Bound states of the Klein－Gordon equation for ring-shaped Kratzer-type potential

The exact normalized bound state wavefunctions and energy equations of Klein－Gordon equation with equal scalar and vector ring-shaped Kratzer-type potential have been obtained.     

Bound states of the Klein－Gordon and Dirac equation for scalar and vector pseudoharmonic oscillator potentials

The exact bound state solutions of the Klein－Gordon equation and Dirac equation with scalar and vector pseudoharmonic oscillator potentials are obtained in this paper. Furthermore, we have used the supersymmetric quantum mechanics, shape invariance and alternative method to obtain the required results.     

双势阱产生正负电子对过程中的正电子波干涉与克莱因隧穿现象

通过将狄拉克场量子化并且数值求解狄拉克方程的方法研究在一维情况下双势阱激发正负电子对产生的过程.研究发现双势阱激发的正电子波在双势阱之间会出现干涉现象,过程中伴随着克莱因隧穿效应,并且在双势阱之间的距离取正电子波对应的驻波条件时,在双势阱之间会表现出驻波形式的正电子干涉波.并且驻波的出现对正负电子对的产生过程也存在相应的影响,驻波最终会通过克莱因隧穿效应衰减消失.     

马氏瓶回流原理分析

为了研究马氏瓶发生回流时水位变化的规律,利用理想气体定律和压强理论对马氏瓶的回流原理进行了推导,得到了引起马氏瓶回流水量的计算公式,并结合试验对公式进行了验证,发现水量的计算值与实际值基本一致,表明了计算公式的适用性。同时发现回流水不仅进入马氏瓶进气管,也会进入马氏瓶内,回流到瓶内的水将压缩水面上部的空气,使瓶内空腔体积减小,试验结果进一步揭示了马氏瓶回流过程的规律。     

综合性实验——纯净水与果汁瓶材料的剖析

设计了一个高分子材料与工程专业的综合性教学实验。利用FT-IR、UV-Vis和DSC三种方法,对生活中常见的纯净水瓶(PET)和果汁瓶(PP)材料进行了剖析,确认出两种材料的组成,合理解释了当沸腾后的热水倒入纯净水瓶时,瓶体会明显变软、变形,而果汁瓶不发生变形的原因。该实验加深了学生对常用高分子材料结构与性能的认识,已应用在三届学生的专业实验教学中,教学效果良好。     

A note on finite-sheeted covering maps from 2-dimensional compact Abelian groups

We consider finite-sheeted covering maps from 2-dimensional compact connected abelian groups to Klein bottle weak solenoidal spaces, metric continua which are not groups. We show that whenever a group covers a Klein bottle weak solenoidal space it covers groups as well, moreover it covers the product of two solenoids. The converse is not true, we give an example of group which covers groups with any finite number of sheets, but does not cover any Klein bottle weak solenoidal space.     

Aut(X, σ) and Aut(X/σ) are not isomorphic in the category of surfaces with nodes

A symmetric Riemann surface is a pair (X,?σ) where X is a Riemann surface and?σ?is an anticonformal involution. We denote by Aut(X,?σ) the subgroup of Aut(X) defined by the automorphisms commuting with σ. There is a natural isomorphism between Aut(X,?σ) and Aut(X/σ). In this article we shall show that this isomorphism does not stand if X is a Riemann surface with nodes.     

Effect of the graft ratio on the properties of polythiophene‐g‐poly(ethylene glycol)

Graft copolymers formed by anchoring poly(ethylene glycol) (PEG) chains to conjugated polythiophene have been prepared by copolymerizing two compounds: unsubstituted α‐terthiophene (Th₃) and a thiophene‐derived macromonomer having an α‐terthiophene conjugated sequence and one Th₃ bearing a PEG chain with molecular weight of 2000 as substitute at the 3‐position of the central heterocycle (Th₃‐PEG₂₀₀₀). The grafting ratio of the resulting copolymers (PTh₃^*‐g‐PEG), which were obtained using 75:25 and 50:50 Th₃‐PEG₂₀₀₀:Th₃ weight ratios, is significantly smaller than that of copolymers derived from polymerization of macromonomers consisting of a α‐pentathiophene sequence in which the central ring bears a PEG chain of M_w = 2000 (PTh₅‐g‐PEG). The electroactivity and electrochemical stability of PTh₃^*‐g‐PEG is not only higher than that of PTh₅‐g‐PEG but also higher than that of PTh₃, the latter presenting a very compact structure that makes difficult the access and escape of dopant ions into the polymeric matrix during the redox processes. Furthermore, the optical π‐π^* lowest transition energy of PTh₃^*‐g‐PEG is lower than that of both PTh₅‐g‐PEG and PTh₃. These properties, combined with suitable wettability and roughness, result in an excellent behavior as bioactive platform of PTh₃^*‐g‐PEG copolymers, which are more biocompatible, in terms of cellular adhesion and proliferation, and electro‐compatible than PTh₅‐g‐PEG. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 239–252