Kirchhoff方程的相对常值特解及其Lyapunov稳定性

对于超细长弹性杆静力学的Kirchhoff方程，用动力学的概念和方法研究其常值特解 和稳定性问题.计算了Kirchhoff方程相对固定坐标系、截面主轴坐标系以及中心线Frenet 坐标系的常值特解，进行了Kirchhoff动力学比拟，用一次近似理论分别讨论了它们的Lyapu nov稳定性，导出了若干稳定性判据，并在参数平面上绘出了稳定域. 关键词： 超细长弹性杆 Kirchhoff方程 常值特解 Lyapunov稳定性     

光纤光栅选频掺Yb3+双包层光纤激光器

利用相位掩模法 ,在D形内包层掺Yb3 双包层光纤一端直接写制出Bragg光栅 ,用作双包层光纤激光器的输出腔镜 .试验得到了线宽为 0 196nm ,波长为 10 5 8 2nm ,最高输出功率为 5 70mW的稳定激光输出 ,解决了激光器中模式竞争造成的输出不稳定现象 .从速率方程出发 ,对激光器的输出功率与抽运功率、光栅反射率的关系以及最佳光纤长度进行了理论分析 ,结果与实验符合很好     

The canonical solution operator of $ {\bar \partial } $ on weighted spaces with holomorphic coefficients

On weighted spaces with strictly plurisubharmonic weightfunctions the canonical solution operator of and the ‐Neumann operator are bounded. In this paper we find a class of strictly plurisubharmonic weightfunctions with certain growth conditions, so that they are Hilbert‐Schmidt operators between weighted spaces with different weightfunctions, if they are restricted to forms with holomorphic coefficients. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Piecewise Deterministic Markov Control Processes with Feedback Controls and Unbounded Costs

The control of piecewise-deterministic processes is studied where only local boundedness of the data is assumed. Moreover the discount rate may be zero. The value function is shown to be solution to the Bellman equation in a weak sense; however the solution concept is strong enough to generate optimal policies. Continuity and compactness conditions are given for the existence of nonrelaxed optimal feedback controls.     

On a class of preconditioners for solving the Helmholtz equation

In 1983, a preconditioner was proposed [J. Comput. Phys. 49 (1983) 443] based on the Laplace operator for solving the discrete Helmholtz equation efficiently with CGNR. The preconditioner is especially effective for low wavenumber cases where the linear system is slightly indefinite. Laird [Preconditioned iterative solution of the 2D Helmholtz equation, First Year's Report, St. Hugh's College, Oxford, 2001] proposed a preconditioner where an extra term is added to the Laplace operator. This term is similar to the zeroth order term in the Helmholtz equation but with reversed sign. In this paper, both approaches are further generalized to a new class of preconditioners, the so-called “shifted Laplace” preconditioners of the form Δφ−k²φ with . Numerical experiments for various wavenumbers indicate the effectiveness of the preconditioner. The preconditioner is evaluated in combination with GMRES, Bi-CGSTAB, and CGNR.     

On a resolvent estimate of the Stokes equation with Neumann–Dirichlet‐type boundary condition on an infinite layer

This paper is concerned with the standard Lp estimate of solutions to the resolvent problem for the Stokes operator on an infinite layer with ‘Neumann–Dirichlet‐type’ boundary condition. Copyright © 2004 John Wiley & Sons, Ltd.     

Existence and uniform decay for Euler–Bernoulli beam equation with memory term

In this article we prove the existence of the solution to the mixed problem for Euler–Bernoulli beam equation with memory term. The existence is proved by means of the Faedo–Galerkin method and the exponential decay is obtained by making use of the multiplier technique combined with integral inequalities due to Komornik. Copyright © 2004 John Wiley & Sons, Ltd.     

Analysis of finite dimensional approximations to a class of partial differential equations

In this paper, a unified approach for analysing finite dimensional approximations to a class of partial differential equations boundary value problems (second‐kind Fredholm differential equations) is introduced. The approach is shown to be general despite of its extremely simple form. In particular, it is expected to be useful in the convergence analysis of finite element methods for solving PDE problems. Three specific examples are presented to illustrate the broad applicability of the approach. Copyright © 2004 John Wiley & Sons, Ltd.     

On the Zeros of Orthogonal Polynomials: The Elliptic Case

Constructive Approximation - Let E = [–1, α] \cup [β, 1], –1 &;lt; α &;lt; β &;lt; 1, and let (pn) be orthogonal on E with respect to the weight function...