收敛性的

In Chapter 2, we will use one-parameter subgroups of the Lie group to develop a version ofNewton\'s method on an arbitrary Lie group for maps from a Lie group to its correspondingLie algebra which is independent of affine connections on the Lie group and differs fromNewton\'s method for sections on Riemannian manifolds.

在第2章中，我们主要研究关于从李群到其李代数的映射f的Newton法的收敛性。利用李群的单参数子群来给出关于映射f的Newton迭代点列，此Newton迭代与李群上的联络无关，也与第1章中研究的Newton迭代不同。

We introduce the general sigma point selection framework, and give two kinds of efficient methods: a reducing the computing complexity by decreasing the number of the sigma point; b scaling the sigma points to influence the effects of the higher order moments, then improve the accuracy of the UT; c Convergence analysis of the UKF, when used as an observer for nonlinear deterministic discrete-time system, is presented. Based on the UKF that captures the posterior mean and covariance accurately to the second or third order term (in terms of Taylor series expansion) for any form of nonlinearity, sufficient conditions to ensure local asymptotic convergence are established.

论文介绍了sigma点的一般选取规则，并给出了两种有效的方法：a通过减少sigma点集合的元素的数目来减少计算复杂度，b通过增加参数来逼近泰勒展开的高阶项，从而提高UT变换的精度；c论文研究了UKF算法应用于非线性确定性离散时间系统时的收敛性问题。

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。

This dissertation deeply studied the theory of CMAC neural networks from learning convergence, generalization ability and the improving of the network model and algorithm, and studied the applications of CMAC neural networks in tank barbette control system combining the national defense research project"Control Algorithm Study of Tank Barbette System". These works are meaningful to enrich the architecture of CMAC theory and to improve the performance of tank gun control system.

本文着重从学习算法的收敛性、网络的泛化能力以及对算法和模型的改进等几个方面深入研究了CMAC神经网络理论，并结合国防95预研项目"坦克炮塔系统控制算法研究"对CMAC神经网络在坦克炮塔控制系统中的应用进行了研究，这些工作对于丰富CMAC神经网络的理论体系，提高坦克炮控系统的性能具有重要的意义。

The primary work of this paper includes: 1 The general process and the fundamental theory of genetic algorithm is introduced systematically, which is also be applied to an example; 2 The penalty function method and the constraint tournament method are introduced in the paper, which are used to process the constraint limit. Via analyzing the basic principle of NSGA-II ,which is elaborated in the paper, the fast non- dominated sorting method, congestion distance and its comparison operator, the elite strategy and the main process of NSGA-II is researched particularly. 3 Via modeling the fire distribution problem, the model is computed by the algorithm of NSGA-II, which is combined with both the penalty function method and the restraint league tournament method The optimization of two goals are also realized in the paper. The results derived from the VC++6.0 indicate that, two algorithms both have the high convergence, simultaneously the Pareto optimal solution also maintain the variety of distribution.

本文所作的主要工作如下：系统地介绍了遗传算法的一般流程和基本理论，并应用于一个函数优化的实例；研究了用于处理约束限制的罚函数法和约束联赛法，论述了NSGA-II的基本原理，并对其提出的快速非支配排序法、拥挤度及其比较算子、精英策略及NSGA-II的主要流程作了详细的研究；建立了火力分配问题的模型，并将NSGA-II算法分别与罚函数法和约束联赛法相结合对该模型进行了计算，实现了对两个目标的最优化；用VC++6.0编程计算后所得的结果表明，两种算法均具有很好的收敛性，同时Pareto最优解也保持了好的多样性分布。

to reduce the impact of carrier frequency offset in ofdm system,this thesis designs a new carrier frequency offset estimation scheme for ofdm system.the carrier frequency offset estimation includes acquisition and tracking.we adopt variable step size adaptive algorithm.the acquisition range of the proposed algorithm is as large as one half of the overall signal bandwidth.through this method we can not only avoid the feedback by using forward error correction,but also reduce the times of complex multiplication in order to reduce the power consumption of the system.this algorithm not only has low complexity and fast convergence nut also can improve the demodulation performance of ofdm system.computer simulation illustrates the superior performance of the proposed algorithm with regard to estimation accuracy in both awgn channel and multi—path channel.

