变分方程

First,the basic formulas solving the artificial earthquake wave compatible with object response spectra are established;the integration equations are translated into the algebraic equations by interpolation function.

首先，从单质点系在地震作用下的反应出发，直接推导了求解与目标反应谱拟合的人造地震动基本公式；随后，利用插值函数将积分方程变换为代数方程组，进而从反应谱的变分求得人造地震动的时域变分。

To one kind of variational inequalities, some researchers give an alternating direction method, which solve a linear variational inequality and a system of nonlinear equations in each iteration.

针对一类变分不等式，有研究者给出了一种交替方向法，在每一步迭代中分别要求解一个线性变分不等式和一个非线性方程。

By using thenatural boundary element method which is set up by professor Feng Kang,the Neu-mann boundary problem of the harmonic equation on the half-upper plane is reducedto the Hadamard type singular integral equation,the integral region of which is un-bound,and then we turn it into corresponding bilinear form.

通过由冯康教授开创的自然边界元方法，将上半平面调和方程的Neumann边值问题归化为Hadamard型强奇异自然边界积分方程，并且此积分方程是无界域上的强奇异自然边界积分方程，然后将它转化为相应的变分形式。

The aim of this paper is to study the existence of solution and multiply results for quasilinear elliptic system in bounded domain and the whole space, semilinear elliptic equation in two dimension space, second order nonlinear difference equation by variational methods. The main results are listed in the following:1. An abstract compactness theorem is proved, and then, under weak Boccardo and De.

本文主要利用变分法，分别研究了有界区域和全空间上拟线性椭圆型方程组、二维空间上半线性椭圆型方程和二阶非线性差分方程问题的解与多重解的存在性，具体内容如下： 1。

This method is variational method, which will be much faster and more efficiency than other method.Firstly we use gauss integral method to disperse the least potential energy of barrette pile group, with the help of vertical settlement finite series and Mindlins equation, we derived vertical load-settlement solution of barrette pile group.

另外，目前有关壁板桩群桩水平承载特性的研究也比较少，因此，为了加深对壁板桩群桩承载特性的理解，本文利用变分法对壁板桩群桩竖直或水平受荷情况下的承载特性进行了初步的研究，通过变分法直接得出荷载位移显式方程，较之以往方法更加快捷。

Based on the analogy of structural mechanics and optimal contro1, and a1so based on carrying the minimum potential energy variational principle in elastici- ty to the generalized one, the theory of Hami1tonian system can be introduced into theory of e1asticity and e11iptic PDE. The transverse eigensolutions of the Hamiltonian operator matrix and its expansion solution method can be deduced.

利用结构力学与最优控制相模拟的理论，将弹性力学势能变分原理导向部分一般变分原理，并将哈密尔顿体系的理论引入到弹性力学与椭圆型偏微分方程之中，导出一套横向哈密尔顿算子矩阵的本征函数向量展开解法。

The main contents include: Some preliminary theory (introduction to Sobolev spaces and variational formulations for differential equations); finite element methods for one-dimensional elliptic problems; the construction methods for general finite elements; error estimates for interpolation operators and inverse inequalities for finite element spaces; a priori and a posteriori error estimates for the finite element method for high-dimensional elliptic problems; some typical spectral methods for partial differential equations; error analysis for the spectral approximation for some linear and nonlinear partial differential equations.

主要内容有：准备知识（Sobolev空间的基本概念和主要结果，微分方程的变分描述）；一维椭圆型方程有限元方法；一般有限元的构造；插值算子误差估计和逆不等式；高维椭圆型方程的先验、后验误差估计；求解偏微分方程的几类谱方法；线性与非线性问题谱逼近的误差分析等。

In this paper, we present a class of equation model for image denoising and edge enhancement. The model is based on robust statistics error norm and variational theory.

本文基于稳健统计误差模函数及变分原理构造了一类用于图像去噪、增强边缘的方程模型，对相关参数进行了分析，设计了该方程有限差分数值求解的并行算法，并对分块模型及实现过程进行改进，提高了并行效率，在此基础上完成了并行数值实验，并对结果就误差模选取、并行效率等方面进行了分析。

In this paper, we present a class of equation model for image denoising and edge enhancement. The model is based on robust statistics error norm and variational theory. By analysing the parameters of the equation and designing the methods of module partitions, the numerical experiments reach a good result and the parallel efficiency has been improved remarkably with finite difference method.

本文基于稳健统计误差模函数及变分原理构造了一类用于图像去噪、增强边缘的方程模型，对相关参数进行了分析，设计了该方程有限差分数值求解的并行算法，并对分块模型及实现过程进行改进，提高了并行效率，在此基础上完成了并行数值实验，并对结果就误差模选取、并行效率等方面进行了分析。

During the calculation of the early age temperature field, the early age physical and mechanical performance of concrete varies with its age, therefore in the second chapter we discuss the early age physical and mechanical performance of concrete and its development regulation with time, we emphasize elastic module and the development about the early age strength of concrete varying with time, at the same time consider the effect of shrink and creep upon the early age of concrete, in succession discuss how to confirm the physical parameter of thermodynamics of concrete.

之后讨论了混凝土的热物理参数的确定。为了能够正确合理的应用有限元方法求解早期混凝土温度场问题，第三章论述了求解温度场的有限元方法。第三章首先对热传导的微分方程作了阐述。之后确定温度场的边界条件。本章采用变分原理推导有限单元法计算温度场的公式。因此在第二小节叙述了变分原理，然后阐明了不稳定温度场的计算的三种方法，确定第四章分析中将采用向后差分法求解0#箱梁早期的温度场。

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。