Hitting times for random walks on subdivision and triangulation graphs

Let G be a connected graph. The subdivision graph of G, denoted by S(G), is the graph obtained from G by inserting a new vertex into every edge of G. The triangulation graph of G, denoted by R(G), is the graph obtained from G by adding, for each edge uv, a new vertex whose neighbours are u and v. In this paper, we first provide complete information for the eigenvalues and eigenvectors of the probability transition matrix of a random walk on S(G) (res. R(G)) in terms of those of G. Then we give an explicit formula for the expected hitting time between any two vertices of S(G) (res. R(G)) in terms of those of G. Finally, as applications, we show that, the relations between the resistance distances, the number of spanning trees and the multiplicative degree-Kirchhoff index of S(G) (res. R(G)) and G can all be deduced from our results directly.     

The energy and spanning trees of the Aztec diamonds

The Aztec diamond was extensively studied in both graph theory and statistical physics. Knuth obtained a formula of the number of spanning trees of the Aztec diamond with the constrained boundary condition, which solved a conjecture posed by Stanley in 1994. In this paper, We give the formulae of the energy and the number of spanning trees of the Aztec diamond with the toroidal boundary condition.     

Resonance tuning and broadening of bowtie nanoantennas on graphene

Metallic bowtie antennas are used in nanophotonics applications in order to confine the electromagnetic field into volumes much smaller than that of the incident wavelength. Electrically controllable carrier concentration of graphene opens the door to the use of plasmonic nanoantenna structures with graphene so that the resonant nature of nanoantennas can be tuned. In this study, we demonstrated with the Fourier transform infrared (FTIR) spectroscopy and the Finite Difference Time Domain (FDTD) method that the intensity and resonance peak of bowtie nanoantennas on monolayer graphene can be tuned at mid-infrared (MIR) wavelength regime by applying a gate voltage, since the optical properties of graphene change by changing the carrier concentration.     

Numerical simulation for the three-dimension fractional sub-diffusion equation

Fractional sub-diffusion equations have been widely used to model sub-diffusive systems. Most algorithms are designed for one-dimensional problems due to the memory effect in fractional derivative. In this paper, the numerical simulation of the 3D fractional sub-diffusion equation with a time fractional derivative of order $\alpha$ $(0<\alpha <1)$ is considered. A fractional alternating direction implicit scheme (FADIS) is proposed. We prove that FADIS is uniquely solvable, unconditionally stable and convergent in $H^1$ norm by the energy method. A numerical example is given to demonstrate the efficiency of FADIS.     

反反相色谱-串联质谱法直接测定植物源性食品中草甘膦及其代谢物残留

采用反反相色谱-串联质谱法建立了直接测定植物源性食品中草甘膦(GLY)及其主要代谢物氨甲基膦酸(AMPA)的方法。样品用水提取,阴离子交换柱(MAX)净化,以5 mmol/L的乙酸铵溶液和5%水-95%乙腈的乙酸铵溶液为流动相,反反相色谱分离,采用电喷雾离子源、负离子扫描模式和多反应监测模式质谱检测,外标法定量。草甘膦和氨甲基膦酸的线性范围分别为10～500μg/L和20～1 000μg/L,相关系数(r2)均大于0.99。方法的检出限(S/N=3)均为0.01 mg/kg,定量下限(S/N=10)分别为0.02 mg/kg和0.04 mg/kg。在6种基质中,GLY和AMPA在3个加标水平下的回收率为78%～113%,相对标准偏差(RSD,n=6)为3.2%～11.0%。方法的灵敏度和回收率高,选择性好,能满足日常食品检测工作的要求。     

全自动固相萃取/高效液相色谱-串联质谱法（HPLC-MS/MS）测定深海鱼中雪卡毒素残留量

建立了深海鱼鱼肉中雪卡毒素残留的高效液相色谱-串联质谱检测方法。虎鳗等样品经甲醇-正己烷(4∶1)提取,HLB柱净化后,采用高效液相色谱-串联质谱分析,外标法定量。质谱分析采用电喷雾电离,正离子扫描,多反应监测模式。定性离子对为m/z 1 128.9/1 057.6、1 128.9/1 039.9、1 128.9/1 075.8。实验结果表明,HLB柱净化后基质效应明显降低,样品中添加0.01～0.1μg/kg的雪卡毒素,其回收率为70%～84%,相对标准偏差(n=6)小于7%;雪卡毒素的检出限为0.01μg/kg,定量下限为0.02μg/kg。该方法样品前处理简单、分析时间短、灵敏、可靠,适用于深海鱼中雪卡毒素含量的检测。     

考虑退货不确定性的多层次多站点逆向物流网络选址优化研究

在退货量不确定情况下,为追求电商企业逆向物流网络成本最小化,建立了多层次多站点的混合整数规划模型。将目标区域进行网格化处理,通过球上距离公式计算相邻备选站点、不同层次备选点间的运输距离,使用蒙特卡罗法模拟退货量,并设计了双染色体编码的遗传算法进行求解。算例验证了模型算法的可行性,并且得出了逆向物流网络成本最小时,快递站点和退货处理中心的选址,快递站点的选址与退货量大小存在对应关系,研究客户退货量会使物流网络选址得到优化。     

L-fuzzy保序算子空间的ωθ-收敛理论

研究L-fuzzy保序算子空间的ωθ-收敛理论问题。在L-fuzzy保序算子空间中引入分子网和理想的ωθ-极限点和ωθ-聚点等概念,系统讨论了这些概念的特征性质以及它们之间的关系。同时,利用分子网和理想的ωθ-收敛性概念,证明了序同态的(ω1,ω2)θ-连续性的若干充分必要条件。     

单回路物流配送问题的新算法——吞圈法

提出解决单回路物流配送问题的一个新启发式算法——吞圈法,通过实验证明,该方法的求解性能稳定,运算次数少,且求解质量较高,优于经典的最近邻点法和最近插入法,也优于大部分智能化算法,是求解单回路物流配送问题的有效方法.