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Based on chapter two, In chapter three, the method of multiple scales is introduced to the study of the multiple-dimensional nonlinear stochastic systems under random external excitation. Using method of multiple scales, we strictly deduce the equation of modulation of amplitude and phase. The effects of random excitations are analyzed; numerical simulations verify the results. Theoretical and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may be changed from a limit cycle to a diffused limit cycle.

在第二章基础上，第三章将多尺度法引入到相应的随机系统的研究中；严格推导了系统的约简方程，用矩方法求出稳态解应满足的方程，获得一些结果；并且数值模拟结果与理论推导的结果是一致的；并注意到，与其对应的确定性系统相比较，系统响应从周期解变为近似周期解，系统的相轨线从极限环变为扩大的近似极限环；随着激励带宽的增大，此扩大的近似极限环的宽度将增大。

In this paper, we introduce the estimation and algorithm o f p arameter and some diagnostic statistics. We deduce the computation formula of curvature and conformal normal curvature for four perturbations of models.

本文主要介绍了指数族非线性模型的参数估计及其算法，若干诊断统计量，并将保形法曲率应用到指数族非线性模型中，推导了模型四种扰动方式的曲率和保形法曲率计算公式。

When normal distribution of subordinate function was considered, we can further deduce fussy reliable formulas that forces and intensities were lognormal distribution, that forces and intensities were weibull distribution, that forces were exponential distribution and intensities were normal distribution, that forces and intensities were exponential distribution. 3. Coincide methods of skip-ratio curve were gotten by deducing and skip-ratio functions of standard road in common use was gotten by theoretic and algebraic calculation.

并以此为基础选取了广义而精确的正态分布隶属函数，进一步推导了应力和强度均为对数正态分布时的模糊可靠性公式、应力和强度均为威布尔分布时的模糊可靠性公式、应力为正态分布和强度为威布尔分布时的模糊可靠性公式、应力为指数分布和强度为正态分布时的模糊可靠性公式、应力和强度均为指数分布时的模糊可靠性公式。

From the NYT article, it is natural to deduce that the author meant "commercial success".

从NYT的原文中可以明显看出原作者的"最成功的"的意思是指商业方面的成功。

In addition, the kinetic energy Ek as a function of R will be different if the ρDE is different. Thus we can observationally measure the Ek of galaxies, compare it will our results here, and then deduce the ρDE in our universe.

而且动能 Ek 随著至星系中心距离 R 的变化，会因ρDE 的不同而不同，因此可以试图量测宇宙中星系的 Ek ，然后和这里的结果比对，即可推导出宇宙中的ρDE 。

In this paper, the Maslov theory was introduced. By τ-p transform, seismic data is transformed from space to ,〖WTBX〗 and phase ( p s, p r ,τ) space. Then it is combined with Born inversion, and deduce the high-frequency asymptotic solution of migration operator amplitude in phase domain.

引人Maslov理论，利用τ-p变换将数据从空间分别变换到和及( p s ， p r ，τ)空间中，并将其结合到Born反演中，推导出了相空间偏移算子振幅的高频渐近解。

This chapter makes use of satellite orbit space geometry to deduce mathematic model and formulas of judgment.

本章通过卫星轨道空间几何关系，推导得出用户判断所在波束的数学模型和计算公式。

The variation of density with depth is expressed as a function of n order polynomial function to deduce general gravity anomaly formula for 2 D density variable body having arbitrary and regular shapes.

本文把密度随深度的变化表示成任意次多项式函数，推导出了计算任意和规则形状二度变密度体重力异常的通用解析公式。

He seeks apodictically certain ways by which, within his own pure inwardness, an Objective [2] outwardness can be deduced.

他试图寻找绝然确定的方式，通过这些方式，在他自己的纯粹内在性『pure inwardness』中，能够演绎出『deduce』客观外在性『an Objective outwardness』。

Analysis whether this pressure sensors fluxsystem be applicable smaller then 1 cm, and whether the pipe geometricalappearance and flow status influence the flux detection system .and relate velocityof flow、compressive stress、pipe configuration、laminar flow and overfall、differenceof the pipe radius、and so on Use the related principle of the hydromechanics , deduce the method of presswith 2 points and 3 points to measure the flux detection, analyzed the possibility ofmake use of MEMS compressive stress transducer to survey flux detection.possibility and related influence factors from the theories.

对实现压差式测量中多点压力传感器设置间距提出了小于1cm的设想，并用有限元分析模型模拟分析了在压力传感器间距小于1cm条件下流量测量的性能，取得了有意义的实验数据，证明了实现这一设想的可行性。

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。