双调和

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

Based on the boundary integral formula and natural boundary integral equation for the boundary value problems of biharmonic equation , the non-symmetrical banding solutions to the circular plate under thermal boundary conditions are gained by the Fourier series and convolution formulae.

根据双调和方程边值问题的边界积分公式和自然边界积分方程，利用傅立叶级数及卷积的几个公式，求得了相应变温边界条件下非对称载荷圆板的弯曲解，从实践上证明了此方法的可行性。

Secondly, we discuss the boundary value problem of two dimensional biharmonic equation in a rectangular field and its variational problem,discretize it by using dual tensor product of and the direct product and lining up of matrices, we get some special matrices which are the presupposition in exploring the fast computation, then solve the system of linear equations.

其次本文讨论了矩形域上二维双调和方程边值问题及其相应的变分问题，利用二元张量积小波分析和矩阵的直积、拉直技巧将变分问题离散化，从而使求解偏微分方程问题变为求解线性方程组的问题。一维情况两组基的张量积下得到的系数矩阵分别为块状七对角阵和稀疏矩阵。这些特殊结构为以后快速算法的研究打下一个基础。

It is not only introduced the two measures taken to solve the biharmonic equations , but the topical grids of H-type、C-type 、 and O-type are generated with this equation.

文中不仅对数值求解双调和方程的两种不同方法作了介绍，还利用该方程生成了典型的H型、C型、O型网格。

The grid generation technique for body_fitted coordinate system by means of numerical solution of biharmonic equations is studied, then the topical H_type grid and the flow field is generated and simulated numerically, respectively.

本文对利用双调和方程微分法生成贴体坐标网格的技术进行了探讨和尝试，生成了典型的H型网格，并对流场进行了数值模拟。

Noindent \hskip 20pt In chapter two, we prove the existence and multiplicity results of some nonlinear biharmonic equations by using lower semicontinuity method and minimax method.

在第二章中，通过下半连续方法和极大极小方法，我们证明了一类非线性双调和方程解的存在性和多解性的结论。

In this paprer, the usual notions of superlinearity and sublinearity for Biharmonic problems $\Delta^2 u + c\Delta u =f $ are given a local form and extended to infinite nonlinearities.

在本文中，我们给出了双调和超线性和次线性问题$\Delta^2 u + c\Delta u =f $的一个局部形式且扩展为不定的非线性形式。

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

On closer examination, though, this is not a vote for multilateralism but just the opposite.

仔细审视后我们发现，这并非是对多边主义投出的赞成票，而是恰好相反。

Uncovering their weak spots, so I can defeat them.

揭露出他们的弱点，这样我就可以打败他们了。