特征方程的根决定了系统的稳定性以及对各种输入的响应特性。
The roots of the characteristic equation determine the stability of the system and the general nature of the transient response to any input.
本算法通用性强，不须求解方程的根就可绘制各种代数函数及超越函数曲线；
This algorithm has a large adaptability of both algebraic and transcendental curves and solving the root of the function are not needed.
求解高次实系数代数方程的根，对于控制系统的分析和综合设计有着重要意义。
Solving the algebra equation with real-coefficients of nth degree is of great importance for analysis and synthesis of a control system.
根据总体稳定性判据，闭环系统稳定，当且仅当所有的特征方程的根有负面真正的部分。
According to the General Stability Criterion, a closed loop system will be stable if and only if all the roots of the characterized equation have negative real parts.
进一步，即使可以精确地得到特征方程，我们依然无法在有限精度的限制下去计算方程的根。
Furthermore, even if the exact characteristic equation can be obtained, we could not compute the roots of the equation in the demanding precision.
从前求一元一次方程和一元二次方程的根，要求输入方程的系数，数据间逗号或空格分隔，输出方程的根。
Once upon, slover the root equation of a degree and equation of two degree that need input coefficient of equation, data separate need comma or space, output the root equation.
FORTRAN77编制的求一元一次方程和一元二次方程的根，实现了输入方程字符串，输出方程的根。
The program use The FORTRAN77 language slover the root equation of a degree and equation of two degree, It is succeed that input string of equation, output the root equation.
本文提出的这种方法，它的特点在于：我们不是用牛顿迭代法去直接逼近方程的根，而是用牛顿迭代法去逼近方程的二次因子。
The method presented in this paper is not to approximate directly with Newton iterate the roots of a polynomial but to approximate its second order factors.
本文指出了弱粘弹性材料结构的特征值是一组有理分式多项式方程的根，并给出了关于这些有理分式多项式方程根的一个定理。
It is pointed out that the eigenvalues of these structures are the roots of a series of rational fraction polynomial equations. A theorem about the roots of these equations is proved in the paper.
也就是求这个方程序的根。
最后一件讽刺的事情发生在1950年，82岁的密立根发表了他的自传，其中第九章的标题为“光子存在的实验验证—爱因斯坦光电方程”“the Experimental Proof of the Existence of the photon—einsteins Photoelectric Equation .”。
One final irony: in 1950, at age 82, Millikan published his Autobiography, with Chapter 9 entitled simply "the Experimental Proof of the Existence of the Photon — Einstein's Photoelectric Equation."
也考虑了在根与解的问越上代数方程与具有滞后的代数方程的等价性。
The equivalauce of roots and solutions between algebraic equation and algebraic equation with time lags is considered.
文中也提出了利用分划曲线来判定系统特征方程具有全部负实部根的方法。
Methods of using the D-decomposition curves to judge whether all the roots of the characteristic equation possess a negative real part are also discussed.
本文利用微分方程稳定性理论，研究了城市交通容量中两种交通方式的竞争关系，它们适合于根舍模型；
Using the theory for differential equation stability, this paper investigates a struggle relationship between two traffic modes in city traffic volume , and shows they suit Gause' s model.
提出了一个新的迭代公式，用此公式求解非线性方程根收敛速度快，且绝对收敛。
This paper presents a new iterative formula by which the solution of nonlinear equation had rapid and absolute convergence.
不动点迭代方法是求解非线性方程近似根的一个重要方法，其应用非常广泛。
Fixed-Point Iteration method is an important technique to solve nonlinear equations for calculating approximate roots and applied widely.
通过分析相应特征方程根的性质，给出系统稳定的一个充分条件。
By studying the properties of roots for the corresponding characteristic equation, the sufficient conditions under which the equation is stable are given.
常用的试算法在确定马斯京根方程参数时一般得不到最优结果，且计算较繁杂。
The parameter of Muskingum equation is usually ascertained by the trial way that were complex and the optimized results not gotten.
本文提出一种通过对数复变换求非线性方程实数根数值解的方法。
A method to find real numerical solution of the nonlinear equation by logarithm complex conversion is presented in this paper.
本文利用特征方程根的性质，研究了开口圆柱薄壳精确微分方程的特征方程的渐近解。
Using the root of the characteristic equation, this paper studies the asymptotic solution of the characteristic equation of the open circular cylindrical thin shells.
对特征方程利用根与系数的关系，导出了一个计算基频的简便公式，并结合实例说明其有一定的实用价值。
A simple formula for finding basic frequency is derived by use of relation of root and coefficient, and an example is enumerated to illustrate its application.
本文介绍了一种求实系数高次代数方程全部根的新方法。
This paper presents a new method in which all roots of a higher degree algebraic equation with real coefficients can be found out.
解方程时要进行一系列移项和同解变形，最后求出它的根，即未知量的值。
To solve the equation means to move and change the terms about without making the equation untrue, until the root of the equation is obtained, which is the value of unknown term.
众所周知，时滞系统的特征方程对某一固定的时滞来说有无穷多个根，并且这些根也是很难解出的。
As everyone knows that the characteristic equations of the delay systems have infinite roots for a fixed delay and it is hard to solve for them.
从而解决了任意一元三次方程的实数根的分布的问题。
Thus solves the distributed problem of optional simple cubic equation's real root.
该一维有限元列式只需对扇形区域在角度方向上离散，最后的总体方程为一个二次特征根方程。
Discretization in angular coordinate is needed only and the global equation is a second order characteristic matrix equation.
该文还阐明了对二阶对称张量成立的关于特征方程的重根与重向的一些结论对非对称二阶张量不一定成立。
The paper illustrates the conclusions about the multiple root of characteristic equation and characteristic vector which fit symmetric tensor of rank two may unfit unsymmetric tensor.
本文通过构造迭代函数，利用逐次逼近的方法给出了一类方程根的存在性与唯一性的判断的一种解决方案。
By means of constructional iterative equation, this paper presents a way to give out the existence and singularity of a type of equational root with gradual approach method.
由于根轨迹方程中未出现可变增益K，从而使计算大为简化。比传统的伊文思法要简便准确得多。
The computation will be simplified, since the variable gain K would not appear in the equation of the root loci.
由于根轨迹方程中未出现可变增益K，从而使计算大为简化。比传统的伊文思法要简便准确得多。
The computation will be simplified, since the variable gain K would not appear in the equation of the root loci.
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