阶矩

The building rules of GLCM （ the best gray levels and pixels interval） were confirmed by experiment. GLCM texture parameters of 300 wood specimens were calculated and assayed, and then placed into a Competitive Neural Network for classification output. The results are as follows: 1） GLCM parameters Angular Second Moment contrast , correlation , entr

以"角二阶矩"、"对比度"、"相关"、"熵"、"方差"、"逆差矩"作为描述木材纹理的特征参数是合适的。2）在比例为1：1的512×512木材图像情况下，生成灰度共生矩阵的最佳像素间距为4，最佳图像灰度级数为128.3）木材纹理图像灰度共生矩阵的"角二阶矩"、"相关"和"熵"值最大的方向为纹理方向。4）竞争神经网络的分类正确率为88％。

A higher moment method with the basis of Chebyshev polynomial ｛T_k｝ is presented,which is used in the reliability analysis of engineering structures.

1引言在工程结构的可靠性分析中，一次二阶矩法(包括中心点法、JC法、映射变换法和实用分析法)以及二次二阶矩法得到了广泛应用[1，2]。

In general quantum case the equal-time kinetic hierarchies for the energy moments of the covariant Wigner function were established.

在普遍量子情形下，建立了协变Wigner函数的能量矩的等时动力论链和链的截断方案，得到了与低阶矩相关的物理密度量的输运方程和约束方程，并且证明高阶矩都能通过低阶矩表示。

In the aspect of multivariate modeling, three forms of multivariate GARCHSK model includes vector form, diagonal form and simplify form, are put forward and compared. The famous dimension disaster exists in multivariate GARCHSK model also. Based on Independent Component Analysis, multivariate volatilities of conditional higher moments are estimated through IC-GARCHSK model, which make dynamic relation of higher moment risk between multi-assets to be possible.

鉴于多元 GARCHSK 模型存在严重的"维数灾难"问题，基于独立成分分解技术提出 IC-GARCHSK 模型，给出多元条件高阶矩波动率的估计方法，使得同时度量多个资产高阶矩风险之间动态关系成为可能，为利用组合投资方式分散高阶矩风险的影响奠定了方法论基础。

They concentrate on discussing the dynamic character of the first and second moment of time series. Under normal distribution, the problem of dynamic financial risk measure and elusion can be solved effectively. However, it becomes invalid or is short of effectiveness.

他们的工作主要集中于讨论时间序列的一阶矩和二阶矩的动态性质，能够有效地解决正态分布条件下动态金融风险的测度与规避问题，对于非正态分布条件下相关主题的讨论具有一定的局限性。

This project also obtained several limit theorems for some important dependent random variables and stochastic processes, such as the Strassen law of the iterated logarithm for negatively dependent random variables, strong limit theorems for mixing random vectors in Banach spaces, sample path properties for two-parameter fractional Wiener processes, and so on.

随机环境中的随机变量与随机过程的研究在国内外相当活跃，本项目主要研究它们的极限性质，着重研究了随机风景中随机变量与随机过程的极限性质，主要取得了以下几个结果：首先对简单对称的Kesten-Spitzer随机游动在低阶矩的条件下给出了强逼近，大大减弱了前人要求任意阶矩的条件，然后对独立风景中的一般随机变量给出了强逼近的一般性结果，由此导出在风景和随机变量都只具有低阶矩的条件下的独立但不同分布、混合相依变量的强逼近，在只有弱高于二阶矩的条件下得到了重相对数律和弱收敛；给出了连续时间参数的Brown风景中Brown运动和稳定风景中稳定过程的滞后增量和连续模等精确样本轨道性质；同时给出了一些重要的相依随机变量和过程的若干极限定理，如负相关随机变量的Strassen重对数律、抽象空间上混合相依变量的一些强极限定理成立的充分必要条件、两参数分数Wiener过程的样本轨道性质等。

The model of programmed crystallization of SPM was proposed based on the moment transformation of the population considering the agglomeration. The optimal temperature-time curves in a batch crystallizer which maximized the terminal mean size and mean weight size can be determined from the application of the Pontryagin Maximum Principle. The calculated crystallization results heating under optimal temperature were compared with ones under linear or natural heating temperature.

根据第四章所得到的螺旋霉素晶体二次成核和晶体生长和布朗扩散引起的聚集动力学，利用第六章所描述的晶体尺寸分布的各阶矩对时间的一阶导数所构成的自封闭的一阶常微分方程组，采用庞得里亚金极大值原理，以温度为控制变量，在满足某些约束条件下，以最大平均尺寸和最大晶体重量平均尺寸为性能指标，计算出了螺旋霉素间歇结晶的最优温度—时间曲线，并同线性加热和自然方式进行了比较。

In Chapter 3 Firstly, the exponential stability in mean square and almost sure exponential stability for neutral stochstic neural networks with time-varying delay can be discussed by using the linear matrix inequality and the semimartingale convergence theorem; And our sufficient conditions are less conserative; Secondly, by utilizing the fixed point theorem, some sufficient and necessary conditions ensuring the asymp- totic stability in mean square for neutral stochastic neural networks with time-varying delays can be given.

第三章首先，利用线性矩阵不等式方法和半鞅收敛定理，考虑了一类具变时滞中立型随机神经网络的二阶矩指数稳定性和几乎必然指数稳定性，所得到的条件保守性要好；其次，采用不动点方法，给出了具变时滞中立型随机神经网络的二阶矩渐近稳定性的充要条件。

The equations of optimal probability density function of stochastic variable or limit state function are derived by use of the higher moments of the function.

一次二阶矩法主要利用随机变量的均值和方差信息以及分布概型来计算结构的失效概率，属于低阶矩法。

Throughout comparing the above estimating methods, we have the following results: the estimators of the moments of the errors does not depend on the random effects, and that of the random effects does not depend on the errors, and then the corresponding asymptotic variances are very simple and optimal; when the random effects are multivariate, we can not construct different estimating equations for the random effects and errors respectively, which results that the asymptotic covariances of estimation are very complex and then the estimating efficiency is bad.

比较上述两种估计法，我们发现：当随机效应是一维的时侯，误差的各阶矩的估计不依赖不可观测的随机效应，随机效应的估计也不依赖误差，因此，估计的渐近方差结构特别简单也是最优的；而当随机效应是多维的，因为随机效应的协变量的影响，我们没有办法针对随机效应和误差的各阶矩分别建立估计方程，这导致所得的估计的渐近方差或者协方差矩阵特别复杂，从而估计的效果不是很好。

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。