New insight into the crystallization behavior of poly(ethylene terephthalate)/clay nanocomposites

Crystallization behavior of poly(ethylene terephthalate) (PET)/clay nanocomposites has been investigated in terms of differential scanning calorimeter (DSC) analysis, polarizing optical microscopy (POM), and scanning electron microscopy (SEM) observation. The nanocomposites for investigation were prepared via in situ polycondensation. Crystalline morphologies were observed through POM and SEM. The nonisothermal and isothermal crystallization rates of different samples were determined for comparison based on DSC data. Secondary nucleation analysis was also performed based on bulk crystallization data derived from DSC analysis. The results revealed that nucleating abilities of montmorillonites (MMT) depended on the dispersion state of clay in matrix, the surface modification status, and the metallic derivatives released from MMT during in situ synthesis. The quantities of metallic elements released were measured by inductively coupled plasma (ICP) analysis. The results showed that the release of these metallic derivatives was also affected by surfactant molecules anchored on the surface of MMT. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2380–2394, 2008     

Molecular design of efficient white‐light‐emitting fluorene‐based copolymers by mixing singlet and triplet emission

A new strategy to realize efficient white‐light emission from a binary fluorene‐based copolymer (PF‐Phq) with the fluorene segment as a blue emitter and the iridium complex, 9‐iridium(III)bis(2‐(2‐phenyl‐quinoline‐N,C³′)(11,13‐tetradecanedionate))‐3,6‐carbazole (Phq), as a red emitter has been proposed and demonstrated. The photo‐ and electroluminescence properties of the PF‐Phq copolymers were investigated. White‐light emission with two bands of blue and red was achieved from the binary copolymers. The efficiency increased with increasing concentration of iridium complex, which resulted from its efficient phosphorescence emission and the weak phosphorescent quenching due to its lower triplet energy level than that of polyfluorene. In comparison with the binary copolymer, the efficiency and color purity of the ternary copolymers (PF‐Phq‐BT) were improved by introducing fluorescent green benzothiadiazole (BT) unit into polyfluorene backbone. This was ascribed to the exciton confinement of the benzothiadiazole unit, which allowed efficient singlet energy transfer from fluorene segment to BT unit and avoided the triplet quenching resulted from the higher triplet energy levels of phosphorescent green emitters than that of polyfluorene. The phosphorescence quenching is a key factor in the design of white light‐emitting polyfluorene with triplet emitter. It is shown that using singlet green and triplet red emitters is an efficient approach to reduce and even avoid the phosphorescence quenching in the fluorene‐based copolymers. The strategy to incorporate singlet green emitter to polyfluorene backbone and to attach triplet red species to the side chain is promising for white polymer light‐emitting diodes. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 453–463, 2008     

On the convergence of stochastic dual dynamic programming and related methods

We discuss the almost-sure convergence of a broad class of sampling algorithms for multistage stochastic linear programs. We provide a convergence proof based on the finiteness of the set of distinct cut coefficients. This differs from existing published proofs in that it does not require a restrictive assumption.     

非对称线性方程组的二阶段分裂迭代法

本文针对非对称正定矩阵提出了一个收敛分裂, 给出了分裂收敛的充要条件. 在此基础上, 提出系数为非对称正定矩阵的线性方程组的二阶段算法, 并讨论了算法的收敛条件. 最后, 通过数值例子展示了算法的有效性.     

The cutoff phenomenon for randomized riffle shuffles

We study the cutoff phenomenon for generalized riffle shuffles where, at each step, the deck of cards is cut into a random number of packs of multinomial sizes which are then riffled together. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Free boundary problem for a fully nonlinear and degenerate parabolic equation in an angular domain

This paper concerns with the problem of how to running an insurance company to maximize his total discounted expected dividends. In our model, the dividend rate is limited in $[0,M]$ and the company is allowed to transfer any proportion of risk by reinsuring. So there are two strategies which we call dividend strategy and reinsurance strategy. The objective function and the corresponding optimal two strategies are the solution and the two free boundaries of the following Barenblatt parabolic equation

$v_t?\underset{0\le a\le 1}{\max }?(\frac{1}{2}{a}^2{\sigma }^2{v}_{xx}+a\mu v_x)+cv?\underset{0\le l\le M}{\max }?[(1?v_x)l]=0$

under certain boundary conditions on an angular domain

$Q_T=\{(x,t)|0<x<Mt,0<t\le T\}.$

The main effort is to analyze the properties of the solution and the free boundaries to show the optimal decision for the insurance company.     

Global weak solutions for a two-component Camassa-Holm shallow water system

In this paper, we prove the existence of global weak solution for an integrable two-component Camassa-Holm shallow water system provided the initial data satisfying some certain conditions.     

复指数系统在$L_{\alpha}^{p}$空间的不完备性

A necessary and sufficient condition is obtained for the incompleteness of complex exponential system in the weighted Banach space Lαp = {f：∫＋∞∞ ｜f（t）e-α（t）｜pdt ＋∞},where 1 ≤ p ＋∞ and α（t） is a weight on R.     

Global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system

This paper is concerned with global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system. A new global existence result and several new blow-up results of strong solutions to the system are presented. Our obtained results for the system are sharp and improve considerably earlier results.