In this paper the problem of topological classification of ordinary 3D)and planar(2D)spin states in a ferromagnet including an annular cavity is discussed. It is verified that the set of homotopy classes of either 3D ...In this paper the problem of topological classification of ordinary 3D)and planar(2D)spin states in a ferromagnet including an annular cavity is discussed. It is verified that the set of homotopy classes of either 3D or 2D spin states in such ordered medium can be constructed into the groups isomorphic to Z, the additive group of integers.展开更多
A fractal square F is essentially a planar self-similar set satisfying the set equation F=(F+D)/n with n≥2 and D?{0,1,...,n-1}~2.In this paper,we study the topological classification of fractal squares in the case of...A fractal square F is essentially a planar self-similar set satisfying the set equation F=(F+D)/n with n≥2 and D?{0,1,...,n-1}~2.In this paper,we study the topological classification of fractal squares in the case of n=4 and |D|=4.展开更多
Equilibrium points and periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as deep space exploring missions. The dipole segment is a g...Equilibrium points and periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as deep space exploring missions. The dipole segment is a good alternative model to study qualitative dynamical properties near dumbbell-shaped asteroids. In this paper, the dipole segment model and its equilibrium points are simply introduced. The stability of the two triangular equilibrium points of the system is numerically examined. Next, periodic orbits are presented around the dipole segment model in two different cases, in which triangular equilibria are linearly stable and unstable,respectively. New types of periodic orbits are illustrated in detail, including their orbital shapes, periods and the Jacobi integral.The orbital stability, topological classification and bifurcations of these orbits are also analyzed with numerical continuations.展开更多
文摘In this paper the problem of topological classification of ordinary 3D)and planar(2D)spin states in a ferromagnet including an annular cavity is discussed. It is verified that the set of homotopy classes of either 3D or 2D spin states in such ordered medium can be constructed into the groups isomorphic to Z, the additive group of integers.
基金Supported by the Soft Science Research of Xiangyang City in 2019。
文摘A fractal square F is essentially a planar self-similar set satisfying the set equation F=(F+D)/n with n≥2 and D?{0,1,...,n-1}~2.In this paper,we study the topological classification of fractal squares in the case of n=4 and |D|=4.
基金supported by the National Natural Science Foundation of China(Grant Nos.11602019&11572035)the Young Elite Scientist Sponsorship Program by China Association for Science and Technology(Grant No.2016QNRC001)Excellent Young Teachers Program of Beijing Institute of Technology(Grant No.2015YG0605)
文摘Equilibrium points and periodic orbits in irregular gravitational fields are significant for an understanding of dynamical behaviors around asteroids as well as deep space exploring missions. The dipole segment is a good alternative model to study qualitative dynamical properties near dumbbell-shaped asteroids. In this paper, the dipole segment model and its equilibrium points are simply introduced. The stability of the two triangular equilibrium points of the system is numerically examined. Next, periodic orbits are presented around the dipole segment model in two different cases, in which triangular equilibria are linearly stable and unstable,respectively. New types of periodic orbits are illustrated in detail, including their orbital shapes, periods and the Jacobi integral.The orbital stability, topological classification and bifurcations of these orbits are also analyzed with numerical continuations.
