查询词典 biharmonic equation

A quasi one-dimensional, time dependent system model based on the parallel compressor theory was used to compute the effect of inlet distortion on turbine engine stability; Through Modifying steady state continuum equation, momentum equation and energy equation, the effect of power extraction and additional bleed on turbine engine running line was computed. Unsteady state continuum equation, momentum equation and energy equation were solved for computing the effect of acceleration on turbine engine running line.

其中，进气畸变对发动机气动稳定性影响的计算采用平行压气机模型，基于李亚普诺夫理论的方法完成；附加引气、功率提取对发动机气动稳定性的影响采用通过对发动机转子间质量、动量、能量守恒方程进行修正的方法进行；加速过程对发动机气动稳定性的影响采用欧拉方法求解动态的质量、动量、能量守恒方程的方法完成；最后采用&层迭&的方法进行各种降稳因素的综合评估。

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。

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。

FENG Kang, YU De-hao and some other scholars of our country are the first ones to create the natural boundary element method, and they have successfully studied the natural boundary reduction method for the boundary value problems of harmonic equation and biharmonic equation.

我国学者冯康、余德浩等首创自然边界元法，并已成功地研究了调和方程及双调和方程边值问题的自然边界归化方法。

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。

The finite difference is used to approximate differential operation; the reflectance map equation described by the first order nonlinear differential equation is transformed into an algebraic equation about the unknown surface heights, and then the objective equation is constructed by the reflectance map equation and gradient information of image. Moreover, the Newton iterative algorithm is utilized to obtain the numerical solution and 3D shape of the surface.

采用有限差分近似微分运算，将一阶非线性微分方程所描述的反射图方程转化为关于未知表面高度的代数方程，再由反射图方程和图像梯度信息构造目标方程，进而用Newton迭代算法求出该方程的数值解，得到表面三维形状。

We develop and apply the Hirota bilinear-θfunction method,Jacobi elliptic function expansion method,linear superposition method and F-expansion method respectively to solve many 2+1 dimensional nonlinear wave models including 2+1 dimensional 2DsG equation,the coupled ZK equation,2+1 dimensional KdV equation,2+1 dimensional long wave short wave resonance interaction equation and 2+1 dimensional dispersive long wave equation,abundant Jacobi elliptic function doubly periodic solutions are derived.These solutions show various periodic wave shapes and special periodic characters.

发展和应用Hirota双线性-θ函数方法，雅克比椭圆函数展开法，线性叠加法，F-函数展开法等分别求解2+1维2DsG方程，耦合ZK方程，2+1维KdV方程，2+1维长波短波共振相互作用方程，2+1维色散长波方程，获得丰富的雅克比椭圆函数双周期波解，描述了一些周期波形态及周期特性。

In the solution of the problems in algebraic equation, differential equation and integral equation, we usually resort the sotution of equation to the fixed point of mapping in metric space. The contraction mapping principle can be used to solve many problems of the existence and uniqueness of equation solution.

在代数方程、微分方程和积分方程的求解问题中，通常把所求的解归结为度量空间中映射的不动点，然后应用压缩映象原理来统一处理许多方程解的存在性和唯一性问题。

On the basis of gas migration equation -Darcy Law,coal seam gas content equation -parabola equation ,ideal gas state equation and the continuity equation s of the gas flow,a dynamic model of gas unilateral flow in the coal seam is set .

根据基本假设，对煤层瓦斯流动规律进行了研究，运用瓦斯运动方程—达西定律、煤层瓦斯含量方程—抛物线方程、理想气体状态方程以及气体流动的连续性方程，建立了煤层单向瓦斯流动的动力学模型，并根据边界条件和初始条件，对动力学模型进行了求解，推导出煤壁单位面积的瓦斯涌出量的计算公式，分析了瓦斯涌出量的影响因素，利用测得的数据，进行了实例计算，并用vc编制了计算机程序。

Diabetes is a social disease that affects several million people worldwide.

糖尿病是一个社会性疾病，全世界有数百万人罹患此病。

I'll call you on Friday to see if we can reschedule our luncheon meeting at your convenience.

我星期五会给您打电话在您方便的时候我们重新安排我们的午餐约会。