系统函数

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

A conditional probability density function of the SAR imaging systems is derived, These works lay a foundation for further research.

将SAR成象系统视为一个多元接入信息系统，在深入分析系统构成的条件下，求出该系统的传递概率密度函数。

Then the stationary joint probability density, the conditional reliability function, the mean first-passage time of the optimally controlled system are obtained from solving the reduced FPK equation, the backward Kolmogorov equation and the Pontryagin equation, respectively of fully averaged systems.

求解与之相应的Fokker-Planck-Kolmogorov方程得最优控制系统的联合概率密度，进而求得最优控制系统的平均幅值；求解与之相应的后向Kolmogorov方程得最优控制系统的条件可靠性函数，进而求得首次穿越时间的条件概率密度；求解与之相应的Pontryagin方程得最优控制系统的平均首次穿越时间。

The system parameters are determined by optimizing an output-error cost function. To deal with the non-uniqueness of the fully parameterized state-space system, a projected gradient search algorithm is presented by restricting the update of the parameters to the tangent space to the manifold of observationally equivalent state-space systems. The sufficient condition to employ L-M algorithm for optimizing parameters is also introduced. The proposed hierarchical optimization identificationmethod includes two steps: First, the parameter search direction is determined by the proposed adaptive L-M projected gradient approach; Second, the optimum step size is computed according to a line search method.

通过极小化输出误差目标函数获得了系统参数估计；提出了正交梯度搜索方法用于解决系统参数的非唯一性问题，正交梯度搜索的本质是在输入-输出等价类相切平面的正交垂空间更新系统参数；给出了用 L-M 算法进行参数优化的充分条件；提出的系统参数递阶优化辨识方法包括两步：首先用给出的自适应 L-M 算子正交梯度方法确定参数优化方向；其次由一维搜索方法计算最佳步长。

At last the results have been applied to the tracking problem of a class of mechanical systems with discontinuous friction term. Chapter 3 mainly deals with uniformly ultimate boundedness of a class of nonautonomous systems with discontinuous right-hand sides and corresponding perturbed systems (in the sense of Filippov solutions). The definitions of globally uniformly strongly ultimate boundedness and globally uniformly weakly ultimate boundedness of discontinuous systems and the definition of globally equiuniformly strongly ultimate boundedness of corresponding perturbed systems are presented firstly.

首次给出不连续系统全局强一致最终有界、全局弱一致最终有界的定义，以及针对于扰动系统的全局强等度一致最终有界性的定义，并基于非光滑的Lyapunov函数得到了不连续系统全局一致强、弱最终有界的Lyapunov定理和扰动系统全局强等度一致最终有界性的Lyapunov定理。

According to the characteristics of elevator group control system ,dispatching software of the system is designed.

根据电梯群控系统的特性，设计了系统的调度软件，使用统计的方法判断群控系统的客流交通模式，确定了电梯目标评价函数，同时介绍了系统的控制模块设计方法。

For the infective subsystem, we obtain the existent condition of the subsystem equilibrium point and the uniqueness of the positive equilibrium point by the no infectious subsystem's conclusion and the image analysis. The partial stability of the subsystem equilibrium points is discussed by analyzing eigenvalue. The condition that the system has no limit cycle is obtained by the Dulac function.

对染病子系统，利用无病子系统所得结论及图像分析法，得到了系统平衡点的存在条件，正平衡点的存在唯一性；利用特征根方法判断了系统平衡点的局部稳定性；利用Dulac函数得到了系统不存在极限环的条件；利用极限方程理论得到了系统疾病消除平衡点和地方病平衡点的全局稳定性。

The flood activity is one child system in this system, it also has an extremely strong nonlinearity relation with the weather system, and it is very difficult for the analysis means based on explicit function and linear measure and the mathematical model in simulating the gradual progress course and gradual progress method of flood reasonably.

水文水环境系统是一类与自然资源、生态环境和社会活动紧密相关的、极其复杂的大系统，洪水活动作为该系统的一个子系统，还与天气系统具有极强的非线性相关关系，这使得基于显函数和线性假设的分析手段与数学模型很难合理地模拟洪水的演进过程和演进规律。

Finally, based on the characteristics of transient responses and the Morlet wavelet, a family of wavelet functions is introduced and used in the simulation of modal analysis.

文中分析了在众多小波基函数中Morlet小波更适合对动态结构系统进行模态分析的原因，结合Morlet小波的性质和结构系统对脉冲响应信号的特性，构造了一小波族，实现了利用Morlet小波变换对多自由度系统进行模态解耦和对时变系统进行模态参数辨识的方法。

Moreover,using Ito differential formul a to the constructed Lyapunov function along solutions of lto stochastic differential systems,Lyapunov method is adopted to set up the fundamental theory of dissipativity in the module corresponding to the theory on the dissipativity of deterministic ordinary dif- fere.

提出了有关Ito型随机微分系统耗散性理论的新概念：按模耗散、按模等度耗散和按模一致耗散，并利用Lyapunov方法，借助于Ito 微分公式沿着Ito型随机微分系统的解对所构造的Lyapunov函数求导数，给出了Ito型随机微分系统有关按模耗散理论的一些代数判据，获得了与确定性常微分系统耗散性理论相对应的结论，最后的算例证明了该方法的有效性和可行性。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。