计算多项式

Prove the formulas with related the Bernoulli polynomials of higher order and Euler polynomials of higher order.

证明了与高阶Bernoulli多项式和高阶Euler多项式相关的无穷积分的计算公式。

In chapter 3, a new method that gives the universal unfolding of the bifurcation functions is established.

第三章以多项式理论为基础，创建了计算普适开折的多项式计算法。

The main purpose is to construct cubature formulae on an arbitrary spherical triangle. Firstly a method for accurately computing the definite integral of spherical polynomial functions on a spherical triangle is proposed.

本文主要研究定义在球面三角形上函数的数值积分，通过积分的插值多项式函数构造具有多项式精度的插值型求积公式，以及给出精确计算球面三角形上多项式函数方法。

The inverse polynomial and the invertible affine transformation exist by the finite field, linear algebra and matrix theory. The invertible affine transformation and the inversion in are easily realized by using lookup table. An algorithm can be used to get the inverse element of modulo .

本文运用有限域、线性代数和矩阵理论，论证了逆多项式和逆仿射的存在性，并且应用查表法简捷地实现了中元素的求逆和逆仿射变换；设计了一个易于在在计算机上实现的算法，来求形如的多项式模时的逆元，该多项式的系数在上。

In this dissertation, we mainly focus on the computation of Jones polynomial and some its related polynomials of links in knot theory and analyze the distribution of their zeros.

本论文主要研究扭结理论中链环的Jones多项式和一些相关多项式的计算以及Jones多项式的根的分布，使用的方法基本上是组合方法。

Simulations are carried out upon square-aperture beam using Legendre polynomial. Conjugate gradient method is used and optimization is performed for several steps to reduce executing time.

针对方光束口径，利用 Legendre 多项式模拟光束波前分布，利用共轭梯度算法对多项式系数进行了优化计算；优化过程分为几步进行以减少计算时间。

In order to calculate the satellite orbit in GPS data process,it is more efficient to use polynomial methods to fit the orbit curve with the parameters of GPS broadcast ephemeris.

利用多项式拟合的方法计算GPS卫星在轨坐标时，使用正交多项式可有效避免计算过程中出现的病态矩阵。

From our results we know that the average error of the Lagrange interpolation sequence and the Hermite interpolation sequence based on the Chebyshev nodes in the 1-fold integrated Wiener space equal weakly to the average error of their corresponding optimal approximation polynomial in the 1-fold integrated Wiener space,and as a kind of information-based operation,they have simple form and their recover functions are polynomials,in the 1-fold integrated wiener space,their average error equal weakly to the corresponding minimal information radius whose permissible information operators class is function values.

通过我们的结果可以知道，基于第一类Chebyshev多项式零点的Lagrange插值算子列和Hermite插值算子列在1-重积分Wiener空间下的平均误差弱等价于相应的最佳逼近多项式在1-重积分Wiener空间下的平均误差，并且作为形式简单且恢复函数为多项式的一种信息基算法，其在1-重积分Wiener空间下的平均误差弱等价于相应的以函数值计算为可允许信息算子的最小平均信息半径。

A new method that transforms bitlevel waveform polynomial to word-level polynomial model is given, allowing for simple composition This method offers an efficient way to determine whether two descriptions from different design levels are equivalent, so component reuse, synthesis and verification across design levels can be realized. In addition, an experimental system using C language is established, including modules such as representation of waveform polynomial, decision of path senstization, delay computing, clocking based on single-period sensitization, clocking based on multi-period sensitization, test generation considering noise and transformation from bit-level waveform polynomial to word-level polynomial model. They respectively used to test models and techniques proposed in this paper.

另外，基于C语言本人设计开发了一个实验软件系统，该系统包括波形多项式表示模块、敏化通路判定模块、延时计算模块、单周期敏化的最小时钟周期精确确定模块、多周期敏化的最小时钟周期确定方法模块、考虑噪声的测试生成模块和位级波形多项式描述转化成字级多项式描述模块，分别用于对本文各章中提出的自动化设计的模型和方法进行实验验证。

Highly precise quadra order non-linear formula is set up, which gives the satisfactory density value of highly pure aluminum (99.999~99.99999 %) at 20 oC.Linear approximate formula for the density calculation of 99.75% primary aluminum (molten point in the range of 658.7℃～1100℃) derived f...

以Jagrangian插值的二次多项式和一次多项式导出的 99.75 %原铝(熔点 6 5 8.7℃～ 1 1 0 0℃)的密度计算的线性近似式、该式子较文献〔1〕所述的还要简单，而数值计算结果却高度吻合。

This is not an ordinary box, which is used as a background picture of the dialog box, very pretty.

详细说明：这可不是一个一般的对话框，它是用图片作为背景的对话框，非常好看。

Conceal me what I am,and be my aid for such disguise as haply shall become the form of my intent.

遮掩我的身份，帮助我，我的面具将成为我的目的。