查询词典 boundary value problem

We can not apply Galerkin methods with radial basis functions to the first boundary value problem (the Dirichlet boundary value problem) of the second-order elliptic equation, because it requires that the approximate functions should fit the essential boundary condition, while the spaces spanned by the radial basis functions fails to satisfy this kind of boundary condition, and it is the same for the higher-order elliptic equation.

我们不能直接应用这样的无网格算法求解二阶椭圆型方程的第一类边值问题(Dirichlet边值问题)，因为第一类边界条件是本质边界条件(对二阶椭圆型方程为Dirichlet边界条件)，而径向基函数的支集通常是全空间，由它们所生成的近似函数空间一般不满足这样的条件。

In the last chap-ter,the natural integral equation and natural boundary element method forharmonic problem on exterior elliptic domain are introduced.Then,based onthis,the natural boundary reduction method for a kind of exterior problem ofanisotropic constant coefficients elliptic equation is discussed, the natural inte-gral equation and its solving method on circular boundary and elliptic bound-ary are obtained.These results can be directly applied in coupled methodand DDM for exterior boundary value problem.

最后，讨论了椭圆外区域调和问题的自然积分算子即D-N算子及自然边界元方法，并基于此研究了一类各向异性常系数椭圆型方程外问题的自然边界归化方法，首次得到其在圆周边界及椭圆边界上的自然积分方程及其求解方法，并将这些结果直接应用于外边值问题的耦合算法。

LBIE, based on the local boundary equation, adopts the traditional moving least squares approximation which depends on only the values of the nodes in the domain of the problem or along its boundary. The whole process of integration is carried on over a local domain or its local boundary centered at the node in question. The local boundary equation can be rewritten to represent the values of the unknown function at the point of interest, and the essential boundary conditions can be directly and easily enforced by using the Green formula and the characters of the Dirac function.

它以局部边界积分方程为基础，采用移动最小二乘近似函数，从而只需要分布在问题域内及其边界上的节点的信息值，无需划分单元；整个积分是在以节点为中心的局部域及其边界上实现，所以不需要背景积分网格；借助于格林公式及Dirac函数的性质，将局部边界积分方程转化为所考虑点的未知函数的边界积分表达式，便于直接施加本质边界条件。

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。

Coordinate sequence method is made up of the instruct information of polygon boundary x, y coordinate. It is the easiest polygon vector encoding method. The file structure of this method is easy, but because of the polygon boundary has stored two times, it will produce data redundancy, moreover, short of neighbor threshold information; Tree index encoding method make all the boundary points digitizing, store the coordinate sequence, connect the point index to boundary line, and then connect the line index to other polygons, so as to the tree index structure has came into being. It eliminates neighbor polygons boundary data redundancy problems; Topology structure encoding method is a method which by setting up a complete topology relationship structure, resolve the neighbor threshold and island information process problem. However, it makes arithmetic more complicated and makes database bigger.

坐标序列法是由多边形边界的x，y坐标对集合及说明信息组成，是最简单的一种多边形矢量编码法，文件结构简单，但多边形边界被存储两次产生数据冗余，而且缺少邻域信息；树状索引编码法是将所有边界点进行数字化，顺序存储坐标对，由点索引与边界线号相联系，以线索引与各多边形相联系，形成树状索引结构，消除了相邻多边形边界数据冗余问题；拓扑结构编码法是通过建立一个完整的拓扑关系结构，彻底解决邻域和岛状信息处理问题的方法，但增加了算法的复杂性和数据库的大小。

According to the principles of total economic value, the first step of the evaluation of assets value of wetland is to classify the assets value into two categories: use value and nonuse value , the former include direct use value and indirect use values , and the later includes existence value and Bequest value , the option value belongs to non-use value because its use value can not be realized.

对湿地资源资产价值的核算，应根据总经济价值的原理，首先将其资产价值分为使用价值和非使用价值两大类；使用价值又进一步分为直接使用价值和间接使用价值；非使用价值则包括存在价值和遗产价值；选择价值由于目前无法实现其使用价值，因此属于非使用价值的范畴。

In Chapter 1, two solutions to the elliptical boundary value problem have been constructed through a monotone iterative process, and they might be identical. In Chapter 2, the author expresses the local solution to the parabolic initial boundary value problem taking advantage of Green function. In Chapter 3, the asymptotic solution to the initial value problem of Duffing equation is obtained and the method for finding the approximate solution to the inverse problem is put forward.This paper is planned with a view to the author's research means.

