曲面的定向

In this paper, firstly, the embeddability of near-triangular graphs on the orientable surface is studied. By using Petersen's Theorem about 1-factor, we first prove that for a near-triangulation on the orientable surface, its geometry dual graph has a 1-factor; then after a procedure of operation leaded by the 1-factor, we show that if a graph G triangulates some orientable surface S_g, then G has a near-triangular embedding in S_h for h = g,g + 1,...,β(G/2」, where β is the Betti number of G. Hence we obtain a conclusion: A near-triangulation of the orientable surface is upper-embeddable. As a generalization, a class of near-quadrangulation is studied, and similar results are obtained.

本文首先研究了近三角剖分图的可定向曲面嵌入性质，通过运用Petersen关于1-因子的定理，首先证明了对于可定向曲面上的三角剖分图，其几何对偶图具有1-因子；然后在1-因子的导向下，通过做一系列增加亏格的手术，证明了如果一个图G三角剖分可定向曲面S_g，那么G可以近三角剖分可定向曲面S_h，这里h=g，g+1，…，「β(G／2」，β是指图G的Betti数，从而得出推论：可定向曲面上的三角剖分图是上可嵌入的，作为推广，又研究了一类近四角剖分图的可定向曲面嵌入性质，并得到类似的结论。

Theorem Let M be a orientable or non-orientable closed surface, and f a C°-flow whose every singular point is isolated. Then f has POTP if and only if the following three conditions hold

定理 设M是任一个可定向或不可定向的闭曲面，f是M上任一个奇点均孤点的C〓-流，则f具有伪轨跟踪性质的充分必要条件是

Using combinatorial thoughts and topological methods,a closed curve system that contains the most number of non-contractible,pair-wise disjoint and pair-wise non-homotopic closed curves on the orientable surface is investigated.

利用组合数学的思想、拓扑的方法研究在可定向曲面上，一类含有个数最多的不可收缩的、两两不相交、互不同伦的圈系统及其性质，得出了关于这些圈的一些拓扑定性性质，并给出这些圈在曲面上的位置分布。

Motivated by this problem, in this paper, we give an upper-embeddable property of one kind of digraphs in orientable surfaces.

受此问题的启发，本文给出了一类有向图在可定向曲面上是上可嵌入的性质。

Secondly, we investigate C°-flows on orientable closed surfaces having POTP, and obtain a necessary and sufficient condition of such flows.

剖析了这些轨道的邻域的轨线结构，还考虑了经过Poisson稳定点及几乎周期点的横截圈和相应的回归映射，其中本文讨论了可定向闭曲面上具有伪轨跟踪性质的C〓-流，得到了可定向闭曲面上C〓-流具有伪轨跟踪性质的较为简洁的充分必要条件；最后本文借助于从可定向的闭曲面到不可定向闭曲面的复叠投射，讨论了不可定向闭曲面上的C〓-流与其提升的轨线之间的联系，解决了不可定向闭曲面上C〓-流具有伪轨跟踪性质的判定问题。

We establish several unique embedding results for 3-connected graphs on orientable surfaces which admit relatively large facial walks and representativity and hence generalize Thomassen's uniqueness theorem on LEW-embeddings.

本文给出了几个关于一般可定向曲面上嵌入图的唯一性定理。结果表明：一些具有大的面迹的可定向嵌入仍然具有唯一性。这在本质上推广了C.Thomassen在LEW-嵌入方面的工作。

Oriented boundary of surface.

曲面的定向边界。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。