An upper bound for the crossing number of augmented cubes

A {\it good drawing} of a graph $G$ is a drawing where the edges are non-self-intersecting and each two edges have at most one point in common, which is either a common end vertex or a crossing. The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a good drawing of $G$ in the plane. The {\it $n$-dimensional augmented cube} $AQ_n$, proposed by S.A. Choudum and V. Sunitha, is an important interconnection network with good topological properties and applications. In this paper, we obtain an upper bound on the crossing number of $AQ_n$ less than $26/324^{n}-(2n^2+7/2n-6)2^{n-2}$.Comment: 39 page

The crossing number of locally twisted cubes

The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a drawing of $G$. Motivated by the recent work [Faria, L., Figueiredo, C.M.H. de, Sykora, O., Vrt'o, I.: An improved upper bound on the crossing number of the hypercube. J. Graph Theory {\bf 59}, 145--161 (2008)] which solves the upper bound conjecture on the crossing number of $n$-dimensional hypercube proposed by Erd\H{o}s and Guy, we give upper and lower bounds of the crossing number of locally twisted cube, which is one of variants of hypercube.Comment: 17 pages, 12 figure

Dual terahertz comb spectroscopy with a single free-running fibre laser

Dual THz comb spectroscopy has the potential to be used as universal THz spectroscopy with high spectral resolution, high spectral accuracy, and broad spectral coverage; however, the requirement for dual stabilized femtosecond lasers hampers its versatility due to the bulky size, high complexity, and high cost. We here report the first demonstration of dual THz comb spectroscopy using a single free-running fibre laser. By tuning the cavity-loss-dependent gain profile with an intracavity Lyot filter together with precise management of the cavity length and dispersion, dual-wavelength pulsed light beams with slightly detuned repetition frequencies are generated in a single laser cavity. Due to sharing of the same cavity, such pulsed light beams suffer from common-mode fluctuation of the repetition frequency, and hence the corresponding frequency difference between them is passively stable around a few hundred hertz within millihertz fluctuation. This considerably stable frequency difference enables dual THz comb spectroscopy with a single free-running fibre laser. While greatly reducing the size, complexity, and cost of the laser source by use of a single free-running fibre laser, the dual THz comb spectroscopy system maintains a spectral bandwidth and dynamic range of spectral power comparable to a system equipped with dual stabilized fibre lasers, and can be effectively applied to high-precision spectroscopy of acetonitrile gas at atmospheric pressure. The demonstrated results indicate that this system is an attractive solution for practical applications of not only THz spectroscopy but also THz-pulse-based measurements.Comment: 29 pages, 7 figure

Optimal Design of Wetland Ecological Water in the Shuangtaizi Estuary, Panjin

AbstractThe protection and utilization of wetland have been more and more important. According to measured water levels, discharge and cross-sections of the Shuangtaizi River network, this paper builds a hydrodynamic model to simulate water and salt movement based on the Mike11. The model was calibrated and validated by measured water levels of July, 2009. A series of irrigation scheme for the reed field were designed according to the hydrological characteristics of the wetland. The results show that volume of water shortage is 65.1 million cubic meters in dry years, 4.2 million cubic meters in average years and 40.5 million cubic meters in wet years. With the expansion of water facilities, the water shortage reduced to 30.6 million cubic meters, 16.3 million cubic meters and 17.4 million cubic meters respectively in dry years, average years and wet years. In wet years and average years, salinity of tidal prism water can satisfy the requirements of irrigation. However, due to high tide salinity in dry years, irrigation can not be directly used for the reed field