On Hermite–Hadamard inequality for $${\varvec{}}$$-convex stocastic processes

In this paper, we investigate the Hermite–Hadamard type inequality for the class of some h-convex stochastic processes, which is an extension of the Hermite–Hadamard inequality given by Barráez et al. (Math. Æterna 5:571–581, 2015). We also provide the estimates of both sides of the Hermite–Hadamard type inequality for h-convex stochastic processes, where h is any non-negative function with \(h(t)+h(1-t)\le 1\) for \(0\le t\le 1\).     

银/金纳米线阵列表面增强拉曼基底的制备及对孔雀石绿的高灵敏度检测

利用种子介导的软模板生长方法制备了金纳米线(Au NWs)阵列, 通过调节生长温度控制Au NWs阵列的形貌, 最后在经硼氢化钠(NaBH₄)清洗过的Au NWs阵列上化学沉积银纳米颗粒(Ag NPs), 制得银/金纳米线(Ag/Au NWs)阵列作为表面增强拉曼散射(SERS)基底. 选用罗丹明6G(R6G)作为拉曼探针分子测定了Ag/Au NWs阵列的SERS性能. 结果表明, Ag/Au NWs阵列作为SERS基底具有高灵敏度、 优异的信号均匀性和良好的稳定性. 使用Ag/Au NWs阵列对孔雀石绿(MG)检测的检出限可低至1×10^-8 mol/L, 线性范围为 1×10^-8~1×10^-4 mol/L. NaBH₄可以在不影响SERS性能的情况下去除Ag/Au NWs阵列上吸附的分子, 使得 SERS基底可以重复使用. 使用Ag/Au NWs阵列对湖水中的MG进行检测, 得到了可靠的回收率, 证明Ag/Au NWs 阵列在检测环境水体中的孔雀石绿上具有应用潜力.     

A superconvergent fitted finite volume method for Black–Scholes equations governing European and American option valuation

We develop a superconvergent fitted finite volume method for a degenerate nonlinear penalized Black–Scholes equation arising in the valuation of European and American options, based on the fitting idea in Wang [IMA J Numer Anal 24 (2004), 699–720]. Unlike conventional finite volume methods in which the dual mesh points are naively chosen to be the midpoints of the subintervals of the primal mesh, we construct the dual mesh judiciously using an error representation for the flux interpolation so that both the approximate flux and solution have the second‐order accuracy at the mesh points without any increase in computational costs. As the equation is degenerate, we also show that it is essential to refine the meshes locally near the degenerate point in order to maintain the second‐order accuracy. Numerical results for both European and American options with constant and nonconstant coefficients will be presented to demonstrate the superconvergence of the method. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1190–1208, 2015     

Free radical initiated low temperature crosslinking of phenylethynyl (PE) end‐capped oligomides

A relatively low‐temperature crosslinking method for phenylethynyl (PE) end‐capped oligomides was developed. PE end‐capped oligomides are typically cured into crosslinked polyimides at 370 °C for about 1 h. The addition of a low viscosity mixed‐solvent of N‐methylpyrrolidinone (NMP)/dimethyl ether of polyethylene glycol (M = 250 g/mol), NMP/DM‐PEG‐250, or NMP/polyethylene glycol (M = 400 g/mol), NMP/PEG‐400, as film forming medium for PE‐end‐capped oligomides was investigated. Fourier transform infrared spectroscopy and ¹³C NMR showed that the mixed solvent addition was effective for achieving low‐temperature crosslinking of the ethynyl end‐caps over the temperature range 200–250 °C. The low temperature crosslinking process was explained by thermolysis of the PEG molecules over this temperature range forming free radical species such as ～CH₂CH₂O· or ～CH₂CH₂^· which initiate cure of the ethynyl groups resulting in a cross linked polyimide membrane. The PEG solvents also provide a radical source for the degradation polymerization of the solvents to a water and NMP insoluble polymer, which formed a miscible blend with the crosslinked membrane. Glass transition temperature (differential scanning calorimetry) data and thermo gravimetric analysis data provide evidence for the miscible blend. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3950–3963, 2010.     

Boundedness,persistence and extinction of a stochastic non-autonomous logistic system with time delays

This paper investigates the stochastic non-autonomous logistic system with time delays. Under two simple assumptions on the environmental noise, it is shown that the stochastic system has a unique global positive solution, and this positive solution is asymptotically bounded. The conditions for extinction, weak persistence of solutions are also obtained by the exponential martingale inequality. Finally, a numerical example is provided to illustrate our results.     

Stochastic stability in one-way flow networks

This paper considers one-way flow network formation games in which transmission through a series of agents is subject to decay. We analyze the myopic best-response dynamics of network formation games, occasionally perturbed by state-dependent random noises. Specifically, if an agent is isolated or has a direct neighbor who is better paid, it is more likely that the agent will make mistakes. Our main result identifies that only empty and wheel networks are candidates for long-term outcomes.     

The effects of medium phonon lifetime on pulse compression ratio in the process of stimulated Brillouin scattering

The performances of stimulated Brillouin scattering (SBS) media with short phonon lifetimes on temporal compression are studied in this paper. In the experiment, FC-72, HT-135 and FC-40 (phonon lifetimes are 1.2 ns, 0.4 ns and 0.2 ns, respectively) are used to study the influence of phonon lifetime on pulse compression in a compact two-cell SBS system. High pulse compression ratio is obtained by a medium with a short phonon lifetime when input energy is high. These results are useful in the generation of picoseconds pulse for Shock Ignition of thermonuclear fuel for ICF.     

基于CdTe量子点自组装的超分支结构的制备及发光特性

提出了一种简单高效制备立体型纳米结构的方法.利用强偶极相互作用,CdTe量子点通过层级自组装形成超分支纳米结构.场发射高分辨透射电子显微(HRTEM)照片显示,制备的超分支纳米结构的构建单元即为原始的CdTe量子点,即组装后的结构保留了原始量子点的量子局限特性.该结构形态受熟化时间、环境pH值以及沉淀剂比例的影响.荧光实验发现,该结构良好地保持了原始量子点的线性光学特性.由于其超分支形态与量子局限效应同时存在,因此该种结构在光伏转换和传感等领域有着重要的潜在应用价值.     

Controlling the evolution of polypropylene microstructure during melt free radical modification using zinc dithiocarbamate with different N-substituted groups

The effects of zinc dithiocarbamates on degradation and branching of polypropylene (PP) were studied during melt radical modification using a tri-functional monomer (trimethylol propane triacrylate (TMPTA)). High-temperature size-exclusion chromatography (HT-SEC) coupled with differential refractive index detector (DRI), light scattering detector (LSD) and viscometer detector (VD) and rotational rheometry were used to analyse the microstructure of modified PP samples. The chemical structure of the N-substituted group showed an important influence in controlling the evolution of PP microstructure during melt radical reaction. The chain cleavage of PP was controlled in the presence of zinc N, N-dimethyldithiocarbamate (ZDMC), and a substantial long chain branched (LCB) fraction was formed. Without co-agent, the molecular weight of PP decreased measurably, and only a minor LCB fraction was formed. Importantly, considerable amounts of highly branched (microgel and hyperbranched) structures were formed in this case.