多项式

According to the orthonormality of Legendre polynomials in the function approximation theory, the exact boundary of the ball Bézier surface was optimally squarely approximated in polynomial form.

依据函数逼近论中Legendre多项式的正交性，得到了采用多项式形式表示的球域Bézier曲面的精确边界的最佳平方逼近。

Orthogonal polynomials with weight equaling 1 are used to make least square approximation, so morbidity phenomenon in solving equation is avoided and better results can be obtained. Advantages and disadvantages of Legendre polynomial and Gram-Schmidt polynomial are also discussed.

比较了Legendre多项式和Gram-Schmidt正交化构造的多项式在处理时间漂移方面的优缺点，并介绍了通过随机误差的平稳性来检验处理结果优劣。

Secondly, we embedded a Legendre polynomial of 5 orders into fixed effects, additive genetic and permanent environment effects were characterized by using Legendre polynomials with from three to eight orders.

其次，固定效应镶嵌5阶Legendre多项式，加性遗传效应和永久环境效应分别镶嵌3到8阶的Legendre多项式。

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。

Recurrent formulas for calculating the coefficients of the Legendre polynomial and the expressions for calculating the sedimentation coefficient are deduced analytically.

为了研究多分散低Péclet数沉降问题，我们先以Legendre多项式展开法得到了计算对分布函数的普遍递推式，以及由Legendre多项式的系数表示的沉降积分。

Based on in comparison of all statistical criteria and behavior of estimated parameter the RRM with a fifth-order Legendre polynomial for both fixed effects and additive genetic effects, a seventh-order Legendre polynomial for permanent environment effects is equally well equipped to model all effects, which is the best model among different RRMs.

通过各种统计指标和估计参数行为的比较，确定固定效应和加性遗传效应镶嵌5阶Legendre多项式，永久环境效应镶嵌7阶Legendre多项式的随机回归模型为最优模型。

This are algorithmic need the linear combination that seeks control quantity to express to be disperse Legendre orthogonal polynomial, will beg control to measure problem translate into to beg question of coefficient of disperse Legendre orthogonal polynomial.

该算法把待求控制量表示为离散Legendre正交多项式的线性组合，将求控制量新问题转化为求离散Legendre正交多项式系数新问题。

By using matrix norm, matrix singular value, non-negative matrix theory, the regions of numaerical range and spectum of operator polynomial and the regularity of operator linear pencil are obtained.

8应用矩阵范数理论、矩阵的奇异值理论、非负矩阵的理论、友矩阵、算子的谱理论为工具，获得了算子多项式数值域具有的特性及其包含范围，算子多项式数值域与n-次数值域的关系，最后研究了算子线性束正则性的等价条件及谱分布情况。

We obtain new lower bounds for the sum of degrees of simple and distinctirreducible factors of the polynomial f1 +···+ fn, where fi(1≤i≤n) are pairwise relatively prime polynomials of several variables with coefficients in C.

七我们对形如f1 +···+ fn的多项式的单重不可约因子的次数和及不同不可约因子的次数和的下界分别作出新的估计，其中fi(1≤i≤n)为系数在C中的两两互素的不可约多项式。

Firstly, the function sinx that appears in the simple pendulum equation is replaced with a polynomial of degree 3 using Maclaurin series expansion and Chebyshev polynomial approximation. Subsequently, the resulting equation which is a Duffing type equation is approximately solved with combing Newton's method and the harmonic balance method.

首先，利用Maclaurin展开和Chebyshev多项式加速技术将单摆振动方程中的正弦型恢复力用三次多项式近似代替，得到一个Duffing型方程；然后，将牛顿法与谐波平衡法结合起来建立Duffing方程的解析逼近周期及周期解，从而给出单摆振动的解析逼近解。

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。