一般方程

The method that simple cubic equation was changed from general to standard was introduced and the distribution of standardized real root was illustrated, which solved the problem of the distribution of any real root for simple cubic equation.

摘要介绍了一元三次方程一般式化为标准式的方法，结合图形给出了标准式的实数根的分布情况，从而解决了任意一元三次方程的实数根的分布的问题。

This equation is the evolutionary equation of the reduced density matrix which is useful for the study of general master equation.

这个方程式约化密度矩阵的演化方程，它对一般主方程的研究很有用。

The main contents and the contributions are as the follows:(1) The general form of the movement equations in terms of Taylor series is derived, for the first time the movement equations of electric power system is expressed by matrices, the characteristics of the coefficients of Taylor series is studied.

所得的主要研究成果如下：（1）推导了电力系统运动方程的高阶泰勒展开的一般形式，首次将电力系统状态方程的泰勒展开用矩阵表达，研究了泰勒展开系数的特性。

In this part, the distribution of stable states of a system is worked out under the condition of unbalanced attention parameters on basis of analyzing elementary dynamic equation and synergetic potential function, which improved the discussion of relevant properties of basic synergetic equations. Then, with the analysis of effects of attention parameters in synergetic dynamics, a set of elementary properties are presented to give light how the attention parameters work on pattern recognition process. In the end, in view of geometric sense in synergetic order parameters, some elementary properties are studied, by which a new construction method of order parameters is established so as to provide a general way to constitute new relations of prototype patterns according to practical requirements.

首先在分析了协同模式识别的基本动力学方程及协同势函数的基础上给出了注意参数不平衡情形下系统稳定状态的分布，完善了对协同模式识别基本方程相关性质的讨论；其次，分析了注意参数在协同动力学过程的作用，并给出了注意参数的一些基本性质，指出了注意参数对模式识别过程产生的影响；然后，从协同序参量的几何意义出发，研究了协同序参量的基本性质，并在指出其局限性的同时建立了新序参量的构造方法，从而能够更一般地根据要求建立模式间的新关系，促进识别过程的进行。

A constant in an equation that varies in other equations of the same general form, especially such a constant in the equation of a curve or surface that can be varied to represent a family of curves or surfaces.

参数，参量在相同一般类型的等式中取值变化的等式中的常数或常量，尤其是曲线方程和平面方程中能代表一类曲线或平面的常量

According to axisymmetric unsteady heat conduction equation of orthogonal aniso tropic material and boundary conditions,the equilibrium equation of a system of finite elements is deduced with triangular element of high accuracy,and programs are designed.

根据均匀正交各向异性材料轴对称热传导方程及其边界条件，利用变分法及欧拉理论，选取 6 节点的高精度三角形单元类型，推导了一般轴对称非定常热传导有限元基本方程。并编制了相应的计算程序。

We can not apply Galerkin methods with radial basis functions to the first boundary value problem (the Dirichlet boundary value problem) of the second-order elliptic equation, because it requires that the approximate functions should fit the essential boundary condition, while the spaces spanned by the radial basis functions fails to satisfy this kind of boundary condition, and it is the same for the higher-order elliptic equation.

我们不能直接应用这样的无网格算法求解二阶椭圆型方程的第一类边值问题(Dirichlet边值问题)，因为第一类边界条件是本质边界条件(对二阶椭圆型方程为Dirichlet边界条件)，而径向基函数的支集通常是全空间，由它们所生成的近似函数空间一般不满足这样的条件。

In this paper, the idea of " centrifugal potential field ",which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established.

本文从离心力势场的概念出发，应用Hamilton原理建立了具有动力刚化效应的刚柔耦合系统的运动方程，证明了该方程解的周期性，并采用了Frobenius方法给出了其精确解的一般形式。

The Hankel transformation method has been used to turn the basicdisplacement equations and displacement-stress constitutive equations intoa system of first order non-homogenous ordinary differential equations inwavenumber domain,and by us of the matrix method,the transfer matrix ofthe medium layered is established.

利用Hankel变换，将轴对称静力问题的位移基本方程和位移应力本构方程转化为波数域内非齐次一阶常微分方程组，利用矩阵法，建立了介质层的传递矩阵，导出了层状弹性半空间轴对称静力问题奇异解的一般解析表达式。

For this method, although the variable time steps can be employed and the initial conditions can be determined in a more natural way, it investigated a special kind of hyperbolic equation with separable coefficients.

该方法虽然不受等时间步长的限制，对初始条件的选取也更具灵活性，但是它是针对一类变量分离系数型的特殊双曲型方程进行讨论的，对一般形式的双曲型方程则没有提及。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