Motivated by the connection with the genus of the corresponding link and its application on DNA polyhedral links,in this paper,we introduce a parameter smax(G),which is the maximum number of circles of states of the link diagram D(G)corresponding to a plane(positive)graph G.We show that smax(G)does not depend on the embedding of G and if G is a 4-edge-connected plane graph then smax(G)is equal to the number of faces of G,which cover the results of S.Y.Liu and H.P.Zhang as special cases. 相似文献
A bounded linear operator T acting on a Hilbert space is called Coburn operator if ker(T ? λ) = {0} or ker(T ? λ)*= {0} for each λ ∈ C. In this paper, the authors define other Coburn type properties for Hilbert space operators and investigate the compact perturbations of operators with Coburn type properties. They characterize those operators for which has arbitrarily small compact perturbation to have some fixed Coburn property.Moreover, they study the stability of these properties under small compact perturbations. 相似文献
This paper presents a long-term analysis of one-stage extended Runge–Kutta–Nyström (ERKN) integrators for highly oscillatory Hamiltonian systems. We study the long-time numerical energy conservation not only for symmetric integrators but also for symplectic integrators. In the analysis, we neither assume symplecticity for symmetric methods, nor assume symmetry for symplectic methods. It turns out that these both types of integrators have a near conservation of the total and oscillatory energy over a long term. To prove the result for explicit integrators, a relationship between ERKN integrators and trigonometric integrators is established. For the long-term analysis of implicit integrators, the above approach does not work anymore and we use the technology of modulated Fourier expansion. By taking some adaptations of this technology for implicit methods, we derive the modulated Fourier expansion and show the near energy conservation.