查询词典 biharmonic function

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。

With the solutions of the biharmonic equation at boundary value in a semi-infinite stripe,a weighted energy function is established.

对半无限带状区域上双调和方程边值问题建立了能量衰减估计，证明了以方程的解建立的加权能量随着与区域有限端距离的增长，该能量呈指数式衰减。

In this paper we study the method of interpolation by radial basis functions in H~k(k ≥ 1) and give some error estimates. By means of such interpolation with a special kind of radial basis function, we construct a basis in H~k(k ≥ 1). Combined with the Galerkin method, this theory can be applied to solve boundary value problems for elliptic partial differential equations (such as the third boundary value problem for Poisson equation and the corresponding problem for the biharmonic equation), and some numerical experiments are also given.

本文从求解偏微分方程的角度出发，在被逼近函数u属于一般的Sobolev空间H~k(k≥1)的情形，引入了一种径向基函数插值方法，并建立了相应的误差估计；再利用这种插值性质，从一类特殊径向基函数出发构造Sobolev空间的一组基，针对Poisson方程第三类边值问题和重调和方程类似边值问题，为用无网格算法求解偏微分方程边值问题建立了相应的理论，并通过算例来验证了这一算法。

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。

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。