变分方程

We first got the PML equations by making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Grding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experiments which show that this method is feasible to a certain extent.

首先通过复化极径得到PML方程，然后在关于吸收参数的假设下，证明了PML问题变分形式中的半双线性形式满足Grding不等式，进而证明了PML问题解的存在惟一性，并给出了数值实验。实验结果表明，该方法有一定的可行性。

We first got the PML equationsby making the radius complex, and then proved that the sesquilinear form in the weak formulation of the PML problem satisfies the Garding inequality under the hypothesis of the absorption factor, and further could prove the existence and uniqueness of the solutions of the PML problem, finally, we gave the numerical experimentswhich show that this method is feasible to a certain extent.

首先通过复化极径得到PML方程，然后在关于吸收参数的假设下，证明了PML问题变分形式中的半双线性形式满足Garding不等式，进而证明了PML问题解的存在惟一性，并给出了数值实验。实验结果表明，该方法有一定的可行性。

The formal solution of partial differential equations is given on characteristic line, the existence of the optimal control is proven by using Ekeland\'s variational principle, Gronwall Lemma and adjoint system, then the necessary condition of optimality is obtained by means of the conception of normal cone.

用特征线法表示出偏微分方程的形式解，利用Ekeland变分原理，Gronwall引理和共轭系统证明了最优控制的存在性，并借助于法锥概念得到了最优控制的必要性条件。

We give the fundamental solution of adjoint transport equation and take it into variational form.

给出伴随输运方程的基本解，再将其带入变分形式中，对关于空间和角度的两个积分进行化简。

Equations and boundary conditions for tilt angle and twist angle of director are obtained with variation theory.

通过变分理论得到指向矢倾角和扭曲角满足的方程和边界条件。

In this paper We study existence of solutions of variational inequalities in a reflexive Banach Space,and acquire several existence results.

本文研究自反Banach空间中的变分不等方程解的存在性，得到了存在性的几个结果。

Firstly, we discuss the boundary value problem of one dimensional biharmonic equation in an interval and its variational problem,multiresolution analysis in the Sobolev space , then solve it with wavelet-Galerkin methods.

首先本文讨论了一维双调和方程边值问题及其相应的变分问题，定义Sobolev空间的多分辨分析，用小波–伽辽金方法进行数值求解，两组基下得到的系数矩阵为七对角阵和块状对角阵。

Hybrid Dynamic; time-varying systems; finite horizon; optimal control; Quasi-Variational Inequality; viscosity solution; lower semicontinuous solution; uniqueness; Dynamic Programming; Viability Theory; inventory systems; mathematical model; proximal subdifferential; parabolic equation; nonlinear boundary

基础科学，数学，控制论、信息论混合动态；时变系统；有限时间；最优控制；拟变分不等式；粘性解；下半连续解；唯一性；动态规划；生存定理；库存系统；数学模型；邻近次微分；抛物型方程；非线性边界

In this text we used the method of volume integral equation base on tensor Green's function to study the forward of 4D transient electromagnetic response.

本文采用基于张量格林函数的体积分方程法进行四维模型瞬变电磁响应的正演研究，文章中首先说明了四维瞬变电磁法模拟的可行性及程序实现，然后分别设计了两个三维异常体模型，采用两种观测方式(激发与接收平行、激发与接收垂直)进行正演模拟计算，并对所得的二次总场的数据进行了分析。

Based on variational principle and split-based interpolation finite element method for fast and accurate analysis of normal mode helical antenna,Combination of genetic algorithm and then load the normal mode helical antenna loaded on the value of lumped elements,Load location,and matching network integrated optimal design parameters,And using Sherman-morrisorr Woodbury formula to quickly solce the load component values and load the changed position of the impedance matrix equation to improve the efficiency of optimized design.

采用基于变分原理和剖分插值为基础的有限元法来快速精确分析法向模螺旋天线，然后结合遗传算法对加载法向模螺旋天线上的加载集总元件的值、加载位置以及匹配网络参数进行一体化优化设计，并采用Sherman-Morrisorr Woodbury公式来快速求解加载元件值和加载位置改变后的阻抗矩阵方程，提高优化设计的效率。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。