对边点

In this paper,we study the problem finding basic circle in plane graph,in which the number and coordinate of nodes and the node number of two ends of the side is given,we create a method,which is enlightened by the"proble of find way in labyrinth",to find way in branch point and then to find basic circle.

论文讨论了平面图形中存在着节点和边，在已知节点的坐标、标号以及边的标号和边两端的节点标号情况下，对其中存在的一阶环进行计算机搜索问题，提出了受"走迷宫"问题启发的一种在分叉点沿一定的方向进行搜索的方法。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

Firstly, some basic concepts about ECC are introduced;then the scalar multiplication under affine coordinate is discussed, we make a research and analysis of the side channel attack of scalar multiplication used in portable device, give out a new scalar multiplication algorithm which has the advantage of efficiency over other protected algorithm; and an improvement of the standard scalar multiplication algorithm proposed by IEEE1363 is made with the efficiency increasing by about 10%; at last, we deal with the using of complex multiplication in scalar multiplication algorithm, we generalize the methods and deduce a complete computing procedure, with proposing a new method which used several different fast endomorphism ,we give out an approach to boost the scalar multiplication with fast endomorphism.

本文首先介绍了椭圆曲线密码的有关基本概念；其次介绍了椭圆曲线上点的标量乘法在仿射坐标下的计算，对一般便携设备上的椭圆曲线点的标量乘法的边信道攻击做了研究与分析，给出了一种在效率上优于其它可抵抗边信道攻击的标量乘法的新算法，并对IEEE P1363 标准给出的标量乘法做了改进，使得标量乘法的运算效率提高了近10%；最后介绍了利用复乘计算标量乘法的方法，对已有的方法进行总结归纳，得出完整的计算过程，并针对两类超奇异椭圆曲线给出了一种利用多个可快速计算的复乘的标量乘法，得出一类普遍的结果，并给出了进一步用复乘加快标量乘法的思路。

According to the principle of the diameter of a circle corresponding to the right angle and the principle of short side for little angle in right triangle, projecting the initially-chosen point to the hyper-planes of the linear equation group in which every linear equation can be regarded as a hyper-plane and the projection points can be obtained. The initially-chosen point, and one arbitrary projection point, and the solution point are all on the surface of the relative hyper-geometry ball, therein-to, there is a projection point which is nearest to the solution point and it can be regarded as the next iterative initially-chosen point, so the solution problem of the linear equation group can be changed as an iterative problem of approaching the solution on the surface of a hyper-geometry ball.

根据直径对应的圆周角足直角以及直角三角形中短边对小角的原理进一步知道，当将初始点向线性方程组中各个方程所代表的超平面上投影得到投影点时，初始点和其任何一个投影点及方程组的解点都将位于一个相应的超球面上，其中必定存在一个投影点离问题解点的距离最短，即把该点作为下一次迭代的初始点，从而可将线性方程组求解的问题变成球面上逼近解点的迭代问题。

With the help of the fundamental theory to singular measure differential system, Green's function matrix expression of solution and well-posed boundary condition are given, together with discussing the properties of the Green's function matrix under the influence of impulsive effect In section 5, based on Lyapunov function method, we investigate that the existence of the first boundary value problem to second-order singular system by macthing the solutions to the second boundary value problem; and the existence and uniqueness of three-point boundary value problem to third order singular system by macthing the solutions to two-piont boundary value problem.

第五部分借助Lyapunov函数法，通过将第二类边值问题的解对结成第一类边值问题的解，得到了二阶广义系统的第一类边值问题解的存在性；通过将两点边值问题的解对结成三点边值问题的解，得到了三阶广义系统的三点边值问题解的存在性和唯一性。

However, methods and references for difference equation are relatively less. The new method proposed in this paper transfer the complex boundary value problem into the existence and uniqueness of the solution of the linear equations. For linear case , we obtained the necessary and sufficient conditions for the existence and uniqueness of the solution for the BVP; For the nonlinear case ,we got a series of new sufficient conditions by using contraction mapping theory and cone theory .

而差分方程边值问题的研究方法和文献还很少，文中新的研究差分方程边值问题的方法是将复杂的边值问题求解转化为代数理论中的线性方程组解的存在和存在唯一问题；对线性情形，较容易地获得了边值问题的解存在以及唯一的充分必要条件，而对非线性情形，则通过压缩原理和锥理论等各种不动点定理，获得了一系列新的充分条件。

This study chose the dahongshan mine which has very important significance to the developing of yunnan iron and steel industry as our work station in which we build six runoff plots according to loss type and chose three place to earth up to observe the rule of the soil moving on the mullock stone and study the eroding rule of the barren side slope with eroding nail experiment.

本研究选择新建的、对云南钢铁工业发展具有重要意义的大红山铁矿进行矿山水土流失研究，按土壤侵蚀类型建立六个径流场进行观测，利用侵蚀钉对人工堆积边坡、裸露自然边坡和公路边坡侵蚀进行研究，在废石场选择三个点进行覆土实验对废石场覆土的潜移和管状侵蚀量进行观测。

In fact, on one hand, it is often found that two graphs with the same number of verticesand the same connectivity(edge-connectivity) may result in entirely different forms after a minimum disconnecting set of vertices is removed, one may be totally disconnected while the other may consist of a few very stable components, and thus be much easier to reconstruct.On the other hand, we often face this question: how easily can we disrupt a system at the least cost, on the contrary, when we set up a system, especially a communication system, we try our best to make it as stable as possible that it can be reconstructed easily if it do get disrupted .

对于两个具有相同点数，具有相同点连通度的图，从图中分别去掉使图不连通的点集后，所得图的结构可能完全不同，这是因为点连通度、边连通度和局部点、边连通度等连通性参数仅反映了系统被破坏的难易程度，而对系统遭受破坏的程度并没有明确的反映。

The above results are of general importance and can be used to improve the solder joint reliability of surface mount components with castellated solder fillet, the design level and the manufacturing process in SMT.

本文研究从提高SMT焊点可靠性、提高组装密度和避免焊点缺陷的角度出发，对高可靠性SMT焊点形态的设计和评价建立了四点规则，对提高有边堡钎料圆角形态表面组装元件的焊点可靠性、提高SMT工艺设计水平具有普遍意义。

The algorithm makes the discrete points sort in scan manner, and secondly it constructs convex hull and triangulates the sorted points by the optimal convex hull technology which is proved by the author, and optimizes triangles utilizing topological structures of directed edges.

该算法对离散点进行扫描线方式排序，利用最优凸壳技术进行凸壳的生成和三角网联结，最后利用有向边的拓扑结构进行三角网优化。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。