求解非线性方程的一个新方法

提出了一种求解非线性方程的数值方法，此方法不需要导数的计算，其收敛阶与抛物线法相同，但计算量要比抛物线法小得多。     

The Hamiltonian Canonical Form for Euler-Lagrange Equations

Based on the theory of calculus of variation, some suffcient conditions are given for some Euler-Lagrangcequations to be equivalently represented by finite or even infinite many Hamiltonian canonical equations. Meanwhile,some further applications for equations such as the KdV equation, MKdV equation, the general linear Euler Lagrangeequation and the cylindric shell equations are given.     

RICE CONDITION NUMBERS OF CERTAIN CHARACTERISTIC SUBSPACES

This paper proposes the Rice condition numbers for invariant subspace, singular sub-spaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are derived by applying perturbation expansions of orthogonal projection operators.     

有界连通区域上Dirichlet空间及其算子

本文主要讨论了有界连通区域Dirichlet空间上Toeplitz算子的Fredholm性质,计算了符号在C1中的Toeplitz算子的本性谱和Fredholm指标．     

An LQP Method for Pseudomonotone Variational Inequalities

In this paper, we proposed a modified Logarithmic-Quadratic Proximal (LQP) method [Auslender et al.: Comput. Optim. Appl. 12, 31–40 (1999)] for solving variational inequalities problems. We solved the problem approximately, with constructive accuracy criterion. We show that the method is globally convergence under that the operator is pseudomonotone which is weaker than the monotonicity and the solution set is nonempty. Some preliminary computational results are given.The author was supported by the NSFC grants Nos: 70571033 and 10571083.     

关于PFI-代数与剩余格

本文提出了一种强FI代数-PFI代数,并且深入研究了它的性质,借此进一步揭示了FI-代数和剩余格之间更加密切的联系,进而以FI-代数为基本框架建立了R0-代数、正则剩余格等逻辑系统的结构特征(包括对隅结构)及其相互关系．这种以FI-代数为基础来统一处理剩余格和R0-代数的方法,同样适合于格蕴涵代数和MV代数等代数结构,而且从中更能清楚地看出它们之间的密切联系,也将有助于对相应形式逻辑系统与模糊推理的研究．     

关于消失平均振动的一个注记

本文得到了极大算子的几个不等式,并从这些结果推广了函数f∈L_(loc)~1(R,dx)属于VMO(R,dx)的一个必要条件。     

推广的Kantorovich算子在Ba空间中的逼近

利用Ditzian-Totik光滑模,研究了推广的Kantorovich算子在Ba空间中的逼近,得到逼近的正定理与等价定理.所得结果改进、推广和统一了一些作者的结果.     

An implicit method for linear ill‐posed problems with perturbed operators

An implicit iterative method is applied to solving linear ill‐posed problems with perturbed operators. It is proved that the optimal convergence rate can be obtained after choosing suitable number of iterations. A generalized Morozov's discrepancy principle is proposed for the problems, and then the optimal convergence rate can also be obtained by an a posteriori strategy. The convergence results show that the algorithm is a robust regularization method. Copyright © 2006 John Wiley & Sons, Ltd.