(Anti-)de Sitter Black Hole Entropy and Generalized Uncertainty Principle

We generalize the method that is used to study corrections to Cardy-Verlinde formula due to generalized uncertainty principle and discuss corrections to Cardy-Verlinde formula due to generalized uncertainty principle in (anti)-de Sitter space. Because in de Sitter black hole spacetime the radiation temperature of the black hole horizon is different from the one of the cosmological horizon, this spacetime is a thermodynamical non-equilibrium spacetime.     

Positive periodic solution for a two-species ratio-dependent predator-prey system with time delay and impulse

A two-species ratio-dependent predator-prey model with time delay and impulse is investigated. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.     

2-巯基苯并咪唑保护的铜纳米团簇的制备及银离子检测

以2-巯基苯并咪唑为保护剂,聚乙烯吡咯烷酮为稳定剂,水合肼为还原剂,“一锅法”合成2-巯基苯并咪唑保护的,高稳定性、强荧光、大斯托克斯位移的铜纳米团簇(Cu NCs),并用于检测水样中的银离子含量。采用透射电子显微镜(TEM)和X射线光电子能谱(XPS)对铜纳米团簇的结构进行表征,通过荧光光谱和紫外可见光谱对其光学性能进行研究。研究表明:该铜纳米团簇的最大激发和发射波长分别为340和558 nm,在日光灯和紫外灯下分别为无色和橙色。Cu NCs具有较高的分散性,尺寸大小为2~3 nm。在最佳反应条件下,铜纳米团簇可以选择性地被银离子猝灭,且灵敏度高,线性范围为1~40μmol/L,检测限为0.5μmol/L。该方法用于检测实际水样(自来水、湖水)中银离子的浓度,结果令人满意,表明在环境监测中有非常高的应用价值。     

Influence of the laser parameters on the space and time characteristics of an aluminum laser-induced plasma

In this work, an aluminum laser plasma produced in ambient air at atmospheric pressure by laser pulses at a fluence of 10 J/cm² is characterized by time- and space-resolved measurements of electron density and temperature. Varying the laser pulse duration from 6 ns to 80 fs and the laser wavelength from ultraviolet to infrared only slightly influences the plasma properties. The temperature exhibits a slight decrease both at the plasma edge and close to the target surface. The electron density is found to be spatially homogeneous in the ablation plume during the first microsecond. Finally, the plasma expansion is in good agreement with the Sedov's model during the first 500 ns and it becomes subsonic, with respect to the velocity of sound in air, typically 1 μs after the plasma creation. The physical interpretation of the experimental results is also discussed to the light of a one-dimensional fluid model which provides a good qualitative agreement with measurements.     

Study of the Optimal Integrated Control of a Dengue Transmission Model北大核心CSCD

建立了一个登革热在蚊子和人之间传播的模型,引入了Wolbachia、自我保护和杀虫剂三种控制措施,分别从常数控制和时变控制两个方面进行探讨。首先,分析了常数控制对模型基本再生数的影响,研究发现:Wolbachia有助于减小基本再生数,且基本再生数与自我保护和杀虫剂呈负相关。其次,以使得感染数最少且实施成本最低为目标,使用Pontryagin极值原理讨论最优控制。最后,通过数值模拟展示了最优控制的效果。     

M-矩阵平方根的一类迭代法

矩阵平方根在数学的许多应用中起着重要的作用.本文研究M-矩阵平方根的计算问题,提出一种计算正则M-矩阵平方根的迭代方法.首先将这个问题转化为M-矩阵代数Riccati方程,进而提出一种有效的方法来求解这个特殊的MARE.理论分析表明,该方法在一定条件下是收敛的.数值实验表明该方法是可行的,且优于二项式迭代法.     

Weak Graph Map Homotopy and Its Applications∗

The authors introduce a notion of a weak graph map homotopy (they call it M-homotopy), discuss its properties and applications. They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001. The difference between them is that the weak graph map homotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages over the graph homotopy transformation. As its applications, they investigate the mapping class group of a graph and the 1-order MP-homotopy group of a pointed simple graph. Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.