简化方程

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。

Finally, by means of analysing and analogizing the tendency of dynamic impedence of soil against the circular frequency, a simplified model of soilstructure system is proposed.

最后，本文通过对大量地基动力刚度和阻尼的计算结果的分析，引入了等效刚度质量和等效阻尼质量的概念，从而简化了土—结构体系的运动方程，建立了一个简化的等效模型。在此模型的基础上，使得原本在领域内很难求解的方程可以在时域内进行求解。

The nonlinearity of Einstein′s field equation brings a lot of difficulties to solving of general relativity theory in case of weak field.

爱因斯坦场方程的非线性性给广义相对论的求解带来许多困难，在弱场情况下，可用近似处理的方法，把高度非线性的场方程变为线性场方程，简化了方程的求解。

In the case of simply supported ends, the Galerkin method is used to simplify the integro-partial-differential equation into an integro -differential equation. The equation is further simplified into a set of ordinary differential equations by introducing an additional variable. Finally, the numerical methods in modern nonlinear dynamics such as phase plane trajectory, power spectrum and Lyapunov exponents are adopted to investigate the dynamical behavior of the beam.

对于两端简支的情形，采用Galerkin方法简化为常微分－积分方程；然后通过引进附加变量的方法进一步简化为常微分方程；最后利用相平面图、功率谱和Lyapunov指数等非线性动力学中的数值方法识别梁的动力学行为。

From K-G Equation and Dirac equation,using 2-D invariant line element, the radius equation and event horizon formula of particles are obtained.A simpler method to the research of quantum effect of the scalar and vector particles in black hole with spherical symmetry is singgested.

分别从K-G方程和Dirac方程入手，利用简化后的二维不变线元，直接给出了粒子的径向方程和视界面方程公式，为研究球对称黑洞中标量粒子和矢量粒子的量子效应提供了一个更简单的方法。

By introducing reasonable fundamental assumptions and the Green strain in orthogonal curvilinear coordinates,geometric equations expressed by the Green strain tensor for solving thin shells with large deformation are derived in this paper.

将正交曲线坐标下的格林应变张量引入到薄壳大变形分析，通过建立恰当的基本假设，直接导出了用格林应变张量表示的壳体变形几何方程，将该方程代入到本构方程，由能量原理得到了小应变非线性变形平衡方程、内力方程和边界条件，在此基础上提出了大应变变形的简化分析方法。

The simplified spherical harmonics method is utilized to discrete the angular variables of Self-Adjoint Angular Flux neutron transport equation as spherical harmonics method has the dis-advantage of large amount of calculation.

针对球谐函数方法求解中子输运方程时计算量大的缺点，将简化球谐函数方法用于离散二阶自共轭中子输运方程的角度变量，同时应用有限元方法在非结构几何下进行空间离散，研究了简化球谐函数方法在SAAF方程中的应用。

Through the analysis of the flowing character of metal injection molding, a set ofessential equations describing the flowing process of metal ring injection molding areestablished on the bases of the general principles of hydrodynamics and calorifics.

通过对金属粉末注射成形流动过程规律的分析，从流体力学和传热学的基本原理出发，建立了一组描述圆筒形金属粉末注射成形流动过程的基本微分方程，经过假设与简化，得到一组简化的控制方程，采用有限差分法求解了这组微分方程，得到温度场。

On the basis of design of a new type bilateral excitation electromagnetic vibrating head, a simplified mathematic model was set up through predigesting electromagnetic field to electromagnetic route method, and motion function of the system was also obtained based on variational theory and non-conservative system Lagrange function.

在设计了一种新型的双边激励的电磁式振动头的基础上，采用将磁场简化为磁路进行分析计算的方法建立振动头的简化数学模型，并根据变分原理及非保守系统拉格朗日方程得出系统的运动方程。

Three displacement functions w,Gand ψare introduced in this paper tosimplify motion equations of elasticity problenis in spherically isotropic media to an indepen-dent partial differential equation concerning one displacement function ψand simultaneous equations concerning two other displacement functions w and G.

本文引入三个位移函数，将球面各向同性弹性力学运动方程，简化为关于ψ的二阶偏微分方程，和关于W和G的联立方程。在静力学问题中，联立方程可进一步简化，w和G可用另一位移函数F表示，而F满足一个四阶偏微分方程。

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。