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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。

To be specific,its generalized characteristic polynomial has positive double roots,which we proved further has only a double,root by using the affine transformation and inverse affine transformation.

为了更好地进行干涉判断，根据椭圆-椭圆外切的代数条件——广义特征多项式具有正的重根，以及进一步证明出的该正重根的唯一性结论，利用仿射变换和逆变换方法，推导出了椭圆-椭圆的不适合边界解析方程。

To be specific, its generalized characteristic polynomial has positive double roots, which we proved further has only a double, root by using the affine transformation and inverse affine transformation, his easy to detect interference accurately between two ellipses using NFB analytic equation.

根据该解析方程不仅可以直接对任意两个椭圆之间的干涉性做出精确判断，并且可由此绘出NFB的轨迹图，同时使用可视化方法给出了快速粗略的判断。

Eigenvalue method is one of the fundamental methods that solve polynomial system.

特征值方法是求解多项式方程组的基本方法之一。

Through the polynomial approximation to function, resulting in more than a Peano-type and Lagrange remainder of the Taylor formula, using elementary functions Maclaurin expansions to address the limits and the approximate evaluation of the problem.

通过多项式来逼近函数，从而得到带有佩亚诺型余项和拉格朗日余项的泰勒公式，利用初等函数的麦克劳林展开式来解决极限及近似求值的问题。

In addition, elementary number theory, the matrix also can be used for elementary transformation to bring more than once and the division of congruence, and promotion to general-in addition to polynomial.

另外，在初等数论中，还可以用矩阵的初等变换来求一次带余除法的商及余式，并将其推广到一般除式为次多项式。

Furthermore, the integer programming method is exploited as the mathematical tool for the generation of a polynomial algorithm producing the optimal set elementary siphons.

在此基础上，以整数规划算法为数学工具给出了时间算法复杂度为多项式的最优基本信标的计算方法。

As a result, the concept of an optimal set of elementary siphons is proposed and also the algorithm which can be finished in polynomial time to find such a set. With the set of optimal elementary siphons, net supervisors can generally produce maximalreachable states.

但是上述理论虽然只需要控制基本信标即可以控制整个系统，但是由于从属信标满足一定的可控性条件才能完全受控，这意味着在控制算法的生成过程中所有的信标都要参与，从而大大增加了系统控制的复杂性。

In Chapter 3, a certain polynomial Hamilton system with 3 degree is given. By elliptic integral formulas, the monotonicity of the periodic orbits of this system is verified.

在众多文章中，讨论次谐轨的分岔都需要一个条件，那就是在同宿轨附近的周期轨是单调的，第三章给出了一个具体的三次平面Hamilton系统，利用椭圆积分公式验证了这个系统的一对同宿轨附近的周期轨的周期是单调的，这包含了三种情况，周期轨在右边同宿轨内部，在左边同宿轨内部以及在整个同宿轨圈外部。

These new APN polynomial functionsare not Carlet-Charpin-Zinoviev equivalent to Dobbertin functions, and arenot equivalent to the known functions under certain conditions.

该APN函数不Carlet-Charpin-Zinoviev等价于Dobbertin函数，且在特定条件下不等价于已知的函数。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。