特解

When scaled factor circulant matrices are nonsingular, we can find the single solution of the scaled factor circulant matrix equation; When scaled factor circulant matrices are singular, we can find the special as well as the general solution of the scaled factor circulant matrix equation; There is only an error of approximation when the fast algorithm is implemented on computers, and only the elements in the first row of the scaled factor circulant matrix and the constants in the diagonal matrix are needed by the fast algorithm.

当鳞状因子循环矩阵非奇异时，该快速算法求出线性方程组的唯一解；当鳞状因子循环矩阵奇异时，该快速算法求出线性方程组的特解与通解。该快速算法仅用到鳞状因子循环矩阵的第一行元素及对角矩阵中的对角上的常数进行计算。在计算机上实现时只有舍入误差。

This paper discusses the broad-sense relation between solution and coefficient of some special kinds of second order variable coefficient and homogeneous linear differential equation,and have a try of giving a general form of common solution and the coefficient decision formula of special solution.

探讨了某些特殊类型二阶变系数齐次线性常微分方程的解与系数的广义关系，尝试了从理论上给出通解的一般形式和特解的系数决定式。

One kind is using the particular solution of the indefinite equation, which can be obtained by the property of the prime number , and the foundation system of solution of its corresponding homogeneous equation ,obtains its solution formula. Another kind is under the foundation of the matrix primary line transformation, and with the aid of some knowledge of numeral theory, obtains its solution formula.

一种是利用该不定方程的一个特解和其相对应的齐次方程的一个基础解系，得出该不定方程的求解公式，而这个特解可以由素数性质得到；另一种是在矩阵的初等行变换基础上，借助一些数论知识，得出该不定方程的求解公式。

The model is usually an inhomogeneous system of linear equations. It is pointed out that the general solution of the homogeneous system of linear equations can satisfy the request of making the wires tight, and the special solution of the inhomogeneous system of linear equations are not smaller than zero, so their sum is greater than a given mumble.

由于多自由度绳牵引并联机构的静力学模型一般是一个非齐次线性方程组，本文指出可让对应齐次方程组的通解的最小值满足绳保持张紧的条件；让非齐次线性方程组的特解非负，而避免利用对应齐次线性方程组的通解保证非齐次线性方程组的解不小于给定的最小值。

In order to obtain more general solution of second order linear differential equation with constant coefficients, which is important in theory and practice, on the basis of knowing a special of the second order linear differential equation with constant coefficients and by using the method of variation of constant, the second order linear differential equation with constant coefficients is transferred to the reduced differential equation and a general formula of the second order linear differential equation with constant coefficients is derived.

为了更多地得到理论上和应用上占有重要地位的二阶常系数线性非齐次微分方程的通解，这里使用常数变易法，在先求得二阶常系数线性齐次微分方程一个特解的情况下，将二阶常系数线性非齐次微分方程转化为可降阶的微分方程，从而给出了一种运算量较小的二阶常系数线性非齐次微分方程通解的一般公式，并且将通解公式进行了推广，实例证明该方法是可行的。

Then is a particular solution of the original equation.

的特解，则就是原方程的一个特解。

According to the plane cross section assumption, configuration of a rod is expressed as a history of the cross section with arc coordinate. A special solution which stands for equilibrium in straight line state is obtained from differential equilibrium equation. Linear perturbation equation is derived and its general solution is obtained in which the integral constants are determined by constrained conditions at two ends of the rod. The condition of existence of non zero solution of the integral constants gives to the Greenhill formula of exact elastic rod model, which shows that the boundary of stable area is a closed curve and of symmetry, and inference of shearable and extensible to stability of the rod is depend on three factors: difference between flexibility of shear and extension of a section of the rod, bending stiffness and the length of the rod.

基于平面截面假定，弹性杆的位形表达为截面的弧坐标历程，根据平衡微分方程得到了两端受力螺旋作用时的直线平衡特解，导出了线性化扰动方程及其通解，积分常数根据两端铰支时的边界条件确定，并根据其存在非零解的条件得到弹性直杆精确模型的Greenhill公式，表明稳定域为一对称的封闭区域，拉/压和剪切对稳定性的影响取决于：拉/压柔度与剪切柔度之差，抗弯刚度和杆长这三个因素

The asymptotical properties of KdV equation and KP equation exhibit the soliton behavior when some conditions are satisfied, and in some cases the parameter matrices describing the interaction between two solutions is quite simple. Two kinds of solutions of the second coupled equations of AKNS hierarchy are provided and applied to NLS equation. A systemical way of construction of special solutions is also tried for DS equation. Most of the results on a scalar equation can often be directly generalized to some matrix equation, and the difference between the ω in scalar form and ω in matrix form lies only in the replacement of vector p, q by matrices p, q.

对KdV方程和KP方程渐近性质的讨论显现出解在一定条件下的孤子特性，从而使得一些情形下，同类解的相互作用体现在参数矩阵上变的较简单；我们给出了AKNS方程的两类不同解，并约化到NLS；对DS方程，我们从另一个方面初步探讨了形式化推导矩阵方程特解的方法；把这些有关标量ω的结果推广到ω为矩阵上往往只要把p，q变为矩阵即可，进而可以再推广到方程组上。

A special analytical solution is derived for the simultaneous differential equations of a dynamic mathematical model for the evaporating surface in supercritical pressure boilers given by Ref.

对文献［1］给出的超临界压力锅炉蒸发受热面的动态数学模型所建立的三个联立偏微分方程组，导出了假定工质压力不随时间变化条件下的解析特解，阐明了该特解的物理意义。

With the conditions of the variables, a standard linear programming model is established and therefore the special solution of the inhomogeneous system of linear equations can be available easily by the simplex method.

对于非齐次线性方程组的特解求解，本文巧妙的利用绳牵引并联机构的拉力应满足的条件建立了一个线性规划的标准模型，由单纯形法可以很容易的获得非齐次线性方程组的特解。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。