Rehabilitation of the Gauss-Jordan algorithm

Summary In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.     

O在Au(111)表面吸附的密度泛函理论研究

应用密度泛函理论，本文系统地研究了O在Au(111)表面上的吸附能、吸附结构、功函数、电子密度和投影态密度，给出了覆盖度从0.11ML到1.0ML的范围内，O的吸附特性随覆盖度变化的规律.研究发现O的稳定吸附位为3重面心立方(fcc)洞位，O在fcc洞位的吸附能对覆盖度比较敏感，其值随着覆盖度的增加而减小；O诱导Au(111)表面功函数的变化量与覆盖度成近线性关系，原因是Au表面电子向O偏移，形成表面偶极子；O—Au的相互作用形成成键态和反键态，且反键态都被占据，造成O—Au键很弱，O吸附能较小. 关键词： 表面吸附 Au(111)表面 密度泛函理论 电子特性     

光码分多址系统中光学相关接收机判决阈值的分析

介绍了光码分多址系统中常用地址码（一维扩时码、二维码和三维码）的特点，并对它们各自的互相关均值和方差进行了理论分析。基于非相干光码分多址系统中光学相关接收机的基本原理，结合不同的用户地址码，对系统误码率性能进行了分析，得到了接收机最佳判决阈值与地址码基本特性参数和系统同时用户数间的关系。最后，给出了数值仿真结果。结果表明，对于采用特定地址码的光码分多址系统，只有选择合适的接收机判决阈值，系统的误码率性能才能达到最佳。研究结果对光码分多址系统中接收机判决阈值的选取具有一定的参考作用。     

非傍轴平顶高斯光束M2因子两种定义的比较研究

基于功率密度的二阶矩方法，推导出了非傍轴平顶高斯(FG)光束束宽和远场发散角的解析表达式.研究表明，当w0/λ→0时，远场发散角趋于渐近值θmax=63.435°，与阶数无关.使用非傍轴高斯光束代替傍轴高斯光束作为理想光束，研究了非傍轴FG光束的M2因子，并与传统定义的M2因子作了比较.在非傍轴范畴，非傍轴FG光束的M2因子不仅与阶数N有关，而且与w0/λ有关.按照定义，当w0/λ→0时，非傍轴FG光束的M2因子不等于0，对阶数N=1, 2, 3时，M2因子分别趋于0.913,0.882和0.886.当N→∞时，M2因子取最小值M2min=0.816.     

K(o)the-Bochner空间的凸性

本文利用K(o)the函数空间的性质以及K(o)the函数空间与K(o)the-Bochner空间的关系,讨论了K(o)the-Bochner空间E(X)的凸性,主要结果如下:(a)给出E(X)的端点的充分条件,得到了E(X)严格凸的判据,相应地推广了Lp(μ,X)以及LΦ(X)的结果;(b)讨论了E(X)的弱局部一致凸和局部完全k-凸;(c)刻画了E(X)的强凸,给出了E(X)强凸的充要条件.     

具有某种断面的半群的研究进展

本文综述了几类具有特殊断面的半群的近期研究结果。在介绍逆半群和正则半群的一般结构之后，概述了具有逆断面的正则半群的结构和同余格的研究成果。总结了作为逆断面的推广的可裂断面，纯正断面，正则^*－断面和恰当断面。提出了可以进一步研究的重要的问题。     

掺钕聚甲基丙烯酸甲酯的光学特性

研究了制备的掺钕螯合物Nd(DBM)3Phen材料的吸收光谱、激发光谱、荧光光谱,应用Judd-Ofelt理论计算了该材料的强度参量．分析了钕离子激发态4F3／2的辐射寿命(631 μs)和4F3／2→4IJ′跃迁的受激发射截面和荧光分支比．     

On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation

In this article, we will derive an equality, where the Taylor series expansion around ε = 0for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted.By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-B(a)cklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-B(a)cklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.     

弱(L_1,L_2)-BLD映射的正则性

本文首先将文［１］中的ＢＬＤ映射推广为弱（Ｌ１，Ｌ２）－ＢＬＤ映射，并证明了如下正则性结果：存在两个可积指数 Ｐ１＝Ｐ１（ｎ，Ｌ１，Ｌ２）＜ｎ＜ｑ１＝ｑ１（ｎ，Ｌ１，Ｌ２），使得对任意弱（Ｌ１，Ｌ２）－ＢＬＤ映射ｆ∈（Ω，Ｒｎ），都有ｆ∈（Ω，Ｒｎ），即ｆ为（Ｌ１，Ｌ２）－ＢＬＤ映射．     

Asymptotique de la norme $L^2$ d'un cycle géodésique dans les revêtements de congruence d'une variété hyperbolique arithmétique

Let M be an arithmetic hyperbolic manifold and be a codimension 1 geodesic cycle. In this paper, we study the asymptotic growth of the -norm of the lifts of F in the congruence tower above M. We obtain an explicit value for the growth rate of this norm. In particular, we provide a new proof of a celebrated result of Millson [Mi] on the homology of the arithmetic hyperbolic manifolds. The method is quite general and gives a new way of getting non zero homology classes in certain locally symmetric spaces. Received: 20 April 2001; in final form: 26 September 2001 / Published online: 28 February 2002