热敏性功能材料聚N-乙烯基己内酰胺的辐射聚合

具有低临界相变温度（LCST）的温度敏感性高聚物是一类特殊热性能的高聚物。当环境温度低于LCST时,其在溶液中的溶解性会随着温度升高缓慢降低。但一旦温度升高到LCST附近很小范围里,其溶解性会突然降低,出现热沉降,而且这种变化是可逆的。这类高聚物中研究较多也最具代表性的是聚N－异丙基丙烯酰胺（PNIPAAm）和聚N-乙烯基己内酰胺（PNVCL）,因为这两种聚合物的LCST都处于生理温度范围内（30－40℃）,使它们的系列高聚物在生物和医药材料中有极其广泛的应用前景^[1,2]。相比而言,PNVCL的研究与应用不PNIPAAm开展得早和完善,但其具有比PNIPAAm更好的生物相容性。所以近年来在生物大分子的分离、浓集、固定化以及药物的包埋和缓释等方面对PNVCL的研究也逐渐开展起来^[3,4,5]。目前,热敏性PNVCL高聚物主要采用化学法合成^[6,7],辐射合成几乎未见报道。为此,本文采用γ辐射聚合聚N－乙烯基己内酰胺（PNVCL）的可溶性链状高聚物。研究辐射条件对其热敏性、平均分子量等的影响。     

Using polymers to control substrate,ligand, or catalyst solubility

The attributes and design of soluble polymer supports for catalysis and synthesis are discussed. By manipulating polymer structure, polymer supports can be prepared so that the solubility of an attached reagent, substrate, or ligand is affected by heating, cooling, pH, or solvent identity. Supports with such engineered solubility are useful both in organic synthesis and catalysis. They can be used as purification handles in organic synthesis as a way to recover catalysts, as a way to turn reactions on or off, and more generally, as a handle for separations. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2351–2363, 2001     

Recent approaches for clickable poly(2-oxazoline)-based functional stimuli-responsive polymers and related applications

Abstract

Poly(2-oxazoline)s (POxs) are well-known thermo-responsive polymers that exhibit reversible hydrophilic–hydrophobic phase transitions at the lower critical solution temperature (LCST). Using living cationic ring-opening polymerisation, various functional groups can be introduced into POxs. Several clickable POxs with propargyl or azide end groups have been designed and subsequently reacted with various functional groups to prepare multifunctional POxs that respond to stimuli such as temperature, pH, chemicals and light. In this article, we briefly review recent approaches for clickable POx-based functional stimuli-responsive polymers and related applications.     

Divided-difference equation and three-term recurrence relations of some systems of bivariate q-orthogonal polynomials

Partial divided-difference equations and three-term recurrence relations satisfied by the bivariate Askey–Wilson and the bivariate q-Racah polynomials are computed in this work. By using limiting processes, partial divided (or q)-difference equations and three-term recurrence relations are also provided for each of the following families of orthogonal polynomials: the bivariate continuous dual q-Hahn, the bivariate Al-Salam-Chihara, the bivariate continuous q-Hahn, the bivariate q-Hahn, the bivariate dual q-Hahn, the bivariate q-Krawtchouk, the bivariate q-Meixner, and the bivariate q-Charlier polynomials.     

General decay of solutions of a wave equation with memory term and acoustic boundary condition

In this paper, the global solvability to the mixed problem involving the wave equation with memory term and acoustic boundary conditions for non‐locally reacting boundary is considered. Moreover, the general decay of the energy functionality is established by the techniques of Messaoudi. Copyright © 2016 John Wiley & Sons, Ltd.     

An equilibrium version of set-valued Ekeland variational principle and its applications to set-valued vector equilibrium problems

By using Gerstewitz functions, we establish a new equilibrium version of Ekeland variational principle, which improves the related results by weakening both the lower boundedness and the lower semi-continuity of the ob jective bimaps. Applying the new version of Ekeland principle, we obtain some existence theorems on solutions for set-valued vector equilibrium problems, where the most used assumption on compactness of domains is weakened. In the setting of complete metric spaces(Z,d), we present an existence result of solutions for set-valued vector equilibrium problems, which only requires that the domain XZ is countably compact in any Hausdorff topology weaker than that induced by d. When(Z, d) is a Féchet space(i.e., a complete metrizable locally convex space), our existence result only requires that the domain XZ is weakly compact. Furthermore, in the setting of non-compact domains, we deduce several existence theorems on solutions for set-valued vector equilibrium problems,which extend and improve the related known results.     

非线性Sturm—Liouville边值问题的多重非负解

利用上下解方法,锥理论,Schauder不动点定理,Amann不动点定理以及映射度理论研究Sturm—Liouville边值问题（SL．ρ）,在某些特定条件下,得到了有多重非负解的存在性结论．从而一定程度上推广和改进了最近的相关结果．     

A new approach to constant term identities and Selberg-type integrals

Selberg-type integrals that can be turned into constant term identities for Laurent polynomials arise naturally in conjunction with random matrix models in statistical mechanics. Built on a recent idea of Karasev and Petrov we develop a general interpolation based method that is powerful enough to establish many such identities in a simple manner. The main consequence is the proof of a conjecture of Forrester related to the Calogero–Sutherland model. In fact we prove a more general theorem, which includes Aomoto's constant term identity at the same time. We also demonstrate the relevance of the method in additive combinatorics.     

Dynamics and optimal control in a spatially structured economic growth model with pollution diffusion and environmental taxation

In the first part of this paper we present a spatially structured dynamic economic growth model which takes into account the level of pollution and a possible taxation based on the amount of produced pollution. In the second part we analyze an optimal harvesting control problem with an objective function composed of three terms, namely the intertemporal utility of the decision maker, the space–time average of the level of pollution in the habitat, and the disutility due to the imposition of taxation.