可解方程

The derivative nonlinear Schrodinger equation is, however, an open and important issue both in theoretical and applied aspects. The DNLS equation with nonvanishing boundary conditions is solved by introducting an affine parameter and we find that it supports a rich set of soliton solutions.

大部分完全可积的(1+1)维非线性偏微分方程，特别是有明确物理应用的方程的孤子解已经用反散射变换等方法得到，但还剩下一些难题，变形的非线性薛定谔方程在非零边值下的反散射变换就是其中一个。

By transforming the interlace series type linear differential equation with coefficient containing binomial coefficients and arrangement number into the linear differential equation of successive integral,the theory and method for solving this kind of equation are determined.

通过把系数含有二项式系数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程，找出了求这类方程通解的方法与理论，把所得定理给出了严格的证明，并通过实例介绍了它的应用。

The other is the difference of the original wind and the harmonic part, which is the solution of Poisson equation with homogeneous boundary condition and can be expanded into double Fourierism cosine series.

第一部分是Laplace方程在给定边界条件下的解，由于Laplace方程的解是调和函数，这个部分可称为调和部分，又因为其与区域内部值无关，也称外部部分。

Apparently, the approximate controllability doesn"t hold for generally linear parabolic equations with bounded control. It doesn"t hold for the semilinear heat equations presented there,either. Then, it is proved by analyzing its" solutions that no matter how long the time T is , there are targets that can"t be approximated by the solution of heat equation with Dirichlet boundary conditions;If a given target satisying certain conditions can be reached by the solution of heat equation .

本文先针对两个具体的半线性热方程系统证明了控制加约束后系统是不能控的；然后通过分析方程的解，对带位势及Dirichlet边界条件的热方程系统，无论时间多大，都存在不能控的目标；文中还证明了满足一定条件的目标可达。

In this paper, a new method used to deal with the motion ability is studied deeply based on Routh-Hurwitz Criterion. The advantage of this kind of analysis method consists in the fact that after establishing the equation in differential calculus for the motion system, there is no need to know a root of the equation, if you know the root signs, you can judge the zero solution stability of the system.

本文利用劳斯－赫尔维茨判据(Routh-Hurwitz Criterion)对机械系统中离心转速调节器的运动德定性进行了分析，这种分析方法的优点就在于：建立系统运动微分方程的特征方程后，不必求解特征方程的根，只需知道根的符号就可判断系统的零解稳定性。

In §2, four met0hods for solving the integrable second order homogeneous linear ordinary differential equation with variable coefficientsy +py'+Qy=0 are given. Thus, the equation can be solved by means of elementary integrals and algebra.

给出了二阶变系数线性方程y＂＋py＇＋Qy＝0在可积的条件下的几种不同的求解方程，从而说明了这种可积的二阶方程不仅能用初等积分法求解而且也可以把它代数化，并使其通解公式化。

For different polynomials g, if the characteristic polynomial of a n matrix A is irreducible, then we get some theorems to determine matrix equations g =A solvable; if it is reducible, then, to see n-dimension space vectors M over a field F as F-module, we use module theory to determine these equations solvable such that it is simpler and clearer to investigate these questions.

对于不同多项式g，当n阶矩阵A的特征多项式为不可约的，我们给出了矩阵方程g=A有解的判定定理；当A的特征多项式为可约的，把域F上的n维线性空间M作为由A导出的F -模，我们利用模论知识来决定矩阵方程g=A有解性，从而使这一问题变了简单，研究思路更加清晰。

In Chapter 4, new Miura type transformation between nonlinear dis- persive wave equations is established.

本方法的特点是可直接从较简单方程的解得到目标方程的行波解。

If α had been determined,the dissociation and non-dissociation species photolysis rate constants could be calculated by the tangent equation of the power function.

任意解离度条件下的解离态和非解离态光解速率常数，可根据幂函数的切线方程来确定。

From the Maxwells equations in integral form directly, the Maxwell Grid Equations are derived through discretization of the solution space and the equations, and thereout the common equation of arbitary structures. Secondly, the solution uncertainty of a common electro-magnetic equation is proved and a strategy is advised to get the unique solution of the finite integration equation.

直接从积分形式麦克斯韦方程组出发，通过空间离散与方程离散得到麦克斯韦网格方程组，由此得到任意结构的一般方程；深入分析了麦克斯韦网格方程组的代数特性，论证了其解的不确定性，并指出了一种可避免解不确定性的措施。

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。