非线性

Base vectors are selected for formulating the nonlinear mapping. An approximate explicit expression is formed by using the Nystrm method for nonlinear mapping which is not available originally. The data in the nonlinear input space is mapped into some linear feature subspace and fisher linear discriminant analysis is computed for the mapped data.

首先提取基向量；然后采用Nystrm方法，以基向量为训练样本，将形式未知的非线性映射近似表达为已知形式的非线性映射，这种近似的非线性映射将变量由非线性的输入空间转换到线性的特征子空间；最后对映射数据进行线性Fisher判别分析。

Under the fixed and clamped boundary conditions, a nonlinear differential oscillation equation with quadric and cubic items was presented by the Galerkin method, and a nonlinear free oscillation equation of the shallow reticulated shells with damage was solved.

基于Lematire等效应变损伤原理，计及扁球面网壳各个杆件的损伤影响，根据薄壳非线性动力学理论推导出含有损伤扁球面网壳非线性动力学方程和协调方程，在固定夹紧边界条件下，用Galerkin方法得到一个含二次和三次非线性振动微分方程，并对具有损伤扁球面网壳的非线性自由振动方程求解。

The experiment data of paramecium from Gause was used to investigate the efficiency of the method. And the twelve nonlinear real examples from "Agricultural Experimental Statistics" written by Mo Huidong were used to compare the difference between results fit by the Excel and the linear transformation method, respectively. The result showed that the Excel fitting method is not only simple and efficient for the parameter estimation but can fit various complex nonlinear equations also.

采用Gause的4组草履虫数据，研究了用Excel的"规划求解"工具进行非线性方程拟合的有效性，并以莫惠栋的《农业试验统计》一书中的12个非线性方程实例，比较了用Excel拟合与用常规线性转换方法拟合的差异，结果表明：用Excel进行非线性方程的拟合不仅简单易行、获得更优的参数估计，而且可以拟合各种复杂的非线性方程。

Based on the nonlinear dispersion relation of electromagnetic wave in relativistic plasma, the nonlinear controlling equation for linearly polarized mode is obtained using Karpman's method. The modulation instability of intense laser pulse propagating through relativistic plasma is analyzed and the modulation instability growth rate as a function of perturbation wave number for laser beam propagating through relativistic plasma is given.

从相对论等离体中电磁波的非线性色散方程出发，利用Karpman方法获得了线性偏振波模所满足的非线性控制方程，在非线性色散方程和非线性控制方程的基础上对线性偏振激光在相对论等离体中传播的调制不稳定性进行分析，给出了调制不稳定的时间增长率与扰动态波数之间的函数关系。

Also the response amplitude will be changed with the initial conditions due to the nonlinear properties of the cables.Taking the bending stiffness, cable sag and cable inclination into consideration, the space vibration control of the cables using the visco-elastic dampers in cable-stayed bridges is investigated by joining the center difference method and the state space strategy. Both the maximum modal damping ration and the optimal damper size are obtained, then the practical suggestions are proposed for the design of the dampers. The space nonlinear vibration equations of the cable-damper system are derived, and anew hybrid method for solving the cable-damper system is presented by combing the Newmark method and Pseudo-force technology. According to the known properties of the cable-damper system, the nonlinear transient responses are analyzed under all kinds of excitations. Based on the transient response, the control effectiveness of the visco-elastic dampers is further demonstrated.

综合考虑了拉索抗弯刚度、垂度的影响，研究了粘弹性阻尼器对斜拉桥拉索的空间振动控制，联合中心差分方法及状态空间法，得出了拉索面内、外振动各阶模态可能达到的最大阻尼比及相应的最优阻尼器系数，并对斜拉桥拉索的阻尼器设计提出了参考建议：考虑拉索抗弯刚度、垂度及几何非线性，导出了索-阻尼器系统的空间振动非线性方程组，结合Newmark方法及伪力(Pseudo-Force)方法，创新地提出了求解非线性方程组的杂交方法，根据拉索-阻尼器系统的阻尼特性，在各种荷载作用下，对索-阻尼器系统的非线性瞬态振动响应进行了研究，从系统响应的角度更加直接地验证了阻尼器的控制效果。

The estimation problem of the fuzzy nonlinear complexity of the random vector is studied, and some upper bounds are given. The limit properties of fuzzy nonlinear complexity of random vector are studied, and the limit theorem and the upper bound of variance limit of the fuzzy nonlinear complexity of random vector are given.(3) Enumeration of lst-order correlation-immune functions is discussed further.

首次提出了模糊非线性复杂度的概念，对随机向量的模糊非线性复杂度的均值进行了估计，给出了若干上界估计公式，并研究了随机向量模糊非线性复杂度的极限性质，给出了随机向量模糊非线性复杂度的极限定理及其方差极限的上界。

Three types of nonlinear element are introduced, one is the existing elastic-plastic flexural column element for reinforced concrete columns, the other two are nonlinear bearing element and nonlinear restrainer element developed by the author.

论述了用逐步积分法进行多点激励下非线性地震反应分析的过程，其中包括三种非线性单元的建立（前人发展的钢筋混凝土弹塑性梁柱单元，作者发展的非线性支座单元、非线性挡块单元）。

In the analysis, a nonlinear wave vibration equation of the thin cylindrical shell including damping and items due to geometric nonlinearities was established and then transformed by Galerkin's method. With different combinations of modes different nonlinear differential equations in modal coordinates were obtained. The Runge Kutta method was used to solve the equations numerically and some features of nonlinear wave vibration were discussed.

在研究过程中，首先，考虑阻尼并引入几何非线性项，建立薄壁圆柱壳的非线性波动方程，然后，采用Galerkin方法对波动方程进行转换，选取不同的模态组合，得到相应模态坐标下的非线性微分方程，最后用Runge-Kutta法进行数值计算并对圆柱壳的非线性波动振动特性进行了分析。

The conditional nonlinear optimal perturbation is a new theoretical method proposed by Mu,et al in 2003, which is an extension of the linear singular vector to nonlinear regimes. It has become a powerful tool to study some issues of nonlinear systems like predictability, sensitivity and so on, because it overcomes the defect of LSV for not representing the fastest developing perturbation of a nonlinear system.

条件非线性最优扰动是Mu等2003年提出的一个新的理论方法，它是线性奇异向量在非线性情形的推广，克服了线性奇异向量不能代表非线性系统最快发展扰动的缺陷，成为非线性系统可预报性和敏感性等研究新的有效工具。

The conditional nonlinear optimal perturbation is a new theoretical method proposed by Mu , et al in 2003, which is an extension of the linear singular vector to nonlinear regimes. It has become a powerful tool to study some issues of nonlinear systems like predictability, sensitivity and so on, because it overcomes the defect of LSV for not representing the fastest developing perturbation of a nonlinear system.

摘要条件非线性最优扰动是 Mu 等2003年提出的一个新的理论方法，它是线性奇异向量在非线性情形的推广，克服了线性奇异向量不能代表非线性系统最快发展扰动的缺陷，成为非线性系统可预报性和敏感性等研究新的有效工具。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。