The triangular kagomé lattices revisited

The dimer problem, Ising spins and bond percolation on the triangular kagomé lattice have been studied extensively by physicists. In this paper, based on the fact the triangular kagomé lattice with toroidal boundary condition can be regarded as the line graph of 3.12.12 lattice with toroidal boundary condition, we derive the formulae of the number of spanning trees, the energy, and the Kirchhoff index of the triangular kagomé lattice with toroidal boundary condition.     

Connections between Wiener index and matchings

Let T be an acyclic molecule with n vertices, and let S(T) be the acyclic molecule obtained from T by replacing each edge of T by a path of length two. In this work, we show that the Wiener index of T can be explained as the number of matchings with n−2 edges in S(T). Furthermore, some related results are also obtained MSC: 05C12 Weigen Yan: This work is supported by FMSTF (2004J024) and NSFF(E0540007) Yeong-Nan Yeh: Partially supported by NSC94-2115-M001-017     

Asymptotic energy of lattices

The energy of a simple graph G arising in chemical physics, denoted by E(G), is defined as the sum of the absolute values of eigenvalues of G. As the dimer problem and spanning trees problem in statistical physics, in this paper we propose the energy per vertex problem for lattice systems. In general for a type of lattice in statistical physics, to compute the entropy constant with toroidal, cylindrical, Mobius-band, Klein-bottle, and free boundary conditions are different tasks with different hardness and may have different solutions. We show that the energy per vertex of plane lattices is independent of the toroidal, cylindrical, Mobius-band, Klein-bottle, and free boundary conditions. In particular, the asymptotic formulae of energies of the triangular, 3³.4², and hexagonal lattices with toroidal, cylindrical, Mobius-band, Klein-bottle, and free boundary conditions are obtained explicitly.     

ZigBee技术在塔吊安全监测预警系统中的应用

针对建设工程塔吊安全监测的现状,将ZigBee技术应用于塔吊安全监测预警系统,设计专用WSN节点,实现位移、压力和距离监测功能;将现场监测数据通过WSN节点及时上传到监控中心PC机进行实时显示和处理,如果监测数据超出报警值,立即发出报警信号,从而有效地预防塔吊事故发生,确保塔吊运行安全;经组网调试,系统性能稳定可靠,测量数据误差小于5%,传输距离可达1 km 以上,具有较高的性价比和推广应用价值。     

具收获项的Ⅱ类功能反应的捕-食系统的定性分析Ⅱ

在文[7][8]的基础上,分析一类食饵具常数收获项的Ⅱ类功能反应的捕食系统．通过对两鞍点分界线相互位置仔细的分析,得到了比较完备的定性结论,特别是第一次在生态系统的讨论中得到了三个极限环的存在性．