精确解

Mainly, we deriver time-accurate wavelet-based schemes for convection equation ,furthermore, we use it for numerical solution of convection equation and make a comparison with exact solution and solution derived from WGM.

主要的，对于对流方程，推导出了时间精度高的基于正交小波基的小波泰勒伽略金格式，进一步用这个格式计算了对流方程的数值解，并和WGM格式得到的数值解以及精确解作了比较，从而验证了格式的正确性。

Using algebraic methods which include extended Tanh-method,some new solitary solutions to the DBM and Log-DBM equation,such as singular solitary solutions,double singular peakon solitary wave solutions,double solitary wave solution with peakon and singular periodic solitary wave solutions are obtained..With the aid of an auxilitary function combined with the elliptic integral of the first kind,periodic solitary solution,singular and periodic singular solitary solutions can be obtained.

第三章利用扩展的Jacobi椭圆函数展开法研究了方程，并给出ZK-MEW方程的Jacobi椭圆函数解，特别的，当模数m→0和m→1时，其中一部分解退化为三角函数解和孤立波解；其次使用sn-cn拟设法，研究了K(k，s，1)方程，得到了k=s=3时的新的精确解，并在模数m→0和m→1时得到了丰富的三角函数和孤立波解。

Thirdly, on the base of the existent error estimate of elliptical Galerkin projection operator, obtain semi-discrete and complete-discrete error estimates betwent EFG solution and exact solution of parabolic partial differential equation. Semi-discrete error estimate show that the rank of r is accordance with the approximation rank of subspace S_h. Complete-discrete error estimates show that it not only have relation with radius r of domain of influence, but also have relation with the step length of time variable and the way of discrete.Lastly, give typical examples and draw up procedures of MATLAB.

再次，在"椭圆Galerkin投影"算子的误差估计的基础上，对用EFG法解抛物型偏微分方程的EFG解与精确解之间作了半离散和全离散的误差估计，半离散的误差估计表明所给出的误差界限关于r的阶是与子空间S_h的逼近阶相一致的，全离散的误差估计表明所产生的误差不但与影响域半径r有关，而且与离散时间变量的步长τ及其离散方式有关。

The thought based on the hyperbola function method is extended,and more explicit and exact solutions are successfully derived,including shock wave type solutions with break point and exponential function type solutions .

在此基础上又对双曲函数法的思想进行了推广，从而获得了其更多的显式精确解，包括间断型激波解和指数函数型解。

It is found that the later is better than the former greatly, due to the fact that accurate solution by gaussian elimination is zero error. But zero error is ideal situation and it is difficult to reach in practice. So all we can do is to search an optimal solution under many restriction conditions, and the optimal can represent the solution of the question better.

咎其原因，高斯消元法是求解问题的精确解，而在实际生产科研工作中，这种理想状况是很难达到的，因此，遗传算法在多个约束条件下寻找当前最优解作为问题的解，才具有实际意义。

Therefore,it is necessary to research diffusion equation for suspended sediment because it describes the sediment move process in the water body.The equation is a various coefficients second-order linear partial differential equa-tion,such equation under complex boundary condition is very difficult to get its analytical solution,while its numerical solution relative analytical solution is more easier and has the obvious superiority:simple,the computation convenience.but to get a kind of difference format which is good accuracy and stability is not easy.

泥沙扩散方程实际上是一个变系数的二阶线性偏微分方程，这样的方程在各种复杂边界条件下求解是十分困难的，求它的解析解在数学上存在着难以克服的障碍，无法求出其精确解，因此常用数值方法求它的近似解，相比较而言，数值方法有着明显的优势：即简单灵活、计算方便快捷，但要寻找一种精度高、稳定性好、计算方便的差分格式也并非易事。

It isverified that the method for using little deformation condition was true with accurate solution of three-piece straightening curve.

文摘：基于三段矫直曲线应变速率的假设，通过计算三段矫直曲线的精确解，验证了使用小变形条件的正确性；考虑高温铸坯蠕变性能，对铸坯的力学行为进行了分析，得出了使用三段矫直曲线方法，铸坯应变速率、应力及应变在矫直区内变化较为平缓，可有效避免铸坯内裂纹的形成；使用本文三段矫直曲线精确解，调整辊列位置，可进行连铸机的在线技术改造。

It isverified that the method for using little deformation condition was true with accurate solution of threepiece straightening curve.

文摘：三段矫直曲线应变速率的假设，通过计算三段矫直曲线的精确解，验证了使用小变形条件的正确性；考虑高温铸坯蠕变性能，对铸坯的力学行为进行了分析，得出了使用三段矫直曲线方法，铸坯应变速率、应力及应变在矫直区内变化较为平缓，可有效避免铸坯内裂纹的形成；使用本文三段矫直曲线精确解，调整辊列位置，可进行连铸机的在线技术改造。

In many fields, such as society, economy, business and physical science, factor analysis models is applied in the multi-index system of these fields, but factor analysis models and theory is not complete, which cumbers the application and development of factor analysis.

摘要本文应用因子分析模型L及其解，求出了经典因子分析模型中公因子载荷、公因子、特殊因子的精确解，解决了经典因子分析模型和理论存在的9个问题，进一步，指出了经典因子分析模型及其解根本的局限性问题：公因子解没有排除观测误差的干扰，不能达到降维的目的等。

By analysing the quantum-mechanical behavior of two ions, we obtain the exact quantum states with parameters in the experimental region.

dinger方程的精确解的基础上，我们设计程序计算了精确解——包含展开系数和系统的能谱。

He and Nina moved to California and lived at 2005 Ivar Street, Apt.

他和Nina搬到加州，并在2005年伊瓦尔街，公寓生活。

Droperidol （ potently inhibits transfected HERGchannels and this is the probable mechanism for QT prolongation.

氟哌利多有效地抑制了转染的 HERG 钾通道，可能是 QT 间期延长的机制。