四阶椭圆问题有限元导数恢复技术与超收敛性

1引言有限元导数恢复技术是近年来发展起来的计算有限元导数并获得导数逼近超收敛性的一种新的后处理技术.对于一维和二维区域上的二阶椭圆边值问题,文[1,2]提出了Z-Z小片插值技术,得到了有限元导数逼近在小片恢复区域上的一阶超收敛结果和剖分节点处二阶强超收敛性;文[3,4]则建立了更为实用的小片插值恢复技术并得到与文[1,2]相平行的超收敛结果;文[5]对两点边值问题构造了一种积分形式的导数恢复公式,利用这个公式可获得剖分节点处有限元导数逼近的O(h~(2k))阶超收敛估计.本文将对一维四阶椭圆     

Greatest Descent Algorithms in Unconstrained Optimization

We show that, for an unconstrained optimization problem, the long-term optimal trajectory consists of a sequence of greatest descent directions and a Newton method in the final iteration. The greatest descent direction can be computed approximately by using a Levenberg-Marquardt like formula. This implies the view that the Newton method approximates a Levenberg-Marquardt like formula at a finite distance from the minimum point, instead of the standard view that the Levenberg-Marquadt formula is a way to approximate the Newton method. With the insight gained from this analysis, we develop a two-dimensional version of a Levenberg-Marquardt like formula. We make use of the two numerically largest components of the gradient vector to define here new search directions. In this way, we avoid the need of inverting a high-dimensional matrix. This reduces also the storage requirements for the full Hessian matrix in problems with a large number of variables. The author thanks Mark Wu, Professors Sanyang Liu, Junmin Li, Shuisheng Zhou and Feng Ye for support and help in this research as well as the referees for helpful comments.     

电饭锅自动控温电路的设计和安装

本文紧紧抓住学生对“自动控温”这一普通现象的好奇 ,积极引导学生去探索和研究 ,使学生在掌握“自动控温”原理的基础上 ,按照自己的意愿和设想来设计一个电路并能动手组装和检验。     

Synthesis of amphiphilic graft copolymer brush and its use as template film for the preparation of silver nanoparticles

A microphase‐separated, amphiphilic graft copolymer consisting of a poly (vinyl chloride) (PVC) backbone and poly(oxyethylene methacrylate) (POEM) side chains, (PVC‐g‐POEM at 62:38 wt %) was synthesized via atom transfer radical polymerization (ATRP). Nuclear magnetic resonance (¹H NMR), FTIR spectroscopy, and transmission electron microscopy (TEM) clearly revealed that the “grafting from” method using ATRP was successful and that the graft copolymer molecularly self‐assembled into discrete nanophase domains of continuous PVC and isolated POEM regions. The self‐assembled graft copolymer film was used to template the growth of silver nanoparticles in solid state by introducing a AgCF₃SO₃ precursor and a UV irradiation process. The in situ formation of silver nanoparticles in the graft copolymer template film was confirmed by TEM, UV–visible spectroscopy, and wide angle X‐ray scattering. FTIR spectroscopy and X‐ray photoelectron spectroscopy also demonstrated the selective incorporation and in situ formation of silver nanoparticles within the hydrophilic POEM domains, presumably due to strong interactions between the silver and the ether oxygen in POEM. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3911–3918, 2008     

结合部切向接触刚度分形模型研究

根据球体与平面接触的切向接触刚度和粗糙表面的接触分形理论，从理论上首次建立了结合部切向接触刚度分形模型，该模型具有尺度独立性。通过对所建模型的数字仿真，直观地给出了结合部切向接触刚度与其影响因素之间的非线性关系，并与实验研究结果具有较好的一致性，从而说明了该模型是合理的。     

分子动力学研究V82A和L90M变异对HIV PR-IDV复合物的影响

为了说明V82A和L90M变异对蛋白酶(PR)和茚地那韦(IDV)复合物的影响,进行了5.5ns的MD模拟.用MM-PBSA方法计算了体系的结合自由能,计算和实验结果一致.分解自由能为不同能量项说明,这两个变异引起熵的贡献变化大于焓的贡献变化.分解自由能到每个残基说明Wild,V82A和L90M具有相似的结合模式,结合能的贡献主要来源于A28/A28',I50/I50'和I84/I84'这六个残基组,详细分析了Wild和IDV的结合模式,对比分析了V82A和L90M变异引起结合模式的细小变化.V82A变异引起结合模式的变化是由于变异后位阻减小导致的.L90M变异引起D25和L90间的作用增强并引起结合模式的细小变化.研究结果有助于更好地理解变异对抑制剂和HIV-1PR结合模式的影响,并可以用来帮助设计更高效的PR抑制剂.     

Synthesis of water-tolerant indium homoenolate in aqueous media and its application in the synthesis of 1,4-dicarbonyl compounds via palladium-catalyzed coupling with acid chloride

The first water-tolerant, ketone-type indium homoenolate was synthesized via the oxidative addition of In/InCl(3) to enones. The reaction proceeds exclusively in aqueous media. Both indium and indium(III) chloride are necessary for the smooth conversion of the reaction. Similar results were obtained when InCl or InCl(2) was used in place of In/InCl(3). The synthetic utility of the indium homoenolate was demonstrated through the synthesis of 1,4-dicarbonyl compounds via palladium-catalyzed coupling of indium homoenolate with acid chloride.     

Multilayer graphene nanoribbons exhibit larger capacitance than their few-layer and single-layer graphene counterparts

This article demonstrates that it is not always beneficial to exfoliate graphitic structures to single-layer graphene to achieve maximum electrochemical performance. Using electrochemical impedance spectroscopy, we show that multilayer graphene nanoribbons with cross sections of 100 × 100 nm provide larger capacitance (15.6 F/g) than do few-layer graphene nanoribbons (14.9 F/g) and far larger capacitance than single-layer graphene nanoribbons (10.9 F/g) with the same cross section.     

Method of sensitivity improving in the non-dispersive infrared gas analysis system

A method of interference correction for improving the sensitivity of non-dispersive infrared (NDIR) gas analysis system is demonstrated. Based on the proposed method, the interference due to water vapor and carbon dioxide in the NDIR NO analyzer is corrected. After interference correction, the absorbance signal at the NO filter channel is only controlled by the absorption of NO, and the sensitivity of the analyzer is improved greatly. In the field experiment for pollution source emission monitoring, the concentration trend of NO monitored by NDIR analyzer is in good agreement with the differential optical absorption spectroscopy NO analyzer. Small variations of NO concentration can also be resolved, and the measuring correlation coefficient of the two analyzers is 94.28%.