摘 要：为了减小正交频分复用系统受频率偏差的影响，在ofdm系统中设计了一种新的载波频偏估计算法。频偏估计包括跟踪和捕获两个阶段，文中采用变步长自适应算法来进行跟踪，这个跟踪算法的捕捉范围是整个信号带宽的一半。通过此方法，不但可以利用前向纠错的方式来避免反馈，而且可以缩减复数乘法的次数以降低计算复杂度和系统功耗。该方法运算复杂度低，并具有较好的收敛性，能改善odfm的解调性能。从计算机的仿真效果可以看出无论是在awgn信道上还是在多径信道上都表现出了卓越的性能。

The study shows the neural network model of hydro turbine can describe its nonlinear characteristic really and ensures the continuity of its derivative function, so improved the convergence for hammer calculating and is a better description of hydro turbine hill chart for science research and engineering design.

利用所述方法建立的水轮机特性神经网络模型能真实地表达水轮机的特性，并且解决了插值法的导数不连续问题，从而确保了水击计算的收敛性，为用于工程计算和科学分析的水轮机特性表达开辟了新的途径。并利用所建立的数学模型，开发了基于MATLAB的可视化软件仿真平台。

The relationship between the topology and convegence of networks is approached and the reason causing overtraining and overfitting is analysed. Then the redundant weights and nodes in the network are defined by using improved activity function and a new algorithm called the BPNSO for determining the network structure for any application is proposed, which use dual optimization objective function combining the mean squre error of the network output with network complexity penalty function.

文章对网络拓扑结构与网络收敛性和稳定性的关系进行了探讨，分析了网络出现Overtraining或Overfitting的原因和解决的目标，提出了神经网络结构优化的策略，改进了活化函数，定义了冗余权值和冗余节点的概念，为辨识和删除冗余权值和冗余节点，提出采用优化目标函数中增加网络复杂度罚函数的双重优化目标函数，并对罚因子提出了基于学习误差和权值的自适应动态调整公式，论文定义了这种BP网络结构优化方法为BPNSO，并给出了完整的计算流程。

In Chapter 2, starting from the basic fractional ordinary differential equations,weapply a high order approximation of fractional derivative advanced by Lubich to frac-tional differential equation, construct a high numerical difference scheme to solve thefractional differential equation, present error analysis of the algorithms theoretically,and prove the consistency ,convergency and stability.

接下来的第二章中，首先从基本的分数阶常微分方程出发，对Lubich提出的一个关于分数阶导数的高阶近似，将其应用于分数阶微分方程，构造高阶数值差分格式来进行分数阶微分方程的数值求解，并在理论上给出这一算法的误差分析，证明了它的相容性，收敛性和稳定性。

At present, however, the Government in this regard is very weak, and the specific problems: First, land use planning behind the reality of the development of land resources survey of the status quo is not clear; Second, land-use planning and urban master planning a lack of effective convergence, often contradictions and conflict, especially large cities, but also the preparation of regional planning, the current work in this area has not carried out; Third, land-use plans and the actual occurrence of the final match of poor demand for land, planning the actual situation can only cover 30 % targeted and guidance very poor.

但是，目前政府在这方面非常薄弱，和的具体问题：首先，土地利用规划的现实背后的发展，土地资源调查的现状是不明确；其次，土地利用规划和城市总体规划缺乏有效的收敛性，往往矛盾和冲突，特别是大城市，而且还编制区域规划，目前在这一领域的工作没有进行；第三，土地使用计划和实际发生的最后一场比赛穷人对土地的需求，规划的实际情况只能满足30 ％的目标和指导很差。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。