边界点

The most-used numerical method for solving direct boundary integral equation is collocation method, which is simple and faster. Seldom have been used the Galerkin scheme in this case.

一般来说，直接边界积分方程可以很方便的用配点法求解，还未见有实际用Galerkin边界元来解的报道。

Based on the fundamental solution of plane piezoelectric problems and the basic thought of the virtual boundary element method for elasticity, this paper presents a virtual boundary element-equivalent collocation method for plane piezoelectric materials.

利用压电材料平面问题的基本解和弹性力学虚边界元方法的基本思想，提出了压电材料平面问题的虚边界元-等额配点解法。

The main purpose of the dissertation is to introduce the concept of "generalized parameter" to the Boundary Element Method.

本文的创新点在于尝试将"广义参数"的概念引入到边界元法的分析中，尝试探寻边界元法求解断裂力学的新理论和新途径。

On the basis of the conclusion above, the nonlinear weak controllable vectors can be obtained, which compose the second class of weak controllable matrix, by means of matrix transfermations of the first class of weak controllable matrix. Furthmore the second criterion of weak controllability, accessibility and strong accessibility, which is more standard, more succinct and more practical, is obtained. On the basis of the first criterion and the second criterion, several important problems about nonlinear controllability are discussed, which include 1 local controllability; 2 three classes of local controllable decomposition, separately by means of local coordinate changes in the neighborhood of a nonsingular point, a point on a singular surface or a designated point x〓 with a designated input u〓; 3 the character of controllability of the ith state variable x〓 in different controllable areas and their boundaries.

在第一判别定理和第二判别定理的基础上，我们分析了非线性系统受控性质中的几个重要问题，所得到的结论包括i得到了非线性系统在可平衡点附近的能控性判别定理；ii分别给出了非线性系统在非奇异点、s阶奇面以及在状态空间内给定的一点x〓和输入u〓上的三种状态分解形式以及相应的求解方法；利用系统的Ⅰ型弱能控矩阵与Ⅱ型弱能控矩阵秩相等的条件，得到了只用系统的前n个弱能控向量来判断系统的弱能控性的判别定理；iii通过引入系统状态分量的三类受控区域边界的定义及相应的求解方法，初步探讨了非线性系统各个状态分量在不同的受控区域及其边界上的受控性质。

At first, preprocessing with the image pyramid and diffusion-filtering technology; then abstracting the boundary-outline information; carrying on the logarithmic coordinate transformation of the abstracted boundary-outline information to get bar chart of the logarithmic coordinate; calculating the value of Cs to get all the phase match points; calculating the value of the degree of approximation to judge the shape matching.

本发明涉及一种基于Shape Context的人脸形状匹配方法，首先采用图像金字塔及扩散滤波技术进行预处理；再利用Canny边缘检测算法和轮廓提取算法提取边界轮廓信息；对提取的边界信息进行对数极坐标变换，得到对数极坐标直方图；通过计算Cs值，获得所有相匹配点；计算相近似度值，进行形状匹配判断。

In this paper, a least-square collocation formulation for solving Helmholtz equation with Dirichlet and Neumann boundary conditions was established.

对于Helmholtz方程问题，其微分方程和边界条件可表示为法应用于Helmholtz方程问题的研究，建立了 Helmholtz方程问题的最小二乘配点格式，分别研究了Hdmholtz方程的波传播问题和边界层问题。

In this thesis, the virtual boundary integral equation is based on double layer potential with the virtual density to be determined on virtual boundary. Since this integral equation related to double layer potential only involves the computation of the normal derivative and second normal derivative of fundamental solution, the exponential integral function is not involved in it, so numerical computation for the exponential integral function is avoid.

本文则基于双层位势，引入虚拟矩密度函数来建立虚边界积分方程，并首先对时间变量进行解析积分，在虚、实边界上采用常单元和等额配点离散，该方程只涉及含基本解的法向导数及其二阶法向导数项的计算，对时间变量进行解析积分后，不会出现对指数积分函数的空间变量的积分计算。

Constructing geometric model of analyzed object is the first step of mesh generation, in this research subject, we mainly analyze the medical encephalon CT picture ,so we select digital instrument to extract border characteristic points from encephalon CT picture and create the analyzed object geometric model.

进行网格剖分首先要建立分析对象的几何模型，鉴于本文的分析对象是医学脑CT扫描图像，为此采用数字化仪从脑CT扫描图像中提取边界特征点，以此形成分析模型的边界轮廓，从而建立分析模型的几何模型。

Since a skeleton pixel should be in the middle point of one of a pair object boundary, based on the discussion of some commonly used thinning algorithms, a fast thinning algorithm based on midpoints of multi-orientation slices was put forward.

在对几种常用细化算法进行探讨之后，提出了利用骨架上的像素点至少在某个方向上应处于该方向对象边界的中心点处的特点，从多个方向对细化对象进行切片，并利用这些切片中心点集作为原始数据集，以快速产生对象骨架的方法。

Based on the survey of the traffic flow in Changchun city arteries, the scatter charts of vehicle speed-low data were plotted, the linear regression equations of scatter plots and their boundaries were derived and compared with the curve of Greenshields speed-flow model and the scatter plot of the freeway data, thus the speed-low characteristics in urban arteries were established, being of help for the traffic managers to determine the traffic signal control strategy.

以长春市干线道路的交通流实测数据为依据，绘制了速度流量的散点图，建立了散点图及边界的线性回归方程，并与Greenshields速度流量理论模型曲线、高速公路的速度-流量散点图进行了对比，分析了城市道路的速度-量特性。实际应用表明，该特性分析能为交通管理者确定信号控制策略提供速度流量依据。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新