单连通区域

讨论了4个变量的双解析函数在有界单连通区域上的Dirichlet问题，建立在四元数分析基础上的结果有理论和实践的意义。

Dirichlet problem of bi analytic functions of four variables on the bounded simply connected domain with smooth boundary is studied . The results , based on quaternionic analysis theory , are of both theoretical and practical interest .

本文用复分析方法处理单连通区域上二阶线性椭圆型复方程非正则斜微商问题的数值解。

In this paper , the complex function method is used to deal with numerical solutions of the irregular oblique derivative problem for linear elliptic complex equations of second order in a simply connected domain .

利用Riemann映射性质将单位圆内Hp（p≥1）空间的定义推广到了在一般单连通区域上定义Hp（p≥1）空间。

Expand the definition of Hp ( p ≥ 1 ) space in unit circle to the simply connected region using Riemann mapping .

研究了计算平面单连通区域Voronoi图的波前传播（Wavefront-propagation）算法。

Voronoi diagram is widely applied in the field of CAD / CAM . We first studied the wavefront propagation algorithm for computing Voronoi diagrams for single connected domain .

基于边界标注的单连通区域扫描线填充新方法

A Novel Edge-Labeled Algorithm for Simple Connected Area Scan Filling

无论是单连通区域还是复连通区域，算法相同，无需对复连通区域进行特殊处理。

No matter whether simple connection or complex connection , the algorithm is same .

稍后我们会知道，在一个单连通区域上也可以。

Or , as we will see soon , in a simply connected region .

提出一种基于边界标注的单连通区域扫描线填充快速算法。

A novel edge - labeled algorithm for simple connected area scan filling is presented .

给出了单连通区域和多连通区域中的一般级数表达式及确定级数项系数的方法。

A series expansion and a method to determine the coefficients of the series expansion are given .

那么我们是在哪里利用了，“定义在单连通区域”的假设呢？

OK , so where do we use the assumption of being defined in a simply connected region ?

研究了二阶拟线性双曲型方程在一般单连通区域上的斜微商边值问题。

The oblique derivative problem for quasilinear hyperbolic equations of second order in general simply connected domains is discussed .

本文把在单连通区域上成立的曲线积分与路线无关性定理推广到复连通区域。

In this paper the theorem in which a curve integral is independent of the integral path on a single connected region is generalized .

证明了拟常曲率流形中二维极小子流形上一个单连通区域为稳定的充分条件。

Sufficient conditions for a simply-connected domain of 2-dimensional minimal submanifold immerged in 2 + p-dimensional manifold of quasi-constant curvature to be stable were proved .

借助保形变换将单连通区域及其边界化为上半平面与实轴。

With the help of the conformal transformation , we transform a simply connected region and its boundary into the upper half plane and real axis .

本文提出一种算法实现单连通区域的线性四元树表示转换成区域边界的4-方向链码描述。

An algorithm is presented for converting the linear quadtree representation of a simply connected region into a 4-direction chain code description of the region 's boundary .

这里，为了使得完全成立，不得不假设，这定义在一个单连通区域，否则就有可能得到，和先前一样的奇怪事情。

And here , to be completely truthful , I have to say defined in a simply connected region . Otherwise , we might have the same kind of strange things happening as before .

对比传统单连通区域扫描线填充法，新方法算法效率高，实现简单，对复杂区域的填充同样适用。

Compared with the normal algorithms , the new one is efficient in algorithm , simple in realization for scan filling of simple connected area and also applicable to the filling of the complex area .

实际上最好的结论是，如果向量场定义在一个单连通区域上，而且旋度为零，那么它就是梯度场。

So , in fact , the actual optimal statement you can make is if a vector field is defined in a simply connected region , and its curl is zero , then it 's a gradient field .

，如果知道了，向量空间在单连通区域内处处有定义，那么就可以毫无顾忌地，在这个区域里使用格林公式了？

Well , if you know that your vector field is defined everywhere in a simply connected region , then you don 't have to worry about this question of , can I apply Green 's theorem to the inside ?

期末考也可能会用得上，实际上，真的不会有十分复杂的问题，不过你们也要大概地了解一下，这个关于单连通区域的知识点。

And , maybe on the final it would be , there won 't be any really , really complicated things probably , but you might need to be at least vaguely aware of this issue of things being simply connected .

一个向量场，如果定义在单连通区域并且旋度为零，那么它就是一个梯度场，并且其上的线积分与路径无关。

OK , so , we 've seen that if we have a vector field defined in a simply connected region , and its curl is zero , then it 's a gradient field , and the line integral is path independent .

文中还定义了平面单连通多边形区域的所谓分层三角剖分，并确定了此剖分下二次样条空间的维数。

Then , a new kind of so-called stratified triangulation of a simply connected planar polygonal region is introduced .

本文介绍了一种基于边界追踪的freeman链码获取算法，算法可以快速获取二值图像中连通体边界线的freeman链码，不仅适用于单连通的简单区域，对于多连通的孔洞区域同样有效。

An algorithm based on contour tracing for obtaining freeman codes is proposed in this paper . The proposed algorithm can obtain freeman codes of the components ' contours in a binary image . And this algorithm fits not only for single-connected region but also for multi-connected region .

该算法能处理多个区域的情况和区域为单连通或复连通区域的情况；

The improved algorithm can deal with multiple regions , single connected domain and multiple connected domain .