离散

Mesh fairness problem We propose the conception of discrete curvature vector for meshes, and suggest a new fairness criterion that a mesh is fair if changes in discrete curvature vectors of this mesh are gradual and uniform Based on this fairness criterion, two algorithms are presented.

网格的光顺问题本文提出了离散曲率向量的概念，并以其变化平稳均匀作为网格光顺的准则，这一准则兼顾了曲率大小及法向的变化。

The discrete curvature vector based method to fair mesh by modifying vertex positions We first low-pass filter the discrete curvature vector function to make it change more gradually and uniformly, and then modify the vertex positions according the resulted function to improve the fairness of mesh.

以此为基础，给出了两个算法：网格改点光顺的离散曲率向量法基本思想是先用低通滤波算子修匀曲率向量，并由此修改顶点的位置以改善网格的光顺性。具体算法吸取了优化问题中Zoutendijk可行方向法的基本思想。

The body of the paper is to design and carry out some experiments for different methods of curvature estimation above.

本文主要工作是针对代表性的离散曲率计算方法进行大量的实验并对实验结果加以比较分析。

A New Method to Obtain Discrete Cutting Points of Space Curve in Three-Dimensional Laser Cutting.

激光三维切割空间曲线的刀位点离散方法。

Detail are introduced as following: transfering the LS equation to difference equation, setting the initial conditions for different shape explosive at different initiation way (point, line, plane, divergent or convergent); the dealing method of different edge conditions; how to draw the curve graph in two dimensional space or surface graph in three dimensional space with the calculated data.

本文提出了在三维直角坐标系中爆轰波传播LS方程离散化方法，建立了相应的差分方程，研究了对不同形状炸药在多种起爆形式（点、线、面、散心、聚心）下初值条件的设定，以及各种边界条件的处理方法。

Chaikin algorithm is the simplest discrete curve modeling method.In thepaper planar Chaikin algorithm is generalized into sphere,and the practicability ofthe algorithm as well as the continuous differentiable property of the generatingcurve is proved.It is shown that the curve generated by Chaikin algorithm is apiecewise spherical Bezier curve of second kind of order two.Furthermore,generalspherical corner-cutting algorithms are discussed,and it is pointed out that thecurve generated through corner-cutting has"Spherical Variation DiminishingProperty".3Curve interpolation method restricted on a smooth surface based ontransformation.

Chaikin算法是最简单的离散曲线造型方法，文中将Chaikin算法推广到球面，证明了算法的可行性和生成曲线的连续可微性，指出球面Chaikin算法得到的曲线是分段的二次第二类球面Bezier曲线，并给出了用球面Chaikin算法构造球面插值曲线的算法；进一步，文中讨论了一般的球面割角算法，指出由球面割角算法得到的曲线具有"球面变差缩减性质"。3基于变换的约束在光滑曲面上的曲线插值方法。

A numerical method, where the pressure is used as a primary dependent variable, is presented for the solution of the two-dimensional steady Navier-Stokes equation in general curvilinear coordinates. SIMPLE (Semi-Implicit Method for Pressure Linked Equations) is mainly adopted.

本文首先详细推导了二维任意曲线坐标系下张量形式的流动控制方程及其和压力修正方程的离散形式，应用求解压力速度耦合的SIMPLE算法，以压力为主要求解变量对Navier-Stokes方程进行数值求解。

Detailed studies are made as follows: Searching the key internal factors which can affects slope stability. According to the geological data which was gained by exploration investigation, establishing a geological model which can reflect rock mass characteristics;With analyzing the internal and exterior factors synthetically, the deformation and possible failure mechanism and mode of the cut slopes was confirmed which combines with stereoic projection and other techniques;The stabilities of the 14 high slopes are estimated synthetically by applicable design codes and guidelines. With the estimate result and some other analysis methods, the rock mass mechanical parameters of slope are identified;As a results, 14 high slopes fall into 4 categories based on rockmass characteristics and discontinuities. The stability and deformation of some typical slopes was analyzed with distinct element method by UDEC;The safety factor of some dangerous slopes are calculated by rigid limiting equilibrium method for coMParison.

首先着重研究影响边坡稳定性的内在因素，主要是通过地质勘探、测量、现场观测等手段取得研究区地质体的基础地质资料，建立起能够反映地质体结构特征的地质模型；随后综合分析潜在的内外部影响因素，并结合赤平投影对边坡可能的失稳模式或破坏机制作出判断；运用已有岩体质量分类方法对沿线14个高陡边坡稳定性进行初步的评价，并结合试验研究、经验判断、工程类比等手段确定了坡体的岩体力学参数；根据稳定性初步评价结果将研究区14个高陡边坡按开挖方式分为4大类，并利用离散元程序UDEC对各类典型高陡边坡进行了稳定性计算分析；对潜在危险边坡利用刚体极限平衡法求出了不同工况下的安全系数。

In this paper a discretization algorithm based on importance of cut point .

提出一种基于断点重要性的离散化算法。

In the last, three different algorithms (namely, the proposed algorithm, the traditional cutting plane method, and the discretization method) have been implemented for same problems.

最后，基于提出的修正算法，并与传统割平面方法、普通离散方法对同一问越作了初步的数值比较实验。

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