Some inequalities for the Bell numbers

In this paper, we present derivatives of the generating functions for the Bell numbers by induction and by the Faà di Bruno formula, recover an explicit formula in terms of the Stirling numbers of the second kind, find the (logarithmically) absolute and complete monotonicity of the generating functions, and construct some inequalities for the Bell numbers. From these inequalities, we derive the logarithmic convexity of the sequence of the Bell numbers.     

基于局部均值的K-近质心近邻光谱分类

天体光谱包含着许多重要的关于天体的物理和化学信息,如天体表面的有效温度、重力加速度以及化学丰度等,天体光谱的处理和分析对天文研究具有重要的科学意义。一些大型巡天计划的实施(如SDSS,LAMOST等)使我们获得了海量的天文光谱数据,因此天文光谱数据的自动分类成为重要的科学研究课题,然而面对如此海量的光谱数据,一些传统的光谱自动分类方法已经不适用,迫切需要寻找高效率的光谱自动分类技术。研究了基于局部均值的K-近质心近邻(local mean-based K-nearest centroid neighbor,LMKNCN)算法在恒星(Star)、星系(Galaxy)和类星体(Quasar,QSO)的光谱分类中的应用。LMKNCN算法的基本思想是根据近质心近邻原则,从每一类训练样本集中为待测样本点选取k个近质心近邻点,然后根据每一类中所选取的k个近质心近邻点的均值点到待测样本点x的距离来判别x的所属类别。针对美国SDSS-DR8的天体光谱数据,对比了K-近邻、K-近质心近邻、LMKNCN三种算法在恒星、星系和类星体的光谱分类中所表现的性能,结果表明三种方法中,LMKNCN算法对这三种光谱的识别率高于其他两种算法或者与其相当,而且其平均分类正确率高于另外两种算法,特别是在类星体的识别率上表现的更好。表明了该算法对天文光谱大数据的快速处理和有效利用具有重要的意义。     

折射率正负梯度交替表面的研究

利用不均匀材料提出了一种折射率正负梯度交替表面, 并利用几何光学法和电磁场数值仿真方法对其机理进行了研究与验证, 发现其可以操控电磁波的传播: 在一定的参数下, 其可以将空间中的入射电磁波一直束缚在介质中, 或在介质中传播一定距离后再实现电磁波的释放; 同时该结构具有宽带、极化无关等特性. 利用该结构可引导能流, 减小后向散射截面, 可用作隐身表面.     

石墨烯基双曲色散特异材料的负折射与体等离子体性质

基于有效介质理论研究了石墨烯/介质周期结构的电磁性质, 研究发现这种复合结构的等频面在太赫兹和远红外波段为双曲线, 可用来实现石墨烯基双曲色散特异材料. 通过改变石墨烯的费米能级、介质层厚度和单元结构中石墨烯的层数, 可很容易地调节双曲色散存在的频段. 由于等频面的双曲色散特性, 石墨烯基双曲色散特异材料在远低于截止频率的范围内, 对斜入射的电磁波具有负的能量折射率和正的相位折射率, 并支持局域体等离子体模式. 基于衰减全反射结构, 研究了体等离子体的激发, 探索了体等离子体在可调的光学反射调制器中的应用.     

Synthesis,Characterization, DNA Binding Properties,and Antioxidant Activity of Novel Copper(II) and Zinc(II) Complexes with Bis(pyrrol‐2‐yl‐methylamine) Ligands

Three novel ligands H₄Lⁿ (n = 1–3) and their copper(II) and zinc(II) complexes were prepared and characterized on the basis of elemental analyses, molar conductivity, ¹H NMR, UV/Vis, and IR spectroscopy as well as mass spectrometry. DNA binding properties of the ligands and their complexes were investigated by absorption spectroscopy, ethidium bromide displacement experiments, and viscosity measurements. The experimental results indicate that the new ligands and their complexes can bind to DNA and the binding affinities of the complexes are higher than those of the ligands. In addition, the antioxidant activity of the ligands and complexes was determined by superoxide and hydroxyl radical scavenging methods in vitro, indicating that the complexes exhibit more effective antioxidant activity than the ligands alone.     

Piezoelectric atrazine sensor based on a molecularly imprinted film of titanium dioxide

We have developed a piezoelectric sensor for the determination of atrazine. It is based on the modification of a molecularly imprinted film of TiO₂ that was placed on a quartz crystal via a surface sol?Cgel process. The resulting sensor exhibits high selectivity for atrazine, a re-usability that is better than that of other sensors, a response time of 3?min, a wider linear range (0.0005?C8?mM), and a lower detection limit (0.1???M). The analytical application of the atrazine sensor confirms the feasibility of atrazine determination.

An extension of an inequality for ratios of gamma functions

In this paper, we prove that for $x+y>0$ and $y+1>0$ the inequality $\frac{{[\Gamma (x+y+1)/\Gamma (y+1)]}^{1/x}}{{[\Gamma (x+y+2)/\Gamma (y+1)]}^{1/(x+1)}}<{\left(\frac{x+y}{x+y+1}\right)}^{1/2}$ is valid if $x>1$ and reversed if $x<1$ and that the power $\frac{1}{2}$ is the best possible, where $\Gamma \left(x\right)$ is the Euler gamma function. This extends the result of [Y. Yu, An inequality for ratios of gamma functions, J. Math. Anal. Appl. 352 (2) (2009) 967–970] and resolves an open problem posed in [B.-N. Guo, F. Qi, Inequalities and monotonicity for the ratio of gamma functions, Taiwanese J. Math. 7 (2) (2003) 239–247].     

高阶广义微扰KdV方程的弱解(英文)

By using the theory of compensated compactness,we prove that there exists a sequence {uδε} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms,namely we prove the existence of the weak solution.     

SYNCHRONIZATION OF TWO COUPLED HINDMARSH-ROSE NEURONS BY A PACEMAKER

This paper considers the synchronization of two coupled Hindmarsh-Rose neurons by a pacemaker.Based on the stability theory of differential equations,the complete synchronization of this pacemaker neuron model is reached.Moreover,we also show that pacemaker can enhance or induce synchronization.Numerical simulations are given to illustrate the main results.