From Rosochatius System to KdV Equation

The Rosochatius system on the sphere, an integrable mechanical system discovered in the nineteenth century, is investigated in a suitably chosen framework with the sphere as an invariant set, to avoid the complicated constraint presentations. Higher order Rosochatius flows are defined and straightened out in the Jacobi variety of the associated hyperelliptic curve. A relation is found between these flows and the KdV equation, whose finite genus solution is calculated in the context of the Rosoehatius hierarchy.     

Theoretical Study on the Reaction of Thymine with Iodomehane in the Water Phase

The reaction mechanisms of carcinogenic methylating agent iodomethane (MeI) with keto and enol tautomers of thymine (K- and E-thymine) were studied by using the B3LYP/6-311+G (d, p) method in water phase. The solvent effects were examined using the polarizable continuum model (PCM). Specifically, PCM single-point calculations at the same level of theory were performed in acetone and CCl4 that represent a range in nonpolarity. The calculated results show that the reaction of K-thymine with MeI is a two-step mechanism, whereas that of E-thymine is a one-step mechanism. Our calculations reveal that K-thymine is appreciably more stable than the enol form in the water phase or in the two solvents. The K- and E-form reaction barriers are 135.6 and 222.1 kJ/mol, respectively in water phase. These findings indicate that the reactions mentioned above could not occur efficiently in biological media in the absence of catalyst. Our conclusions are in agreement with the previous studies on the reactions of guanine with methyl chloride and methyl bromide.     

SOME TRACE FORMULAS FOR THE SCHRDINGER EQUATION WITH ENERGY-DEPENDENT POTENTIAL

The importance of the inverse scattering problem for the Schrdinger equation with energy-dependent potential:     

南京大学举行第十届科学报告会——化学学科进行国际学术交流活动

5月20日,南京大学隆重集会,庆祝建校七十七周年,并举行为期十天的第十届科学报告会。应邀前来参加庆祝活动的日本名古屋大学和美国威斯康星大学代表团的化学学者、正在该校化学系讲学的美国专家以及来自北大、复旦、南开、科学院上海有机所等十三个单位的化学工作者和在宁高校及有关单位的代表参加了化学系的报告会。中、日、美科学家济济一堂,进行了国际和校际的学术交流活动。     

Banach空间中扰动增生算子的迭代程序

给出两类扰动增生算子的迭代程序,并证明它们的收敛性.     

非自治拉曼多色孤子的管理和传输

以变系数的非自治非线性薛定谔方程为模型,考虑了一种色散、非线性和自发拉曼散射效应管理下的非自治系统,通过简单变换显式给出了该系统的精确非自治拉曼多色孤子解。基于精确孤子解,解析研究了该拉曼多色孤子在非自治管理系统中的演化特性,发现孤子的中心位置、波数与色散和非线性以及拉曼效应有关,而孤子频移仅与拉曼效应的参数决定,拉曼效应主导了非自治孤子的自频移,引起了孤子的频移在传输过程中不断的发生变化,导致了孤子的多色性。另外,我们数值讨论了该非自治孤子的传输稳定性,结果表明:该非自治拉曼多色孤子在有限的扰动下具有较好的稳定性。     

离子热法合成多级孔CuAPO-5分子筛

采用丁二酸、氯化胆碱与四乙基溴化铵三元低共熔体为溶剂和模板剂,借助微波辐射快速合成了具有多级孔结构的CuAPO-5分子筛。系统地考察了P2O5/Al2O3、HF/Al2O3与Cu O/Al2O3的物质量之比,铝源及铜源对CuAPO-5分子筛合成的影响。利用X射线衍射(XRD)、扫描电镜(SEM)、透射电镜(TEM)和N2物理吸脱附等检测手段对合成产物的结晶度、形貌和孔结构等进行了表征。通过SEM可知在一定的条件下,可得到具有六角纳米盘状特殊形貌的CuAPO-5分子筛。N2物理吸脱附、SEM和TEM分析表明该分子筛是一种同时存在微孔和介孔的多级孔磷酸铝分子筛材料。     

Theoretical Study of the Reactivity of Mn~+ with CS_2

The reactions of Mn+(7S,5S) with CS2 have been studied at the B3LYP/TZVP level on both septuplet and quintet potential energy surfaces(PESs).The overall energies have been refined at the CCSD(T) level.The calculated results indicate that the reactions of Mn+(7S,5S) with CS2 proceed via an insertion-elimination mechanism.Calculations show that the quintet reaction is more favorable than the septuplet under high energy conditions.The spin-forbidden reaction Mn+(7S) + CS2 → MnS+(5Π) + CS proceeds through a septuplet-quintet surface and the crossing seam is approximately determined.All results have been compared with the existing experimental and theoretical data.     

DNA甲基化-非甲基化碱基间堆积作用的理论研究

运用二级Mфller-Plesset(MP2)理论方法和cc-pVDZ基组优化了6-甲基鸟嘌呤(O6-MethylG),4-甲基胸腺嘧啶(O4-MethylT)以及5-甲基胞嘧啶(C5-MethylC)与DNA碱基鸟嘌呤(G),腺嘌呤(A),胞嘧啶(C),胸腺嘧啶(T)之间的堆积构型.在MP2/aug-cc-pVXZ//MP2/cc-pVDZ(X=D,T)水平上,采用完全基组外推方法校正了堆积碱基对间的相互作用能,并用完全均衡校正法(CP)校正了基组重叠误差(BSSE).MP2计算结果表明,DNA碱基甲基化使得嘧啶-嘧啶、嘧啶-嘌呤堆积碱基间的平行旋转角发生明显改变,并使堆积碱基间的相互作用能增大.在MP2/cc-pVDZ计算级别上得到了各堆积碱基对的全电子波函数,并用分子中的原子理论(AIM)分析了堆积碱基对间的弱相互作用.AIM分析结果显示,甲基化增强了堆积碱基间的π-π作用,且甲基氢与相邻碱基间形成H2CH…X(X=O,N,CH3,NH2)等类型的氢键.甲基化损伤使碱基间重叠程度增大、π-π作用增强以及堆积碱基间形成多个氢键,是堆积作用能增加的主要原因.     

受压橡胶海绵圆筒的轴对称平面应变问题研究

针对橡胶海绵材料圆筒受压问题,根据欧拉-拉格朗日变分原理,建立了基于Blatz-Ko材料模型的轴对称平面应变问题的非线性微分方程. 采用参数变换的方法,获得了该问题的参数形式解析解. 并通过相应数值算例,得到了径向应力和切向应力沿圆筒径向的变化规律,以及过盈量对径向应力和切向应力影响规律.