Shock waves for the hyperbolic balance laws with discontinuous sources

In this paper, we are concerned with the behavior of shock waves in a 2 × 2 balance law with discontinuous source terms. We obtain the existence of a local shock wave solution of this problem and deduce that the discontinuous source terms create a weak discontinuity in this solution. Copyright © 2013 John Wiley & Sons, Ltd.     

富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.     

Inducing a high twisted conformation in the polyimide structure by bulky donor moieties for the development of non-volatile memory

Two polyimides, PI(DAT-6FDA) and PI(DAPT-6FDA), from N-(2,4-diaminophenyl)-N,N-diphenylamine (DAT) or N-(4-(2′,4′-diaminophenoxy)phenyl-N,N-diphenylamine (DAPT) and 4,4′-(hexafluoroisopropylidene)diphthalic anhydride (6FDA) were prepared to clarify the structural effect on the resulting memory properties. The memory device based on PI(DAT-6FDA) showed an unstable volatile behavior, while the device based on PI(DAPT-6FDA) with a more bulky donor (D) unit exhibited a stable non-volatile FLASH type memory characteristic with a long retention time over 10⁴ s. The theoretical simulation based on the density functional theory (DFT) suggested that the greater distinct charge separation between the ground and charge transfer (CT) states led to a highly stable memory behavior. Also, it was clarified that PI(DAPT-6FDA) had a highly twisted conformation compared to PI(DAT-6FDA) in the ground state, and a more twisted dihedral angle between the D and acceptor (A) units was induced in the CT state, which led to the non-volatile memory characteristic.     

Stability criteria in terms of two measures for functional differential equation with variable‐time impulses

This paper focuses on the stability in terms of two measures for functional differential equation with variable‐time impulses. Being different from most of existing literatures, the impulses of functional differential equation are assumed to be closely associated to the current state. We propose a new comparison principle for the considered systems and establish several stability criteria in terms of two measures. Also, the theoretical results are applied in a class of delayed neural network systems with variable‐tine impulses, and numerical simulations are introduced to illustrate the effectiveness of our results. Copyright © 2014 John Wiley & Sons, Ltd.     

Existence results of stochastic impulsive systems with expectations‐dependent nonlinear terms

In this paper, sufficient conditions are established for the existence and uniqueness of global solutions to stochastic impulsive systems with expectations in the nonlinear terms. The maximal interval and the estimate of mild solutions are also discussed. These results are obtained by using the fixed point theorem, interval partition, and Lyapunov‐like technique. Finally, examples are given to illustrate the theory. Copyright © 2014 John Wiley & Sons, Ltd.     

大学基础化学教学中的知其所以然*

针对大学本科一年级基础化学如“化学概论”等课程教学中,学生对于不断出现的专业名词及物理化学含义的理解问题,以“焓”“熵”等外来词汇以及角动量l、能级分裂单位“Dq”等缩写为例,从专业名词来源开始讲解,使学生在学习过程中既知其然又知其所以然,更好地理解化学专业词汇,尤其是外来词汇的内涵与物理化学意义。     

形状记忆聚氨酯研究进展

对形状记忆聚合物(主要以聚氨酯为例)的总体研究概况、合成方法、表征手段、数学模型等方面进行了综述。     

一类具有粘性项的拟线性抛物型方程组*

研究了一类具有非线性源项和粘性项的拟线性抛物型方程组的初边值问题．通过构造稳定集, 证明了此问题整体解的存在性, 并建立了解的长时间行为．同时在放松函数的适当假设条件下, 得到了初始能量非负时解的爆破性质及解的生命区间估计．     

密闭高温高压溶样ICP-MS测定24个国际地质标样中的Sb和Bi

研究了ICP-MS分析中Bi,Sb,Te和As产生的记忆效应,其记忆效应Bi>Sb>Te>As。在低浓度硝酸介质中(0.01%～1%),贮存样品的聚丙烯瓶和ICP-MS的进样管道会对Bi元素产生严重的吸附作用。0.1%氢氟酸的清洗效果优于6%的硝酸,而6%的硝酸的清洗效果要优于0.1%高氯酸。在给定的仪器操作条件下,Sb和Bi的检出限分别为0.001和0.000 1 ng·mL-1。采用该清洗方法,结合密闭高温高压溶样,测定了24个国际地质标样中的Bi和Sb。大部分标样的测定结果与已有参考值吻合较好。文章还给出了国际标样AGV-2(安山岩)、BHVO-2(玄武岩)和BCR-2(玄武岩)中Bi和Sb的测定值。     

Improvement of permanent memory effect in PDLC films using TX-100 as an additive

A number of polymer dispersed liquid crystal (PDLC) films based on dimethacrylate monomers were synthesised by polymer-induced phase separation (PIPS) using polyethylene glycol p-(1,1,3,3-tetramethylbutyl)-phenyl ether (TX-100) as an additive up to total solution weight of 10% aiming to modify the initial anchorage force of the liquid crystal (LC) molecules to the polymeric matrix. The effects of the addition of this additive to the PDLC films were studied resorting to electro-optical studies. Using a fitting model, several parameters were correlated such as the permanent memory effect (PME), the voltage required to achieve 90% of maximum transmittance (E90), the average elastic constant (K) and the rotational viscosity of the director (γ). The use of TX-100 results on an increase on the PME and γ, and decrease on the E90 and K.