边界点

The method is to add a term into the original singular kernel while it subtracts its analytical solution from the original equation. Since the singularity of Green's function can be eliminated by such a mathematical technique, shape function does not need to be supposed while solving the unknown. The calculation can be directly applied to the real shape of the object by taking the integral points distributed on the object as nodes that satisfy boundary conditions.

由於格林函数的奇异性经过数学上的技巧加以消除，因此当求解未知数时已经不需要再假设形状函数，即可直接使用物体真实的外型来做计算，也就是直接将物体上分布的积分点视为满足边界条件的节点。

Non-linear singular perturbation problems;rational collocation method; Sinh transform;boundary layer;internal transition region.

非线性奇异摄动问题；有理配点法；Sinh变换；边界层；内部过渡区域

Available features: Auto-Trim, Crop, Deskew, Flip, Mirror, Resample, Resize, Rotate, Shear, Add Noise, Anti-Alias, Average, Bending, Border Remove, Brightness, Buttonize, Color Resolution, Colored Gray, Contour, Contrast, Cylindrical, Despeckle, Dilate, Dot Remove, DPI Resolution, Edge Detector, Emboss, Erode, Etch, Gamma Correct, Gaussian Blur, Glow, Gradient, Grayscale, Half-Tone, HistoContrast, Hole Punch Remove, Hue, Impressionist, Intensity Detect, Invert, Invert Text, Laplacian, Line Remove, Line Segment, Max Filter, Median, Min Filter, Mosaic, Motion Blur, Multiply, Oilify, Old Photo, Pixelate, Polar, Posterize, Prewitt, Punch, Radial Wave, Ripple, Saturation, Sharpen, Smooth, Sobel, Solarize, Swirl, Unsharp, Wave, and more!

可用的功能：自动修剪，作物， deskew ，倒装，是一面镜子，重新取样，大小，旋转，剪切，添加噪音，抗混叠，平均而言，弯曲，边界消除，亮度， buttonize ，色彩解析度，色灰，轮廓，对比度，圆筒形， despeckle ，扩张，点删除， dpi解析度，边缘检测， emboss ，侵蚀，腐蚀， Gamma修正，高斯模糊，辉光，梯度，灰阶，半色调， histocontrast ，孔冲床删除，色调，印象派，强度检测，反转，反转文本，拉普拉斯，删除线，线段，最高过滤器，中位数，闵过滤器，马赛克，运动模糊，乘， oilify ，旧照片， pixelate ，极地， posterize ， prewitt ，冲床，径向波，涟漪，饱和度，锐化，平滑，索贝尔，曝光，漩涡，锐化，波浪，及其他更多功能！

By introducing the concept of"nihility point"and the method of"spherule bounding" in the algorithm, we have simply and effectively realized boundary discretization in 3-D space.

这种算法采用"虚点"概念，按照一定的规则用"小球跳跃法"简单而有效地实现了三维场域边界的三角形离散。

Aimed at the problem of choosing the initial value when the Newton method is used to compute the controlling unstable equilibrium point, a practical and rigorous solving scheme was presented: by identifying the controlling load bus of the given fault, and using the Thevenin equivalent circuit to represent the rest of the system at the state of the post disturbance stable equilibrium point, using the steady equivalent circuit to represent the induction motor in composite load, and then using the torque characteristics of induction motor, a point near the CUEP is gained to be the initial value. The second order normal forms was used to approximate the stable manifold of CUEP, and the local approximating boundary of the region of attraction of the post disturbance stable equilibrium point was gained. Then just by simulating the state of the system at the fault clearing time, the transient voltage stability of the system could be determined.

针对采用牛顿法求取故障后系统主导不稳定平衡点(controlling unstable equilibrium point，CUEP)存在的初值选取难题，提出一种实用但不失严谨的解决方案：通过识别给定故障的主导负荷母线，对主导负荷母线以外系统由故障后稳定平衡点处的状态进行戴维南等值，对负荷中感应电动机部分采用其稳态等值电路，再由感应电动机的转矩特性求得CUEP附近的一个点作为近似的CUEP，以此为迭代初值可靠求得CUEP；采用二阶正规型来近似CUEP的稳定流形的方法求得近似的局部吸引域边界；由仿真得到故障清除时刻系统的状态并根据该状态是否位于吸引域内判断系统的暂态电压稳定性。

On the base of these work, the theory and technique which deal with ecological modeling ,two-dimension ecological dynamic model and stochastic eutrophication model was researched thoroughly.

本文获得的主要创新点为：提出了建立能很好拟合复杂边界的二维生态动力学富营养化模型的方法。

Ical modeling ,two-dimension ecological dynamic model and stochastic eutrophication model was researched thoroughly.

本文获得的主要创新点为：提出了建立能很好拟合复杂边界的二维生态动力学富营养化模型的方法。

Based on nonsmooth analysis theory, the viability criterion is verified under the condition that the set-valued mapping in the right hand side is a polytope and the boundary function of the region is subdifferentiable and its subdifferential is a convex hull of finitely many points.

当右端集值映射为多面体，边界为次可微函数，且次微分为有限点集凸包时，基于非光滑分析理论，给出了在一点处检验生存性条件是否成立的方法。

Since the deflections of the seven plates mentioned above satisfy the differential equation of plates, we can simply superpose the corresponding quantities and make them satisfy all the boundary conditions and supporting conditions.

2上述的七种板的挠度满足板的微分方程，因而只要把它们迭加，以满足边界及支承点的条件，即得其解。

At the production point the production possibility frontier must be tangent to a line whose slope is minus the price of manufactures divided by that of food.

在生产点上，生产可能性边界一定和一条斜率等于负的制造品价格除以粮食价格的直线相切

James, son of Zebedee, and John the brother of James, whom he named Boanerges, that is, sons of thunder

载伯德的儿子雅各伯和雅各伯的弟弟若望，并为他们起名叫"波纳尔革"，就是"雷霆之子"

The southern Hungarian university city of Szeged will host part of the project, amounting to 40 percent of the total investment, which will mostly be paid for through Hungary's EU structural funds.

位于塞格德南部的匈牙利大学将负责部分项目，总计占总投入资金的40%。大部分资金将由匈牙利的欧盟结构基金会支付。