准晶体中八方晶系点群的对称性与矩阵表示

从理论上对准晶体中八方晶系各点群进行了研究.运用八方晶系各点群的极赤投影图,列出了各点群的所有对称操作;填出了固有点群822的群乘表.运用坐标变换和群论在自定义的八方坐标系中,推导出八方晶系点群所有对称操作的矩阵.这32个3×3矩阵的结构是相当简洁的,它们的矩阵元只有5种可能取值:0,±1,±2.其中2是反映八方晶系准晶体所具有的准周期性的特殊无理数.     

关于矩阵方程X+A*X-nA＝I的正定解

本文对任意正整数n界定了矩阵方程X A*X-nA=I的正定解的特征值的范围,给出了它的极大正定解一个充分条件.     

一种可能的简并谱NNS分布

利用随机矩阵理论,通过对一特殊情形的简并谱展开研究,得到了简并谱一种可能的最小相邻间距NNS分布函数．研究表明,由于简并的存在,简并谱不仅可分解成随机谱和规则谱两个子谱,同时还影响其规则谱,使规则谱的能级斥力减少．     

Nonlinear Effects for Bose Einstein Condensates in Optical Lattices

Cold atoms and, more recently, Bose-Einstein condensates （BEC＇s） in optical lattices have attracted increasing interest since their first realization. In particular, the formal similarity between the wavefunction of a BEC inside the periodic potential of an optical lattice and of the electrons in a crystal lattice has triggered theoretical and experimental efforts alike. Many phenomena from condensed matter physics, such as Bloch oscillations and Landau-Zener tunneling have been shown to be observable also in optical lattices. An important difference between electrons in a crystal lattice and a BEC inside the periodic potential of an optical lattice is the strength of the self interaction and hence the magnitude of the nonlinearity of the system. Electrons in a metal are almost noninteracting, whereas atoms inside a BEC interact strongly. A＇ perturbation approach is appropriate in the former case while in the latter the full nonlinearity must be taken into account. From this feature new physics is expected. Most experiments to date have been carried out in the regime of shallow lattice depth, for which the system is well described by the mean field Gross-Pitaevskii equation with a periodic potential. Moreover, the nonlinearity induced by the mean-field of the condensate has been shown, both theoretically and experimentally, to give rise to instabilities in certain regions of the Brillouin zone. These instabilities are not present in the corresponding linear system, i.e. the electron system. Experimental and theoretical results on the subject of nonlinear Landau-Zener tunneling and nonlinearity-induced instabilities in a Bose-Einstein condensate interacting with an external periodic potential will be presented.     

关于圈的完全正矩阵实现

本文给出了一个关联图为圈的非负、半正定矩阵A为完全正的一个充要条件.我们还证明了这样的矩阵A（当A为完全正时）的分解指数即为A的阶数.     

全光纤反射式马赫曾德尔干涉型多波长滤波器的研究

对反射式的马赫－曾德尔干涉型多波长滤波器的性能作了较详细的研究，得出了两个耦合器的分光比和两臂的臂长差对其输出谱线的影响，结论对设计制作不同性能指标的该型多波长滤波器具有重要的参考价值。实验上用光纤熔融拉锥法制作了该种器件，实验结果与理论相符合。     

贝塞尔-高斯脉冲光束在色散介质中的时间和光谱特性

 对等衍射长度贝塞尔-高斯脉冲光束在色散介质中的时间和光谱特性作了研究，结果表明，通过选择适当的空间参数，贝塞尔-高斯脉冲光束沿轴上传输时，脉冲宽度不变。传输距离小于无衍射长度时，随衍射角增加，功率谱形状未变，脉冲波形保持不变；传输距离大于无衍射长度时，随衍射角增加，光谱由蓝移变为红移，脉冲展宽。     

K_(1,n)-free图具有给定性质的[a,b]-因子的一个充分条件

图G称为K1,n-free图,如果它不含K1,n作为其导出子图.对K1,n-free图具有给定性质的[a,b]-因子涉及到最小度条件进行了研究,得到一个充分条件.     

关于一类具有相同非负群逆和M-P逆的非负矩阵的进一步研究

1引言设A是n阶非负方阵．设矩阵方程(1)AXA=A,(2)XAX=X,(3)(AX)~T= AX,(4)(XA)~T=XA,(5)AX=XA．A具有非负广义逆是指存在非负方阵X满足方程(1)～(4),并记为A~(?)．A具有非负群逆是指存在非负方阵X满足方程(1),(2),(5),并记为A~#．在A~(?)存在的前提下,两者相同的充分必要条件有(a)AA~(?)=A~(?)A；(b)A~(?)=p(A),其     

Σ-原子能级的理论计算与分析

通过对Σ-原子的理论分析,数值求解了相应的Dirac方程,得到 了一组Σ-原子的能级值,与实验数据相当吻合;其结果连同K-原子的情况支持了Batty 光学模型势在奇异原子中应用的正确性,进而表明核子间的强相互作用力为吸引力.