Fabrication of Melamine/Tb3+-Intercalated Polydiacetylene Nanosheets and Their Thermochromic Reversibility

Polydiacetylene (PDA) is one kind of the conjugated polymer with layered structure, which can serve as a host to accommodate the guest components through intercalation. In these intercalated PDAs, some of them were reported to have a nearly perfect organized structure and perform completely reversible thermochromism. Till now, these reported intercalated PDAs were made by only introducing a single component for intercalation. Here, we chose 10, 12-pentacosadiynoic acid (PCDA) as the monomer, of which the carboxyl-terminal groups can interact with either Tb\begin{document}$ ^{3+} $\end{document} ions or melamines (MAs). When the feeding molar ratio of PCDA, MA, and Tb\begin{document}$ ^{3+} $\end{document} ion was 3:267:1, only Tb\begin{document}$ ^{3+} $\end{document} ions were intercalated though excess MAs existed. Such Tb\begin{document}$ ^{3+} $\end{document}-intercalated poly-PCDA exhibited completely reversible thermochromism, where almost all the carboxyl groups interacted with Tb\begin{document}$ ^{3+} $\end{document} ions to form the nearly perfect structure. When the feeding molar ratio of PCDA, MA, and Tb\begin{document}$ ^{3+} $\end{document} ion was 3:267:0.6, both Tb\begin{document}$ ^{3+} $\end{document} ions and MAs were intercalated. There existed some defects in the imperfect MA-intercalated domains and at the domain boundaries. The MA/Tb\begin{document}$ ^{3+} $\end{document}-intercalated poly-PCDA exhibits partially reversible thermochromism, where the backbones near the defects are hard to return the initial conformation, while the rest, those at nearly perfect organized domains, are still able to restore the initial conformation.     

Symmetric duality with (p, r) − ρ − (η, θ)-invexity

In this paper we introduce a new type of generalized invex function, called (p, r) − ρ − (η, θ)-invex function and study symmetric duality results under these assumptions. In our study the nonnegative orthants for the constraints are replaced by closed convex cones and their polars. We establish weak and strong duality theorems under (p, r) − ρ − (η, θ)-invexity assumptions for the symmetric dual problems. We also give many examples to justify our results.     

二氢黄酮类化合物的核磁共振碳谱模拟研究

采用表征分子内部化学微环境的结构描述子原子电负性作用矢量(Atomic Electronegativity Interaction Vector, AEIV)对255个共振碳原子进行了结构表征,应用多元线性回归技术建立了结构描述子AEIV与这些碳原子的¹³C NMR化学位移的定量相关模型.该定量结构谱图关系(定量构谱关系/QSSR)模型的复相关系数达到R_MM=0.915,标准偏差为SD_MM=14.879. 采用留一法交互检验的结果为R_CV=0.909,SD_CV=15.324. 结果表明,模型具有良好的估计力和稳定性.     

内积在溶液浓度测定中的应用

提出内积的溶液浓度测定方法。该方法计算已知浓度溶液透光率曲线与0号溶液（浓度最低的溶液）透光率曲线的内积ρ,确定溶液的ρ-C曲线,然后测定未知溶液的透光率曲线,计算其与0号溶液透光率曲线的内积,并利用已建立好的ρ-C曲线进行插值以估计溶液浓度。由于该方法利用了透光率曲线的全部信息,因此对溶液浓度的估计精度较高。对K2Cr2O7溶液浓度的测定实验结果表明,该方法对溶液浓度的估计相对误差小于1.00%。     

Description of Rotation Bands in^157,158Er at Ultrahigh Spin

Properties of the four rotation bands, ^157Er（1,2） and ^15SEr（1,2）, at ultrahigh spin are investigated within the supersymmetry scheme including many-body interactions and possessing the SO（5） （or SU（5）） symmetry on the rotational symmetry. Quantitatively good results of the 7-ray energies and the dynamical moments of inertia in the rotation bands in ^157 Er and ^158 Er at ultrahigh spin are obtained. We theoretically predict that the competition between the anti-pairing and pairing effects may exist in ^157 Er（1,2） and ^158Et（2） bands states. In ^158Er（1） band state, the favourepairing effects may exist and the SO（5） （or SU（5）） symmetry play a dominant role. There may be sphere coexisting with headecupole deformed in ^158Et（1） rotation band state.     

Characterization of compact quantum group

Given a C^＊-algebra A and a comultiplication Ф on A, we show that the pair （A, Ф） is a compact quantum group if and only if the associated multiplier Hopf ^＊-algebra （A, ФA） is a compact Hopf ^＊-algebra.     

The Cauchy Problem for the Generalized Korteweg-de Vries-Burgers Equation in _H

The Cauchy problem for the generalized Korteweg-de Vries-Burgers equation is considered and the local existence and uniqueness of solutions in L^q(0, T;L^p) ∩ L^∞(0, T; \dot{H}^{-s})(0 ≤ s < 1) are obtained for initial data in \dot{H}^{-s}. Moreover, the local solutions are global if the initial data are sufficiently small in critical case. Particularly, for s = 0, the generalized Korteweg-de Vries-Burgers equation satisfies the energy equality, so the initial data can be arbitrarily large to obtain the global solution.     

湖北网湖^137Cs、^210Pb计年与沉积速率研究

采用放射性核素^137Cs和^210Pb计年法测定百年来湖北网湖沉积物的年代，据此计算出网湖的沉积速率．结果表明：2种计年方法测得的沉积速率基本一致，以1954年和1963年为时标，^137Cs测得的沉积速率分别为0．594cm·a^-1和0．557cm·a^-1。^210Pb计年法CIC模式计算得到网湖平均沉积速率为0．56cm·a^-1．CRS模式得到百年来网湖沉积速率变化较大，20世纪50年代以前，平均沉积速率为0．2cm·a^-1左右；50年代至80年代中期，平均沉积速率上了一个台阶，约为0．4cm·a^-1；80年代中期以后平均沉积速率攀升至约0．6cm·a^-1，网湖沉积速率变化与湖区自然环境的改变和人类活动的影响密切相关．     

从$A^{p}_{\alpha}$到$A^{\infty}(\varphi)$的加权复合算子

设$u \in H(D), \ \phi$为$D$上的解析自映射,定义$H(D)$上的加权复合算子为$u C_{\phi}(f)=$$uf\circ\phi$, \ $f\in H(D)$.本文得到了从$A^{p}_{\alpha}$到$A^{\infty}(\varphi)\ (A_{0}^{\infty}(\varphi))$的加权复合算子$u C_{\phi}$的有界性和紧性的充要条件.     

带Markov调制的随机微分延迟方程的稳定性

本文采用了一例特定的Lyapunov函数,来研究带Markov调制的随机微分延迟方程的p阶指数稳定性,并对其几乎必然指数稳定性也进行了探讨.