A Numerical Approach of the sentinel method for distributed parameter systems

In this paper we consider the problem of detecting pollution in some non linear parabolic systems using the sentinel method. For this purpose we develop and analyze a new approach to the discretization which pays careful attention to the stability of the solution. To illustrate convergence properties we give some numerical results that present good properties and show new ways for building discrete sentinels.      

聚醚砜酮涂层纤维顶空固相微萃取-气相色谱法分析水中痕量的酚类化合物

应用自制的聚醚砜酮(PPESK,30 μm)涂层纤维,采用顶空固相微萃取-气相色谱法测定水中痕量的酚类化合物。优化了固相微萃取温度、萃取时间、pH值和离子强度。方法的检出限为0.003～0.041 μg/L,相对标准偏差低于16%(n=5)。将PPESK涂层纤维与商品化的聚丙烯酸酯涂层纤维对比,结果表明PPESK萃取酚类化合物有较高的萃取富集倍数。用所制备的PPESK萃取头分析自来水、海水等实际水样,20 μg/L添加水平下的回收率分别为100.5%～111.8%和94.8%～117.3%。     

Grafting of Poly（lauryl acrylate） onto Nano-silica by ‘Click Chemistry’

Poly（n-alkyl acrylate） with long side groups,namely,poly（lauryl acrylate）（PLA） was synthesized by reversible addition-fragmentation chain transfer（RAFT） polymerization,and the trithioester terminal groups were converted to thiol by reducing reaction.Grafting of the obtained polymer onto nano-silica modified with 3-（methacryloxy）propyl-trimethoxysilane（SiO2-MPS） was conducted by thiol-ene ‘click chemistry＇.PLA was characterized by proton nuclear magnetic resonance（1H NMR） and gel permeation chromatography（GPC）.Fourier transform infrared（FTIR） spectrometry and thermogravimetric analysis（TGA） were used to demonstrate the grafting reaction,and the grafted hairy nano-silica（SiO2-g-PLA） was viewed under a transmission electron microscope（TEM）.According to TGA,grafting ratio and grafting density of SiO2-g-PLA are 30.27％ and 0.013 chain/nm2,respectively.The static water contact angle of SiO2-g-PLA is （80.10±2.97）°,which ensures its hydrophobicity.Dispersion experiment was carried out to confirm its dispersibility in mixed solvents,indicating its potential application in coatings or composites.     

辛普生公式中间点的渐近性(英文)

辛普生公式是数值积分中的著名公式.利用泰勒公式,讨论了当区间的两个端点都趋于其内一定点时辛普生公式中间点的渐近性,得到了具有一般性的结果.     

非傍轴部分相干厄米-高斯光束的相干和非相干合成

推导出二维非傍轴部分相干厄米-高斯（H-G）光束相干合成和非相干合成的交叉谱密度和光强的解析公式,并分析了一些特例. 合成光束的光强不仅决定于f参数,f_σ参数,离轴参数,合成光束的束数和阶数以及传输距离z,而且还决定于合成方式. 对部分相干光的相干合成和非相干合成概念做了物理诠释,其正确性为数值计算例证实. 关键词： 部分相干光的相干和非相干合成 非傍轴部分相干厄米-高斯（H-G）光束 自由空间中的传输方程     

Integrable Coupling of （2＋1）-Dimensional Multi-component DLW Integrable Hierarchy and Its Hamiltonian Structure

A new multi-component Lie algebra is constructed, and a type of new loop algebra is presented. A （2＋1）-dimensional multi-component DLW integrable hierarchy is obtained by using a （2＋1）-dimensional zero curvature equation. Furthermore, the loop algebra is expanded into a larger one and a type of integrable coupling system and its corresponding Hamiltonian structure are worked out.     

Limit theorems for random walks

We consider a random walk $S_{\tau }$ which is obtained from the simple random walk $S$ by a discrete time version of Bochner’s subordination. We prove that under certain conditions on the subordinator $\tau$ appropriately scaled random walk $S_{\tau }$ converges in the Skorohod space to the symmetric $\alpha$-stable process $B^{\alpha }$. We also prove asymptotic formula for the transition function of $S_{\tau }$ similar to the Pólya’s asymptotic formula for $B^{\alpha }$.     

Higher-order implicit strong numerical schemes for stochastic differential equations

Higher-order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed. These are based on a stochastic Taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero. The regions of absolute stability of these implicit and related explicit methods are also examined.