级数的和

Via the stochastic averaging method, the four-dimensional system is reduced to a two-dimensional one. Through the logarithmic polar transformation , and then Girsanov theorem and Feynmann-Kac formula, the backword differential operator is then obtained. By expanding the eigenfunctions as a Fourier cosine series, the approximate analytic expansion of the moment Lyapunov exponent is then obtained.

首先在经典二元机翼颤振方程加入随机激励，通过随机平均法，Girsanov定理和Feynmann-Kac公式得到关于矩Lyapunov指数的特征值问题，其次采用Fourier余弦级数对特征函数进行正交展开得到系统矩Lyapunov指数的近似解析式。

Based on Reddy higher-order shear deformation plate theory and general von Kármán-type equations, the analytical solutions for free vibration and dynamic response of simply supported functionally graded plates with piezoelectric layers in thermal environments are described with double Fourier series, where temperature-dependent material properties are taken into account.

基于Reddy高阶剪切变形理论和广义Kármán 型方程，用双重Fourier级数展开法求得了热环境下带压电层的功能梯度复合材料混合层合板的自由振动及动力响应的解析解，分析中考虑了材料热物参数对温度变化的依赖性，讨论了环境温度和控制电压对固有频率及动力响应的影响。

The distribution function of the system response and state function is approximately determined by the standard normal distribution functions using Edgeworth series, and its reliability is obtained.

在结构系统响应和状态函数的前四阶矩的一般数学表达式的基础上，使用 Edgeworth级数把未知响应和状态函数的概率分布展开成标准的正态分布表达式，并放松了对随机参数的分布概型和激励类型的限制，从而确定了系统的可靠度

Although these tribal systems may be arranged as above so as to seem to form a progression, of which the extremes are pure exogamy on the one hand, and endogamy –transmuted into caste of the Mantchu and Hindu types- on the other, we have at present no right to say that these systems were developed in anything like this order in tribal history.

虽然这些部落体系可以被安排成如上看起来象形成级数，其端点一是纯外婚制，另一是变成Mantchu和印度型的纯内婚制，现在我们还没有权力说在部落历史上这些体系被发展成了象这个序列的东西。

When they built up the quantum Liouville equation inthe phase-space representaiton and discussed the mathematicaltransformation of the wave functions between the coordinate ormomentum and phase space,Torres-Vega and Frederick alwaysassumed the positive series expansion in coordinate of potentialsof systems.This is obviously incomplete because potentials ofreal systems contains in general negative powers of coordiante.

Torres-Vega和Frederick在建立相空间中的量子Liouville方程以及讨论和推导相空间波函数和坐标或动量空间中的波函数之间的的数学变换时，总是假定体系的相互作用势仅能展成坐标的正项级数，这显然是不全面的，因为实际体系的相互作用往往都含有坐标的负幂项。

The finite summation of real Fourier series approximation of a time pusle.

时间脉冲的实部傅立叶级数接近的有限和。

The new wine is then classified as fino or oloroso according to its natural progression.

新葡萄酒的级别象fino和oloroso一样是根据它的自然级数进行。

In this thesis, first, the basic principles and properties of the Generalized Frequency Response Function and the Volterra Series are introduced.

首先讨论了非线性系统相关理论，包括Volterra级数和广义频率相应函数的基本原理，基本性质，以及以此为基础的非线性系统故障诊断。

Harmonic proportion and progression are the essence of the created universe.

调和比例和级数是创造的宇宙的本质。

In Chapter 3, by means of Carlitz inversion formulas and a transformation of basic hypergeometric series obtained by Chu, we give new proofs for several Rogers-Ramanujan type identities.

第三章：在第二章内容的基础上，使用Carlitz-反演公式和初文昌获得的一个级数变换公式再次证明了许多Rogers-Ramanujan类型恒等式。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。