从研究结果看：第一章通过单调迭代过程构造出椭圆型方程的边值问题的两个解，并且指出二者可能是同一个解；第二章利用格林函数给出了抛物型方程的初边值问题的局部解的解析表达式；第三章中，先对Duffing方程的初值问题写出解的渐近展开式，再对其反问题提出一种求近似解的方法。

The second chapter is the main part of this paper, in which the formulation of the Riemann boundary value problem of non-normal type on the real axis, the solution method of homogeneous problem, the relation between the two kinds of different derivatives and the inhomogeneous problem will be thoroughly given. In this paper, the solution and the solvability of the Riemann boundary value problem of non-normal type on the real axis will be given. Furthermore, it is shown that the twokinds of derivatives of the function Ψ are existing and equivalent in the case ofthe solution about the original problem, therefore, we get uniformly Hermite interpolatory polynomial. The relation between the two kinds of different derivativesof the function Ψ are similar for smooth closed contours by means of the same proof.

第二章是本文的主要部分，分别给出了实轴上一类非正则型Riemann边值问题的提法、齐次问题的解法、两种导数的关系及非齐次问题的求解，本文运用杜金元教授[11]的方法获得了实轴上非正则型Riemann边值问题的封闭解及可解性条件，且在问题可解的情况下论证了函数Ψ的非切向极限导数和Peano导数存在且相等，从而获得了统一的Hermite插值多项式，同样关于封闭曲线上非正则型Riemann边值问题，采用本文论证方法证得了函数Ψ的非切向极限导数和Peano导数存在且相等，从而较好地统一了[10]、[11]中的Hermite插值多项式。

Second order incident boundary condition on fixed incident boundary is derived for numerical simulations, based on the cnoidal or sinusoidal motions of wave maker paddle, which shows that the prediction with second order incident boundary condition is more accurate than the prediction with first order incident boundary condition. 2 The analytical solution for higher-order Boussinesq equations is derived and its applicable range is discussed. 3 A 2-D fully non-linear numerical model using boundary element method is developed to obtain wave forces acting on rectangular obstacle. 4 The three-dimensional fully non-linear waves are studied in a numerical wave tank using finite element method.The studies on the coupled numerical model combined Boussinesq equations with Laplace equation are following.

非耦合非线性波浪计算模型：1 根据造波板做椭圆余弦运动或正弦运动速度，推导出数值模拟波浪水槽时固定入射边界上的二阶波浪入射边界条件，数值计算结果和实验结果的对比表明采用二阶入射边界条件对波面升高的预报比采用一阶入射边界条件对波面升高的预报更为精确；2 推导了波浪水槽造波板做正弦运动所产生波浪的高阶Boussinesq方程摄动展开解析解，讨论了该解析解的适用范围；3 对整个波浪水槽应用边界元方法数值模拟了波浪对物体的非线性作用；4 用有限元法求解三维Laplace方程模拟了三维完全非线性波浪水槽。

According to the different orientations of domain walls with respect to the (100) observation plane of a foil, 90°domain boundaries may be divided into two kinds. one is thin lens or ring shaped a-a 90°domain boundary, and the domain wall lies on the {110} plane; Usually, most of these domain boundaries are uncharged; according to the extinction rules for the (011) domain walls, the displacement vector 〓 along 〓 can be dertermined, which is parallel to the line of intersection between the domain wall and the plane consisting of spontaneous polarization vectors on both sides of domain boundary; from selected area electon diffraction of crystals including domain boundary, we not only examine slight difference in the crystal parts on both sides of the domain boundary, but also obtain crystallographic relationship between them, that is, there exists a 180°rotation symmetry operator along a normal of domain wall. The other is Z or ring shaped a-c 90°domain boundary along {010} direction, and the displacement vector 〓 runs along 〓 direction.

根据界面相对于样品中(100)观测面取向的不同，90°畴可分为两类：一类为薄透镜片状或环状的a-a90°畴，其界面平行于{110}，多数不带电，由消光规律可确定其位移矢量平行于畴界面与自发极化所在平面的交迹，即，〓方向，而从包含畴界的选区电子衍射图可知，这种不带电的90°畴界两侧存在微小的取向差，其界面两侧的结晶学关系为以界面法线为二次轴的旋转关系；另一类为Z状或环状的a-c90°畴，其界面平行于[010]或[001]，相应的位移矢量为〓方向。

Putt your way through 36 fun-filled holes of minigolf on 3D designed courses with elevated greens, bunkers, bridges and water hazards, among other crazy obstacles.

您的推杆方式，通过36个有趣的填孔迷你的三维设计的课程，以提升绿党，掩体，桥梁和水的危害，除其他疯狂的障碍。

Some participles can be used either as attributes or as predicatives.

有些分词既可当定语用，也可当表语用。