This paper provides a functional equation astisfied by the generating function for enumerating rooted loopless planar maps with vertex partition. A kind of applications in enumerating, by providing explicit formulae, ...This paper provides a functional equation astisfied by the generating function for enumerating rooted loopless planar maps with vertex partition. A kind of applications in enumerating, by providing explicit formulae, a type of rooted loopless planar maps with the maximum valency of vertices given are described. Meanwhile, the functional equation for enumerating rooted loopless planar maps (connected) with the edge number and the valency of root-vertex as the parameters is also derived directly.展开更多
In this paper we enumerate the rooted dual loopless nonseparable near-triangular maps on the sphere and the projective plane with the valency of root-face and the number of inner faces as parameters. Explicit expressi...In this paper we enumerate the rooted dual loopless nonseparable near-triangular maps on the sphere and the projective plane with the valency of root-face and the number of inner faces as parameters. Explicit expressions of enumerating functions are derived for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for the rooted 2-connected triangular maps on the projective plane, from which asymptotics evaluations are derived.展开更多
The functional equation satisfied by the vertex partition function of rooted loopless Eulerianplanar maps is provided. As applications, the enumerating equations for general and regular casesof this kind of maps are a...The functional equation satisfied by the vertex partition function of rooted loopless Eulerianplanar maps is provided. As applications, the enumerating equations for general and regular casesof this kind of maps are also discussed.展开更多
Terminologies not explained here refer to [1] on enumeration, to [2, 3] on functional equations, and to [4] on combinatorial maps. Let (?) be a set of all rooted planar maps. For N∈(?); let m(N) and n_i(N), i≥1 repr...Terminologies not explained here refer to [1] on enumeration, to [2, 3] on functional equations, and to [4] on combinatorial maps. Let (?) be a set of all rooted planar maps. For N∈(?); let m(N) and n_i(N), i≥1 represent the valency of the root-vertex and the number of non-root-vertices with valency i in N. All maps considered here are rooted loopless Eulerian planar maps. Let ? be a set of展开更多
It is shown that the lower bound on the maximum genus of a 3-edge connected loopless graph is at least one-third of its cycle rank. Moreover, this lower bound is tight. There are infinitely such graphs attaining the b...It is shown that the lower bound on the maximum genus of a 3-edge connected loopless graph is at least one-third of its cycle rank. Moreover, this lower bound is tight. There are infinitely such graphs attaining the bound.展开更多
传统单相级联H桥(cascaded H-bridge,CHB)变流器采用dq控制,在电网电压畸变情况下,控制性能受锁相环影响较大。为此,文章提出电网电压畸变下的单相CHB变流器无锁相环控制方法。首先通过构造级联延迟信号消除(cascaded delayed signal ca...传统单相级联H桥(cascaded H-bridge,CHB)变流器采用dq控制,在电网电压畸变情况下,控制性能受锁相环影响较大。为此,文章提出电网电压畸变下的单相CHB变流器无锁相环控制方法。首先通过构造级联延迟信号消除(cascaded delayed signal cancellation,CDSC)模块,快速提取电网电压基波信号;然后将其矢量化,根据瞬时有功功率、无功功率和电压、电流之间的关系计算参考电流信号,完成对有功电流、无功电流的独立控制。此外,通过电网电压前馈进一步减轻电网电压畸变对电网电流的影响;并由此完成各H桥直流侧的电压平衡控制。与传统的dq控制相比,无锁相环控制方法消除了构造正交电流信号造成的延时。三单元CHB变流器的仿真和实验结果证明了所提方法在电网电压畸变情况下的有效性。展开更多
基金This research was partially supported by the U. S. National Science Foundation under Grant Number ECS 85-03212 and by the National Natural Science Foundation of China as well. And, it was completed during the author's stay at RUTCOR, The State Univerity
文摘This paper provides a functional equation astisfied by the generating function for enumerating rooted loopless planar maps with vertex partition. A kind of applications in enumerating, by providing explicit formulae, a type of rooted loopless planar maps with the maximum valency of vertices given are described. Meanwhile, the functional equation for enumerating rooted loopless planar maps (connected) with the edge number and the valency of root-vertex as the parameters is also derived directly.
基金NNSF of China(10271048, 60373030)the Tenth Five Year Plan of the 211 Project Foundation of Central University for Nationalities
文摘In this paper we enumerate the rooted dual loopless nonseparable near-triangular maps on the sphere and the projective plane with the valency of root-face and the number of inner faces as parameters. Explicit expressions of enumerating functions are derived for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for the rooted 2-connected triangular maps on the projective plane, from which asymptotics evaluations are derived.
基金This project is supported partially by the National Natural Science Foundation of China Grant 18971061
文摘The functional equation satisfied by the vertex partition function of rooted loopless Eulerianplanar maps is provided. As applications, the enumerating equations for general and regular casesof this kind of maps are also discussed.
基金Project supported by the National Natural Science Foundation of China
文摘Terminologies not explained here refer to [1] on enumeration, to [2, 3] on functional equations, and to [4] on combinatorial maps. Let (?) be a set of all rooted planar maps. For N∈(?); let m(N) and n_i(N), i≥1 represent the valency of the root-vertex and the number of non-root-vertices with valency i in N. All maps considered here are rooted loopless Eulerian planar maps. Let ? be a set of
文摘It is shown that the lower bound on the maximum genus of a 3-edge connected loopless graph is at least one-third of its cycle rank. Moreover, this lower bound is tight. There are infinitely such graphs attaining the bound.
文摘传统单相级联H桥(cascaded H-bridge,CHB)变流器采用dq控制,在电网电压畸变情况下,控制性能受锁相环影响较大。为此,文章提出电网电压畸变下的单相CHB变流器无锁相环控制方法。首先通过构造级联延迟信号消除(cascaded delayed signal cancellation,CDSC)模块,快速提取电网电压基波信号;然后将其矢量化,根据瞬时有功功率、无功功率和电压、电流之间的关系计算参考电流信号,完成对有功电流、无功电流的独立控制。此外,通过电网电压前馈进一步减轻电网电压畸变对电网电流的影响;并由此完成各H桥直流侧的电压平衡控制。与传统的dq控制相比,无锁相环控制方法消除了构造正交电流信号造成的延时。三单元CHB变流器的仿真和实验结果证明了所提方法在电网电压畸变情况下的有效性。
基金Supported by NSFC(No.10271017,No.11371133)Natural Science Foundation Project of Chongqing(No.cstc2012jjA00041)Chongqing Innovation Fund(No.KJTD201321)
