查询词典 solution set of equation

The fact that solution of wave equation is equivalent to the extreme value of quadratic function solution was verified, and the existence and uniqueness of the quadratic function solution was also proved.

证明了波动方程的解和二次泛函极值解的等价性，以及二次泛函极值解的存在唯一性，为其在液压传动中流体瞬变分析的进一步应用提供了理论依据。

Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier–Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack subjected to internal impulsive pressure are given by dynamic weight function method.

首先采用静态内压下的应力强度因子作为参考解，得到了带径向边裂纹厚壁圆筒的权函数；然后用振型函数方法推导无裂纹厚壁圆筒在冲击内压下的动应力响应，分析中将相应的弹性动力学方程解分为满足非齐次边界条件的准静态解和满足齐次边界条件的动态解的叠加，利用傅立叶-贝塞尔级数展开，推导出了厚壁圆筒内动应力的响应历程和分布规律；最后由动应力权函数方法导出带径向边裂纹厚壁筒在冲击内压下的动态应力强度因子计算公式。

This paper discusses the broad-sense relation between solution and coefficient of some special kinds of second order variable coefficient and homogeneous linear differential equation,and have a try of giving a general form of common solution and the coefficient decision formula of special solution.

探讨了某些特殊类型二阶变系数齐次线性常微分方程的解与系数的广义关系，尝试了从理论上给出通解的一般形式和特解的系数决定式。

The solitary wave can be generated considering Goring and Raichlen's movement of a paddle. The proposed original linear solution for the solitary wave generation is expressed in the hypergeometric function. Two disadvantages of the original solution with large trailing wave and skewed wave profile are found by comparing with the theory of solitary wave derived from Boussinesq's equation. The difference between the original linear solution and the solitary wave theory results from the nonlinearity and dispersion of generated waves in the flume.

本文并以弱非线性的孤立波造波问题做为解析之对象，由於孤立波造波板速度为一超越函数，造成解析上的困难；本文以 hypergeometric 函数推求常微分方程式之全解，并与理论波形解比较后，发现由於未考虑非线性及分散性过强等问题，使得线性暂态解较理论波形拉长与歪斜，可能无法有效描述孤立波造波问题，故针对线性之分散关系做出修正。

The direct method of solution for non-normal type of singular integral equation with Hubert kernel is discussed. Their solution have form of integral and the condition of solution have form of the system of equations.

给出了具有Hilbert核非正则型奇异积分方程的直接解法，对核密度函数k在附加某些条件下，得出了方程积分形式的解和方程组形式的可解条件。

Based on the maximum principle,we construct the blowing-up lower solution by the relations of parameters and solution of the ordinary differential equation and then the blow-up properties are studied.We use the maximal principle to analyse the derivative profiles of the solution and get the lower bounds and upper bounds of blow-up rate through the complicated analysis technology and the inequality theory.

基于最大值原理的比较理论，通过一些特定的参数关系，利用相关常微分方程的解构造合适的爆破形式的下解，由此得到退化反应系统初边值问题的爆破解；然后，对爆破解的性质进行进一步的研究，利用极大值原理对解的导数特性进行了分析，给出了解的爆破速率的上、下界估计。

Based on inverse equation, the forward solution model of position is presented in this thesis through method of successive approximation, for parallel robots possess characteristic of easy inverse solution and difficult direct solution. The method is proved to be highly effective by simulation example.

根据6-SPS并联机器人反解容易、正解较难的特点，本论文基于位置反解方程，通过杆长逐次逼近的思路建立了位置正解模型，并对该方法进行了实例验证。

In chapter 6, we discussed the wavefront solution of a kind of lattice differential equation which derives from diverse fields. We obtained the wavefront solution by using sup-subsolution iteration when the coupled functions are quasimonotone, and by applying Schauder fixed point theorem, we also obtained the wavefront solution when the coupled functions have a different quasimonotone property.

在第六章中，我们对一类从实际问题中抽象出来的二阶时滞格微分方程的行波解进行了讨论，用单调迭代的方法讨论了耦合函数具有拟单调性时行波解的存在性，用不动点的方法讨论了耦合函数具有指数拟单调性时行波解的存在性。

In Chapter two, it is given of the three-dimensional boundary element and the boundary element space, Sobolev space for the contact boundary element problem with friction; it is proved of existence and uniqueness of the solution by variation inequality for the contact Boundary Element Method matrix equation under two kinds of condition that the contact zone is fixed and the contact zone is increasing along with the load; it is given of the expressionfor the error of the exact solution and the boundary element solution.

第2章，给出三维边界单元及边界元空间、有摩擦接触边界元问题的Sobolev空间，利用变分不等式证明了不变接触区和随载荷可变接触区两种情况下的接触边界元法矩阵方程解的存在唯一性，给出了准确解与边界元解的误差表达式，还证明了三维弹塑性摩擦接触问题凝缩矩阵解的存在唯一性，为三维弹塑性摩擦接触边界元法奠定数学基础。

By means of the undetermined coefficient method ,which is submitted in reference for solving nonlinear wave equations for their peaked soliton solutions ,three kinds of peaked soliton solutions are obtained for two important nonlinear wave equations— Korteweg-de Vries equation and Benjamin-Bona-Mahonyequation,respectively. One kind of peaked compacton solution ,which has the characteristics of both peaked soliton solution and compacton solution ,is obtained for above two equations with the aid of transformation relation between triangle function and hyperbolic function,. By use of above solutions, two kinds of periodic peaked traveling wave solutions are constructed.

摘 要：利用文献中提出的求非线性波方程尖峰孤子解的方法，分别求解了两个重要的非线性波方程—Korteweg-de Vries 方程和Benjamin-Bona-Mahony BBM）方程，得到了3类尖峰孤子解；借助双曲函数与三角函数间的变换关系得到了1类尖峰紧孤子解，该型解兼有尖峰孤子解和紧孤子解的特点；在上述结果的基础上构造了2个周期性的尖峰行波解。

The second is to cut a mere 100 calories from your diet , which is the equivalent of a tablespoon of butter.

第二个就是从你的饮食中减少一百卡路里，只是相当于一大汤匙的黄油。

This is where the Rorschach test comes in.

现在，罗氏测试就出现了。