查询词典 initial approximation

Numerical simulations show that similar to their counterpart in deterministic nonlinear system some symmetry-breaking bifurcation may occur in the stochastic Duffing-Van der pol system, and Chebyshev polynomial approximation is an effective approach in solving dynamical problems of nonlinear system with random parameter.

数值模拟显示随机Duffing-Van der pol系统与确定性均值参数系统有着类似的对称破裂分岔行为，文中的主要数值结果表明Chebyshev多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法。

Numerical results for the original stochastic Duffing-van der Pol system obtained separately by the Mento-Carlo method and the Chebyshev polynomial approximation are compared to show the effectiveness and efficiency of the latter method in solving the nonlinear dynamical problems of system with bounded random parameters.

数值模拟结果显示，Chebyshev正交多项式逼近法是研究含有界随机参数的耦合非线性动力学系统的一种有效方法。

Spectral element methods for partial differencial equation is introduced in this study from viewpoint of the collocation approximation of Chebyshev polynomial. Wave Equation and its space discretization are deduced. Two time integral methods, central difference method and implicit Newmark method, are introduced, and their stability and applicability are also discussed in some details. The significance of absorbing boundary conditions in spectral element methods for Aeroacoustics is explained, and Clayton-Engquist-Majda absorbing boundary conditions is emphasized and introduced, then the discrete scheme of this boundary conditions is deduced and applied to spectral element methods for wave equation.

本文从Chebyshev多项式逼近理论出发，详细介绍了谱元方法求解偏微分方程的过程；推导了流体中的声波动方程并在空间上对其进行了谱元离散；详细讨论了两种时间积分方法──中心差分法和Newmark方法，分析了它们的稳定性条件，并从理论上对比了两种方法的优缺点和适用范围；将吸收边界条件推广应用于谱元方法求解气动声学问题中，重点介绍了Clayton-Engquist-Majda吸收边界条件的原理和公式，推导了该吸收边界条件的变分形式，并将其引入波动方程的离散形式中。

The stochastic Bonhoeffer-Van der Pol system is first transformed into an equivalent deterministic system using the Chebyshev polynomial approximation, so that the problem of controlling stochastic chaos is reduced to the problem of controlling deterministic chaos in the equivalent system.

首先运用Chebyshev多项式逼近的方法，将随机Bonhoeffer-Van der Pol系统转化为等价的确定性系统，使原系统的随机混沌控制问题转换为等价的确定性系统的确定性混沌控制问题，继而可用Lyapunov指数指标来研究等价确定性系统的确定性混沌现象和控制问题。数值结果表明，随机Bonhoeffer-Van der Pol系统的随机混沌现象与相应的确定性Bonhoeffer-Van der Pol系统极为相似。

In this paper, the elemntary knowledge of oblique circulant matrix is described briefly and three inverse eigenvalue problems which a-re denoted by Ⅰ,Ⅱ,Ⅲ and best approximation problem which is denoted byⅣ on oblique circulant matrix are presented.

本文介绍了斜循回方阵的基本内容，提出了斜循回方阵的特征值反问题Ⅰ，Ⅱ，Ⅲ及其最佳逼近问题Ⅳ，给出了它们有解的充分必要条件及求解算法，并举出了相应的数值例子。

A fast algorithm for calculating the inverse and Moore-Penrose inverse of the permutation factor circulant matrix is presented. Then, a fast algorithm for the product of the permutation factor circulant matrix is given. Finally, The least-square solutions of inverse problems and the optimal approximation problems for the permutation factor circulant matrix are discussed.

首先给出了一种求n阶置换因子循环矩阵的逆阵、自反g-逆、群逆、Moore-Penrose逆的快速算法，然后给出了计算两n阶置换因子循环矩阵之乘积阵的一种快速算法，最后给出了其反问题的最小二乘解的存在性定理及它的一般表示，并证明了逼近矩阵的存在唯一性且给出它的具体表达式。

When scaled factor circulant matrices are nonsingular, we can find the single solution of the scaled factor circulant matrix equation; When scaled factor circulant matrices are singular, we can find the special as well as the general solution of the scaled factor circulant matrix equation; There is only an error of approximation when the fast algorithm is implemented on computers, and only the elements in the first row of the scaled factor circulant matrix and the constants in the diagonal matrix are needed by the fast algorithm.

