带跳的非线性随机微分方程的Lyapunov指数的估计

本文研究了带跳的非线性随机微分方程Lyapunov指数的估计,在适当的条件下,确定其Lyapunov指数q的值．对于给定的步长h,考虑此微分系统的Euler离散化模型,给出了的理论误差估计.     

Study of photon-induced L3 vacancy alignment for elements La to U

Alignment of photon-induced L₃ vacancies is studied in rare earth and highZ elements at energies of experimental interest, near thresholds to 60 keV, under nonrelativistic dipole approximation. Numerical calculations of the matrix element are undertaken to produce theoretical data for comparison with the experimental findings. The A₂ values being s>0.1 at photoelectron energies <20 keV are certainly higher than 5–8% uncertainties quoted in experimental results. Present findings are from a very basic model, hydrogen-like and can further be treated as reference to observe the impact of screening, relativistic, multipole and retardation corrections to the model     

解可分离约束双凹规划问题的一种外逼近方法[英文]

在本文中，我们提出了双凹规划问题和更一般的广义凹规划问题。我们给出了双凹规划问题的整体最优性条件，并构造了一个有限终止外逼近算法。     

On error bounds for lower semicontinuous functions

We give some sufficient conditions for proper lower semicontinuous functions on metric spaces to have error bounds (with exponents). For a proper convex function f on a normed space X the existence of a local error bound implies that of a global error bound. If in addition X is a Banach space, then error bounds can be characterized by the subdifferential of f. In a reflexive Banach space X, we further obtain several sufficient and necessary conditions for the existence of error bounds in terms of the lower Dini derivative of f. Received: April 27, 2001 / Accepted: November 6, 2001?Published online April 12, 2002     

HIGH ACCURACY FINITE VOLUME ELEMENT METHOD FOR TWO-POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

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CONVERGENCE OF AN ITERATION METHOD WITHOUT DERIVATIVE

In this paper, we give a convergence theorem and error estimates for an iteration method under new Kantorovitch-Ostrowski type condition using the information of higher derivatives at initial points. Compared with the corresponding study in [3],the convergence determination is established under one global condition, instead of two , on the function.     

NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD, the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1-and L2-norm space estimates and the 0((△t)2) estimate for time variable are obtained.     

Energy inconsistency of Galerkin approximationsfor plane Couette flow

For classical solutions of the incompressible Navier-Stokes equations (NSE) the energybalance between kinetic energy, work done by external forces, and viscous dissipation holds rigorously true. It is shown in this paper that standard Galerkin approximations violate energy balance in the case of plane Couette flow, whereas Poiseuille flow turns out to be energy consistent at any cutoff. The main reason for this discrepancy is seen in the different boundary conditions between the stationary linear shear flow and its disturbances. In our analysis, essentially, we introduce an auxiliary external force field which enforces the finite dimensional Galerkin approximation to fulfil the NSE. It is exemplarily demonstrated how the energy discrepancy decreases when the number of disturbed modes is increased which couple to the stationary shear flow.     

谱约束下对称正交对称矩阵束的最佳逼近

讨论了对称正交对称矩阵的广义逆特征值问题，得到了通解表达式和最佳解的表达式。     

Inexact Newton methods for the nonlinear complementarity problem

An exact Newton method for solving a nonlinear complementarity problem consists of solving a sequence of linear complementarity subproblems. For problems of large size, solving the subproblems exactly can be very expensive. In this paper we study inexact Newton methods for solving the nonlinear, complementarity problem. In such an inexact method, the subproblems are solved only up to a certain degree of accuracy. The necessary accuracies that are needed to preserve the nice features of the exact Newton method are established and analyzed. We also discuss some extensions as well as an application. This research was based on work supported by the National Science Foundation under grant ECS-8407240.