Numerical methods for finding multiple eigenvalues of matrices depending on parameters

Summary. Let be a square matrix dependent on parameters and , of which we choose as the eigenvalue parameter. Many computational problems are equivalent to finding a point such that has a multiple eigenvalue at . An incomplete decomposition of a matrix dependent on several parameters is proposed. Based on the developed theory two new algorithms are presented for computing multiple eigenvalues of with geometric multiplicity . A third algorithm is designed for the computation of multiple eigenvalues with geometric multiplicity but which also appears to have local quadratic convergence to semi-simple eigenvalues. Convergence analyses of these methods are given. Several numerical examples are presented which illustrate the behaviour and applications of our methods. Received December 19, 1994 / Revised version received January 18, 1996     

环状连续强激光下光学薄膜的瞬温和热畸变

详细研究了非冷却光学薄膜元件在环形激光光束辐照下的瞬态温度分布和随后的热畸变，并且用泰曼干涉仪实际测量了连续波氧碘激光辐照各种非冷却光学元件的热畸变量并与理论计算相比较，分析结果表明理论和实验相一致。     

Effect of absorbed pump power on the quality of output beam from monolithic microchip lasers

The dependence of the beam propagation factor (M ² parameter) with the absorbed pump power in the case of monolithic microchip laser under face-cooled configuration is extensively studied. Our investigations show that the M ₂ parameter is related to the absorbed pump power through two parameters (α and β) whose values depend on the laser material properties and laser configuration. We have shown that one parameter arises due to the oscillation of higher order modes in the microchip cavity and the other parameter accounts for the spherical aberration associated with the thermal lens induced by the pump beam. Such dependency of M ² parameter with the absorbed pump power is experimentally verified for a face-cooled monolithic microchip laser based on Nd³⁺ -doped GdVO₄ crystal and the values of α and β parameters were estimated from the experimentally measured data points.     

Surface grating formation and erasing on a-Se films

Surface relief formation at holographic recording on amorphous selenium films was demonstrated and investigated. The presence of this optical phase modulation component is essential for ensuring significant, stable and erasable optical recording in a-Se films at 290–320 K temperatures, where conventional photodarkening was known as insignificant and unstable. Photocrystallization can only be observed in super-exposed a-Se films at the given experimental conditions of hologram recording. Erasing behavior of surface relief gratings under heat treatment was also investigated in order to reveal further details of the mechanism. Photoinduced structural transformations within the amorphous phase, connected to local ordering under the condition of light-induced fluidity, are proposed as an explanation for the relief formation and erasing. The observed reversible optical recording process may be useful for the various optoelectronic applications of photoconductive a-Se layers. Received: 12 June 2000 / Accepted: 6 June 2001 / Published online: 30 August 2001     

An algebraic characterization ofB-convergent Runge-Kutta methods

Summary In the analysis of discretization methods for stiff intial value problems, stability questions have received most part of the attention in the past.B-stability and the equivalent criterion algebraic stability are well known concepts for Runge-Kutta methods applied to dissipative problems. However, for the derivation ofB-convergence results — error bounds which are not affected by stiffness — it is not sufficient in many cases to requireB-stability alone. In this paper, necessary and sufficient conditions forB-convergence are determined.This paper was written while J. Schneid was visiting the Centre for Mathematics and Computer Science with an Erwin-Schrödinger stipend from the Fonds zur Förderung der wissenschaftlichen Forschung     

Point approximation of a space-homogeneous transport equation

Summary We present an approximation method of a space-homogeneous transport equation which we prove is convergent. The method is very promising for numerical computation. Comparison of a numerical computation with an exact solution is given for the Master equation.     

Ag+掺杂的立方相Y2O3:Eu纳米晶体粉末发光强度研究

采用化学自燃烧法制备了不同Ag⁺掺杂浓度的Y₂O₃:Eu纳米晶体粉末样品(［Y³⁺］∶［Eu³⁺］∶［Ag⁺］=99∶1∶X，X=0—3.5×10^-2)，以及通过退火处理得到了相应的体材料.根据X射线衍射谱确定所得纳米和体材料样品均为纯立方相.实验表明在纳米尺寸样品中随着Ag离子浓度的增加，荧光发射强度随之增加，当X=2×10^-2时达到最大值，其发光强度比X=0时提高了近50%.当Ag离子浓度继续增加，样品发光强度保持不变.在相应的体材料样品中则没有观察到此现象.通过对各样品的发射光谱，激发光谱，X射线衍射图谱，透射电镜(TEM)照片和荧光衰减曲线的研究，分析了引起纳米样品荧光强度变化的原因是由于Ag离子与表面悬键氧结合，从而使这一无辐射通道阻断，使发光中心Eu³⁺的量子效率提高；Ag⁺的引入所带来的另一个效应是使激发更为有效.这两方面原因使发光效率得到了提高.     

Yb3+掺杂KY(WO4)2激光晶体生长、结构与光谱分析

采用顶部籽晶提拉法(TSSG)生长出Yb:KY(WO₄)₂(Yb:KYW)激光晶体.对预烧后的原料及晶体进行了XRD分析，结果表明，分别在920℃和600℃预烧8h后的熔质和助熔剂基本上形成一相，抑止了实验中的挥发问题；所生长的晶体为β-Yb:KYW，计算其晶格常数为a=1.063nm，b=1.034nm，c=0.755nm，β=130.75°.测得不同厚度样品的吸收光谱，结果表明样品在933nm和981nm有较强的吸收峰，计算出主峰981nm的吸收截面σ关键词： Yb:KYW TSSG法 晶体结构 光谱参数     

纳米级精度分光路双频干涉度量系统的设计

为完成快速、精确的外观轮廓度量,设计了一种新型纳米级精度分光路双频干涉度量系统。系统由低频差双频激光干涉度量模块和微探头及二维工作台两部分组成。微探针以轻敲式接近样品至几十纳米时,受原子力作用发生偏转,利用双频干涉模块度量其纵向偏转量,并对样品进行梳状式度量得到外观形貌。根据双频激光的实际光源,对原有双频干涉度量理论进行了改进提高。进行了系统组建和实验验证。结果表明:系统具有纳米级精度,可用于超精样品外观轮廓度量。     

Angle theorems for the Lagrangian mean curvature flow

We prove that symplectic maps between Riemann surfaces L, M of constant, nonpositive and equal curvature converge to minimal symplectic maps, if the Lagrangian angle for the corresponding Lagrangian submanifold in the cross product space satisfies . If one considers a 4-dimensional K?hler-Einstein manifold of nonpositive scalar curvature that admits two complex structures J, K which commute and assumes that is a compact oriented Lagrangian submanifold w.r.t. J such that the K?hler form w.r.t.K restricted to L is positive and , then L converges under the mean curvature flow to a minimal Lagrangian submanifold which is calibrated w.r.t. . Received: 11 April 2001 / Published online: 29 April 2002