逼近

Based on the recent situation and trend of the nonlinear systems, we present some recent developments and important problems in stochastic dynamics such as response, bifurcation , chaos, synchronization and control.

摘要介绍了非线性随机动力学的响应、分岔、混沌以及混沌同步与控制的研究现状和发展趋势，探讨了随机复动力系统、时滞系统、逼近方法和数值方法研究中的若干问题及其进展。

With the primary goal function, the optimization problem is changed to a nonrestraint one.

在无约束优化过程中，通过逐步增大罚因子，使无约束优化问题的解逼近原约束优化问题的解，用随机搜索优化方法得到了拱坝的优化体型。

Since the solutions of this problem are the critical points of the associated energy function. One generally needs some compactness such as PScondition or C-condition to prove the existence of critical points of the energy func-tion, but when we study the elliptic equation in R~N, the compactness condition does not always hold since the imbedding of the Sobolev space H_0~(1,2)into L~(2*) is not compact. In this chapter, based on the nonsmooth critical point theory, and by using the approximation technique with periodic function, the existence of nontrivial solution is obtained.

由于该方程的解就是其所对应的能量泛函的临界点，通常都要在一些紧型条件的基础上来证明其所对应的能量泛函临界点的存在性，但当我们在无界域上考虑该椭圆方程解的存在性时，Sobolev空间H_0~(1，2)到L~(2*)的嵌入非紧，从而导致所对应的能量泛函失去紧性，本章在非光滑临界点理论的基础上，应用周期逼近的方法证明该问题非平凡解的存在性。

Exive least-squares solutions, antire?exive least-squares solutions, bisymmetric least-squaressolutions, symmetric and antipersymmetric least-squares solutions, symmetric or-thogonal symmetric least-squares solutions, symmetric orthogonal antisymmetricleast-squares solutions and their optimal approximation to the linear matrix equa-tion AX = B, and solve them successfully. 2. For Problem II, we can convert it to another problem of finding the least-squares solutions with the least norm of a new consistent matrix equation. Onthe base of the solutions of Problem I we can apply the iterative method to get

本文所构造的迭代法的优点在于先利用法方程变换将求矩阵方程的最小二乘解转化为求一个相容矩阵方程的解的问题，再利用迭代法对于任意给定的初始矩阵进行迭代，均可在有限步内迭代出所求问题的一个解；可将问题II转化为求新方程的极小范数解的问题，同样用迭代法求解，从而系统且全面地解决了问题I、II在约束矩阵类如中心对称、中心反对称、自反矩阵、反自反矩阵、双对称、对称次反对称、对称正交对称、对称正交反对称矩阵中的最小二乘解及其最佳逼近问题。

Direct difference is sensitive to noisy data, so a threshold limitation is given, which can not only filter the result from noisy data but also pick edge points up according men's desire. On the other hand, artificial intelligence is used for segmentation in reverse engineering. Because the essence of segmentation is clustering similar characteristics and self-organizing feature mapping is one function of neural network, SOFM network is used for segmentation in the thesis, coordinates and normal of data points is took as the characteristics vector.

第二种方法，基于双向角度微分的边点提取法，针对三维正交模型采用基于截面线的方式组织数据，此方法比基于曲率半径方法更简洁，不用进行曲面拟合，大大提高了计算速度；计算过程中由数据点的直接差分逼近微分，但直接差分对数据误差敏感，为此，本文提出了阈值过滤的方法，一方面过滤了数据误差在计算结果中引起的噪音，另一方面可以按照设计意图控制边点的提取；来决定是否提取光滑交接的边点。

The existence of global weak solution for a class of generalized Ginzburg-Landau equations with an inhomogeneous boundary condition was studied. Some integral indentities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained.

研究具非线性边界条件的一类广义Ginzburg＿Landau方程解的整体存在性·推导了Ginzburg＿Landau方程的非齐次初边值问题光滑解的几个积分恒等式，由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计；通过逼近技巧、先验估计和取极限方法证明了Ginzburg＿Landau方程的非齐次初边值问题整体弱解的存在性

The ill-conditioned normal equations bring numerical problems in construction of macromodel in time domain for power distribution networking using rational function approximation.

摘要有理函数逼近法方程组病态条件数为构建电源分配网络时域宏模型带来了数值问题。

Introduces the notion of Feynman's path integrals and path integrals approach to financial modeling; Derives the path-dependent options pricing formula by making use of the Lagrange form of path integrals; Discusses Ilinski(2003)'s Gauge model which based on path integrals and fibre bundle, and its application for real-options evaluation; Summarizes the general modeling framework of options evaluation, taking advantage of the Hamilton form of path integrals; Applies the Geske-Johnson's analytical approximation in the path integrals form to the real-options evaluation for investment decisions, detailed procedure is presented under the assumption that underlying asset price dynamic follows a geometric Brownian motion, and the integral reduction for multivariate normal integrals and polynomial approximation for real-options evaluation is given.

系统论述了路径积分概念方法及其在期权估值中的应用，利用路径积分方法的Lagrange表述推导了路径依赖期权定价公式：探讨了基于路径积分和纤维丛的Gauge模型思想方法在实物期权价值评估中的应用；利用路径积分的Hamilton表述形式，总结了基于Hamilton表述的期权估值一般化框架；基于路径积分的形式框架建立了一个新的投资期权估值模型，并在具体的估值算法中给出了多重正态积分的降阶计算和期权价值的多项式逼近方法。

To evaluate the precision of solutions obtained by modal series method, normal form method and linear modal method, an error index describing the approximation to the nonlinear simulation is defined and then applied to the same system.

为比较模态级数法、正规形法和线性模式分析法所得解对时域仿真解的逼近程度，定义一误差指标，并在4机2区系统中做相关分析。

These changes are Now, they have begun, they will speed up as you go on towards 2012, Nostradamus and St.

现在，据Nostradamus 和St。 Malachy所说，这些变化已经开始了，而且随着2012的逼近它还会加速。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。