Multiarm star triblock terpolymers via sequential double click reactions

Multiarm star triblock terpolymers were obtained by using two different click reactions sequentially: Cu(I) catalyzed azide–alkyne and Diels–Alder. The synthetic strategy is described as follows: (poly(methyl methacrylate))_n‐(polystyrene)_m‐poly(divinyl benzene)) ((PMMA)_n‐(PS)_m‐polyDVB) multiarm star diblock copolymer was first obtained from an azide–alkyne click reaction of (alkyne‐PS)_m‐polyDVB multiarm star polymer with α‐anthracene‐ω‐azide PMMA (anth‐PMMA‐N₃), followed by a Diels–Alder click reaction of the anthracene groups at the star periphery with α‐maleimide poly (tert‐butyl acrylate) (PtBA‐MI) or α‐maleimide poly(ethylene glycol) (PEG‐MI) leading to target (PtBA)_k‐(PMMA)_n‐(PS)_m‐polyDVB and (PEG)_p‐(PMMA)_n‐(PS)_m‐polyDVB multiarm star triblock terpolymers. The hydrodynamic diameter of individual multiarm star triblock terpolymers were measured by dynamic light scattering (DLS) to be ～24–27 nm in consistent with the atomic force microscopy (AFM) images on silicon substrates. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 1557–1564, 2010     

The Levels-Recursive Algorithm for Vector Valued Interpolants by Triple Branched Continued Fractions

1 Introduction Let Πl,m,n be a set of points in three dimensional space R3, Πl,m,n = {(xi, yj, zk), i = 0, 1, · · · l; j = 0, 1, · · · m; k = 0, 1, · · · n}. Let a d?dimensional vector vi,j,k be given at every point (xi, yj, zk) ∈ Πl,m,n and     

一致凸Banach空间非扩张映象带误差的Ishikawa型的三重迭代序列的收敛性

在一致凸Banach空间上,研究了半紧的非扩张压缩映象‖Tx-Ty‖≤‖x-y‖的Ishikawa型的三重迭代序列的收敛性问题,建立并证明了带误差的Ishikawa三重迭代逼近收敛定理,从而独特的推广了Mann和Ishikawa迭代方法,改进和发展了文献[1]-[7]的主要结果.     

Hill‐climbing to Pasch valleys

Exhaustive enumeration of Steiner Triple Systems is not feasible, due to the combinatorial explosion of instances. The next‐best hope is to quickly find a sample that is representative of isomorphism classes. Stinson's Hill‐Climbing algorithm [ 20 ] is widely used to produce random Steiner Triple Systems, and certainly finds a sample of systems quickly, but the sample is not uniformly distributed with respect to the isomorphism classes of STS with ν ≤ 19, and, in particular, we find that isomorphism classes with a large number of Pasch configurations are under‐represented. No analysis of the non‐uniformity of the distribution with respect to isomorphism classes or the intractability of obtaining a representative sample for ν > 19 is known. We also exhibit a modification to hill‐climbing that makes the sample if finds closer to the uniform distribution over isomorphism classes in return for a modest increase in running time. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 405–419, 2007     

再论一类二次系统的无界双中心周期环域的POincare分支

本文再一次讨论了具有双曲线与赤道弧为边界的双中心周期环域的二次系统的Poincare分支，并构造出了此系统出现极限环的(0，3)分布或出现一个三重极限环的具体例子．     

测度链上非线性微分方程的三正解

运用文[1]中的Leggett—Williams不动点定理，我们给出了测度链上的非线性微分方程-x^△△(t)=f(t,x(σ(t))),t∈[a,b,]关于两点边值条件ax(a)-βx^△(a)=0，γx(σ(b)) δx^△(σ(b))=0三正解存在性准则。     

Additive formulae of theta functions and modular equations of degree five

Ramanujan recorded additive formulae of theta functions that are related to modular equations of degree five. We present elementary and simple proofs.     

李三系与Laurent多项式代数F[t,t~(-1)]

本文通过讨论Laurent多项式代数及其导子代数的对合自同构确定了一类具体的无限维单李三系, 并且提供了一种利用Novikov代数上自然的李代数结构来构造李三系的方法.     

Hydrogen bubbles and formation of nanoporous silicon during electrochemical etching

Many nanoporous Si structures, including those formed by common electrochemical etching procedures, produce a uniformly etched nanoporous surface. If the electrochemical etch rate is slowed down, details of the etch process can be explored and process parameters may be varied to test hypotheses and obtain controlled nanoporous and defect structures. For example, after electrochemical etching of heavily n‐doped (R = 0.05–0.5 Ω·cm) silicon 〈100〉 single crystals at a current density of 10 mA cm^?2 in buffer oxide etch (BOE) electrolyte solution, defect craters containing textured nanopores were observed to occur in ring‐shaped patterns. The defect craters apparently originate at the hydrogen/BOE bubble interface, which forms during hydrogen evolution in the reaction. The slower hydrogen evolution due to low current density and high BOE viscosity allows sufficient bubble residence time so that a high defect density appears at the bubble edges where local reaction rates are highest. Current‐carrying Si? OH species are most likely responsible for the widening of the craters. Reducing the defect/doping density in silicon lowers the defect concentration and thereby the density of nanopores. Measurements of photoluminescence lifetime and intensity show a distinct feature when the few nanopores formed at the ring edges are isolated from each other. Overall features observed in the photoluminescence intensity by XPS strongly emphasize the role of surface oxide that influences these properties. Copyright © 2005 John Wiley & Sons, Ltd.     

完全单半群上同余的两种刻画

给出了完全单半群的相容组和同余结的定义,并利用它们刻画了完全单半群上的同余.