精确解

In this paper,in consideration of air medium inside the hole defects acting on the electric field, a coupled field of antiplane strain problem for the piezoelectric material with an elliptic hole is analyzed with an expression for potential function of complex veriable in Faber series.

考虑椭圆孔内空气介质对电场的作用，用复变函数的Faber级数展开方法，分析了含椭圆孔的压电材料反平面应变问题的耦合场，给出了问题的精确解。

That the coefficient matrix of the reduced linear correction equation has arrow-shaped block structure and can be accurately decomposed into 25 sets of low-dimension linear equations by two algorithms was proposed.

该文指出其修正方程系数矩阵可具有箭形分块结构，可采用两种方法将其精确解耦为25个低维线性方程组。

By using the solutions of a new auxiliary elliptic equation,a direct algebraic method is proposed to construct the exact solutions of some nonlinear evolution equations.The main difference between this method and previous auxiliary elliptic equation methods is that the balance order becomes smaller after using the new auxiliary elliptic equation.Therefore,the derived algebraic equations are greatly simplified.

利用一个新的辅助椭圆方程将求解非线性发展方程精确解的问题转化为一个代数方程组进行求解，与已有的辅助椭圆方程法的主要不同是，应用这一新的辅助椭圆方程后降低了平衡次数，减少了所得的代数方程组的个数和方程的项数，从而大大地简化了代数方程组的求解。

Mathematics mechanization; Symbolic computation; Exact solution; Auxiliary equation method; Soliton

基础科学，数学，数学分析数学机械化；符号计算；精确解；辅助方程法；孤立子

This method can be used to find new exact solutions to other nonlinear evolution equations.

这种方法也可用于寻找其它非线性发展方程的新的精确解。

The improved method can be used to obtain more formal exact solutions to nonlinear partial differential equations.

改进后的方法可以获得非线性发展方程的更多形式的精确解。

On the basis of the dispersion relation, we investigated the properties of nonlinear surface waves. It is shown that there exist backward surface waves, with the phase velocity and group velocity opposite in direction. For transverse electric waves, the nonlinear wave equation is transformed into Bernoulli equation, and the exact solutions of magnetic fields are obtained.

在色散关系的基础上研究了非线性旋磁表面波的频率特性，揭示了该系统能激发后向表面波，其群速度与相速度反向；将反铁磁晶体中TE表面波满足的非线性波动方程变形为伯努利方程，用反函数形式给出了表面波磁场的精确解。

The model of heat and mass transfer of a biological sample in cryopreservation was solved by perturbation and integral methods.

用摄动法和积分法求解了生物样品的传热传质模型，在模型简化时比较了积分解和精确解，探讨了低温保存中细胞的损伤机理，对冷却介质温度随时间线性变化时相变界面的移动作了实验研究，用自己设计和制作的实验台架和测试装置测量了相变界面的移动和温场的分布。

Through a construction of a distribution function,the normal form of KFVS is deduced based on the nocollision Boltzmann equation .

通过构造一个分布函数，利用无碰撞的 Boltzmann方程，推导出求解一般形式的KFVS方法，对一维溃坝进行了模拟，并与精确解进行了比较，说明了这种方法的进步性和可行性

The results show that the infinite method is valid in solving problems in infinite domain and thus high precision can be obtained by eliminating the border effect in finite element analysis.

采用具有精确解的无限厚壁圆筒作有限单元法分析和无限单元法分析，通过对这两种分析方法的分析结果的比较得知：无限单元法是解决无限域问题的一种有效的方法，采用这种分析方法进行隧道及地下工程结构分析，可以消除有限单元法所带来的边界效应，从而使计算精度大为提高。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。