时间尺度上二阶拟线性阻尼动力方程的振动性分析

研究二阶拟线性时滞阻尼动力方程[a(t)|x^Δ(t)|^λ-1x^Δ(t)]^Δ+b(t)|x^Δ(t)|^λ-1x^Δ(t)+p(t)|x(δ(t))|^λ-1x(δ(t))=0的振动性,其中t ₀∈T,而T为任意时间尺度,考虑方程是非正则情形,即$\int^{∞}_{t_0}$[a^-1(s)e_-b/a(s,t₀)]^1/λ Δs < ∞。 通过引入广义Riccati变换,借助时间尺度上的有关理论,并结合不等式技巧,建立了该方程振动的一些新的充分条件,推广、改进并丰富了现有文献中的结果。     

时标上二阶广义Emden-Fowler型动态方程的振荡性

研究了时标上的一类具有阻尼项的二阶广义Emden-Fowler型泛函动态方程的振荡性,利用时标上的微积分理论和广义的Riccati变换及不等式技巧,建立了该方程振荡的若干判别准则, 推广且改进了一些已有的结果,并用具体实例来说明本文的主要结论。     

具非正中立项的二阶非自治延迟动态系统的动力学性质研究

研究了时间测度链T上的一类具非正中立项的二阶非自治延迟动态系统的动力学性质。 利用时间测度链上的有关理论, 结合一些经典不等式, 得到了该系统的一些新的动力学性质, 并举例说明了本文定理的重要性。     

具非正中立项的二阶非自治延迟动态系统的动力学性质研究

研究了时间测度链T上的一类具非正中立项的二阶非自治延迟动态系统的动力学性质。 利用时间测度链上的有关理论, 结合一些经典不等式, 得到了该系统的一些新的动力学性质, 并举例说明了本文定理的重要性。     

时标上二阶广义Emden-Fowler型动态方程的振荡性

研究了时标上的一类具有阻尼项的二阶广义Emden-Fowler型泛函动态方程的振荡性,利用时标上的微积分理论和广义的Riccati变换及不等式技巧,建立了该方程振荡的若干判别准则, 推广且改进了一些已有的结果,并用具体实例来说明本文的主要结论。     

The broadband NIR emission properties of Bi doped La2O3–Al2O3–SiO2 glass

Bi₂O₃ doped 65SiO₂–20Al₂O₃–15La₂O₃ (in mole%) glasses were prepared by the traditional melting–quenching method. The spectroscopic properties and mechanism of NIR broadband emission in these glasses were investigated in this work. Three excitation wavelengths of 500, 700 and 800 nm were used to test emission spectra. The emission band under 500 nm excitation can be regarded as combination of emission bands under 700 and 800 nm excitation. 2.0 mole% is found to be the optimal Bi₂O₃ doping level in this glass. Under 500 nm excitation its emission peak, FWHM and lifetime of emission band are 1160 nm, 300 nm and 569 μs, respectively. The longest fluorescent lifetime reaches 620 μs under 700 nm excitation. The valence state of Bi in these glasses is suggested to be lower than +3 by X-ray photoelectron spectroscopy. With the help of energy matching, we infer that both Bi⁰ and Bi⁺ centers are responsible for the NIR fluorescence of Bi₂O₃ doped 65SiO₂–20Al₂O₃–15La₂O₃ glass.     

Fractional chromatic numbers of tensor products of three graphs

The tensor product $(G_1,G_2,G_3)$ of graphs $G_1$, $G_2$ and $G_3$ is defined by $V(G_1,G_2,G_3)=V\left(G_1\right)\times V\left(G_2\right)\times V\left(G_3\right)$and $E(G_1,G_2,G_3)=\left\{\left((u_1,u_2,u_3),(v_1,v_2,v_3)\right):\left|\{i:(u_i,v_i)\in E\left(G_i\right)\}\right|\ge 2\right\}.$Let ${\chi }_f\left(G\right)$ be the fractional chromatic number of a graph $G$. In this paper, we prove that if one of the three graphs $G_1$, $G_2$ and $G_3$ is a circular clique, ${\chi }_f(G_1,G_2,G_3)=min\{{\chi }_f\left(G_1\right){\chi }_f\left(G_2\right),{\chi }_f\left(G_1\right){\chi }_f\left(G_3\right),{\chi }_f\left(G_2\right){\chi }_f\left(G_3\right)\}.$     

The Electron Spin as a Chiral Reagent

We show that enantioselective reactions can be induced by the electron spin itself and that it is possible to replace a conventional enantiopure chemical reagent by spin‐polarized electrons that provide the chiral bias for enantioselective reactions. Three examples of enantioselective chemistry resulting from electron‐spin polarization are presented. One demonstrates the enantioselective association of a chiral molecule with an achiral self‐assembled monolayer film that is spin‐polarized, while the other two show that the chiral bias provided by the electron helicity can drive both reduction and oxidation in enantiospecific electrochemical reactions. In each case, the enantioselectivity does not result from enantiospecific interactions of the molecule with the ferromagnetic electrode but from the polarized spin that crosses the interface between the substrate and the molecule. Furthermore, the direction of the electron‐spin polarization defines the handedness of the enantioselectivity. This work demonstrates a new mechanism for realizing enantioselective chemistry.     

Dependence of spectroscopic properties on doping content and temperature of bismuth-doped lanthanum aluminosilicate glass

The effects of bismuth doping content and temperature on the absorption property and near-infrared(NIR) luminescence of Bi-doped La2O3-Al2O3-SiO2(LAS) glasses are presented.The emission intensity reaches the maximum when the Bi2O3 content in 3.0Bi-LAS is 1.83%.The emission spectra reach their peaks at 1 190 and 1 117 nm,with full-width at half-maximum(FWHM) values of 330 and 228 nm under 500 and 700-nm excitations,respectively.As the Bi2O3 content increases,the peak wavelengths and FWHMs of emission bands increase,but their lifetimes decrease.The lifetime of 2.0Bi-LAS is 460 μs at 9 K,and is almost temperature independent until 350 K.The NIR emission of Bi in the system has strong resistance to thermal quenching from 9 to 350 K.