Zeros of the Jones Polynomial for Multiple Crossing-Twisted Links

Let D be a general connected reduced alternating link diagram, C be the set of crossings of D and C′ be the nonempty subset of C. In this paper we first define a multiple crossing-twisted link family {D ⁿ (C′)|n=1,2,…} based on D and C′, which produces (2,2n+1)-torus knot family, the link family A _n defined in Chang and Shrock (Physica A 301:196–218, 2001) and the pretzel link family P(n,n,n) as special cases. Then by applying Beraha-Kahane-Weiss’s Theorem we prove that limits of zeros of Jones polynomials of {D ⁿ (C′)|n=1,2,…} are the unit circle |z|=1 (It is independent of the selections of D and C′) and several isolated limits, which can be determined by computing flow polynomials of subgraphs of G corresponding to D. Furthermore, we use the method of Brown and Hickman (Discrete Math. 242:17–30, 2002) to prove that, for any ε>0, all zeros of Jones polynomial of the link D ⁿ (C) lie inside the circle |z|=1+ε, provided that n is large enough. Our results extend results of F.Y. Wu, J. Wang, S.-C. Chang, R. Shrock and the present authors and refine partial result of A. Champanerkar and L. Kofman.     

O-vacancy and surface on CeO2: A first-principles study

Atomic and electronic structures of CeO₂ (1 1 1), (1 1 0) and (1 0 0) surfaces are investigated using the first-principles density functional theory taking into account the on-site Coulomb interaction. Both the stoichiometric and O-deficient surfaces are examined in order to clarify the overall features. The CeO₂ (1 1 1) is found to be the most stable surface, followed by the (1 1 0) and (1 0 0) surfaces, consistent with experimental observations. Three surfaces exhibit different features of relaxation. Large relaxations are found at the (1 1 0) and (1 0 0) surfaces, while very small changes are observed at the (1 1 1) surface. It is found that the O-vacancy occurs more readily at the (1 1 0) surface as compared with the (1 1 1) surface. Furthermore, the formation energies of the O-vacancy in the surfaces are lower than that in the bulk. The energetically favorable O-vacancy locates in the second O-atomic layer for the (1 1 1) while at the surface layer for the (1 1 0). The excess electrons left with the removal of the O atom are distributed in the first two layers with certain (a considerable) fraction filling the Ce-4f states.     

A new chaotic Hopfield network with piecewise linear activation function

This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.     

Design of unobscured reflective zoom system with three mirrors

A method for the design of an unobscured reflective zoom system with three mirrors is described. This method applies the vector aberration theory, which helps designers analyze third-order aberrations for optical systems with decentered and tilted surfaces. As the vector aberration theory presents the variation of third-order aberrations in asymmetric systems through analytic expressions, real ray tracing is unnecessary. Hence, the design with vector aberration theory is faster, and the analytic expressions are more comprehensive and intuitive. To demonstrate the practicability of the method, a design example is given, which shows that the presented method can guide designers achieve a good unobscured reflective zoom system with three mirrors.     

Phase-field modeling droplet dynamics with soluble surfactants

Using lattice Boltzmann approach, a phase-field model is proposed for simulating droplet motion with soluble surfactants. The model can recover the Langmuir and Frumkin adsorption isotherms in equilibrium. From the equilibrium equation of state, we can determine the interfacial tension lowering scale according to the interface surfactant concentration. The model is able to capture short-time and long-time adsorption dynamics of surfactants. We apply the model to examine the effect of soluble surfactants on droplet deformation, breakup and coalescence. The increase of surfactant concentration and attractive lateral interaction can enhance droplet deformation, promote droplet breakup, and inhibit droplet coalescence. We also demonstrate that the Marangoni stresses can reduce the interface mobility and slow down the film drainage process, thus acting as an additional repulsive force to prevent the droplet coalescence.     

Rapid decolorization of azo dyes in aqueous solution by an ultrasound-assisted electrocatalytic oxidation process

In this study, we developed a novel ultrasound-assisted electrocatalytic oxidation (US–EO) process to decolorize azo dyes in aqueous solution. Rhodamine B was decolorized completely within several minutes in this developed US–EO system. Oxidation parameters such as applied potentials, power of the ultrasound, initial pH of the solution, and initial concentration of RhB were systematically studied and optimized. An obvious synergistic effect was found in decolorization of RhB by the US–EO process when comparing with either ultrasound (US) process or electrocatalytic oxidation (EO) one. Additionally, the decolorization of other azo dyes, such as methylene blue, reactive brilliant red X-3B, and methyl orange, were also effective in the US–EO system. The results indicated that US–EO system was effective for the decolorization of azo dyes, suggesting its great potential in dyeing wastewater treatment.     

激光跟瞄仿真系统及两种跟瞄方法

基于OpenGL和大气传输光学分析的3维全数字仿真是激光跟瞄系统的重要研究手段。为提高跟踪和瞄准精度,从激光跟瞄仿真系统整体出发,研究了目标成像中的投影变换、成像与跟踪的关系、高精度跟踪现有算法的控制过程仿真等内容,并提出了基于大视口、目标大气传输图像序列的跟瞄仿真技术。说明了仿真系统中跟瞄精度分析的特点。就某仿真场景,设计了“头部顶点”和“两点提取”两种跟瞄方法,在不同大气湍流条件下得到了它们的跟瞄精度,说明应用该激光跟瞄仿真系统,能够预先设计、测试和验证一些跟瞄方法,帮助进行算法分析和改进,从而提高工作效率和节约成本。     

基于过模波导的高功率微波准相干功率合成器

研究了一种用于功率合成的GW级高功率微波功率合成器。该合成器工作在X波段,输入微波由2路工作频率不同的X波段的微波源产生。为了满足输出功率和功率容量的要求,用于功率合成的微波源工作段波导的过模因子为12.7,这给功率合成器的设计带来了一定的困难。着重讨论了如何利用过模波导设计X波段高功率合成器,研究了如何抑制过模波导的高次模式并提高其功率容量和传输效率。设计的功率合成器单路传输效率达到99.0%以上,允许的最大输出功率达到5.6 GW以上,还可以按照需求适当增大高度,以进一步提高其功率容量而不影响传输效率。     

四种新型仲胺配合物的合成、表征及与ct-DNA相互作用的光谱研究

合成了新型仲胺类配体L(N,N’-二(4-甲基苄基)乙二胺)及其四种过渡金属的硝酸盐配合物,[ML2(H2O)2]2+.2NO3-(M=CuⅡ,CoⅡ,NiⅡ,ZnⅡ),利用元素分析、红外、1H NMR等对其结构进行了表征,其中用X-ray单晶衍射解析了Cu-L单晶结构,为波谱分析推测的分子结构进行了验证。通过紫外、荧光光谱研究了该四种金属配合物与小牛胸腺DNA的相互作用,结果表明配合物与DNA的作用方式均为静电结合,Cu-L,Co-L,Ni-L,Zn-L与DNA的结合常数分别为:1.67×103,2.5×103,1.35×103和9.85×102。     

磁场安培环路定理证明的新方法

大学物理中磁场的安培环路定理是学生重点掌握的内容之一,安培环路定理的证明也是必须要讲解的内容.现有的教材在证明环路不包围电流的情况时多采用圆心角的方法证明,本文给出了两种新的证明方法,此方法借用了环路中包围电流的环路积分结果,方法简单、明了,在国内广泛使用的教材中未见出现此证明方法.