查询词典 perturbation function

The perturbation of my mind during this fifteen or sixteen months'interval was very great; I slept unquietly, dreamed alwaysfrightful dreams, and often started out of my sleep in the night.

同时，我也同他们约定好他们回来时船上应悬挂的信号。这样，他们回来时，不等靠岸我老远就可把他们认出来了。他们出发时，正好是顺风。

A general unstable chaotic solution of the Duffing oscillator in a double-well with weak periodic perturbations is obtained by using the direct perturbation method in this paper.

利用直接微扰的方法求出了双阱中具有弱周期微扰的Duffing 振子混沌解的一般表达式。

Firstly, the integral-differential equation described the radiation field evolution is derived, and then the instability of its solution is also investigated analytically. By using the perturbation and iteration method, the threshold detuning and threshold linear growth rate of the unstable solution are analyzed and discussed in detail.

首先，建立了一个描述辐射场演化的积分一微分方程，解析分析了系统解的不稳定性，并采用线性方程解的微扰迭代方法进一步对系统不稳定解出现的失谐量阈值和线性增长率阈值等作了详细讨论。

On the basics of chapter three, a new scheme of photon acceleration by which the large amplitude nonlinear density perturbation excited by a finite length driving beam in plasmas is used to upshift the frequency of an ultrashort laser pulse.

第四章在第三章研究基础上，提出一种新的光子加速机制，即，利用有限长电子束激励的大振幅非线性等离子体电子密度扰动来对入射的光脉冲进行加速。

Both components of the perturbed vector potential are considered in the equations, as well as the perturbation of the electrostatic potential.

方程包含了完全的电磁扰动：静电场扰动，磁场的垂直扰动和平行扰动。

In order to analyze the stiffness of 3D 4 directional braided composites, the homogenization theory based on the multi-scale perturbation theory was used as the basic theory. The virtual displacement principle was used to educe the homogenization formulation of effective elastic modulus and the schemes to solve the problem using finite element method. The effective elastic modulus of 3D braided composites were predicted by this method and the calculation results agree quite well with experiment results.

在对三维编织复合材料刚度性能的分析过程中，以基于小参数渐近展开和多尺度摄动方法的均匀化理论为理论基础，用虚位移原理导出了等效弹性模量的均匀化列式及其有限元求解方程，从而通过细观和宏观有限元的数值分析方法预测了三维四向编织复合材料的等效弹性模量，预测结果与实验结果较为吻合。

In the sense of Von Karman large displacement, the governing equation of nonlinear dynamic response of the clamped circular plates under impact of a mass is established by using the virtual displacement principle and Galerkin's method in this paper. The effect of coupling between the impact load and the displacement of. the circular plates is considered. The governing equation is solved by applying the time increment method and the singular perturbation theory, and the asymptotic solutions of nonlinear dyna...

本文在Von Kármán大位移的意义上，利用虚位移原理伽辽金方法建立了圆板在物体撞击下的非线性动力响应的控制微分方程，在研究响应问题时，考虑了冲击载荷与圆板位移响应之间的耦合影响，文中使用时间增量法和奇异摄动理论求解问题的控制方程，获得了固支圆板非线性动力响应的近似解，并且求解了具体算例，绘出了圆板位移、应力响应曲线以及冲击力随时间的变化曲线。

In this project, we study the theory of higher order differential equations in Banach spaces and related topics. We solve an open problem put forward by two American Mathematicians and two Italian Mathematicians concerning wave equations with generalized Weztzell boundary conditions, introduce an existence family of operators from a Banach space $Y$ to $X$ for the Cauchy problem for higher order differential equations in a Banach space $X$, establish a sufficient and necessary condition ensuring $ACP_n$ possesses an exponentially bounded existence family, as well as some basic results in a quite general setting about the existence and continuous dependence on initial data of the solutions of $ACP_n$ and $IACP_n$. We set up quite a few multiplicative and additive perturbation theorems for existence families governing a wide class of higher order differential equations, regularized cosine operator families, regularized semigroups, and solution operators of Volterra integral equations, obtain classical and strict solutions having optimal regularity for the inhomogeneous nonautonomous heat equations with generalized Wentzell boundary conditions, gain novel existence and uniqueness theorems,which extend essentially the existing results, for mild and classical solutions of nonlocal Cauchy problems for semilinear evolution equations, present a new theorem with regard to the boundary feedback stabilization of a hybrid system composed of a viscoelastic thin plate with one part of its edge clamped and the rest-free part attached to a visocelastic rigid body. Also we obtain many other research results.

在本研究中，我们对Banach空间中的高阶算子微分方程的理论以及相关理论进行了深入研究，解决了由美国和意大利的四位数学家联合提出的一个关于广义Wentzell边界条件下的波动方程适定性的公开问题，恰当地定义了Banach空间中的高阶算子微分方程Cauchy问题的算子存在族及唯一族，建立了齐次和非齐次高阶算子微分方程Cauchy问题适定性的判别定理，获得了关于高阶退化算子微分方程的算子存在族、正则余弦算子族、正则算子半群、Volterra积分方程解算子族的乘积扰动和混合扰动定理，得到了关于以依赖于时间的二阶微分算子为系数的一大类非自治热方程非齐次情形下的时变广义Wentzell动力边值问题的古典解、严格解的最大正则性结果，获得了半线性发展方程非局部Cauchy问题广义解和经典解存在唯一的判别条件，从实质上推广了现有的相关结果；得到了一部分边缘固定而另一部分附在一粘弹性刚体上的薄板构成的混合粘弹性系统的边界反馈稳定化的新稳定化定理，还建立了一系列其他研究结果。

In section 2, if φ satisfies some conditions, a result is obtained that f can be reconstructed from the sampling values when the sampling set is Z or the sampling set is a small perturbation of Z.

在第二节，我们证明了若φ满足适当的条件，采样节点为整数节点或采样节点为为整数节点的微小扰动时，函数能够由其采样值稳定而且唯一的重建。

Based on the ISC earthquake catalogue data, according to the orbit equations of two-body-problem and the perturbation theory of celestial mechanics, we could determine the projection pole of the sun, and thus calculate the zenith distance from the sun to the epicenter. After calculating all the earthquakes on their zenith distances, we could get the distribution of the solar zenith distance versus the occurring probability of earthquakes.

基于ISC地震记录，利用天体动力学中二体问题的轨道方程和摄动理论，确定发震时刻太阳在地面的投影点位置，并进一步计算出太阳相对震中的地心天顶距，将地震按天顶距的大小进行统计，得到地震的太阳天顶距地震频度分布。

We have something to do in the new stage.

在这段崭新的时期中，我们有一些要做的。

The difference between tourism decision-making under uncertainty and risky tourism decision-making is indistinctive.

其中不确定性旅游决策和风险旅游决策的界线比较模糊，两者的区分是相对的。