算法论

Mathieu function is the base of field theory analysis in elliptical cylinder coordinate system. So, firstly, detail investigation has been given about the problem of numerical analysis of Matheiu functions, based on the predecessor's contribution, an improved faster algorithm of numerical analysis and confirmation algorithm of Matheiu functions has been presented.

Mathieu函数是椭圆柱坐标系统下场论分析的基础，因此本文首先对Mathieu函数的数值计算问题进行了详细研究，并在前人基础上完善并进一步改进了目前被认为较为可行的数值算法，并提出了验证算法。

To solve this problem, based on the concept of graph theory we give a few models and arithmetic designs of virtual backbone in the environment of different application, and propose the corresponding routing mechanism with these virtual backbones. The major achievements are outlined as follows:The state of host's power or the time of host's online plays an important role in keeping stability of a virtual backbone. With a view to this feature, the paper introduces a simple and efficient heuristic algorithm for calculating the virtual backbone by seeking a minimum connected dominating set with maximal weight. The maximality of the weight-based choice of backbone nodes guarantees that the most suitable nodes have been chosen for the role of backbone nodes so that they can properly coordinate all the other nodes and keep stability of the virtual backbone in the network.

为了解决这个问题，本文利用网络图论中的一些理论，在不同的应用环境下给出几种虚拟骨干网的模型、构建及基于稳定性和节能的算法设计，并针对这些骨干网提出相应的分层路由机制，主要研究内容和贡献如下：考虑到主机的功率大小和在线时间长短对虚拟骨干中心的相对稳固性的影响，提出用基于极大权的最小连通支配集模拟虚拟骨干网；并给出其数学模型和相应的启发式算法，确保了性能强的主机担任骨干节点；通过优化规则确保骨干网的极小性，有效地减小了控制分组转发开销；最后进行了仿真验证。

During the pre-processing of the finite element analysis, the interactive subdivision method which combines the computer's high efficiency with human's intelligence is realized. The dummy node method, which is used to solve the subdivision problem about multiply connected region and the region with isolated verge combining the optimization algorithm in topology, is brought forward for the first time in this dissertation.

在有限元分析的前处理中，本文实现了既充分利用计算机的高效性又融合了人工干预的灵活性的交互式网格生成算法，并且首次提出虚拟节点法，结合图论优化算法解决了多连通域及包含孤立边界的任意形状目标区域的网格自动生成问题。

Furthermore, the information dissemination of several topologies is analyzed theoretically, and the statistical properties of canonical topologies and varying neighborhood topology are analyzed from graph theory.

针对传统粒子群优化算法中全连接型拓扑和环形拓扑的特点，引入了一种粒子群信息共享方式——多簇结构，进而基于多簇结构提出了动态可变拓扑策略以协调动态概率粒子群优化算法的勘探和开采能力，并从理论上分析了最优信息在各种拓扑中的传播，同时从图论角度分析了几种经典拓扑以及动态可变多簇结构的统计特性。

In this paper, we first discuss some basic theories about wavelet analysis, including some definitions about wavelet analysis, multi-resolution analysis, the decomposition and reconstruction algorithm of wavelet transform, orthonormal wavelet decomposition of the signal, and a few important properties of wavelet transform.

本论文中，我们首先讨论了小波分析的基本原理，包括了小波分析的基本概念，多分辨分析，小波变换的分解算法和重构算法，信号的正交小波分解，以及小波变换的几个相关的重要性质，这些都是我们进行研究和应用的基础。

Veinott algorithm, which can compute reachable matrix and the period index of strongly connected graphs, respectively.

1即可。算法2 借助了图论中求可达矩阵的Warshall 算法和求强连通图周期指数的Balcer ？

Based on the characteristics above, this paper presents two graph-theory algorithms fast identifying the weakness of networks according to wide area measurement information such as pre-fault network topology and load flow, namely the algorithm of fast search for transmission section based graph theory and the algorithm of fast search for flow transferring Minimal Short Path.

基于潮流转移的上述特点，本文根据事故前的网络拓扑结构、潮流分布状态、输电元件物理参数与系统电压等级等广域测量信息，针对两种不同的网络结构分别提出了相应的快速识别网络薄弱环节的图论方法，即输电断面快速搜索算法与潮流转移最短路径快速搜索算法。

The first one focuses upon the fundamental theory and methods of system identification, including the basic concepts of system description and identification,review of matrix theory, stochastic process and pulse response of linear systems; the first principle models for lumped and distributed parameter systems; modeling of bioreactions; auto regressive moving average model; weighted least square and regressive weighted least square for parameter estimation of ARMA model; Runge-Kutta and Simplex methods; an example of BPNN application; as well as Kalman Filter.

第一部分包括知识驱动建模、数据驱动建模、参数估计和状态估计的基础理论和方法。具体为：(1)系统辨识和系统描述的基本概念，包括矩阵论、随机过程、线性系统的脉冲响应函数等基础知识回顾；(2)基于动态物料和能量衡算的集总参数、分布参数对象的知识驱动建模方法；(3)生物反应系统的建模方法；(4)自回归移动平均模型；(5) ARMAX模型参数的加权最小二乘参数估计一次性算法和递推算法，相应的统计性质；(6)龙格库塔法和单纯形法；BP神经网络应用实例；(7)卡尔曼滤波器，及其与加权最小二乘参数估计递推算法的对比。

of transitive closure based on equivalence relation, method of maximum fuzzy spanning tree based on fuzzy graph, and algorithm Fuzzy C-Means based on partition are more deeply investigated. Respectively, this thesis proposes an algorithm for document fuzzy clustering based on methed of transitive closure and an algorithm for document fuzzy clustering based on methed of maximum fuzzy spanning tree. Moreover, FCM is particularly studied from data standardization method, metrics method, and selection method of initial clustering prototype.

较深入地讨论了基于等价关系的传递闭包法、基于模糊图论的最大树法以及基于划分的模糊C-均值算法，分别提出了基于传递闭包法的文本模糊聚类方法ATCFC和基于最大树法的文本模糊聚类方法ATCMT；重点从改变规格化方式、改变度量方式、改变初始聚类原型选择方式三方面对FCM算法进行研究。

However, the transmission lines among the shortest path from one node of the overloaded line to the other, might suffer from flow transferring most greatly after the overloaded line tripping for a "strong-receiver" system, in which generations and loads are distributed equably and generation capacity in load centre is large.

基于潮流转移的上述特点，本文根据事故前的网络拓扑结构、潮流分布状态、输电元件物理参数与系统电压等级等广域测量信息，针对两种不同的网络结构分别提出了相应的快速识别网络薄弱环节的图论方法，即输电断面快速搜索算法与潮流转移最短路径快速搜索算法。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。