Postfunctionalization of polyoxanorbornene via sequential Michael addition and radical thiol‐ene click reactions

We demonstrated the successful postfunctionalization of poly(oxanorbornene imide) (PONB) with two types of double bonds using sequential orthogonal reactions, nucleophilic thiol‐ene coupling via Michael addition and radical thiol‐ene click reactions. First, the synthesis of PONB with side chain acrylate groups is carried out via ring‐opening metathesis polymerization and nitroxide radical coupling reaction, respectively. Subsequently, the resulting polymer having two different orthogonal functionalities, main chain vinyl and side chain acrylate, is selectively modified via two sequential thiol‐ene click reactions, nucleophilic thiol‐ene coupling via Michael addition and photoinduced radical thiol‐ene. The orthogonal reactivity of two diverse double bonds, vinyl and acrylate functionalities, for the abovementioned consecutive thiol‐ene click reactions was first demonstrated on the model compound. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Nilpotent Steiner loops of class 2

We describe Steiner loops of nilpotency class 2 and establish the classification of finite 3-generated nilpotent Steiner loops of nilpotency class 2.     

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.     

Quaternion-valued admissible wavelets and orthogonal decomposition of L 2(IG(2), ℍ)

A series of admissible wavelets is fixed, which forms an orthonormal basis for the Hilbert space of all the quaternion-valued admissible wavelets. It turns out that their corresponding admissible wavelet transforms give an orthogonal decomposition of L ²(IG(2), ℍ).      

Hemivariational inequality approach to constrained problems for star-shaped admissible sets

The hemivariational inequality approach is applied to establish the existence of solutions to a large class of nonconvex constrained problems in a reflexive Banach space. The admissible sets are supposed to be star-shaped with respect to a ball. Due to a discontinuity property of the Clarke directional differential related to the corresponding distance functions, the proposed method permits one to attain the solution without passing to zero with the penalization parameter. Some applications to nonconvex constrained variational problems illustrate the theory.     

关于某些KKM型定理

本文表明关于KKM定理的某些最近的结果是错误的．     

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