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On the basis of the conclusion above, the nonlinear weak controllable vectors can be obtained, which compose the second class of weak controllable matrix, by means of matrix transfermations of the first class of weak controllable matrix. Furthmore the second criterion of weak controllability, accessibility and strong accessibility, which is more standard, more succinct and more practical, is obtained. On the basis of the first criterion and the second criterion, several important problems about nonlinear controllability are discussed, which include 1 local controllability; 2 three classes of local controllable decomposition, separately by means of local coordinate changes in the neighborhood of a nonsingular point, a point on a singular surface or a designated point x〓 with a designated input u〓; 3 the character of controllability of the ith state variable x〓 in different controllable areas and their boundaries.

在第一判别定理和第二判别定理的基础上，我们分析了非线性系统受控性质中的几个重要问题，所得到的结论包括i得到了非线性系统在可平衡点附近的能控性判别定理；ii分别给出了非线性系统在非奇异点、s阶奇面以及在状态空间内给定的一点x〓和输入u〓上的三种状态分解形式以及相应的求解方法；利用系统的Ⅰ型弱能控矩阵与Ⅱ型弱能控矩阵秩相等的条件，得到了只用系统的前n个弱能控向量来判断系统的弱能控性的判别定理；iii通过引入系统状态分量的三类受控区域边界的定义及相应的求解方法，初步探讨了非线性系统各个状态分量在不同的受控区域及其边界上的受控性质。

For the purpose of validating the effectiveness of the mathematical model, based on a hydrofoil catamaran, HC200B, the simulation research is carried out, by use of Mablab's Simulink toolbox, so that the elevations and trim angles are obtained corresponding to 12 velocity points and the variation of the boat's attitude at the design speed is also obtained.

为了验证模型的有效性，基于一艘高速水翼双体船HC2 0 0B ，使用Matlab的Simulink工具箱进行了仿真研究，给出了在 12个航速点的上浮量和纵倾值，以及在设计航速的船体姿态。

In this paper,a design method of two dimensional Linear Phase Nearly Perfect Reconstruction filter banks based on a new class of cosine modulation systems is presented,which can be described as follow: firstly,the Parks-McClellan algorithm is adopted for designing the prototype filter,then by employing cosine modulation,a series of analysis and synthesis filters can be obtained,accordingly a one-dimensional LP-NPR filter banks can be constructed;Secondly,cascading two one-dimensional LP-NPR filter banks in the form of tree structure and using the unimodular transformation,a two dimensional nonseparable LP-NPR filter banks can be obtained.

提出了一种基于一类新余弦调制系统的二维线性相位-近似完全重构滤波器组的设计方法，设计过程分为两个步骤：首先采用Parks-McClellan算法来计原型滤波器，再经过余弦调制能到一系列的线性相位分析和综合滤波器，从而可以构造一维LP-NPR滤波器组；然后利用树状结构来结合两个一维LP-NPR滤波器组，并运用单位模变换，可以得到二维不可分离LP-NPR滤波器组。

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。

By the experiment, not only the relation between adhesion force and creepage has been obtained, but also the relation between adhesion coefficient and speed has been obtained as well.

试验不仅得到了完整的粘着力与蠕滑率的关系，同时得到了粘着系数与运行速度的关系。

By using the Neighbor-joining method of Molecular Evolutionary Genetics Analysis sofrware, a dengrogram was obtained based on genetic distances. Another dendrogram was obtained by Maximum Likelihood methodv in PHYLIP (3.6) software. The bootstrap values vwere evaluated for each crunode of the dendrogram by means of bootstrap test.

利用分子进化遗传分析软件，采用邻结法构建系统发生树；同时根据等位基因频率，利用PHYLIP(3.6)分析软件，采用最大似然法构建系统发生树，应用自举检验估计系统树中结点的自引导值，并进行了系统发生分析。

Firstly, variables which were acquired for the above two kinds of classification system were obtained from field and laboratory investigation of the core samples as well as test of supersonic waves in drilling holes. Secondly, distribution functions and parameters of all variables are determined using statistic method. Thirdly, 20000 RMR values or BQ values and cumulative distribution function of these RMR or BQ values have been obtained utilizing Monte—Carlo method and the results are plotted. Finally, risk analysis can be made from above results.

风险评价方法步骤如下：（1）首先通过岩芯样品的现场观测和实验室试验及钻孔岩体超声波测试获得两种分类所需的变量；（2）通过统计分析和判断得出各变量的分布函数及参数；（3）运用Monte—Carlo模拟方法获得2万个RMR值或BQ值及相应的累积分布函数，并将结果绘成岩体质量描述图；（4）运用以上结果作出岩体质量风险分析。

An optical system with refraction and total internal reflection was proposed according to the luminous characteristic of LED and the law of energy conservation. The ordinary differential equations satisfying the spots on the contour curve of TIR refractive and reflective planes were established. The coordinates of points on profile curves were obtained by solving these ordinary differential equations using Runge-Kutta method. The profile curves were acquired by curve fitting of the coordinate spots with software UG, and then TIR model of the projector and data of the surface shape suitable for NC manufacture were obtained.

根据LED的发光特性以及能量守恒定律选择采用折射全反射光学系统，通过建立TIR折射面及全反射面轮廓曲线上的点所满足的常微分方程，利用RungeKutta求解常微分方程得到轮廓曲线上点的坐标，再在UG中对坐标点进行曲线拟合得到轮廓曲线，进而得到TIR模型及适合数控加工的面形数据。

A fitting curve between the decay time constant and the film thickness of YBCO was obtained, and the film thickness can be obtained from the fitting.

另外还作出了YBCO薄膜的薄膜厚度与衰减时间常量之间的关系曲线，提出了测量YBCO薄膜厚度的一种新方法。

Thedata was obtained by experiment and linear regression method was used to fit the penetration ratio of X2ray in explosiveunder different conditions. The decay law was obtained by analyzing the fitted results.

通过试验测定，利用线性回归方法对不同情况下测得的X 射线在某炸药中的穿透率进行拟合，分析拟合结果得出X 射线在某炸药中的衰减规律。

More direct, directer ; most direct, directest

径直的，笔直的

Do you know how to use a chain saw?

你知道如何使用链锯吗？