变分方程

The performance function and constraint equation in calculus of variations were constructed by analyzing input and output equations of the system containing parameters to be estimated. The traditional parameter estimation problem could be transformed to that of least squares estimation.

通过分析包含待估参数的系统输入输出方程，构造变分法中的性能范函和约束方程，将传统的参数估计问题化为带约束条件的最小二乘估计问题；利用拉格朗日乘子法，分析参数估计方程，得到参数的最优估计。

When propagating light\|ray passes through two fixed points in the gradient index mediums and a cuspidal variable\|point （at this point the trace equation of propagating light\|ray is non\|differentiable） at the borderline of two different GRIN mediums, the mathematical relationship, which the trace equation of propagating light\|ray and borderline equation of two different GRIN mediums should satisfy, is derived by the Fermat's principle and calculus of variation.

当光线通过梯度折射率介质中两个固定点和两个GRIN介质界线上的可动尖点（光线轨迹方程的不可微点）时，由费马原理和变分法运算推得传输光线的轨迹方程与两种不同GRIN介质的界线方程应满足的微分关系式。

Image processing is an interdisciplinary topic, which is connected to photology, electronics, mathematics, imaging and computer techniques.

基于变分问题和偏微分方程的图像处理技术研究变分方法

A general model of two phase image segmentation based on variational level set method is proposed,and the region model is based on the image general probability distribution function.

基于变分水平集方法建立了两相图像分割的通用模型，其区域模型基于图像的一般概率分布函数，通过变分方法得到水平集函数的演化方程和符合常值分布、Gauss分布及Rayleigh分布的参数估计。

Based on the generalized potential variational principle of nonlinear elasticity theory with large deflection, the incomplete generalized potential energy functional with large deflection is established on the space coupling free vibration of collaborated system structure by considering the effect of axial compressive and shearing strain energy of stiffening girder.

摘要基于大位移非线性弹性理论的广义变分原理，考虑加劲梁轴向压缩应变能和剪切应变能的影响，建立了协作体系斜拉桥空间耦合自由振动的大位移不完全广义势能泛函，通过约束变分导出了协作体系斜拉桥的加劲主梁竖向挠曲振动微分方程。

Based on the generalized potential energy variational principal of nonlinear elasticity theory with large deflection, the incomplete generalized potential energy functional with large deflection is established on the space coupling free vibration of three-span self-anchored suspension bridge by considering the effect of axial compressive and shearing strain energy of stiffening girder.

摘 要：摘要：基于大位移非线性弹性理论的广义变分原理，考虑了加劲梁轴向压缩应变能和剪切应变能的影响，建立了三跨自锚式悬索桥空间耦合自由振动的大位移不完全广义势能泛函，通过约束变分导出了自锚式悬索桥的竖向挠曲振动、横向挠曲振动、纵向振动及扭转振动的基础微分方程，为自锚式悬索桥的固有振动性状分析提供可靠的理论依据。

Deducing the associated Euler-Lagrange equations of the two models, it is analyzed the diffusion performance of the p-harmonic equations and proved the two models have unique solutions in the space of Sobolev.

利用变分原理，推导出两种变分模型所对应的Euler-Lagrange方程；利用图像的局部正交坐标系，分析其扩散能力。

Image restoration ; image inpainting ; image completion ; variational method ; partial differential equation; total variation ; texture synthesis

图像复原；图像修补；图像补全；变分方法；偏微分方程；全变分；纹理合成

Based on variation principle, a free vibration variation-integration equation of cantilever curved pipe for conveying fluid is derived. This is a bending-torsion-fluid tree phase coupled dynamics problem. It is difficult to uncouple and to obtain bending and torsion analytic solution separately. We can only look for approximate solution or numeral results.

根据变分原理导出了悬臂输液曲管的变分－积分方程，这是弯曲－扭转－流体三相藕合的动力学问题，无法解藕而单独求出弯曲和扭转的解析解，只能作近似计算。

In the thesis,the author systematically discusses the novel semi-inverse method ofestablishing GVPs or SGVPs in fluid mechanics,from 1-D unsteady flow to full 3-Dunsteady flow,from direct problems to hybrid ones.

应用该公式，对于任意用二个守恒型方程描述的流体问题，都可以非常方便地求得其广义变分原理，从而使得建立广义变分原理完全格式化了。

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。