当鳞状因子循环矩阵非奇异时，该快速算法求出线性方程组的唯一解；当鳞状因子循环矩阵奇异时，该快速算法求出线性方程组的特解与通解。该快速算法仅用到鳞状因子循环矩阵的第一行元素及对角矩阵中的对角上的常数进行计算。在计算机上实现时只有舍入误差。

Application on circular cylinder particle size distribution based on anomalous diffraction approximation.

反常衍射近似在测量圆柱形粒子粒径分布中的应用。

The phase of optical wave can be recovered by the intensity transport equation under the paraxial approximation For the optical system with diffraction limit, it is difficult to get the boundary radical slope of phase and sample in the circular domain boundary when using the intensity transport equation to recover the phase, consequently, we reviewed an algorithm mentioned in the reference ［4］, namely, the equation, computation domain and boundary condition are changed, then the phase is reconstructed by the multigrid method and corrected at last Moreover, the experiment system is set to testify the algorithm, and the recovered phase from the intensity data detected by CCD is compared with the result from phase retrieval algorithm, it is found that the phase reconstruction error can reach 017 λ in the case of non-uniform intensity distribution, as a result, the method is suitable for the phase recovery with low wavefront sensing accuracy.

在傍轴近似条件下，可以利用光强传播方程对畸变波前进行相位恢复。对于衍射受限的光学系统，很难获得相位的边界径向斜率值作为边界条件，此外，要获得精确的圆域边界采样值也并非易事。为了克服上述困难，进一步研究了相位恢复改进方法，即改变了方程的表示形式、计算区域和边界条件，并用多重网格法进行求解获得重构相位，最后再将其修正。为了验证算法的精确性，搭建了实验系统对算法进行实验验证，将由CCD探测的光强分布进行计算得到的相位分布与相位恢复算法的结果进行比较，证明在光强分布非均匀的情况下，该方法恢复的相位均方根误差能够达到017 λ，可以适用于波前传感精度要求不是很高的相位恢复。标签自适应光学相位恢复相位修正光强传播方程 adaptive optics phase retrieval phase correction intensity transport equation

Common Reflection Surface stack is a brand-new and special ZO imaging method, the theory of CRS stack stems from paraxial ray theory, the biggest difference between CRS stack and conventional ZO imaging method is that it consider a reflector R as a circular reflector segment Cr placed in the vinicity of reflector R, Cr can be seen as the second order approximation of the reflector. The CRS traveltime surface is the multi-coverage reflection response of the reflector mirror assigned to R.

共反射面元（CommonReflection Surface=CRS）叠加技术是一种全新的、特殊的零偏移距剖面成像方法，CRS迭加理论源于傍轴射线理论，它与普通的零偏移距剖面成像方法的最大区别是它认为地下反射层是由许多个小反射弧段互相叠合组成的，认为来自某反射点附近的一个邻域内的反射信息都可以对该反射点的成像作出贡献，因此对该反射点进行零偏移距成像时就应该聚焦更多的能量参与迭加。

Pachomius manual labour was organized as an essential part of the monastic life; and since it is a principle of the monks as distinguished from the mendicants, that the body shall be self-supporting, external work of one sort or another has been an inevitable part of the life ever since.

根据圣pachomius体力劳动组织作为一个重要组成部分寺院生活；以来，这是一个原则的和尚，作为有别于乞丐，该机构应自支撑，对外工作的这种或那种已一个必然的一部分，生活至今。

In order to study the effects of parametrical rolling on the ship movement and tilts, in allusion to ship's navigating in regular following waves, the equation of ship rolling motion is transformed into normal Mathieu equation by proper variable replacement when strong parametrical excitation in restoring moment varied according to sine or cosine wave.

为研究参数横摇对船舶运动和倾覆的影响，通过对船在规则波上随浪航行时，恢复力矩中出现的1个以正余弦规律变化的强参数激励项进行适当的变量置换，将船舶的横摇运动方程转换成标准形式的Mathieu方程。