ON THE CROSSING NUMBER OF THE COMPLETE TRIPARTITE GRAPH K_(1,8,n)

The well known Zarankiewicz' conjecture is said that the crossing number of the complete bipartite graph Km,n (m≤n) is Z(m,n). where Z(m,n) = [m/2] [(m-1)/2] [n/2] [(n-1)/2](for and real number x, [x] denotes the maximal integer no more than x). Presently, Zarankiewicz' conjecture is proved true only for the case m≤G. In this article, the authors prove that if Zarankiewicz' conjecture holds for m≤9, then the crossing number of the complete tripartite graph K1,8,n is Z(9, n) 12[n/2].     

Nonadiabatic quantum dynamics of Br2 in solid Ar: A four-dimensional study of the B to C state predissociation

Quantum dynamics simulations are performed for a diatomics-in-molecules based model of Br₂ in solid Ar which incorporates four nuclear degrees of freedom and four electronic states. The nuclear motions comprise two large amplitude coordinates describing the Br₂ bond distance and an effective symmetry-preserving matrix mode. Two symmetry-lowering harmonic modes are added in the spirit of linear vibronic coupling theory. Initiating the dynamics on the B state by means of an ultrafast laser pulse, nonadiabatic transitions to the two degenerate C states are monitored and the effect of vibrational preexcitation in the electronic ground state is investigated.     

On edges crossing few other edges in simple topological complete graphs

We study the existence of edges having few crossings with the other edges in drawings of the complete graph (more precisely, in simple topological complete graphs). A topological graphT=(V,E) is a graph drawn in the plane with vertices represented by distinct points and edges represented by Jordan curves connecting the corresponding pairs of points (vertices), passing through no other vertices, and having the property that any intersection point of two edges is either a common end-point or a point where the two edges properly cross. A topological graph is simple if any two edges meet in at most one common point.Let h=h(n) be the smallest integer such that every simple topological complete graph on n vertices contains an edge crossing at most h other edges. We show that Ω(n^3/2)≤h(n)≤O(n²/log^1/4n). We also show that the analogous function on other surfaces (torus, Klein bottle) grows as cn².     

弹性半空间地基上四边自由矩形板稳态振动的解析解

采用双重Fourier变换,分析得到弹性半空间地基受竖向稳态荷载作用下的积分变换解．与四边自由矩形板的振动解析解相结合,得出弹性半空间地基上四边自由矩形板稳态振动的解析解．还给出算例及参数影响分析．     

Influence of experimental methods on crossing in magnetic force–gap hysteresis curve of HTS maglev system

The crossing in magnetic levitation force–gap hysteresis curve of melt high-temperature superconductor (HTS) vs. NdFeB permanent magnet (PM) was experimentally studied. One HTS bulk and PM was used in the experiments. Four experimental methods were employed combining of high/low speed of movement of PM with/without heat insulation materials (HIM) enclosed respectively. Experimental results show that crossing of the levitation force–gap curve is related to experimental methods. A crossing occurs in the magnetic force–gap curve while the PM moves approaching to and departing from the sample with high or low speed of movement without HIM enclosed. When the PM is enclosed with HIM during the measurement procedures, there is no crossing in the force–gap curve no matter high speed or low speed of movement of the PM. It was found experimentally that, with the increase of the moving speed of the PM, the maximum magnitude of levitation force of the HTS increases also. The results are interpreted based on Maxwell theories and flux flow-creep models of HTS.     

Asymmetrical edges induced strong current-polarization in embedded graphene nanoribbons

We investigate the electronic structures and transport properties of the embedded zigzag graphene nanoribbon (E-ZGNR) in hexagonal boron nitride trenches, which are achievable in recent experiments. Our first principles results show that the E-ZGNR has a significant enhanced conductivity relative to common ZGNRs due to the existence of asymmetrical edge structures. Moreover, only one spin-orientation electrons possess a widely opened band gap at the magnetic ground state with anti-ferromagnetic configuration, resulting in a full current-polarization at low bias region. Our findings indicate that the state-of-the-art embedding technology is quite useful for tuning the electronic structure of ZGNR and building possible spin injection and spin filter devices in spintronics.     

Aggregation of ferromagnetic and paramagnetic atoms at edges of graphenes and graphite

In this work we report that when ferromagnetic metals (Fe,Co and Ni) are thermally evaporated onto n-layer graphenes and graphite,a metal nanowire and adjacent nanogaps can be found along the edges regardless of its zigzag or armchair structure.Similar features can also be observed for paramagnetic metals,such as Mn,Al and Pd.Meanwhile,metal nanowires and adjacent nanogaps cannot be found for diamagnetic metals (Au and Ag).An external magnetic field during the evaporation of metals can make these unique features disappear for ferromagnetic and paramagnetic metal;and the morphologies of diamagnetic metal do not change after the application of an external magnetic field.We discuss the possible reasons for these novel and interesting results,which include possible one-dimensional ferromagnets along the edge and edge-related binding energy.     

基于三次样条插值的图像多尺度方向边缘重构

为了检测小结构的轮廓以及大目标的边缘,将多尺度边缘检测与小波变换有机地结合起来,利用小波分析方法来研究信号的多尺度边缘特征。针对图像信号的多尺度边缘检测和重构问题,利用二进小波变换的多尺度分析特性,定义了图像在水平和垂直方向的多尺度边缘。同时,利用三次样条插值算法,提出了一种由二进小波变换在水平和垂直方向的极值重构图像信号的算法。实验结果显示多尺度重建方法与著名的交替投影算法相比,算法复杂度低,图像重建速度提高了20倍,而且重建图像质量较好,其峰值信噪比提高了1 dB以上。     

Simulation of pedestrian flow based on cellular automata: A case of pedestrian crossing street at section in China

One of the purposes of pedestrian studies is to evaluate the effects of a proposed program on the pedestrian facilities before its implementation. In order to evaluate the level of service (LOS) of a pedestrian facility, a microscopic model is built to simulate the process of pedestrian crossing street. Most of the existing models focus on the occupant evacuation flow in buildings; however, they are not appropriate for pedestrians in the traffic. According to the characteristics of pedestrian crossing street at signalized crosswalks, we build a model based on cellular automata. Both of the system size and cell size are coordinate with the reality. Depending on the contrast of three parameters of pedestrian flow between simulation data and the reality data, we found that this model is analogous to the real process of pedestrian crossing street at signalized sections. Finally, simulation and its results can provide guidance for evaluating the effects of pedestrian facilities before their implementation.