一簇金刚石晶格上S~4模型的相变

采用重整化群和累积展开的方法,研究了一簇金刚石晶格上S~4模型的相变,求得了系统的临界点.结果表明:当分支数m=2和m 12时,该系统只存在一个Gauss不动点K~*=b_2/2, u_2~*=0;当分支数3≤m≤12时,该系统不仅有Gauss不动点,还存在一个Wilson-Fisher不动点,并且后一个不动点对系统的临界特性产生决定性的影响.     

一种计算液接电势的新方法*

依据液接电势达稳态时通过边界层的净电荷为零这一思想,提出了一种计算液接电势的新方法。对于3类液接电势的计算,特别是Lewis-Sargent公式与Henderson方程的推导,思路清晰易懂,避免了过往液接电势计算方法存在的一些问题。本文所提出的方法能够为液接电势相关内容的教学提供借鉴。     

Geometric Phase for High-Temperature Master Equation

Geometric phase of mixed state is investigated for three-level system obeying a high-temperature master equation. The results show the Berry phase of mixed phase is strongly dependent on the initial condition. For the different initial angle, the turning region is different. In addition, the decrease of Berry phase is most slow around the coupling strength α=5 with an increasing of evolving time.     

外伸梁离散系统模态的若干定性性质

在已证明外伸梁的差分离散模型频率和位移振型基本振荡性质的基础上,首先揭示了两跨外伸梁的共轭系统是一端铰支一端固定并有一个中间铰的两跨连续梁,证明了两跨外伸梁的共轭梁的刚度矩阵是符号振荡矩阵,进而确定了外伸梁的弯矩振型的符号改变数;由此进一步讨论了它的转角振型和剪力振型的符号改变数规律以及位移振型的其他一些定性性质.     

2.0μm附近模拟呼吸气体中~(13)CO_2/~(12)CO_2同位素丰度的高精度实时在线测量

采用可调谐二极管激光吸收光谱技术,结合一新型多通池搭建了一套模拟呼吸气体中CO_2同位素丰度的测量装置.气体的压强、温度和流速被很好地控制且均能保持长期的稳定性;采用三次多项式拟合光谱基线,对光谱进行归一化,很好地消除了功率变化对测量结果的影响;利用移窗-回归技术消除频率漂移对同位素丰度测量的影响.实验结果表明:移窗-回归法的引入不仅延长了系统的稳定时间,还提高了系统的测量精度;小波去噪的应用获得了比多光谱平均法高2倍的信噪比;系统的稳定时间为100 s;Kalman滤波后系统测量精度为0.067‰.     

Polyamine-substituted epoxy-grafted silica for aqueous metal recovery

Glycidoxypropyltriethoxysilane (GPS) was used as a reactive silane to graft metal- complexing ligands onto silica gel in aqueous media under mild conditions. The synthesis entailed the reaction of GPS with silica gel, followed by grafting polyamine onto the epoxy functional group. GPS was added to silica gel in ethanol with 5 vol. % water and the mixture was air-dried for 24 h. Subsequently, excess amounts of polyamines: triethylenetetramine, tetraethylenepentamine, and pentaethylenehexamine were individually added to the silanised silica, followed by solvent evaporation and ovendrying at 60°C. The ligand-grafted silica gel particles showed a rapid heavy metal uptake in batch or flow-through experiments with capacities reaching 0.1 mmol g⁻¹ for copper, zinc, cadmium, or lead ions. Columns packed with the modified particles could be readily regenerated by acid-washing with only a small decrease in activity. The particles could be used for the colourimetric detection of heavy metal pollution or for pre-concentration for analytical purposes. Competition between Cu²⁺, Zn²⁺, Pb²⁺, and Cd²⁺ ions for the three synthesised silica showed that Cu²⁺ ions were adsorbed more strongly than the other metal ions. The general method developed can be applied to graft other molecules with terminal amino groups for other purposes.     

过渡金属催化有机腈和叠氮酸钠反应机理的研究

过渡金属催化有机腈和叠氮酸钠反应机理的研究一直是一个具有挑战性的课题.本工作组合理论和实验方法,对其反应机理作了深入的探讨.基于对两种类型中间体（H₂O）₃M…N₃^-和（H₂O）₃M…NCCH₃稳定性的理论分析和中间体Cd₂（μ₃-N₃）（μ₃-OH）（μ₅-CHDA）（1）和Cd（μ₂-N₃）（μ₃-IBA）（2）（H₂CHDA为1,3-环己二酸,HIBA为4'-（咪唑-1-基）苯甲酸）的成功捕获,首次从实验和理论上揭示了过渡金属离子在反应中起活化叠氮酸根的作用.此外,基于中间体（H₂O）₃M… N₃^-和乙腈分子的静电势盆分析的结果,揭示了叠氮酸根未配位的端基N原子可以进攻氰基N原子发生加成反应,随后可能发生环加成反应生成四唑,在水分子的辅助下,其加成物也可能发生类似于里特反应生成全氮阴离子.该项研究把过渡金属催化有机腈和叠氮酸钠反应引入全氮阴离子合成的新领域.     

分数阶一般退化微分系统的通解

本文研究了系数矩阵不是方阵情形的分数阶一般退化微分系统的解.通过定义可解阵对,获得分数阶一般退化微分系统的通解表达式.该结果推广了整数阶退化微分系统和分数阶常微分系统解的相应结论.