多项式

In this thesis, the limit cycles bifurcated from some kinds of polynomial systems are investigated using the methods of bifurcation theory and qualitative analysis.

本文利用分支理论和定性分析的方法，借助于计算机等辅助工具对几类多项式系统的极限环分支问题进行了研究。

Comparing with deterministic system, the point of bifurcation in stochastic Duffing-van der Pol system is moved as increasing the intensity of random parameter.

进一步的推广证实正交多项式逼近法在实际问题中有广阔的应用前景，它可以解决含有多个随机参数的非线性随机动力学系统的分岔问题。

The bifurcation theory of the plane polynomial vector fields is one important research domain of the theory of ordinary differential equation.

平面多项式向量场的分岔理论是常微分方程定性理论的重要研究领域之一，主要研究依赖于参数的向量场的全局轨线拓扑结构随参数变化的规律。

On two binomial coefficient s and their related combinatorial identities;2. Several identities on binomial coefficient s and trigonometric func tion values of special angles are obtained.

利用组合数学的一些技巧给出了切比雪夫多项式的通项表达式，并得到了一些二项式系数，特殊三角函数值的恒等

Two main aspects of the research work are as follows:(1) The paper introduces the experimental ice forces on semi-circular breakwaters which is made by State Key Laboratory of Coastal and Offshore Engineering of Dalian University of Technology and calculate the ice value for different radius semi-circular component, based on which it speculates on that horizontal ice value and water level accord with biquadratic polynomial function, meanwhile, the paper analyses incidence of ice heap to horizontal ice value of semi-circular component.

论文的主要工作有三部分：(1)主要介绍大连理工大学海岸和近海工程国家重点实验室所做的物理模拟试验，应用水平冰力计算公式计算了不同半径半圆型构件的冰力值；根据这些数值的分析，推测半圆型构件水平冰力与水位符合四次多项式函数关系；同时分析了碎冰堆对半圆型构件水平冰力影响。

Linear, annual, and biyearly variations of GPS height have been analyzed with help of harmonic analysis method.

利用三角多项式拟合方法分析了所有测站高程变化的线性项、周年项、两年项和半年项。

Second, in the viewpoint of crypto analysis, the practical requirement for the cryptographic function is to construct the function that can resist all the known crypto analysis and attacks. In advanced, the main cryptographic properties are compared, and the relation among these cryptographic properties is analyzed, including the trade-off ones. Get the conclusion that the construction of cryptographic Boolean function is to find out the proper Boolean function in the whole vector space under the restriction of several cryptographic properties required for the security system.

然后本文从密码分析的角度，讨论了密码函数的实际需求，即构造能够抵抗已有密码分析与攻击的布尔函数；分析了布尔函数的主要的密码学性质，并比较了这些性质之间的相互关系，包括制约的关系；得出了构造布尔函数的实质的结论，即在向量空间中构造全体布尔函数，以所需的若干密码学性质作为限制条件，用有限域上的多项式、Walsh谱、Hadamard矩阵等数学工具找出适当的布尔函数用于加密体制的设计。

The boundary of interval Ball curves of degree n is discussed and two algorithms for the degree reduction of interval Ball curves are given by means of linear programming and best approximation respectively.

讨论了n次区间Ball曲线的边界的构成；同时通过讨论区间多项式的降阶，利用线性规划法及最佳一致逼近法，给出了区间Ball曲线的的降阶算法。

In this research a new mathematical model - cubic polynom with two given derivatives at end points - was proposed which can good match the S-shpae curve.This model has a number of analytical features:describing the geographic phinomena prosesses in three hierarchies (textural fractal,structural fractal and state fractal); the boundary values of the structural fractal can be considered as the boundary values of interval of scaleless.

在研究中提出了扩展分维表达函数：带导数三次多项式，它能很好地表达反S形分布曲线，具有一系列解析特征：可从三个层次（纹理分形、结构分形和态势分形）上描述地理现象或过程；其中结构分形的边界可近似地看作是非扩展分维无标度区的上下界。

There exist Engel groups for each of which the Engel length of the product of two elements is not bounded by any polynomial function of the Engel lengths of the factors.

定理1。每个团体存在的恩格尔恩格尔产物长度两个因素并不是什么北临多项式函数恩格尔长度因素。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。