近似方法

The main subjects of the volume include:- spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers;- multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations;- Hankel operators and forms;- operator algebras;- the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations;- approximation in holomorphic spaces.

卷包括：主要课程-定期微分算子和延迟方程谱分析，稳定控制器，傅立叶乘数；-多变量算子理论，模型论，换位解除定理，coisometric变现；- Hankel算子和形式；-算子代数；-在奇异积分和谐波分析，奇异积分算子和积分表示贝尔曼函数方法；-在全纯空间近似。

In order to find a stable approximate solution of linear compact operator equation, the article introduces general theories about ill-posed problems, it bases on spectral theory of self-adjiont compact operators and the singular value decomposition for compact operators, avails singular system to give expression of the solution, and explains ill-posedness of compact operator equation roots in the property that the singular values trends to zero. Thereout, it is provided with theoretic support of building up regularization method by inducting regularization filter to weaken or filtrate the influence that the nature of the singular value being very close to zero has on the solutions stability.

为了得到线性紧算子方程稳定的近似解，介绍了不适定问题正则化的一般理论，以自伴紧算子的谱分析与紧算子奇异值分解为理论基础，利用奇异系给出了解的表达式，说明了紧算子方程不适定性的根源在于紧算子的奇异值趋于零的性质，由此通过引入正则化滤子函数来减弱或滤掉奇异值趋于零的性质对解的稳定性的影响，构造正则算子，从而提供了建立正则化方法的理论依据。

In most meshless methods based on weights with compact support, difficulties arise in nonconvex bodies such as bodies containing crack.

大多数的无单元方法都使用具有紧支集特性的权函数。当求解域是非凸区域的时候，无单元的近似函数不能准确的描述裂缝带来的场函数不连续。

For this type of new model,we study it mainly from these ways:First,we make further research on the nature features of their distributions;give out the probability distribution of the mixed stochastic variables,and the statistical features and the approximate distributions of the short-term individual risk models. Also the relationships between the total amount of compound compensation and individual one were investigated.At last we give out a kind of practical calculation method for the individual risk model.That is the calculation of the number of claims translating into the calculation of Vandermonde determinant.Second,a kind of risk model with main claims and by-claims is built under specific conditions.

对于这类有主副理赔的风险模型，我们主要从以下几个方面进行研究：首先，对短期个别风险模型和长期聚合风险模型的理赔总额的分布性质及特征做了较深入的研究，给出了混合型随机变量和的概率分布和短期个别风险模型理赔总额的统计特征与近似分布；在复合分布的框架下，研究了聚合风险模型理赔总额和个别理赔额之间的分布关系，给出了和个别理赔额对应的理赔次数的实用计算方法，即在总索赔额服从复合泊松分布时，把不同理赔额对应的理赔次数的计算转化为线性方程组的计算。

Nonlinear wave system; Exact solution; Approximate solution; Soliton; Riccati equation method; Turing machine; Computable function

非线性波系统；精确解；近似解；孤立波； Riccati方程方法；图灵机；可计算函数

MVFK8vP7Ge+Uu0 Nonlinear wave system; Exact solution; Approximate solution; Soliton; Riccati equation method; Turing machine; Computable function

非线性波系统；精确解；近似解；孤立波； Riccati方程方法；图灵机；可计算函数

Chapter 1 reviews recent investigation in Bose-Einstein condensation, and analyzes critical point and condition of phase transition. Chapter 2 introduces the experiment of Mott insulator and superfluid phase transition in dilute atomic gases, theoretic mode and some studying. In chapter 3, we study the influence of dipole-dipole interaction of two component BEC in optical lattice, by Green function technique and mean-field approach. The results show that long range interaction and dipole-dipole interaction can be strongly influence the phase transition of two component.

本文内容分为四章，第一章对BEC近几年的研究回顾，分析了理想情况下凝聚的临界行为和凝聚条件；第二章我们介绍了光格子中绝缘-超流相变和理论模型及其描述；第三章我们利用格林函数和平均场近似的方法，对偶极-偶极相互作用在光格子中两分量BEC原子的超流-绝缘相变的作用进行了分析，结果表明偶极-偶极相互作用和长程相互作用对绝缘-超流相变有很大的影响。

This paper mainly introduces a new method to approximating the failure probability of structural systems and the method is defined as dimensions reduction method by conditional probability .

本文主要介绍一种新的结构体系失效概率近似计算的方法——条件概率降维法。

Restricted by the assumption of low-order linear displacement approximation in each block, Discrete Element Methods often have to mesh many continuum parts of the problem domain into small discrete blocks when simulating crack propagation problems, and the result is very sensitive to the very way that divides the domain.

一般离散单元计算方法受离散块体低阶线性位移近似的限制，在模拟开裂过程时，需要将大部分实际上连续的区域离散化，离散方式对分析结果有显著影响。

To use linear program, we have to take care of two problems. The first problem is that the actual relationship between intensity and duration is nonlinear convex function. In this study, we propose to use piece-wise linear curve to approximate the nonlinear convex curve. The second problem is that there are many feasible event sequences.

使用线性规划遭遇的困难有二：第一，作业强度与作业时间呈非线性之凸函数关系，因此本研究将使用片段线性曲线(piece-wise linear curve)近似作业强度与作业时间呈非线性之凸函数关系；第二，专案有很多组可能事件顺序，事件顺序的不同会产生不同的资源限制式，本研究提出一个系统化的方法求解问题。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新