估计理论

In this paper we study the method of interpolation by radial basis functions in H~k(k ≥ 1) and give some error estimates. By means of such interpolation with a special kind of radial basis function, we construct a basis in H~k(k ≥ 1). Combined with the Galerkin method, this theory can be applied to solve boundary value problems for elliptic partial differential equations (such as the third boundary value problem for Poisson equation and the corresponding problem for the biharmonic equation), and some numerical experiments are also given.

本文从求解偏微分方程的角度出发，在被逼近函数u属于一般的Sobolev空间H~k(k≥1)的情形，引入了一种径向基函数插值方法，并建立了相应的误差估计；再利用这种插值性质，从一类特殊径向基函数出发构造Sobolev空间的一组基，针对Poisson方程第三类边值问题和重调和方程类似边值问题，为用无网格算法求解偏微分方程边值问题建立了相应的理论，并通过算例来验证了这一算法。

Based on Brune ω~2 source spectrum ,Hanks and McGuire deduced a simplified formula of RMS accelera- tion by stationary random vibration theory and Parseval theorem.

Hanks 和 McGuire 基于 Brune 的ω~2震源谱，借助平稳随机振动理论和 Parseval 定理给出了估计均方根加速度衰减关系的表达式。

Because the central difference method is conditional stable, the critical time step and damping were estimated by model analysis, which can guarantee the computation stability. In this paper, the mesh method was used to described the tool surface.

由于中心差分法的计算是有条件稳定，作者对确定系统临界时间步长和阻尼系数的方法进行了研究，采用模态分析理论估计临界时间步长和阻尼，保证了计算的稳定性。

In this paper,starting with the concept of risk,trying to take the theory of probability,central limit theorem,definition of optimal statistic estimate and economic theory as the basis and according to the concrete situation of the natural gas exploration project,the formula to quantitatively determine the risk is derived.

文章从"风险"的概念入手，尝试以概率论、中心极限定理、最优统计估计量的定义和经济理论为基础，结合天然气勘探项目的具体情况，推导出了定量测定风险的公式。

The results show that the estimated correlation dimension can be taken as the characteristic parameter to define what state the motion of the system is in,and further the results can be used for trend monitoring in different failure situations of the system.

理论分析和计算结果表明，所估计的相关维数在不同状态下有着显著的差别，可以对碰摩转子系统不同的状态进行分类，对碰摩转子运动特性的研究提供了一种新的方法。

Meanwhile, it could be seen that there does not exist a confidence interval with width less than 0.5 because of the property of Poisson distribution. Based on these conditions, the author mainly carried out research into two aspects of this problem as follows. Firstly, by numerical and theoretical analysis, the author compares some existent confidence intervals, for example,"exact" confidence interval, Wald confidence interval and Bayesian confidence interval, and finds some deficiencies points of the confidence intervals, whose modification version has been proposed .Also, several better confidence intervals such asare also presented .Secondly, for given confidence coefficient and interval width, the author constructs a class of asymptotical two-stage interval estimate procedures. At the same time, under varies restriction of confidence coefflcientent interval width, the optional sample size of the first stage has been computed by numerical computation. The numerical computation shows that the method considered in this dissertation have good properties and applied value.

同时，由于Poisson分布的特性，我们知道不存在其参数区间长度小于0.5的置信区间，基于这些情况，我们主要展开了以下两个方面的研究：一是利用数值计算分析与理论分析的方法对现有的若干置信区间如"精确"置信区间，Wald置信区间，Bayes置信区间等进行分析比较，发现了一些缺陷，针对这些缺陷，我们进行适当的修正，并得到几种性质较好的置信区间如：修正大样本区间Jeffreys原则下置信区间二是针对已给定的置信系数与区间长度，我们提出了一种渐近的两阶段区间估计程序，并利用数值计算的方法，在各种置信系数与区间长度限定下，算出了最优的第一阶段观测次数，大量数据表明，本文考虑的方法性态良好，具有应用价值。

In this paper, the problem of the robust stability and decay estimations of such control system is considered. Several new criteria are given by applying the differential theorem, the decay rate for this class of system is also obtained.

根据微分方程理论和矩阵指数特性，提出了具有不确定性的时滞控制系统与时滞相关和与时滞无关稳定的充分性判据，并给出系统衰减速率的估计方法。

Our analysis result shows: in the judgment and decision-making process, the investor cognation biases can be divided into the cognation bias of price fluctuation, the estimate bias of corporate value, the manager bias of risk and wins, the manipulate bias of trading.

本文认为金融市场上投资者所具有的典型性认知偏差包括对股价波动的认知偏差、对上市公司价值的估计偏差、对风险和回报的管理偏差以及股票交易中的操作偏差四种；而深入分析投资者的这些认知偏差很有理论和现实意义。

By using the spectrum approximation theory of compact operator, the approximation of anisotropic nonconforming ?nite element method for Stokes eigenvalue pronlem are presented and the optimal error estimates are obtained, which are as same as those of traditional ?nite element methods.

利用紧算子谱逼近理论，给出了 Stokes 特征值问题的各向异性非协调有限元逼近方法及最优误差估计，得到了与剖分网格满足正则性或拟一致性关键假设下相同的收敛效果。

Some priori estimates, Turing instability and global stability of positive constant steady-state solution are obtained by comparison principle, operator spectrum theory and Turing theory.

利用比较原理，算子谱理论及Turing理论，得到了正解的一些先验估计，正常数平衡态解的Turing不稳定性及正常数平衡态解的一致渐近稳定性。

So that more consumers can enjoy more delicious quality, technology is even better than wine.

让更多的消费者可以品尝到品质更为鲜美，工艺更为精湛的葡萄酒。

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