递归的

The purpose of this paper is to present some ways of transformation based on decomposition of trigonometric reasoned formula of integral calculus, and furthermore, it can promote student s ability of integral calculation and use of recursion serial.

结合积分的计算，分析积分递推式的化归问题，三角有理式在积分中的拆分法的化归问题，有利于促进学生对于积分的计算以及递推序列的巧妙应用等数学能力的培养。

A scanline algorithm for area filling with pushing span -ends has good efficiency but also a shortcoming that one class of special connected fields cann′t be filled completely by this algorithm .

针对压入区段端点的区域填充扫描线算法有可能出现的漏填，分析了漏填现象产生的原因，并在不增加算法复杂度的情况下提出相应的改进办法，给出了具体的算法流程，从而实现了对任意4-连通区域的正确而快速的填充，而且该算法的运行效率比递归种子填充算法以及经典的扫描线种子填充算法有明显提高。

Furthermore,the stability behavior and accuracy characteristics of the algorithmare proven by a spectral decomposition method.

在前人工作的基础上，提出了一种新的用于解决结构动力分析问题的时间积分方法——Taylor级数方法；建立了求解线性问题和非线性项可以表示为多元多项式形式的非线性问题的Taylor级数方法的理论，并给出递归求解通式；阐述了该方法的程序实施过程，给出了计算流程图，并在非线性有限元分析平台NFAP中嵌入了Taylor级数方法的计算模块；利用谱分解的方法分析了该方法的稳定性和精度特性，以封闭的解析形式给出了描述积分法特性的周期延长率和振幅衰减率的表达式；通过对该方法的理论分析和特性研究，阐述了该方法的可行性和高效性。

Secondly, the properties of output sequences of stop-and-go clocked combiners are discussed. It is proved that the output sequences are stationary and obey strong law of large numbers and central limit theorem. Using the probabilistic model properly built, we analyze the rate of coincidence between the output sequences of two kinds of generators with basic operations and corresponding LFSRs sequences. All the computational formulae are derived. A recursive algorithm for efficiently computing the poster probability of partial input strings and corresponding joint probability is introduced. Moreover, divide-and-conquer attacks on this kind of generators which reconstruct the initial states of the input stop-and-go generators individually are proposed.

其次，分析了一般钟控停走组合生成器输出序列的概率分布性质，证明了生成器的输出序列是严平稳的，且服从强大数定律和中心极限定理；考察了钟控加法型组合生成器和钟控乘法型组合生成器的输出序列和相应的常规钟控下线性移位寄存器序列之间的符合率，给出了符合率的具体计算公式；给出了组合器输出序列段和输入序列段之间的联合分布以及部分输入序列段的后验概率的有效递归算法，进一步提出了利用后验概率对钟控组合生成器进行分别征服相关攻击的方法。

Hypercube has many advantages, such as smaller diameter, simple routing algorithm, many parallel paths between any two nodes, and fault-tolerance, on the other hand that the Hypercube nodal degree increased logarithmetically to the number of nodes has limited network population. So we propose a constant nodal degree hierarchical topology to remedy the weakness of Hypercube and take advantages of Hypercube most. Given the definition of FCCN we analyse the basic properties including nodal degree , number of links , extensibility and diameter (maximum network communication delay). Also we proposed a simple and self-routing algorithm applied in FCCN. Although the self-routing algorithm is not optimal, but at more than 82% case it can get the shortest path, and the percent is larger and larger increased with network levels. By the self-routing algorithm the internodal distance is calculated to evaluate the network communication delay more clearly. The average internal distance is in order of the cubic root of the network population that is almost same as logarithmetically relation in a few thousands. FCCN is a highly scalable network due to its recursive construction.

首先在比较了基本互连网络的基础上，看到超立体网络的杰出性能，包括网络直径小、寻路算法简单且为自寻路算法、容错能力好等等，但是由于其节点度随网络的规模的增加而按对数关系增长，使得超立体网络的应用规模受到极大限制，所以为了能最大限度利用超立体网络的优点的同时弥补其节点度方面的不足，作者提出了节点度等于常数4的FCCN网络结构，来最多地利用立方体网络的优点；然后在对FCCN网络进行严格的定义后，分析了网络的节点度、链路数、延伸特性、网络的直径（决定网络的最大通讯延迟）等，并提出了适于FCCN网络的简单的自寻路算法，计算自寻路算法可得到最短路径的比例，看到在多于82％以上的情况自寻路算法都是最优的，而且比例随网络层数的增加而增加；应用所提出的自寻路算法计算了可以更加准确反映网络通讯延迟的参数—网络平均节点距离，计算得到此参数与网络大小的立方根成正比，此比例关系在网络的规模在几千节点以内与对数关系的网络几乎一样；FCCN网络是一高度可扩展结构，这是因为FCCN的递归构成方式，使得网络在增加节点时其原有的拓扑结构可以保持不变，不需对网络进行重新设计，为网络的实用扩展提供了条件；理论分析得出FCCN网络是一种高度可扩展高性能网络的结论。

The paper sees Horton code as a primary characteristic value and generalizing condition of the river network, and selects, simplifies and generalizes river based on scale of before and after generalization,, The main contents of paper include:(1)Reviews generalization concept, arithmetic operators, methods, influence factor and frame of map generalization and design, analyze core theory of feature —oriented map generalization, discuss the main context and applicable method of river feature generalization(2) Summarizes natural form and spatial configuration characteristic of the river network, and describe the river network using digraph Paper mostly researches tree —like river, identifies the direction of river based on the angle of the main and secondary reach, and identifies the main river based on most length and predominant continuation of the flow direction along the major channel , then receives the grade of river by recursion and structuralize river network, builds hiberarchy rank system of river based on Horton coding(3)Designs the model of river network based on Horton code, and organizes the data of node, branch and river.

本论文把Horton编码作为水系网的一个主要特征值并以此作为综合条件，并根据综合前后的比例尺对水系网进行选取、化简和概括。论文的主要工作包括：(1)总结地图综合的概念、算子分解、实现方法、主要影响因素和总体设计框架，分析面向地理特征的制图综合的核心理论支撑，在此基础上讨论水系专题要素综合的主要内容和综合适用的方法。(2)总结水系网的自然形态和空间结构特征，用图论对水系网进行描述。以树状水系作为主要研究对象，依据树状水系的主支流交汇关系确定水系流向，依据水系中主流的长度最长和主流保持原有的流向趋势确定主流，按此递归得到河流的不同级别，对基于河段组织的水系网结构化，自动建立水系的Horton编码。(3)设计基于Horton码的水系网模型，对结点、河段、河流和河系的数据进行有效的组织。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