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.
一些人利用这里的方程，取代平衡常数。
And some people use that equation here instead of equilibrium constant.
然后利用法向量得出切平面的方程。
And then get this equation for the plane using the normal vector.
佩雷尔曼博士利用广为人知的“瑞奇流（Ricci flow）”这样一个热方程来证明了庞加莱猜想。
Dr Perelman proved Poincaré's conjecture by taking an equation normally used to model heat dissipation in three-dimensional objects, known as Ricci flow.
就像内能u一样，我们希望能够利用状态方程的数据，计算出其表达式，这些表达式能方便我们说出即将发生的过程。
Just like u, we'd like to be able to express it in a way that allows us to calculate what happens only from equation of state data.
加州大学戴维斯分校环境科学与政策系教授黑斯廷斯，是世界上利用数学模型(方程组)来理解自然系统的顶级专家之一。
Hastings, a professor in the UC Davis Department of Environmental Science and Policy, is one of the world's top experts in using mathematical models (sets of equations) to understand natural systems.
人们很容易利用方程序对变化的物价水平进行描述，虽然在高等学术界有人质疑，这样的方程序是否具有实际价值。
A version of an equation explaining a shifting price level is not hard to diagram, although there is some doubt, in higher academic circles, as to whether any such equation is of real value.
你还可以利用剪切版这个技巧来复制一个方程通过计算器来计算。比如，复制下面这个方程到剪切版。
You can also use the clipboard trick to copy an equation into the calculator and process it. For instance, copy this to the clipboard.
麦克斯韦方程组用矢量的形式重新表示，并利用狭义相对论你的对称性。
Slide-shows original equations, then equations re-written as vector analysis, then using the symmetry of special relativity.
在已知空间物体表面区域方程的前提下，利用黎曼和可以方便地求出被测物体的体积。
It is very convenient to calculate the object volume to use Riemann sum after obtained the object surface region equation.
利用简单的代数 (代替上述方程式)，我们就会发现存在另一种看问题的角度
Using some simple algebra (substitute from the earlier equations), we find out that there is another way to view this
本文利用声波方程，对阶梯状地表数据进行样条插值处理，得到了与起伏地表比较吻合的四边形网格剖分。
Using acoustic equation, the paper conducts spline interpolation for step surface data and results in quadrilateral grid partition coincident with relief surface.
我们知道什么会引起骚动和讨论，并把考虑把这些利用起来。一级方程序有一个疯狂的社区。
We learnt what generated buzz and discussion and tried to work that into our future thinking. F1 has a crazy community!
一个旋转黑洞的最佳描述是在1963年获得由新西兰数学家罗伊克尔，利用重力爱因斯坦的方程序。
The best description of a spinning black hole was given in 1963 by the New Zealand mathematician Roy Kerr, using Einstein's equations of gravity.
本文利用微分方程的数值解法对时间序列建模预测作了新的尝试。
In this paper a new method of modeling forecasting is given for the time series by using the numerical solution of differential equation.
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.
利用积分方程方法以及半空间并矢格林函数的快速算法对埋地目标体矢量电磁散射进行正演计算。
Forward electromagnetic scattering by buried objects is computed with the integral equation method and efficient algorithm for half-space dyadic Green's functions.
利用这组方程，作者研究了纵向磁化铁氧体柱中的法拉第旋转（铁氧体柱的两端是截面变化的圆锥）。
With these equations, they have investigated the problem of Faraday rotation in a longitudinally magnetized ferrite rod with tapering cross-sections at both ends.
通过对一类相当复杂的变分方程问题的研究并利用其有关结论，我们证明了新模型最佳控制的存在性并刻划出其结构。
From studying some kind of quite complex variational equation problems and applying the conclusion, we prove that the optimal control of new model is existent and characterize its structure.
利用不定方程理论及中国剩余定理，我们设计了一类陷门背包公开钥密码系统，它们具有更好的安全性。
Using the theorem of linear Diophantine equations and the Chinese remainder theorem, we have constructed a class of trap-door knapsack public-key cryptosystems, which have a better security.
主要考虑非线性波方程组的一些简单对称及其构成的李代数，并利用所得对称给出该方程组的一些单参数变换群。
In this paper, the symmetries and Lie algebra of a coupled nonlinear wave equation were discussed. One-parameter transformation groups of this equation were obtained by using the symmetries.
通过解析共线条件方程式，利用相对定向直接法进行像对的相对定向。
By analyzing collinear equation and adopting absolute orientation method, the stereo pair of photos is relatively oriented.
本文根据珩轮的加工原理和齿面方程，利用计算机图形学方法，分别建立了珩轮的表面模型和实体模型。
Based on the machining theories and gear profile equation, using computer graphics, the article builds the surface model and solid model of honner.
本文研究了具有边界摄动的抛物型方程。利用可解性的讨论，得到了原问题的摄动解。
In this paper, the parabolic equation with boundary perturbation is considered. Using discussion of the solvability, the perturbed solution of original problem is obtained.
本文对几类二阶非线性常微分方程，利用首次积分求得了其通积分公式。
This paper has found general integral formulas of some types of two - order nonlinear ordinary differential equations by first integral.
本文利用微分方程的数值解法对时间序列建模预测作了新的尝试。
In this paper, the numerical solution of differential equation is employed to establish the forecasting model of the time series.
分析得出节点型钢腹板的剪应力方程，利用试验数据可求得腹板上测点的应力值。
Stresses in the steel webs were obtained by using the test data in the shear strength equation introduced from the analysis.
采用复变函数将系统的动力学方程简化，利用谐波平衡法分析了系统的稳态解，得到了系统的幅频响应。
The stationary solution of system was solved by harmonic balance method, and the amplitude-frequency response was presented.
采用复变函数将系统的动力学方程简化，利用谐波平衡法分析了系统的稳态解，得到了系统的幅频响应。
The stationary solution of system was solved by harmonic balance method, and the amplitude-frequency response was presented.
应用推荐