Convergence Rate of The Trust Region Method for Nonlinear Equations Under Local Error Bound Condition

In this paper, we present the new trust region method for nonlinear equations with the trust region converging to zero. The new method preserves the global convergence of the traditional trust region methods in which the trust region radius will be larger than a positive constant. We study the convergence rate of the new method under the local error bound condition which is weaker than the nonsingularity. An example given by Y.X. Yuan shows that the convergence rate can not be quadratic. Finally, some numerical results are given. This work is supported by Chinese NSFC grants 10401023 and 10371076, Research Grants for Young Teachers of Shanghai Jiao Tong University, and E-Institute of Computational Sciences of Shanghai Universities. An erratum to this article is available at .     

Some Results behind Dividend Problems

We consider the basic dividend problem of the compound Poisson model with constant barrierstrategy.Some results concealed behind the dividend problem are made explicit in the present work.Differentmethods and some of which are firstly given in this paper.All these results presented certain direct relationshipbetween some important actuary variables in classical risk theory is also revealed.     

0.86μm激光扫描二维成像的实验研究

本文给出作者设计的0.86μm激光二维成像系统的原理框图、成像雷达距离方程和部分物体对0.86μm激光的反射对比度的测试数据,并展示了各类物体激光成像的照片.     

An existence result for a two‐phase Stefan problem arising in metal casting

We present a model arising from the thermal modelling of two metal casting processes. We consider an enthalpy formulation for this two‐phase Stefan problem in a time varying three‐dimensional domain and consider convective heat transfer in the liquid phase. Then, we introduce a weak formulation in a fixed domain, by means of a suitable transformation. Existence of solution is obtained by applying an abstract theorem. The proof of this theorem is done by taking an implicit discretization in time together with a regularization. By passing to the limit in the regularization parameter and in the time step, we obtain the existence of solution of the continuous problem. Copyright © 2005 John Wiley & Sons, Ltd.     

一类非线性常微分方程振荡解的渐近表示

在本文中,我们讨论了非线性常微分方程y"=a0|x|αy3 a1|x|βy2 α2|x|γy α3|x|δ振荡解的渐近表示．在这个方程中将α0,α,α1,β,α2,γ,α3,δ分别换成0,0,6,0,0,0,sgn(x),1就是著名的第一类Painleve方程,而将α0,α,α1,β,α2,γ,α3,δ分别换成2,0,0,0,sgn(x),1,α0,就是著名的第二类Painleve方程．当α0,α,α1,β,α2,γ,α3,δ分别换成-β/3γ,0,0,0,1/γ,1,α,0时,可用于组合KdV方程孤立子解的化简．     

刚性方程组M~.(t)+C~.X(t)+KX(t)=F(t)解的探讨

讨论了刚性常微分方程组(1)的解析解和数值解,给出了解的一般形式和应用该算法的数值例子.     

一类脉冲中立型时滞抛物方程组的振动性

研究一类脉冲中立型时滞抛物方程组解的振动性,得到了该类方程组在两类不同边界条件下所有解振动的若干充分条件.     

Differential algebraic equations with after-effect

In this paper, we are concerned with the solution of delay differential algebraic equations. These are differential algebraic equations with after-effect, or constrained delay differential equations. The general semi-explicit form of the problem consists of a set of delay differential equations combined with a set of constraints that may involve retarded arguments. Even simply stated problems of this type can give rise to difficult analytical and numerical problems. The more tractable examples can be shown to be equivalent to systems of delay or neutral delay differential equations. Our purpose is to highlight some of the complexities and obstacles that can arise when solving these problems, and to indicate problems that require further research.     

新疆红景天红色素的提取及理化性质的研究

对用索氏提取法和乙醇浸取法提取红景天红色素进行了比较，并探讨浸取的浓度，浸取温度等因素，指出了最佳生产工艺条件，从红景天中提取的天红色素是一种安全无毒的食用色素，本文还研究了几种食品添加剂对红景天红色素稳定性的影响，并对色素的耐氧化性进行了探讨，旨在为红景天红色素的开发利用提供有实用价值的信息。