Asymptotic Formulas and Inequalities for the Gamma Function in Terms of the Tri-Gamma Function

Results in Mathematics - In the paper, the authors establish some asymptotic formulas and double inequalities for the factorial n! and the gamma function Γ in terms of the tri-gamma function...     

基于Rietveld精修方法解析Bi2O3的原子热振动

三氧化二铋(Bi₂O₃)是氧离子导电体,为了获得它的原子热振动各向同性温度因子,对该粉末晶体进行X射线衍射实验,建立了晶体结构模型,利用Rietveld 精修方法的RIETAN-2000 程序对所得实验结果进行了晶体结构精修,通过最大熵方法(MEM)解析得到了粉末晶体的等高电子密度分布三维(3D) 和二维(2D)可视化图谱。结果表明,各原子Bi₍₁₎、Bi₍₂₎、O₍₁₎、O₍₂₎和O₍₃₎的原子热振动各向同性温度因子分别为0.004 938 nm²、0.004 174 nm²、0.007 344 nm²、0.007 462 nm²、和0.007 857 nm²,等高电子密度分布的可视化,进一步验证了晶体结构模型和原子位置的准确性,这些参数对研究晶体材料的热性质具有一定参考意义。     

Comparative Analysis of Hydration Layer Reorientation Dynamics of Antifreeze Protein and Protein Cytochrome P450

Antifreeze proteins (AFPs) inhibit ice recrystallization by a mechanism remaining largely elusive. Dynamics of AFPs' hydration water and its involvement in the antifreeze activity have not been identified conclusively. We herein, by simulation and theory, examined the water reorientation dynamics in the first hydration layer of an AFP from the spruce budworm, Choristoneura fumiferana, compared with a protein cytochrome P450 (CYP). The increase of potential acceptor water molecules around donor water molecules leads to the acceleration of hydrogen bond exchange between water molecules. Therefore, the jump reorientation of water molecules around the AFP active region is accelerated. Due to the mutual coupling and excitation of hydrogen bond exchange, with the acceleration of hydrogen bond exchange, the rearrangement of the hydrogen bond network and the frame reorientation of water are accelerated. Therefore, the water reorientation dynamics of AFP is faster than that of CYP. The results of this study provide a new physical image of antifreeze protein and a new understanding of the antifreeze mechanism of antifreeze proteins.     

基于P2 Mo18O6-62@Tb3+溶液可逆变色-荧光开关性质对维生素C和H2O2的光谱检测

基于变色多酸P₂Mo₁₈{\mathrm{O}}_{62}^{6-}与绿光Tb³⁺之间的功能互补及分子间能量转移的原理, 在维生素C(VC)的还原下, P₂Mo₁₈{\mathrm{O}}_{62}^{6-}@Tb³⁺溶液由浅黄色变为蓝色, 发生荧光猝灭; 相反, 在H₂O₂氧化下, 溶液的蓝色褪去, 荧光得以恢复, P₂Mo₁₈{\mathrm{O}}_{62}^{6-}@Tb³⁺溶液呈现出可逆的化学响应变色及荧光开关性质. 利用紫外-可见(UV-Vis)及荧光(PL)光谱法对VC浓度进行定量检测, 分别以800 nm处的吸光度和 547 nm处荧光强度的对数值对VC浓度作图, 获得光谱法对VC检测的线性方程, 检出限分别为3.40×10^-3和0.21 μmol/L; 利用UV-Vis及PL动力学方法对VC和H₂O₂检测的响应速度进行了考察, 响应时间分别为52和320 s; 通过UV-Vis光谱及动力学方法考察了VC检测的选择性及可重复使用性.     

Finite-difference calculation of donor energy levels in a spherical quantum dot subject to a magnetic field

The ground and excited states of a donor impurity at the center of a spherical quantum dot subject to a magnetic field are calculated within the effective-mass approximation. The barriers are infinitely high and the differential equation is solved by combining the finite-difference method with the Richardson extrapolation. The binding and transition energies are more accurate than the available variational values, and excellent agreement is found with the hydrogen atom. The transition energies for a medium-size quantum dot are given.     

Temperature effect on qubit in RbCl quantum rod

We change the ellipsoidal boundary in a quantum rod (QR) into a spherical one by a coordinate transformation, and then study the influences of the ellipsoid aspect ratio and polaron radius on the probability density (PD) and oscillation period (OP) of an electron with the variational method of Pekar type (VMPT). By employing the quantum statistics theory (QST), we investigate the temperature effects on the PD and the OP. Numerical results denote that the electron probability density and the oscillation period increase (decay) with raising temperature in lower (higher) temperature regime. The electron probability density increases (decreases) with increasing ellipsoid aspect ratio when the temperature is in lower (higher) regime. The electron probability density decays (enhances) with increasing polaron radius when the temperature is in lower (higher) temperature regime. The oscillation period is an increasing function of the ellipsoid aspect ratio, whereas it is a decreasing one of the polaron radius.     

四取代酞菁化合物的合成和光谱性质

以3(4)-硝基邻苯二腈为起始原料经过两步反应合成了α(β)-四苯氧基酞菁.通过谱学方法和元素分析表征了其结构,研究了中心离子和取代基位置对酞菁吸收波长、发射波长和荧光强度的影响.结果表明,取代位置对最大吸收波长、最大发射波长和荧光强度的影响较大,而中心离子对荧光强度的影响较大,可降低荧光强度甚至淬灭荧光.     

“Weakley型稀土多金属氧酸盐的制备与发光性质”在无机化学实验教学中的应用

采用理论与实验相结合的方法对稀土多金属氧酸盐的发光性质进行探究。首先,通过常规水溶液法合成了一系列稀土多金属氧簇Na9LnW10O36(Ln^3+=Sm^3+、Eu^3+、Tb^3+、Dy^3+);其次,利用粉末X射线衍射、红外光谱、拉曼光谱对簇合物的结构进行表征;最后,利用紫外-可见光谱、荧光光谱对簇合物的光学性质进行考查。通过系统性的实验使学生对稀土簇合物的结构表征以及发光性质有全面、深刻的认识。     

Constructing infinite sequence exact solutions of nonlinear evolution equations

To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding Bäcklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.