函数的变差

Firstly, the Voronovskaja type formula of asymptotic expansion of this kind of operators is given. Then the approximation of the bounded variation functions by the kinds of operators is discussed.

第一节给出该算子的Voronovskaja型渐近展开公式；第二节讨论该算子对有界变差函数的逼近。

At present, the investigations for the properties of these operators are only limited to the functions of bounded variation.

目前， 关于这类和积分混合型算子的逼近性质仅限于对有界变差函数逼近方面的研究。

A discussion is made of the continuously sufficient and necessary conditions of the bounded variation fon the closed interval in the paper.

讨论了有界变差数 f在闭区间上连续的充要条件以及函数 f在闭区间上有有界变差的充要条件。

In chapter 2, we define the abstract periodic three level bounded variation functions with range in a Banach space ?

其中第二章定义并研究了实Banach空间取值的抽象三级周期有界变差函数用抽象系数三角多项式逼近的性质。

In this paper, we study the rate of convergence of Durrmeyer-Bézier Operaters for functions of bounded variation f and obtain a accurate estimation of coefficient. Our result improves the result of Zeng by making use of probable property of basic functions.

在Zeng等人对有界变差函数f的Durrmeyer-Bézier算子在区间(0，1)上收敛于 1/(a+1f+a/(a+1f 的收敛阶进行研究的基础上，利用基函数的概率性质等方法，对其所给的Durrmeyer-Bézier算子收敛阶估计结果作进一步的改进，得到其收敛阶的精确估计。

The cartoon component of an image is modeled by a bounded variation function;the corresponding incorporation of BV penalty terms in the variational functional leads to solve PDE equations.

图像的卡通部分是由一个有界变差函数来刻画，相应的将BV罚项合并到变分泛函中需要解偏微分方程。

This dissertation firstly introduces the principles of four kinds of simple gridding methods, which are"Linear interpolation based on triangulation","Inverse distance weighted and averaged method","Modified Shepard's method"and"Multiquardirc method". Secondly, it researches the Ordinary Kriging method for geophysical irregular data, which mainly includes the base knowledge of region change and variogram and the principle of Ordinary Kriging method. Thirdly, it researches the Inverse Interpolation for geophysical irregular data, which mainly includes the principle of inverse interpolation and its iterative algorithm, and the principle of Inverse Interpolation to realize the gridding of geophysical data. Finally, it uses these gridding methods to grid theoretical model data of potential field and raw aeromagnetic data, and compares and analyzes the gridding results.

本文首先简单介绍了地球物理不规则分布数据的四种简单网格化方法(即基于三角网的线性插值法、反距离加权平均法、改进的Shepard方法和多元二次函数法)的方法原理；接着，重点研究了地球物理不规则分布数据网格化的普通克里金法，主要研究了区域变化量、变差函数的基础知识和普通克里金法的方法原理；之后，重点研究了地球物理不规则分布数据网格化的反插值法，主要研究了反插值法的方法原理和迭代求解算法，以及反插值法实现地球物理数据网格化的原理；最后，应用这些方法对理论位场模型和实际航磁数据进行了试验、对比和分析。

Another reason is that the degree of linear independence of the variable basis functions composed by sigmoid functions decreases as the hidden nodes increasing, and this lead up to the inferior matrix condition number during learning, which forces the learning step length to decrease and the convergence speed to slow down.

一是因为未知系统复杂时需要较多的隐节点，从而学习的参数过多减慢了学习速度；另一个原因是随着隐节点数增加，由Sigmoid函数构造的可变基函数线性无关程度减弱，从而导致学习过程中矩阵条件数变差，迫使学习步长减小，收敛速度不得不减慢。

By fitting the models of semivariogram of them and analyzing the patterns, it was found that the nugget range of macropterous SBPH and larval SBPH were approaching to that of spiders, as well as the range of structural intensity, but the nuggets of SBPH were not approaching to that of spiders, neither the structural intensity. The spatial pattern of larval SBPH and spiders were aggregation, but that of macropterous SBPH was random sometimes.

通过变差函数模型的拟合及空间格局的分析，得出灰飞虱长翅成虫、若虫与蜘蛛的变程范围相近，结构性强度的范围相近，但同一时间灰飞虱与蜘蛛的变程和结构性强度则均不尽相同；灰飞虱若虫与蜘蛛自始至终为聚集分布，但灰飞虱长翅成虫与蜘蛛的分布型则有差异，在某些时间为均匀分布。

On the approximate uncorrelation property of DWT coefficients of LMSV process in the same scale and different scales, first the quasi maximum likelihood estimation method of parameters and the estimation method of volatility process of LMSV model are presented.

根据小波变换可将过程分解到不同的尺度上以及LMSV过程同一尺度下和不同尺度下DWT系数的近似不相关性，提出了建立局部似然函数的方法，又根据DWT系数和MODWT系数之间的关系，将局部似然函数表示为模型参数和局部小波方差估计的形式，并用该方法对中国股市收益进行了时变LMSV模型参数的估计。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。