Collapsed 5-manifolds with pinched positive sectional curvature

Let M be a closed 5-manifold of pinched curvature 0<δ?secM?1. We prove that M is homeomorphic to a spherical space form if one of the following conditions holds:

(i)

The center of the fundamental group has index ?w(δ), a constant depending on δ;

(ii)

and the fundamental group is a non-cyclic group of order ?C, a constant;

(iii)

The volume is less than ?(δ) and the fundamental group is either isomorphic to a spherical 5-space group or has an odd order, and it has a center of index ?w, a constant.

     

K6‐minors in triangulations and complete quadrangulations

In this paper, we shall prove that a projective‐planar (resp., toroidal) triangulation G has K₆ as a minor if and only if G has no quadrangulation isomorphic to K₄ (resp., K₅ ) as a subgraph. As an application of the theorems, we can prove that Hadwiger's conjecture is true for projective‐planar and toroidal triangulations. © 2009 Wiley Periodicals, Inc. J Graph Theory 60: 302‐312, 2009     

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介绍了在已知环形轴对称等离子体平衡位形的条件下,建立磁力线为直线的坐标系的方法。该坐标系被广泛应用于托卡马克等离子体的磁流体稳定性和动理论物理问题的理论分析,但文献中对坐标系建立方法却很少有介绍。结合几类托卡马克位形和球形环位形,对该类坐标系的特征进行了分析。     

螺绕环的电感

给出了螺绕环电感的准确表达式,并对常见问题作了详细的讨论.     

Hamiltonian cycles in bipartite quadrangulations on the torus

In this article, we shall prove that every bipartite quadrangulation G on the torus admits a simple closed curve visiting each face and each vertex of G exactly once but crossing no edge. As an application, we conclude that the radial graph of any bipartite quadrangulation on the torus has a hamiltonian cycle. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory 69:143‐151, 2012     

Clifton-pohl torus and geodesic completeness by a ‘complex’ point of view

We show that a natural complexification and a mild generalization of the idea of completeness guarantee geodesic completeness of Clifton-Pohl torus; we explicitely compute all of its geodesics.     

Knotted pictures of the GHZ states on the surface of a trivial torus

By means of the torus knot theory method, this paper presents the complete process of obtaining the knotted pictures of eight GHZ states on the surface of a trivial torus from the knotted pictures of eight basic three-qubit states on the surface of a trivial torus. Thus, we obtain eight knotted pictures 121 linkage on the ordinary plane.     

CP~n中具有循环调和序列的平坦极小环面

研究具有循环调和序列的平坦极小浸入ψ:T2→CPn。证明了存在T2的一个有限覆盖p:T2→T2和一个全迷向的平坦极小浸入φ:T2→CPn使得ψ。p=A。φ,其中A:CPn→CPn:[v]→[vA]是线性全纯同胚。     

The dynamical feature of transition of a Hamiltonian system to a dissipative system

The mechanism of generation and annihilation of attractors during transition from a Hamiltonian system to a dissipative system is studied numerically using the dissipative standard map. The transient process related to the formation of attracting basins of periodic attractors is studied by discussing the evolution of the KAM tori of the standard map. The result shows that as damping increases, attractors are mainly generated from elliptic orbits of the Hamiltonian system and annihilated by colliding with unstable periodic orbits originating from the corresponding hyperbolic orbits of the Hamiltonian system. The transient process also exhibits the general feature of bifurcation.