| 1. | It is clear that for any graph g the space r(g) and r(tg) are homeomorphic .
显然，对任意一个图G，空间R（G）和空间R（TG）是同胚的。 |
| 2. | A necessary and sufficient condition on diffeomorphisms
关于微分同胚的一个充分必要条件 |
| 3. | Properties of topologically stable homeomorphism on compact manifold
拓扑稳定同胚的性质 |
| 4. | The present paper presents the chain recurrent set with the expansive homeomorphism and shadowing properties and this connection for the mistake in literature [ 1 ] and its proof
摘要给出具有跟踪性可扩同胚的链回归集的几个性质，指出以往文献中证明链回归集无环性时的错误之处，并给出严格的证明。 |
| 5. | Abstract : the present paper presents the chain recurrent set with the expansive homeomorphism and shadowing properties and this connection for the mistake in literature 1 and its proof
文摘:给出具有跟踪性可扩同胚的链回归集的几个性质，指出以往文献中证明链回归集无环性时的错误之处，并给出严格的证明 |
| 6. | In section 2 . 4 , a sufficient condition is given for a distal homeomorphism not having the potp . in the end of this section , we describe the distal homeomorphisms of intervals and circles . in chapter , we study some other shadowing properties
4节给出了紧致度量空间上的distal自同胚不具有伪轨跟踪性的一个充分条件，并给出了区间上和圆周上distal同胚的等价刻划。 |
| 7. | In the framework , a control mesh may be arbitrary one - dimensional or two - dimensional orientated topological manifold , and the curve or surface is defined on differential manifold homeomorphic to the control mesh with a potential function as its basis functions . this method is an extension of nurbs , which efficiently overcomes the limitations of nurbs
广义有理参数曲线曲面定义在与控制网格拓扑同胚的微分流形上，以高度一般的势函数为基函数，其控制网格可以是任意的一维拓扑流形和二维可定向拓扑流形。 |
| 8. | Its properties and design method is discussed in chapter 4 . for control meshes with arbitrary topology , we present a universal method in chapter 5 to construct parametric curves and surfaces . generalized rational parametric surface can be controlled precisely and flexible , and it is easy to model local features and 3d primitives
然后，在第五章中，我们将控制网格进一步推广到任意可定向二维拓扑流形，提出了一个通用的方法将控制网格映射到与之拓扑同胚的微分流形上，统一了广义有理参数曲线曲面的构造过程。 |
