Synthesis of well‐defined,soluble poly(3‐alkyl‐4‐benzamide) by chain‐growth condensation polymerization

Well‐defined poly(3‐alkyl‐4‐benzamide) was synthesized by means of chain‐growth condensation polymerization of phenyl 3‐octyl‐4‐(4‐octyloxybenzyl(OOB)amino)benzoate ( 1c ) from initiator 2 , followed by removal of the OOB groups on amide nitrogen of poly 1c . Polymerization of 1c with phenyl 4‐(trifluoromethyl)benzoate ( 2b ) in the presence of 1,1,1,3,3,3‐hexamethyldisilazide (LiHMDS) and LiCl in THF at ?10 °C gave poly 1c with a narrow molecular weight distribution (M_w/M_n ≤ 1.08) and a well‐defined molecular weight (M_n = 4480–12,700) determined by the feed ratio of monomer to initiator (from 10 to 30). The OOB groups of poly 1c were removed with H₂SO₄ to give the corresponding N‐unsubstituted poly(p‐benzamide) (poly 1c′ ) with low polydispersity. The solublity of poly 1c′ in polar organic solvents was dramatically higher than that of poly(p‐benzamide), demonstrating that introduction of an alkyl group on the aromatic ring is very effective for improving the solubility of poly(p‐benzamide). © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 360–365     

地球化学模拟在高放废物地质处置中的应用与发展

随着核能事业的发展,高放废物的处理和处置问题日益突出.其中,研究高放废物在环境介质中的吸附、扩散和迁移行为是获取放射性核素对周围环境和人群健康影响的基础参数的最重要和最直接的途径.近年来,人们利用已有的实验数据及核素的基础热力学和动力学数据,附以相应的数学模型,建立了一些地球化学模拟软件,用于分析核素在地质介质中可能发生的连续性和长期性变化.目前,国内外常用的地球化学模拟软件有十多种.本文从热力学平衡计算原理、种态分布计算方法和表面配位模型假设等几个方面对地球化学模拟软件进行了简要介绍,对近年来地球化学模拟软件在核素种态分布计算和表面配位模型模拟两方面的应用进行了举例分析,并以Ca-U-CO3配合物为例,说明完备的热力学数据对地球化学模拟软件发展的重要性,以期促进我国地球化学模型的应用和发展.     

一种一致性排序标度方法

针对层次分析法判断矩阵一致性问题,提出了一种新的排序标度方法,证明了采用新方法形成的判断矩阵具有一致性,最后通过实例运用说明了此方法的可行性和有效性.     

Higher integrability for nonlinear elliptic equations with variable growth and discontinuous coefficients

In this paper, based on the theory of variable exponent spaces, we study the higher integrability for a class of nonlinear elliptic equations with variable growth and discontinuous coefficients. Under suitable assumptions, we obtain a local gradient estimate in Orlicz space for weak solution.     

基于马尔可夫决策过程的医疗检查预约优化模型

医技部门的医疗检查如电子计算机断层扫描（CT）、核磁共振成像设备（MRI）、X射线（X－rays）常常有如下三种病人类型：门诊病人、住院病人和急诊病人。针对不同病人类型的需求特点，运用马尔可夫决策过程原理和动态规划方法，建立了医疗检查设备的预约优化模型，并证明了模型的最优性质，得出了不同病人类型的最优预约策略。数值算例的结果表明：本文的预约策略不仅易于实施，而且，通过该模型获得的最大收益比按传统先来先预约的模式所获得的收益要大。     

Estimator of a change point in single index models

This paper considers the problem of change point in single index models. In order to obtain asymptotically valid confidence intervals for the estimation of the change point, the convergence rate and asymptotic distribution of the change point estimate is studied. Some simulation results are presented which show that the numerical performance of our estimator is satisfactory.     

Water waves trapped by thin submerged cylinders in a two‐layer fluid: Discrete eigenvalue

Exact solutions of the linear water‐wave problem describing oblique water waves trapped by a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross‐section in a two‐layer fluid are constructed in the form of convergent series in powers of the small parameter characterising the “thinness” of the cylinder. The terms of this series are expressed through the solutions of the exterior Neumann problem for the Laplace equation describing the flow of unbounded fluid past the cylinder.     

Statistical inference for Vasicek-type model driven by Hermite processes

Let $Z$ denote a Hermite process of order $q\ge 1$ and self-similarity parameter $H\in (\frac{1}{2},1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $q?2$. In this paper, we deal with a Vasicek-type model driven by $Z$, of the form $d{X}_t=a(b?X_t)dt+d{Z}_t$. Here, $a>0$ and $b\in \mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations.     

Transition probabilities of Lévy‐type processes: Parametrix construction

We present an existence result for Lévy‐type processes which requires only weak regularity assumptions on the symbol with respect to the space variable x. Applications range from existence and uniqueness results for Lévy‐driven SDEs with Hölder continuous coefficients to existence results for stable‐like processes and Lévy‐type processes with symbols of variable order. Moreover, we obtain heat kernel estimates for a class of Lévy and Lévy‐type processes. The paper includes an extensive list of Lévy(‐type) processes satisfying the assumptions of our results.