变分方程

Based on the variational principle of initial post-buckling theory, the neutral equilibrium equation of the arch under uniform compression is derived.

基于初始后屈曲理论的变分原理，导出了圆拱在均匀压力作用下弹性失稳的中性平衡方程，并计算了圆拱反对称屈曲的临界压力，得到了与经典解一致的结果。

In chapter 4, we compute the symmetry group, variational symmetry group, divergence symmetry group of some operator equation.

在第四章中计算了一些偏微分算子方程的对称群，变分对称群以及散度对称群。

In this paper, a general, strain-consistent, third-order displacement field of shells is proposed. On this basis, the nonlinear theory of composite laminated shells including third-order transverse shear deformation and rotary inertia is developed. Hamilton's variational principle is used to derive the nonlinear static and dynamic governing differential equations and the corresponding boundary conditions of composite laminated anisotropic general shells under the orthogonal curvilinear coordinates. And the form of spherical shells is degenerated.

本文提出了一种最普遍的应变协调、三阶壳体位移场，在此基础上建立了考虑三阶横向剪切变形和旋转惯性的复合材料层合壳体非线性理论，用Hamilton变分原理导出了复合材料层合各向异性任意壳体在正交曲线坐标系下的非线性静、动力控制微分方程和相应的边界条件，并将其蜕化为球壳形式。

Choosing parabOlic type confiningpOtential,we solve the unperturbed〓equation andobtain the electron wave function.

选择抛物型的约束势，我们通过求解未微扰情况下的薛定格方程，给出了电子的波函数，在此基础上，应用变分方法来考虑电子和表面声子的相互作用。

First, structure tensor is calculated to gain vector field for characterizing local structure of image. And then, total variation partial difference equation is imposed for smoothing vector field. Based on this we use line integral convolution for guide the stroke to generate virtual special effect image with fluctuant sense. Last, mergering with original real image, cylindrical panorama with virtualized relationship controlled by time can be generated, which accomplished the character of surpass the time and space in virtual reality system.

该方法通过计算结构张量获得图像曲线走向矢量场，以此刻画图像局部结构；并采用全变分偏微分方程对曲线走向矢量场自适应滤波平滑处理；在此基础上利用线积分卷积指导画笔走向模拟生成线条波动感虚化效果图像；最后结合原始真实图像和虚化效果图像，实现了一种基于时间变量的柱面场景虚化关联算法，并为虚拟现实系统超越现实时空的需要提供了一种新思路。

In this paper,the artificial parameter perturbation method and variational iteration method have been applied to nonlinear differential equation with power nonlinearities.

应用人工参数法和变分迭代算法，求解了具有分数阶非线性的一阶常微分方程。

A variational formulation is constructed from the famous Gelfand-Levitan equation to reconstruct the scattering potential.

从著名的Gel＇fandLevitan方程出发，本文构造了一个重建散射位势的变分公式。

The calculus of variations; Euler's equation; the principle of least action;δ-method; the multiplier rule

基础科学，数学，古典数学变分法；欧拉方程；最小作用原理；δ-方法；乘子法则

Furthermore the existence condition and the variation principle of the differential equation are discussed, and the theory gist of the step-time technologies is presented.

应用相关的势算子理论对抛物型偏微分方程的泛函存在条件及变分定理进行了较系统的讨论，进而指出了"时间步进有限元法"各种处理方法的理论依据。

Basing on the variation principle of solid-fluid coupled problem,on the situation of the tank being full filled,the essential method and principle have been found by using the numerical approximation of finite element method.

在罐车满载的情况下，根据固液耦合问题的广义变分原理，使用有限元的近似数值计算方法，找到解决满载罐车液固耦合振动问题的基本方法和原理，建立铁路罐车的固液耦合问题的动力学控制方程，并通过算例验证液体对罐车耦合振动的影响，得到在工程上所需要的分析结果。

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。