Helical Folding of Conjugated Oligo(phenyleneethynylene): Chain‐Length Dependence,Solvent Effects,and Intermolecular Assembly

As a representative folding system that features a conjugated backbone, a series of monodispersed (o‐phenyleneethynylene)‐alt‐(p‐phenyleneethynylene) (PE) oligomers of varied chain length and different side chains were studied. Molecules with the same backbone but different side‐chain structures were shown to exhibit similar helical conformations in respectively suitable solvents. Specifically, oligomers with dodecyloxy side chains folded into the helical structure in apolar aliphatic solvents, whereas an analogous oligomer with tri(ethylene glycol) (Tg) side chains adopted the same conformation in polar solvents. The fact that the oligomers with the same backbone manifested a similar folded conformation independent of side chains and the nature of the solvent confirmed the concept that the driving force for folding was the intramolecular aromatic stacking and solvophobic interactions. Although all were capable of inducing folding, different solvents were shown to bestow slightly varied folding stability. The chain‐length dependence study revealed a nonlinear correlation between the folding stability with backbone chain length. A critical size of approximately 10 PE units was identified for the system, beyond which folding occurred. This observation corroborated the helical nature of the folded structure. Remarkably, based on the absorption and emission spectra, the effective conjugation length of the system extended more effectively under the folded state than under random conformations. Moreover, as evidenced by the optical spectra and dynamic light‐scattering studies, intermolecular association took place among the helical oligomers with Tg side chains in aqueous solution. The demonstrated ability of such a conjugated foldamer in self‐assembling into hierarchical supramolecular structures promises application potential for the system.     

Well-Posedness of Hydrodynamics on the Moving Elastic Surface

The dynamics of a membrane are that of a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the dynamic equations of the two-dimensional fluid, and the incompressible equation, all of which operate within a curved geometry. In this paper, we prove the local existence and uniqueness of the solution to the reduced elastic surface model by reformulating the model into a new system in the isothermal coordinates. One major difficulty is that of constructing an appropriate iterative scheme such that the limit system is consistent with the original system.     

Monotonicity of the matrix geometric mean

An attractive candidate for the geometric mean of m positive definite matrices A ₁, . . . , A _m is their Riemannian barycentre G. One of its important operator theoretic properties, monotonicity in the m arguments, has been established recently by Lawson and Lim. We give an elementary proof of this property using standard matrix analysis and some counting arguments. We derive some new inequalities for G. One of these says that, for any unitarily invariant norm, ||| G ||| is not bigger than the geometric mean of |||A ₁|||, . . . , |||A _m |||.     

Empirical likelihood for AR-ARCH models based on LAD estimation

By employing the empirical likelihood method,confidence regions for the stationary AR(p)-ARCH(q) models are constructed.A self-weighted LAD estimator is proposed under weak moment conditions.An empirical log-likelihood ratio statistic is derived and its asymptotic distribution is obtained.Simulation studies show that the performance of empirical likelihood method is better than that of normal approximation of the LAD estimator in terms of the coverage accuracy,especially for relative small size of observation.     

网络上SIR型传播的随机建模与极限定理

复杂网络本身及其上的传播过程是最近以来的研究热门,但是多数的工作都只有宏观模型,没有微观基础.本文中,我们将边与边之间的连接与个体的状态变化看作为基本的泊松流,从微观角度构造了网络上SIR型传播的随机模型.对任意有限的固定时间区间,在热力学极限下,从随机系统可以得到一个确定性动力系统—所谓的"水动力极限".这样,本文为这一领域的唯象的动力学模型建立了一个合理的微观基础.同时,我们得到了收敛速度的估计.     

可靠性系列知识讲座 第一讲:可靠性的基本统计知识

介绍了可靠性的基本概念、数据类型、寿命分布、参数估计,特别是用于计算置信限和置信区间的统计量方法和样本空间排序法。     

第二讲:成败型情形和指数分布情形的可靠性评定

对于成败型情形,基于成功次数给出了成功率的优良置信限和置信区间;对于产品寿命服从指数分布的情形,针对不同类型的数据(定数截尾、定时截尾、定总时与定数混合截尾、工型区间删失等)分别给出了可靠性参数(平均无故障时间(MTBF),可靠度,可靠寿命)的点估计和置信限。