http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
ENUMERATION OF LOOPLESS MAPS ON THE PROJECTIVE PLANE
Li, Zhaoxiang,Liu, Yanpei 한국전산응용수학회 2002 Journal of applied mathematics & informatics Vol.10 No.1
In this paper we study the rooted loopless maps on the sphere and the projective plane with the valency of root-face and the number of edges as parameters. Explicit expression of enumerating function is obtained for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane, from which asymptotic evaluations are derived.
CHROMATIC SUMS OF ROOTED TRIANGULATIONS ON THE PROJECTIVE PLANE
LI, ZHAOXIANG,LIU, YANPEI 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1
In this paper we study the chromatic sum functions for rooted nonseparable near-triangular maps on the projective plane. A chromatic sum equation for such maps is obtained.
ZHAOXIANG LI,YANPEI LIU 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
A map is bisingular if each edge is either a loop or an isthmus (i.e., on the boundary of the same face). In this paper we study the number of rooted bisingular maps on the sphere and the torus, and we also present formula for such maps with four parameters: the root-valency,the number of isthmus, the number of planar loops and the number of essential loops.
Chromatic sums of rooted triangulations on the projective plane$^{**}$
Zhaoxiang Li,Yanpei Liu 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.18 No.1-2
In this paper we study the chromatic sum functions for rooted nonseparable near-triangular maps on the projective plane. A chromatic sum equation for such maps is obtained.
Li, Zhaoxiang,Liu, Yanpei 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
A map is bisingular if each edge is either a loop or an isthmus (i.e., on the boundary of the same face). In this paper we study the number of rooted bisingular maps on the sphere and the torus, and we also present formula for such maps with four parameters: the root-valency, the number of isthmus, the number of planar loops and the number of essential loops.
Chromatic sums of singular maps on some surface
Zhaoxiang Li,Yanpei Liu 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.15 No.-
A map is singular if each edge is on the same face on a surface (i.e., those have only one face on a surface). Because any map with loop is not colorable, all maps here are assumed to be loopless. In this paper povides the explicit expression of chromatic sum functions for rooted singular maps on the projective plane, the torus and the Klein bottle. From the explicit expression of chromatic sum functions of such maps, the explicit expression of enumerating functions of such maps are also derived.
CHROMATIC SUMS OF NONSEPARABLE SIMPLE MAPS ON THE PLANE
Li, Zhaoxiang,Liu, Yanpei 한국전산응용수학회 2003 Journal of applied mathematics & informatics Vol.12 No.1
In this paper we study the chromatic sum functions for rooted nonseparable simple maps on the plane. The chromatic sum function equation for such maps is obtained . The enumerating function equation of such maps is derived by the chromatic sum equation of such maps. From the chromatic sum equation of such maps, the enumerating function equation of rooted nonseparable simple bipartite maps on the plane is also derived.
Enhanced Li storage performance of ordered mesoporous MoO2 via tungsten doping.
Fang, Xiangpeng,Guo, Bingkun,Shi, Yifeng,Li, Bin,Hua, Chunxiu,Yao, Chaohua,Zhang, Yichi,Hu, Yong-Sheng,Wang, Zhaoxiang,Stucky, Galen D,Chen, Liquan RSC Pub 2012 Nanoscale Vol.4 No.5
<P>Ordered mesoporous tungsten-doped MoO(2) was synthesized by a nanocasting method. The Li storage performance of mesoporous MoO(2) is significantly improved by tungsten doping, which exhibits a reversible capacity of 700 mA h g(-1), better cycling and rate performance. This material combines the advantages of the high theoretical capacity of MoO(2) and the better electroactivity of WO(2).</P>
Saddle point and generalized convex duality for multiobjective programming
Zhaoxiang Yan,Shizheng Li 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.15 No.-
In this paper we consider the dual problems for multiobjec-tive programming with generalized convex functions. We obtain the weakduality and the strong duality. At last,we give an equivalent relationshipbetween saddle point and ecient solution in multiobjective programming.