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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。

The polynomials, such as the Zernike polynomial, the orthogonal Zernike polynomial in square zone and the Legendre polynomial, are used to describe the phase of the wavefront in the algorithm of the Hartmann Sensor's model reconstruction in square zone.

方形区域上的哈特曼波前传感器的波前模式重构算法中可用Zernike多项式、方域上正交的Zernike多项式以及Legendre多项式来重构波前相位。

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。

The VBA macro can extend an antenna element to an arbitrary linear or square array with their amplitudes of the array elements being weighted in the Chevbyshev polynomials or Cosine functions.

宏命令将单元天线扩展为任意线阵或是平面方阵，并对天线阵的幅度进行切比雪夫加权或余弦加权。

It is feasible to simplified curved surface of second degree and solved some polynomials factor decomposition by the theories of the matrix algebra.

用矩阵代数的理论简化二次曲面和解决某些多项式的因式分解的方法是可行的。

Using the steepest descent method of Deift-Zhou,we derive uniform asymptotic formulas for the Meixner polynomials.

利用Deift和Zhou的最速下降线法，我们导出一些关于Meixner多项式的一致渐近公式。

Finally, we present an efficient algorithm for computing the minimal polynomial of a polynomial matrix. It determines the coefficient polynomials term by term from lower to higher degree.

最后，我们给出了一种计算多项式矩阵最小多项式或特征多项式的有效算法，它从低次项到高次项逐项确定最小多项式的系数多项式。

Define Ck =∪rCk,r, where r passesthrough all monic irreducible polynomials of degree k over Zn.

定义Ck=∪rCk，r，这里r跑遍Zn中所有k次首一不可约多项式。

Now he worked in ajoint venture.

现在他在一家合资企业工作。

More troops in Afghanistan won't change any of the foregoing.

更多的在阿富汗的军队也不会改变之前的状况。