Carnot-Caratheodory空间中的变换论

Klein发表著名的埃尔兰根纲领,由群论角度研究了空间变换群的不变量,从而引进了各种不同的几何学．本文利用Felix Klein的观念,研究Carnot-Caratheodory空间{M,Q,g}(又称为次黎曼流形)上的类似问题,给出了次黎曼流形中的共形不变量和射影不变量．本文给出的共形和射影不变量可视为黎曼情形的一种自然推广．由于次黎曼流形与黎曼流形之间有着本质的差异,故此,本文通过次黎曼流形上存在的唯一非完整联络(Nonholonomic connections)来刻画所提的问题．     

A complete global solution to the pressure gradient equation

We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants. The global existence of a smooth solution was established in Dai and Zhang [Z. Dai, T. Zhang, Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics, Arch. Ration. Mech. Anal. 155 (2000) 277-298] up to the free boundary of vacuum. We prove that the vacuum boundary is the coordinate axes.     

The Level-split of the Two-level Entangled Atom in an Optical Field

The behavior of a two-level entangled atom in an optical field with circular polarization is studied in this paper. The interaction of an optical field and one of the entangled atoms is analyzed in detail. A general solution of the SchrAo¨Gdinger equation about the motion of the entangled atom is obtained. The properties of the action are dependent on the initial state of the atom. By detecting the entangled atom out of the field, we can obtain the state of the other atom moving in the field. It is shown that the state of the atom out of the field will influence the energies of the split-levels of the atom in the field.     

Formation of Interfacial Layers in LaAlO3/Silicon during Film Deposition

We have studied the interracial reactions between amorphous LaAlO3 thin films and Si substrates, using high- resolution transmission electron microscopy and x-ray photoelectron spectroscopy. It has been shown that the interracial layer between LaAlO3 film and Si substrate chemical states show that the ratio of La 4d3/2 to Al 2p is SiLaxAlyOz. The depth distributions of La, Si and Al of the interfacial layer remains unchanged with the depth compared to that of the LaAlO3 film. Moreover, the Si content, in the interracial layer gradually decreases with increasing thickness of the interracial layer. These results strongly suggest that the Al element is not deficient in the interracial layer, as previously believed, and the formation of a SiLaxAlyOz interracial layer is mainly due to the diffusion of Si from the substrate during the LaAlO3 film deposition. With the understanding of the interracial layer formation, ones can control the interface characteristics to ensure the desired performances of devices using high-k oxides as gate dielectrics.     

Investigation on nonradiative decay of I13/2→I15/2 transition of Er-doped oxide glasses

Nonradiative decay of ⁴I_13/2→⁴I_15/2 transition of Er³⁺ has been investigated in a series of oxide glasses. For Er³⁺-doped glass samples, the Judd-Ofelt analysis on absorption spectra was performed and the fluorescence lifetime was determined by extrapolating to zero Er³⁺ concentration limit. Infrared spectra were measured in order to investigate the influence of OH⁻ groups in different glasses. The effects of glass matrix on the decay rate were discussed from the viewpoint of phonon energy, variations of effective fields, and OH⁻ groups. Compared to other glasses, phosphate glass presents low quantum efficiency and large nonradiative decay rate due to its high phonon energy and hygroscopic behavior.     

稀磁半导体Zn1-xMnxTe吸收光谱压力红移的理论研究

以自由Mn²⁺离子的径向波函数为基础,通过引入电子云延伸效应系数κ来修正这一径向波函数,得到了稀磁半导体Zn_1-xMn_xTe晶体中Mn²⁺离子的径向波函数.以此波函数为基础,研究了Zn1-xMnxTe晶体吸收光谱的高压谱移特性,并且得到了吸收谱中四条谱线随压力的红移规律.     

The solvability conditions for inverse eigenproblem of symmetric and anti‐persymmetric matrices and its approximation

The problem of generating a matrix A with specified eigen‐pair, where A is a symmetric and anti‐persymmetric matrix, is presented. An existence theorem is given and proved. A general expression of such a matrix is provided. We denote the set of such matrices by ??????_Eⁿ. The optimal approximation problem associated with ??????_Eⁿ is discussed, that is: to find the nearest matrix to a given matrix A* by A∈??????_Eⁿ. The existence and uniqueness of the optimal approximation problem is proved and the expression is provided for this nearest matrix. Copyright © 2002 John Wiley & Sons, Ltd.     

基于分形维数的液体爆炸分散中界面破碎形态研究

通过对爆炸抛撒图象的处理,得到液体界面的曲线.采用盒维数的计算方式,计算界面曲线的分形维数.通过对各时刻液体界面分形维数的变化研究,分析爆炸抛撒近场阶段的变化过程,同时观察到蘑菇状尖顶的出现与破碎,以及空化区域的形成和消失现象。     

稳态锁模产生4ps激光脉冲

首次利用ＧａＡｓ光电导开关，控制Ｎｄ：ＹＬＦ激光器腔内Ｑ值，实现稳态锁模，获得脉宽和能量稳定性极高的４ｐｓ激光脉冲。     

5,10-二(对-氨基)四苯基卟啉和吖啶黄之间激发能量的传递

利用Forster能量传递机制,研究了氯仿溶液中吖啶黄向5、10-二(对-氨基)四苯基卟啉(简称TBP)的激发能量传递和TBP.浓度变化时对能量传递速度常数的影响.实验结果表明,吖啶黄和TBP之间具备能量共振传递的条件,并且计算了能量共振传递的临界距离为0.42nm、传递效率为0.72和传递速度常数为1.42×107s-1.这些数据对复合膜光电转换器件的设计将具有重要意义.