On concentration of solution to a Schrödinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems where λ>0 and is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C¹ functional with a convex lower semicontinuous functional, we prove that for each large enough λ>0, there exists a positive solution for the problem, and that, as λ→+∞, such solutions converge to a positive solution of the limit problem defined on the domain Ω=int(V^?1({0})).     

Some extensions of the operator entropy type inequalities

In this paper, we define the generalised relative operator entropy and investigate some of its properties such as subadditivity and homogeneity. As application of our result, we obtain the information inequality. In continuation, we establish some reverses of the operator entropy inequalities under certain conditions by using the Mond–Pe?ari? method.     

Explosive synchronization in a mobile network in the presence of a positive feedback mechanism

Synchronization is a process that describes the coherent dynamics of a large ensemble of interacting units.The study of explosive synchronization transition attracts considerable attention.Here,I report the explosive transition within the framework of a mobile network,while each oscillator is controlled by global-order parameters of the system.Using numerical simulation,I find that the explosive synchronization(ES)transition behavior can be controlled by simply adjusting the fraction of controlled oscillators.The influences of some parameters on explosive synchronization are studied.Moreover,due to the presence of the positive feedback mechanism,I prevent the occurrence of the synchronization of continuous-phase transition and make phase transition of the system a first-order phase transition accompanied by a hysteresis loop.     

苗族服饰色彩体系构建研究

色彩是民族服饰的核心要素，也是民族文化元素的重要组成部分，构建一套兼具科学性与实用性的色彩体系极具挑战性。在传统色彩地理学方法基础上，通过提取主题色和改进的关联规则挖掘方法，获取色彩数据、寻找色彩规则，并对其进行自然色彩体系（NCS）编谱分析，构建了一套苗族服饰色彩体系（Miao’s costume color system,MCCS）。该体系有助于进一步挖掘苗族服饰的配色规律，实现对苗族服饰色彩的数字化保护，为民族服饰色彩传承机理的探索与研究提供新的思路。     

Homo‐double helix formation of an optically active conjugated polymer bearing carboxy groups and amplification of the helicity upon complexation with achiral and chiral amines

An optically active, m‐terphenyl‐based π‐conjugated polymer bearing carboxy groups was synthesized by the copolymerization of the diethynyl monomer bearing a carboxy group with (S,S)‐2,5‐bis(2‐methylbutoxy)‐1,4‐dibromobenzene using Sonogashira reaction. The copolymer showed a weak circular dichroism (CD) in the main‐chain chromophore region due to a homo‐double helix formation with an excess helical handedness biased by the chiral alkoxy substituents through self‐association. However, upon complexation with achiral amines, such as piperidine, the CD intensity of the polymer significantly increased resulting in the formation of a greater excess one‐handed homo‐double helix via hydrogen‐bonded inclusion complexation with the achiral amines between each strand, leading to the amplification of the helicity. A preferred‐handed homo‐double helix was also induced in the polymer in the presence of nonracemic amines. The effect of the achiral and chiral amines on the homo‐double helix formation was investigated by comparing the CD spectra of the polymer to those of its model dimer. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 990–999     

一种带疏水长链的水溶性偶氮引发剂的合成及端基疏水聚合物疏水缔合效应研究

以偶氮二异丁腈、十二胺为主要原料,通过Pinner反应制备了一种两端各带有12个碳烷基链的水溶性偶氮引发剂——2,2'-偶氮二异丁基十二脒盐酸盐AIBL.采用核磁氢谱、元素分析及液相色谱对AIBL进行了结构及纯度表征,采用TGA、DSC和紫外分光光度计研究了其热分解现象和热分解动力学,采用表面张力仪对其表面活性进行了测定.结果表明,所合成的引发剂AIBL具有预想的结构和较高的纯度,其热分解反应属于一级反应,热分解活化能为134.80 k J/mol,70℃下水中的半衰期约为4 h;AIBL在水溶液中具有表面活性,其临界胶束浓度为0.13 g/L,对应的表面张力为33.57 m N/m.以丙烯酰胺为单体、AIBL为引发剂制备了水溶性端基疏水聚合物SPAM.采用溴化法研究其转化率,应用乌氏黏度法、零切黏度法以及荧光探针对其缔合作用进行了研究.结果表明,AIBL具有良好的引发丙烯酰胺聚合的能力;相对于不带疏水长链的引发剂所合成的聚合物PAM,SPAM具有明显的疏水缔合效应,这说明AIBL成功地将疏水长链引入到聚合物的端基中,从而形成端基疏水聚合物.