双调和函数

With Airy stress function, a plane elasticity problem can be simplified to solve a biharmonic function equation.

通过引入Airy应力函数，平面问题可以归结为在给定的边界条件下求解一个双调和方程。

These application examples indicate that the direct method derived in this paper simplifies the process of constructing the Airy function in specific plane problems.

这些例子说明，利用本文的观察法可以将某些平面问题应力函数构造的过程简单化。关键词双调和函数， Airy应力函数，弹性力学平面问题

This paper, firstly, after a deep study of image mathematical models, sets up two kinds of image models namely Laplace partial differential equation model and biharmonic equation model and then obtains the eigenvectors of image by the methods of eigenfunction expansion and boundary recurrence.

本文首先较深入地研究了图象的数学描述，提出图象的Laplace偏微分方程和双调和方程两种模型，继而采用特征函数展开法和边界递推法分别求得图象的特征矢量。

This paper presents the boundary value problem solved as the biharmonic equation of upper plane and strip domain with Green functional method and it deals with the numerical solution of bihormonic equation, using the Matlab program calculation to realize the visualization of numeric solution.

用Green函数法求解了区域为上半平面和带形区域的双调和泊松方程的边值问题；以及探讨了双调和方程的数值解，并用Matlab编程计算实现了双调和方程数值解的可视化。

Taking beam with rectangular section as an example, the corresponding analytical solution of beam subjected to cosine distribution pressure is given through constructing the stress function satisfying all boundary conditions and biharmonic equation , which is a base of beam subjected to arbitrary distribution pressure.

以矩形截面简支梁为例，通过构造一个满足所有边界条件和双调和方程的应力函数，给出了梁受余弦分布力作用情况下相应的解析解，这为求解梁受任意分布压力作用下解的问题打下了基础

Owing to the anisotropic and the biharmonic nature of microwave radar backscatter on spaceborne scatterometer, and to the scatter model function nolinear and the existence of various noise sources in the measurements in addition to the model function, the

由于卫星散射计探视雷达回波的各向异性的双调和性质，同时由于散射物理模型函数的非线性及信号中存在噪声，使得常规点方式风场反演中风向有多至4个解的多解存在。

Owing to the anisotropic and the biharmonic nature of microwave radar backscatter on spaceborne scatterometer, moreover, scatter model function nonlinear and the existence of various noise sources in the measurements in addition to the model function, the retrieval wind results consist of as many as four wind directions.

摘 要 由于卫星散射计探视雷达回波的各向异性的双调和性质，同时由于散射物理模型函数的非线性及信号中存在噪声，使得常规点方式风场反演中风向有多至4个解的多解存在。

It is the well-known Lame's formulas for the stresses in a hollow circular cylinder subjected to uniform pressures.

在此 ，针对实际问题的需要，在三维空间中构建了一个既满足双调和方程又满足边界条件的新应力函数，推导出厚壁

With the help of the Mountain-Pass Theorem lacking Palais-Smale compactness condition (PSc condition and by adoption of the best attained function of Sobolev embedding, the paper proves the existence of nontrivial solutions of two classes of critical biharmonic equations on boundary conditions by overcoming serial difficulties caused by loss of compactness due to Sobolev embedding.

本文借助于没有 PS 条件的翻山引理，并利用 Sobolev 嵌入的最佳达到函数，克服了由于 Sobolev 嵌入失紧性而带来的系列困难，证明了含临界增长的两类双调和方程边值问题非平凡解的存在性。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。