution at the same time. The result shows that the optimal pulse sequence is the well-known stimulated Raman adiabatic passage (STIRAP) scheme. The detuning of pump pulse and Stokes pulse Δp and Δs with the opposite sign and the chirps χp and χs with the same sign are in favour of the complete and robust population transfer for few-cycle laser pulse. Rabi frequencies Ωp and Ωs have insensitive effects on the complete population transfer during a large scope of their ratio when they are large enough.     

Nonlinear optical properties of 75TeO2－20Nb2O5－5ZnO glasses doped with CeO2

Nonlinear optical properties of 75TeO_2－20Nb_2O_5－5ZnO glasses doped with CeO_2 have been investigated with a self-diffracted time-resolved degenerate four-wave mixing (DFWM) technique at different excitation intensities and lattice temperatures. The DFWM signal exhibits three peaks at higher excitation intensities, where a main peak appears at zero delay time and two rather weak side peaks are located symmetrically at the negative and positive time delay. Due to destructive interferences between the fifth- and third-order polarizations, the line-shape of the main peak around the zero time delay evolves from single peak into a double-peak structure with increasing excitation intensity. Two side peaks emerge at the positive and negative time delay and gradually intensify with increasing excitation intensity or lattice temperature, and their positions are independent of the pulse duration, temperature and excitation intensity, which are attributed to the many-body Coulomb interaction.     

关于一点的投影到一仿射集合的加权扰动分析

本文讨论了在C~n中一点的投影到一个仿射集合的加权扰动分析,我们假定长方矩阵A有任意秩,扰动是任意的这最一般性情形。分别研究了当A有扰动δA后为(?),当rabkA=rank(?)和rankA≠rank(?)两种情况下解x的相对误差界,推广了文献[3][4][11][12]的主要结果。     

飞秒激光诱导瞬态光栅多级衍射

瞬态光栅测量法是一种时间分辨四波混频技术,它是研究介质非线性特性一种重要的手段.这种瞬态光栅测量方法对任何导致介质折射率改变相当灵敏,因而被广泛应用于研究物理和化学动力学过程.在介质中,当两束泵浦光在空间和时间上重合时,就构成一个光栅,光栅空间周期Λ=λex/2sin(θ/2), λex是激发波长,θ是两束激发光束之间的夹角.另外一束探测光(时间延迟)被这个光栅衍射,在布拉格衍射角度上产生一束相干光.在这种情况下,这个光栅形状是正弦的,而且只有一级衍射信号产生.然而,在超快超强激光(飞秒脉冲)作用下,可能在光栅亮区域里诱导一种 "溶解态",这样光栅形状将不再是正弦的,多级衍射信号可能产生.     

Effect of four-wave mixing on electromagnetically induced transparency in Λ-type system with a two-photon probe field

Using density matrix equation, we calculate analytically as well as numerically the effect of the four-wave mixing (FWM) field on electromagnetically induced transparency (EIT) in the rubidium 5S_{1/2}-5P_{3/2}-5D_{5/2} Λ-type system with a two-photon probe field. The calculated results are in good agreement with Fulton's experimental results in 1995 Phys. Rev. A 52 2302.     

COMPETITION EFFECT IN ATOMIC-MOLECULAR SYSTEM

The competition effects among the processes that occur in the two-photon 3S→4D excitation of Na atom in Na-Na₂ vapour mixture are observed: such as atomic ionization, optical-pumped stimulated radiation, four-wave frequency mixing and molecular stimulated diffuse-band radiation, etc. The dip at the two-photon resonance in the excitation spectrum for the diffuse-band radiation under high temperature condition is interpreted as the suppression of population in 4D state.     

长方矩阵常见广义逆的代数扰动

本文详细讨论了长方矩阵常见广义逆的代数扰动理论,并给出了他们代数扰动的表达式,改进了文献3,4的相应结论.     

激光及其相关学科的发展

在物理学家汤斯、肖洛、卜洛赫洛夫和巴索夫等人研究工作的基础上,美国人梅曼于1960年研制出世界上第一台激光器(红宝石激光器)。在梅曼获得成功之后的几个月内,又有好几种激光器研制成功,其中包括第一台连续波运转的激光器——氦氖激光器。以后,各种激光器竞相出现,呈现一派欣欣向荣的气象。