边界格点

Some valuable works in the paper include: First, based on the algorithm of based-cell detection, the paper presented a dynamic adjustment function on "M" which can work out a problem of outliers fault-making on boundary cell.

总结本文的研究内容，主要有如下创新： 1、在基于单元的孤立点数据挖掘算法基础上，针对边界单元格出现的孤立点误判问题，给出了对M值进行动态调整函数。

The origin algorithm has the same time complexity with the improved one, but the latter achieved a notability in dealing with the problem of outliers fault-making on boundary cell.

另外，本文通过实例，对改进的算法进行了验证，结果证明新旧两种算法具有相同的时间复杂度，但新算法在避免边界单元格处孤立点误判问题上达到了明显的效果。

For reducing boundary distortion area, the elevations of grid DEM are viewed as a discrete sequence under a generalized coordinate, so that the boundary problem of two-dimensional discrete wavelet transform is turned into the boundary problem of one-dimensional discrete wavelet transform, which not only greatly reduces the boundary distortion area, improves the precision of reconstructed DEM data near the boundary, but also decreases the number of zeros adding on the boundary for wavelet transform, and boosts the compression ratio. On the basis of analyzing the distribution characteristics of coefficients in low and high frequency bands, a mixed entropy coding plan is applied, and a high efficient quantizator called"self-adaptive hard threshold"is established, which is helpful for improving the precision of the reconstructed DEM data and for enhancing compression ratio.

为了减小小波变换山区格网DEM数据压缩中边界失真区域，将山区格网DEM高程值视为广义坐标下的离散随机序列，把二维离散小波变换中的边界问题转换为一维离散小波变换中的边界问题，不仅大大减少了小波变换边界失真区域，提高了重构DEM数据边界点的精度，而且减少了边界补零个数，提高了压缩比；通过对山区格网DEM数据小波变换低频区和高频区变换系数分布特点的分析，采取了霍夫曼—游程混合熵编码方案，设计了高效、低失真的"自适应硬阈值"量化器，即对低频区变换系数不进行量化，直接进行霍夫曼编码；对高频区变换系数则先用"自适应硬阈值"方法量化处理，再进行游程编码。

For the single objective optimization, the decomposition and coordination method is adopted to build the decomposition and coordination model according to the existing sub-area division conditions of power networks. Then using the Augmented Lagrange method, the minimization problem of decomposition and coordination model can be changed to the saddle point problem of augmented Lagrangian function. Finally, the so called auxiliary problem principle is selected to decompose variables as well as the functions. This transforms the voltage and reactive optimization problem of the wholenetworks to some sub-problems in some sub-areas.

对于单目标无功电压优化，根据实际电网分区情况，采用分解协调法复制各分区的边界节点，建立分解协调模型，采用增广拉格朗日法将求分解协调模型的极小值问题转化为求增广拉格朗日函数的鞍点问题，然后采用辅助问题原理分解变量和增广拉格朗日函数，从而将全网无功电压优化问题分解为多个分区的分布式并行优化问题。

In the surface of the substrate the liquid crystal molecules parallel to the surface as a consequence of the surface potential. Adopting the Lebwohl Lasher model, the mole cular centers of mass are located at the sites of the simple cubic lattice with period boundary conditions.

在基板表面处，液晶薄层受到表面作用势的作用使液晶分子沿面平行排列，采用Lebwohl Lasher模型，将分子质心固定在简单立方晶格的格点上，并对此格点模型赋以周期性边界条件，然后将简立方格点模型分为平行于基板的20个分子薄层，得到各薄层的指向矢分布的数值结果。

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。

Then, the boundary points are extracted. By using Shu's theorems the sum of Legendre polynomial of the boundary points is calculated.

首先使用Yang-离散格林公式将二值图像矩计算中区域内求和转换为沿区域边界求和；然后提取该图像的边界点；再利用Shu提出的公式计算出边界点的Legendre多项式的叠加值。

Given a mesh, we first solve a Poisson equation to construct a scalar field and use it to generate some critical points. The cutting paths between the critical points and the boundaries are solved in the Poisson scalar field using the deepest descent method. For meshes with nonzero-genus, we construct a Harmonic scalar field, and connect the saddle points with the boundaries based on the Morse theory.

对于给定的任意网格，通过求解泊松方程构造标量场来选取临界点，并采用最速下降法给出临界点到边界或者初始点的切割路径；对于亏格不为零的网格，基于Morse理论，通过构造一个调和标量场来得到鞍点，并将它们连接到边界。

If P is a convex lattice polygon, and its pair-wise disjoint family of translates are also lattice polygons, whose union contains every lattice point, it is called a TLP .

若P为凸格点多边形，其内部边界不交平移覆盖平面格点集，则称之为可平移格点多边形TLP。记顶点数为v的TLP的内格点数的下确界为i ，得出i(5)=i(6)=1，i(7)=i(8)=4。

In theory, firstly, the numerical simulation methods, such as the boundary element method, the finite difference method and the finite element method, were utilized to calculate the distribution of electric field intensity and potential of the electron-gun system, the focusing system and the whole equipment, respectively. Then, the trajectories of the electron-beam were traced by using of the Runge-Kutta method and the Monte-Carlo method associatively. The point spread function was also calculated.

在理论分析中，先后采用边界元方法、差分方法、有限元方法等科学数值计算方法，编制程序，对X射线源的电子枪发射系统、聚焦系统以及发射系统与聚焦系统的组合系统等的电场分布进行了严格的计算，在准确求得各系统电场内各个剖分点的电场场强、偏导数等参量的基础上，采用蒙特-卡罗模拟方法和不等距龙格-库塔方法相结合，追踪由LaB_6单晶阴极表面发射出的大量电子束在电场内的运动轨迹，求出点扩展函数，并根据点扩展函数的优劣，反复调节、大量计算对比，挑选出X射线源最佳的电极结构及其组合。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。