重根

The number a is called a double root of the polynomial function f.

数a称为多项式丞数f的二重根。

Lagrange interpolation focus on the application of the formula .The comparison between the method of Transform and that of Lagrange's interpolation formula in square matrix form is made. Also the form of Lagrange's interpolation formula is generalized to include the double root case.The application of the generalized lagrange's interpolation formula in square matrix to solving state equations is found to be effective.

重点介绍了Lagrange插值公式在状态方程求解中的应用，用对角矩阵及相似矩阵的性质证明了，当状态转移矩阵中方阵的特征根相异时，拉格朗日插值公式与Laplace变换法对表达具有一致性，并用极限方法对方阵含二重根时拉格朗日插值公式的应用进行了推导。

In this paper,the authors deeply discussed the relations between the extremum and the multiple roots for some types of functions,and researched how to use the relations in real world.

就一类函数极值与重根的关系作比较深入的探讨，并对这些关系作一些应用研究。

The improvement can maintain the speed of the original convergence and is still effective when there are multiple root s.

对牛顿求根公式作了改进，使其对重根情况仍有效，并保持原有的收敛性

Moreover this article also involves to the revision Newton iterative scheme, as well as this law when asks the multiple root the application.

另外本文还涉及到修正的牛顿迭代格式，以及该法在求重根时的应用。

A criterion for divergence of iteration is given and the covergence speed and covergence acceleration for iteration with multiple root are investigated.

给出迭代发散的一个判定，并讨论重根情形下迭代的收敛速度和迭代加速。

This paper investigates into the method for determining the times of multiple root s of the nonlinear function equation f=0, revising and supplementing the former conclusions,and obtains some more precise results.

文章对一般非线性函数方程重根次数的确定方法进行了探讨，对原有几个结论作了修改和补充，从而得到了更精确的结果。

The division with surplus, the comprehensive division and Eisenstein Test applications on polynomial that can not be divided are mainly discussed; the sufficient condition of that polynomial with coefficient being integer has no integer root, that cubic polynomial with coefficient being integer is irreducible in rational domain and that polynomial with coefficient being integer has not two completely same roots are summed up.

主要论述了带余除法、综合除法及不可约多项式艾森斯坦判别法的应用；总结出了整系数多项式的无整数根的充分性，三次整系数多项式在有理数域上不可约的充分性，整系数多项式无重根的充分性。

Ring. There are comprehensive researchs on the simple root cyclic codes.

本文主要研究了环F_2+uF_2和更一般的有限环Z_(p~2)上重根循环码结构，并讨论了环F_(2~m)+νF_(2~m)(ν~2=ν)上码的性质。

By mean of congruence transformation, when root of a polynomial has zero-root or double-root, a method for diagonalization of some Bezout matrics is given in this paper.

主要通过合同关系，对Bezout矩阵中当多项式存在零根和存在二重根时的对角化问题进行分析，得到一些有意义的结论。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。