Asymptotic approximation for the solution to a semilinear parabolic problem in a thin star‐shaped junction

A semilinear parabolic problem is considered in a thin 3‐D star‐shaped junction that consists of several thin curvilinear cylinders that are joined through a domain (node) of diameter The purpose is to study the asymptotic behavior of the solution u_ε as ε→0, ie, when the star‐shaped junction is transformed in a graph. In addition, the passage to the limit is accompanied by special intensity factors and in nonlinear perturbed Robin boundary conditions. We establish qualitatively different cases in the asymptotic behavior of the solution depending on the value of the parameters {α_i}and {β_i}. Using the multiscale analysis, the asymptotic approximation for the solution is constructed and justified as the parameter ε→0. Namely, in each case, we derive the limit problem (ε=0)on the graph with the corresponding Kirchhoff transmission conditions (untypical in some cases) at the vertex, define other terms of the asymptotic approximation and prove appropriate asymptotic estimates that justify these coupling conditions at the vertex, and show the impact of the local geometric heterogeneity of the node and physical processes in the node on some properties of the solution.     

Separation of three polar compounds from Rheum tanguticum by high‐speed countercurrent chromatography with an ethyl acetate/glacial acetic acid/water system

The separation of polar compounds by high‐speed countercurrent chromatography is still regarded as a challenge. In this study, an efficient strategy for the separation of three polar compounds from Rheum tanguticum has been successfully conducted by using high‐speed countercurrent chromatography. X‐5 macroporous resin chromatography was used for the fast enrichment of the target compounds. Then, the target fraction was directly introduced into high‐speed countercurrent chromatography for separation using ethyl acetate/glacial acetic acid/water (100:1:100, v/v/v) as the solvent system. Consequently, three polar compounds including gallic acid, catechin, and gallic acid 4‐O‐β‐d ‐(6′‐O‐galloyl) glucoside were obtained with purities higher than 98%. The results showed glacial acetic acid could be such an appropriate regulator for the ethyl acetate/water system. This study provides a reference for the separation of polar compounds from natural products by high‐speed countercurrent chromatography.     

Facile One‐Pot Three‐Component Synthesis of Functionalized Pyridylfuran‐2‐amines

The reactive 1 : 1 zwitterionic intermediates generated in situ from the reaction between a series of isocyanides and diaroylacetylenes were trapped by pyridine carbaldehydes to yield highly functionalized 5‐pyridylfuran‐2‐amines in good yields (82–93%).     

Synthesis and properties of novel polyimide/nylon‐6 triblock copolymers

Nylon‐6‐b‐polyimide‐b‐nylon‐6 copolymers were prepared by first synthesizing a series of imide oligomers end‐capped with phenyl 4‐aminobenzoate. The oligomers were then used to activate the anionic polymerization of molten ϵ‐caprolactam. In the block copolymer syntheses, the phenyl ester groups reacted quickly with caprolactam anions at 120 °C to generate N‐acyllactam moieties, which activated the anionic polymerization. In essence, nylon‐6 chains grew from the oligomer chain ends. All of the block copolymers had higher moduli and tensile strengths than those of nylon‐6. However, their elongations at break were much lower. The thermal stability, chemical resistance, moisture resistance, and impact strength were dramatically increased by the incorporation of only 5 wt % polyimide in the block copolymers. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4247–4257, 2000     

β‐cyclodextrin‐based polymeric nano‐receptor: the self‐assembly of cyclodextrin‐appended comb‐copolymer

Well‐defined β‐cyclodextrin (β‐CD)‐appended biocompatible comb‐copolymer ethyl cellulose‐graft‐poly (ε‐caprolactone) (EC‐g‐PCL) was synthesized via the combination of ring‐opening polymerization (ROP) and click chemistry. The resulting products were characterized by ¹H NMR, FT‐IR spectroscopy, and GPC. The synthesized comb‐copolymer could assemble to micelles, with the surface covered by β‐CD. The inclusion with ferrocene derivation was investigated by cyclic voltammetric (CV) experiments, which indicated the potential application of the micelles as nano‐receptors for molecule recognization and controlled drug release. Copyright © 2011 John Wiley & Sons, Ltd.