查询词典 stochastic approximation

The main work of the thesis consists of summarizing the characteristics of the approximation methods,compiling the programs of approximation methods,and getting availability of every approximation method according to examples.

本文的主要工作是总结各种近似方法的特点，编写各近似方法的程序，通过算例总结出各种近似方法的适用性。

It can adjust time interval in light of approximation effect, and the current segment's approximation error is not influenced by other segments'. This method can improve approximation precision of reach set and makes the verification applicable in practical systems.

该方法可根据近似误差自动调节近似时所用的时间间隔，每段的近似误差不受其它段的影响，达到提高近似精度和减少计算量的目的，从而进一步降低验证方法实现的难度。

In the final chapter, we discuss interval polynomial approximation of rational surfaces. Firstly, we briefly state the interval-surface approximation based on the Taylor Expansion, and later, we give out a better interval-surface approximation based on the optimization method, which is also the main work of this paper.

第四章主要介绍了有理曲面的区间多项式的逼近，首先简单介绍了基于泰勒展开来做的区间曲面逼近，后面是本文的主要工作，我们基于优化方法得到了更好的区间曲面逼近，它也是本文的重要部分。

Padé approximation is an effective rational approximation.Using the first derivative of Gaussian function as basic wavelet,Pad conversion is used to obtain its rational fraction approximation.

采用高斯函数一阶导数作为基本小波，用Padé变换获得其有理分式逼近，利用开关电流技术实现小波滤波器可获得小波变换所需的基本小波及其膨胀小波。

Structure-Based Approximation Learning Theory: Under the description of manifold and topological architecture of neural field, we have proposed a learning frameworks of neural networks based on global architecture approximation theory borrowed from the concept of topology and manifold to solve the optimal problems of learning in non-nonlinear and non-Euclidean space, and discussed a few basic components of the learning theory, learning mechanism and learning algorithm in the term of structure-based approximation and global structure analysis.

基于结构的逼近学习理论：通过人工神经网络模型神经场的流形结构和拓扑结构描述，我们提出了在非线性和非欧氏空间中基于整体结构逼近的神经场学习理论框架；用对偶流形理论和拓扑概念作为工具，讨论了神经网络的学习理论、学习机理、学习算法和算法的具体实现。

Direct and inverse theorems of approximation by this kind of operators are discussed, and the Jackson—type integral estimation of approximation and Steckin — Marchaud inequality of weak type of uniform approximation for these operators are obtained.

讨论了一元Bernstein型算子的逼近正逆定理，建立了该算子逼近的Jackson型积分估计式和一致逼近的弱Steckin-Marchaud型不等式。

And the direction query efficiency based on multi-approximate index is compared with that based on taditional external approximation index. 2 The algorithms of nearest neighbor and reverse nearest neighbor about point, line and ploygen based on multi-approximate index are proposed after the virous methods of distance measure are discussed in detail. And the query efficiency of NN and RNN based on multi-approximate index is compared with that based on taditional external approximation index. 3 The basic concept of semi-join and the strategy of distance-direction semi-join are introduced. And the model of distance relationship, direction relationship and the bounding for spatial object are discussed. Then the method is presented about how to implement the query of distance-direction semi-join, and the efficiency of the algorithm based on multi-approximate index is compared with that based on taditional external approximation index.

即：1在方向关系矩阵模型、开域方向模型基础上，讨论了基于多重近似索引下的定性与定量方向检索方法，并通过实验对基于多重近似索引与外部近似索引下的方向检索效率进行了对比分析；2详细讨论了各种距离度量方法，提出了基于多重近似索引下的点、线、面的最邻近查询和反最邻近查询算法，并通过实验对基于多重近似索引与外部近似索引下的最邻近查询和反最邻近查询效率进行比较分析；3介绍了半连接的基本概念，探讨了距离关系、方向关系以及空间对象数量的约束模型，给出了基于多重近似索引下的距离方向半连接实现方法，并通过实验对基于多重近似索引与外部近似索引下的距离方向半连接的效率进行了比较分析。

It also gives the definitions and stochastic properties of pure random process, random walk process and AR(1) autoregressive process, and analyses the simulative data of three typical random processes using wavelet analysis, frequency spectrum analysis and time-correlation analysis. The stochastic properties of time series and the trend component, the time length of time-correlation and the properties of main frequency of these three typical random processes are summarized as the templates for further research.

给出了包括纯随机过程、随机游走过程和 AR(1)自回归过程等在内的基本随机过程的定义和统计特征，并运用小波分析，时间相关和频谱分析对这三种基本随机过程的模拟数据进行分析，归纳出它们在时序上的随机特征、低频信号趋势项特征、时间相关的长短以及主频信号的位置等特点，作为研究 GPS 接收机误差和多路径效应的随机特征的模板。

In part 2, we study the properties of the solution z of backward stochastic differential equation and backward doubly stochastic differential equation.

第二部分分别研究了倒向随机微分方程和倒向重随机微分方程中解z的性质。

Huang and Lin proposed the weak solution concept for Backward Stochastic Differential Equation This paper based on the predecessor's work , gives the weak solution concept for Backward Stochastic Differential Equation with continuous martingale,uses the Girsanov transformation, obtains its weak solution of the existence of a necessary and sufficient conditions, and on this basis obtains its weak solution of the existence of sufficient conditions,these sufficient conditions weakened the drifting coefficient which requested in the existence uniqueness of strong solution to satisfy the Lipschitz condition the request.

本文在前人研究的基础上，给出由连续鞅驱动的倒向随机微分方程弱解的概念，利用Girsanov变换，得到其弱解存在的存在的一个充分必要条件，并在此基础上得到了其弱解存在的一些充分条件，这些充分条件减弱了在强解的存在唯一性中要求的漂移系数满足Lipschitz条件的要求。

That snake Alaric named Archbishop...

庇护。。。那个毒如蛇蝎的Alaric被命名为大教主。。。

You have done lots of magical things to be amazed at.

你做了很多神奇的事物感到惊讶。