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Function approximation; best uniform approximation polynomial; deviation point; FPGA

函数逼近；最佳一致逼近多项式；交错点；FPGA实现

For the given endpoint interpolation conditions, a new approximation method of multidegree reduction is presented. Using Chebyshev polynomial approximation theory, the nearly best uniform approximation under the interpolation conditions of endpoints can be obtained.

对于给定的首末端点的各阶插值条件，给出了一种新的一次降多阶逼近算法，应用Chebyshev多项式逼近理论达到了满足端点插值条件下的近似最佳一致逼近。

We divide this interval into several subintervals, based on deviation points, find the best uniform approximation polynomial of each subinterval, and then denormalize the computation result to the final result.

论文摘要：根据切比雪夫定理，提出了一种适于FPGA实现的函数逼近新方法：通过区间映射关系，将函数定义域映射到较小的逼近区间内，并按照交错点对逼近区间进行分段，分别求出每段的最佳一致逼近多项式，对函数进行分段逼近，最后将逼近结果反映射，得到最终的函数计算结果。

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。

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。

In this thesis, we first discuss the algorithms of arithmetic operations over binary fields using a polynomial basis representation.

本文首先讨论了有限域上基本算术运算的算法，对有限域上的椭圆曲线理论进行了研究，分析了椭圆曲线上的核心算法——数乘算法。

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。

Consequently, we get an estimate formula of the number n_1, bounded above by a polynomial of degree 24 in the parameters of F.

从而给出n_1的一个以F的参数的24次方为上界的估计式。

Then we get an estimate formula of the number i\;bounded above by a polynomial of degree 9 in the parameters of F. As pointed by D.

从而给出n_1的一个以F的参数的9次方为上界的估计式。D。

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。