The domination number and the least QQ-eigenvalue

A vertex set $D$ of a graph $G$ is said to be a dominating set if every vertex of $V(G)\setminus D$ is adjacent to at least a vertex in $D$, and the domination number $\gamma(G)$ ($\gamma$, for short) is the minimum cardinality of all dominating sets of $G$. For a graph, the least $Q$-eigenvalue is the least eigenvalue of its signless Laplacian matrix. In this paper, for a nonbipartite graph with both order $n$ and domination number $\gamma$, we show that $n\geq 3\gamma-1$, and show that it contains a unicyclic spanning subgraph with the same domination number $\gamma$. By investigating the relation between the domination number and the least $Q$-eigenvalue of a graph, we minimize the least $Q$-eigenvalue among all the nonbipartite graphs with given domination number.Comment: 13 pages, 3 figure

A New Method for Fast Computation of Moments Based on 8-neighbor Chain CodeApplied to 2-D Objects Recognition

2D moment invariants have been successfully applied in pattern recognition tasks. The main difficulty of using moment invariants is the computational burden. To improve the algorithm of moments computation through an iterative method, an approach for fast computation of moments based on the 8-neighbor chain code is proposed in this paper. Then artificial neural networks are applied for 2D shape recognition with moment invariants. Compared with the method of polygonal approximation, this approach shows higher accuracy in shape representation and faster recognition speed in experiment

Zc(3900)Z_c(3900) as a DDˉ∗D\bar{D}^* molecule from the pole counting rule

A comprehensive study on the nature of the $Z_c(3900)$ resonant structure is carried out in this work. By constructing the pertinent effective Lagrangians and considering the important final-state-interaction effects, we first give a unified description to all the relevant experimental data available, including the $J/\psi\pi$ and $\pi\pi$ invariant mass distributions from the $e^+e^-\to J/\psi\pi\pi$ process, the $h_c\pi$ distribution from $e^+e^-\to h_c\pi\pi$ and also the $D\bar D^{*}$ spectrum in the $e^+e^-\to D\bar D^{*}\pi$ process. After fitting the unknown parameters to the previous data, we search the pole in the complex energy plane and find only one pole in the nearby energy region in different Riemann sheets. Therefore we conclude that $Z_c(3900)$ is of $D\bar D^*$ molecular nature, according to the pole counting rule method~[Nucl.~Phys.~A543, 632 (1992); Phys.~Rev.~D 35,~1633 (1987)]. We emphasize that the conclusion based upon the pole counting method is not trivial, since both the $D\bar D^{*}$ contact interactions and the explicit $Z_c$ exchanges are introduced in our analyses and they lead to the same conclusion.Comment: 21 pages, 9 figures. To match the published version in PRD. Additional discussion on the spectral density function is include

Effects of Mo on the Microstructure and Hydrogen Sorption Properties of Ti-Mo Getters

AbstractThe effects of Mo on the microstructure evolution, porosity and hydrogen sorption properties of Ti-Mo getters are investigated in this work. The results show that the addition of Mo prolongs the densification process of Ti-Mo getters and results in a significant amount of sintered pores. With the Mo content increasing, the porosity of getters firstly increases reaching the maximum value as it attains about 7.5wt.%, and then drops. At the room temperature, the hydrogen sorption property of getters increases progressively with the Mo content increasing, but the tendency is not very clear before its content lies below 2.5wt.%. When the Mo content achieves about 7.5wt.%, the hydrogen sorption property proves to be the best. The discussion is made about the above mentioned phenomena inclusive of hydrogen sorption properties of getters under different activation conditions (from 500–750 °C)

Experimental Equilibrium Moisture Content of Wood Under Vacuum

Wood equilibrium moisture content (EMC) was measured under vacuum by an electronic method. A wafer was used to measure EMC using an in-house designed vacuum instrument. EMC at 4 to 100 kPa and temperature from 30 to 90°C were measured. The relationships among temperature, pressure, and EMC were determined, and a diagram of wood EMC was produced. The results showed there are obvious differences between experimental EMC values obtained and theoretical EMC values of other researchers. It is suggested that corrections should be introduced into theoretical models or a new model for the vacuum condition developed