新型共价交联纳米胶囊的构筑、调控与功能

利用共价自组装的方法，将刚性组装基元与柔性链在一定条件下进行横向交联，可以方便地制备出单层高分子纳米胶囊.相比于传统的非共价超分子囊泡，这种新型的共价纳米胶囊具有结构稳定、尺度可控且分散性优异等诸多优点.因此，如何利用化学合成的手段来制备新型的纳米胶囊，并进一步实现对其结构调控和性能的探究具有十分重要的意义.针对这些问题，分别发展了功能化的柱[5]芳烃、四苯乙烯、卟啉、三嗪、苯硼酸酐等不同类型构筑基元，并使之与两端具有活性位点的柔性烷基链在适当的溶剂中进行聚合反应，最终获得了一系列的共价纳米胶囊.通过对其结构的修饰和调控，发现这些功能化的高分子纳米胶囊在光捕获、人工酶、抗菌材料以及药物载体等领域具有诸多潜在应用价值.未来，新型共价高分子纳米胶囊的开发、功能化以及应用有望得到进一步的拓展.     

一类特殊的Koszul Calabi-Yau DG代数

假设一个连通上链DG代数A的基分次代数A~#或者同调分次代数H(A)是由一次元素x,y生成的代数kx,y/(xy+yx).本文证明A是Koszul Calabi-Yau DG代数.     

2-距离空间中平方型压缩映象的一个新的耦合公共不动点定理

在2-距离空间的框架下, 利用映象对的ω-相容性条件, 建立了一类新的平方型压缩条件, 讨论了此类映象耦合公共不动点的存在性和唯一性.证明了一个新的耦合公共不动点定理, 也提供了一个有效的例子来支持该文的新结果.该文的结果改善了之前文献中的相关结果.     

LOCALIZED PATTERNS OF THE SWIFT-HOHENBERG EQUATION WITH A DISSIPATIVE TERM

In this paper, the normal form analysis of quadratic-cubic Swift-Hohenberg equation with a dissipative term is investigated by using the multiple-scale method. In addition, we obtain Hamiltonian-Hopf bifurcations of two equilibria and homoclinic snaking bifurcations of one-peak and two-peak homoclinic solutions by numerical simulations.     

Computer Simulation Study on Adsorption and Conformation of Polymer Chains Driven by External Force

In this work, Monte Carlo simulations are used to study the critical adsorption behaviors of flexible polymer chains under the action of an external driving force F parallel to an attractive flat surface. The critical adsorption temperature T_c decreases linearly with increasing F,indicating that the driving force suppresses the adsorption of polymer. The conformation of polymer is also affected by the driving force.However, the effect of F is dependent on the competition between the driving force and temperature. Under strong force or at low temperature,the polymer is stretched along the direction of the force, while under weak force or at high temperature, the polymer is not stretched. When the force is comparable to the temperature, the polymer may be stretched perpendicular to the driving force, and below T_c, we observe conformational transitions from parallel to perpendicular and again to parallel by decreasing the temperature. We found that the perpendicular stretched conformation leads the polymer chain to synchronously move along the direction of the driving force. Moreover, the conformational transitions are attributed to the competition and cooperation between the driving force and the temperature.     

大环分子衍生物在人工跨膜离子通道领域中的研究进展

大环分子如环糊精、冠醚等因具备独特的空腔结构, 能够通过主-客体相互作用实现对分子、离子的特异性识别, 因此常被应用于人工跨膜离子传输系统的研究和开发. 与天然的通道蛋白相比, 大环分子具有价格低廉、性质稳定、结构易于修饰和功能化等诸多优点, 因而备受科研工作者们的关注. 本综述详细介绍了大环分子在人工离子通道领域中的研究进展, 按照不同的大环分子进行分类, 系统归纳了基于大环结构的人工跨膜通道的制备方法、结构调控以及其在生物医药领域中的潜在应用. 最后对大环类人工离子通道做了简要的总结和展望, 该综述对于发展新型人工离子通道以及发掘其潜在的应用价值具有重要意义.     

可加稳定过程的自相交局部时

本文研究了可加稳定过程的自相交局部时的问题.利用Borel–Canteil引理等方法,得到可加稳定过程的自相交局部时的Hlder上界,推广了文献[5]中的结果.     

半格分次弱Hopf代数的$G$-Cleft扩张

本文首先将Clifford幺半群代数分解为交叉积的半格直和,然后将这个结果通过$H$-$G$-cleft扩张推广到所谓的$G$-交叉积上.     

Willmore submanifolds in the unit sphere via isoparametric functions

In this paper, we show that both focal submanifolds of each isoparametric hypersurface in the sphere with six distinct principal curvatures are Willmore, hence all focal submanifolds of isoparametric hypersurfaces in the sphere are Willmore.     

Nonparametric estimation of quantiles for a class of stationary processes

We study smoothed quantile estimator for a class of stationary processes. We obtain the convergency rates and the Bahadur representation, as well as the asymptotic normality for this estimator by the method of m-dependent approximation. Our results can be used in the study of the estimation of value-at-risk(Va R) and applied to many time series which have important applications in econometrics.