级数的和

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％。

This article is focused on the use of Mathematica graphics functions to perform some abstract concept of mathematical analysis, the conclusion of the understanding; auxiliary function for the extreme value; and its application in the series.

本文主要讨论的是利用Mathematica的绘图功能来演绎数学分析中某些抽象的概念、结论的理解；辅助求函数的极值；和它在级数中的应用。

The constant term and non-singular terms, which are called general T-stress here, play a significant role in determining the stress and strain fields around a crack tip which in turn can affect the calculation of stress intensity factor of the crack.

裂纹尖端的奇异应力场可以表达为Williams级数展开的形式，其中常数项和非奇异项对裂纹尖端的应力应变场有着很大的影响，这些影响反过来作用于裂纹应力强度因子的计算。

Secondly, the effectiveness and limitation of the classical perturbation, such as the method of multiple scales and the Poincare-Lindstedt method, are discussed in detail through a Duffing oscillator with delayed velocity feedback. It is shown that the two perturbation methods are effective only in solving the approximate solution of the first two orders. An ambiguity or paradox will be encountered when they are used to seeking for the third or higher order approximation of solution.

其次，以一具有时滞速度反馈的Duffing系统为例，研究了经典摄动法如多尺度法，Poincaré-Lindstedt法等在求解时滞微分方程级数解时的适用性和局限性问题，指出利用这些方法只能有效求得系统的前两阶近似解，而在求系统的三次以上近似解时会出现矛盾或二义性。

A new method of fault diagnosis based on the nonlinear spectral analysis for a class of nonlinear systems with the Volterra series solution is given in this dissertation. The new method consists of three elements.

本文对一大类可以用Volterra级数描述的SISO非线性系统进行了研究，在前人研究的基础上，提出了一整套工程可实施的基于非线性系统频域分析的故障检测与诊断理论和方法。

Based on the polynomial fitting of power function, FFT of sinusoidal function and 1-level decomposition of Daubechies wavelet, the simulation shows that the approximation of DT and the gradient depend on the width of horizontal distance spectrum.

文章基于幂级数多项式拟合、三角函数的FFT 和一级Daubechies 小波分解的理论分析以及数字地形的数值仿真，研究了近似地形的精确度与坡度的确定性因素。

One way is to regard them as the random variables submit to a certain distribution; another is to take them as a random process—— we derive random variables form any of its function's time development, and, the diffusion equation could be partially approached by a equation which is similar to the Ito stochastic integral equation so that the Ito stochastic integral equation is inter-related with the diffusion equation. Therefore, this process could basically reflect the uncertainty in different models.

PSFEM法是假定基本随机变量在均值点处产生微小摄动，利用Taylor级数把随机变量表示为确定部分和由摄动引起的随机部分，从而将有限元控制方程转化为一组线性的递推方程，求解得出位移的统计特性，进而求出应力的统计特性。

How to calculate the sum of P-series by Fourier series ;2. Fourier series was utilized to fit the stress and strain of tire in a rolling cycle by means of mechanic-field analytic result.

利用轮胎力学场的数值分析结果，采用傅立叶级数拟合单元在轮胎滚动一周内的应力-应变变化，并根据拟合后的傅立叶系数计算轮胎单元损耗应变能和生热率，分析了轮胎在不同速度时的温度场。

Because the formers mainly used morphological methods, such as step number and elevation of terrace, canyon character, relationship of topographical units, there has no unified conclusion to origin of the Three Gorges.

Willis在1903年提及，迄今已有近100年的历史，但是由于前人主要依据阶地的级数、高程等特征，三峡峡谷特征，地貌间相互关系等地貌学方面的研究，造成三峡成因上的次成谷和先成谷之争、三峡形成时间早晚之争一直难有定论。

The reaction kinetics was studied by selecting control-step method as well as modified Debye-Hückel activity coefficient model and Bromley osmotic coefficient model. The results show that the reaction order is 2 and apparent reaction activation energy 85.8 kJ/mol, and the reaction is mainly controlled by precipitation of KB5O8?4H2O.

采用选取控制步骤法并引入修正的Debye-Hückel活度系数模型和Bromley渗透系数模型研究了该反应的动力学的影响规律，得出反应级数为2，表观反应活化能为85.8 kJ/mol，反应主要受四水五硼酸钾晶体析出的控制。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。