Optical switching and alignment of antiferroelectric liquid crystals containing an azo group

The optical properties of two kinds of photochromic antiferroelectric liquid crystal (AFLC) containing an azo group have been examined. Depending on the substituting group at the chiral centre, these AFLCs showed different photoinduced phase transitions by Ar⁺ laser light irradiation. This phase transition has led to a new form of optical switching controlled by a bias voltage. In addition, it was found that these AFLCs caused an azimuthal photoalignment effect regulated by linearly polarized Ar⁺ laser light irradiation. These phenomena were applied to image storage.     

基于智能数据采集器的研究与实现

针对目前各行业数字化、智能化产品应用日趋广泛，数据的获取、传输、分析、应用尤为重要，如何避免采集设备接口单一、功能固定、实用性差等缺点，提出采用ARM嵌入式工控模块M9080-N20为基础，采用VK3266串口芯片扩展UART串行接口，提出基于73K222AU调制解调器、HR219307变压器实现采集器二线模拟通信，并支持以太网、CAN总线和UART串行通信，可以有效解决数据远程采集、传输和控制，适用于特殊环境设备故障检测、诊断和抢修。实验结果证明，智能数据采集器不仅具有多种型号设备故障诊断功能；还能实现野外快速通信组网，不同类型设备数据远程采集、传输、分析和控制功能，在军民融合产品上具有广阔的应用前景和实用价值。     

Classroom note: Using the binomial series to prove the arithmetic mean–geometric mean inequality

In 1968, Leon Gerber compared (1 + x) ^a to its kth partial sum as a binomial series. His result is stated and, as an application of this result, a proof of the arithmetic mean–geometric mean inequality is presented.     

运用CAFP教学提升学生化学意志素质的教学案例

鉴于当前学生化学意志素质缺乏的问题，探讨以认知、情绪唤醒、情感、意志为主控目标，在预习、尝试学习、交错搭配合作学习中，开展CAFP教学研究，以促成情意因素对认知的调动、动力、强化等功能。     

Areas and the Fundamental Theorem of Calculus

We present a concise, yet self-contained module for teaching the notion of area and the Fundamental Theorem of Calculus for different groups of students. This module contains two different levels of rigour, depending on the class it used for. It also incorporates a technological component.     

不同光场二阶相干度的实验研究

基于Hanbury Brown-Twiss(HBT)实验,我们借助于两个单光子计数模块,一个50/50分束器和一个快速计数卡(FastCom-P7888)研究了不同光场的二阶相干度。我们首先制备了脉冲相干光,连续相干光以及单原子发出的单光子源,并测量这几种不同光场的二阶相干度g(2)(τ)。我们通过测量俘获在磁光阱(MOT)和远失谐偶极阱(FORT)中的单原子在近共振连续激光激发下所辐射的荧光的二阶相干度,分别得到了g(2)(τ=0)=0.08和g(2)(τ=0)=0.09,借助于实验中产生的脉冲光与单原子,接下来我们将进行触发式单光子源的实验研究。     

Analysis of the multiple roots of the Lundberg fundamental equation in the PH (n) risk model

In the study of the Sparre Andersen risk model with phase‐type (n) inter‐claim times (PH (n) risk model), the distinct roots of the Lundberg fundamental equation in the right half of the complex plane and the linear independence of the eigenvectors related to the Lundberg matrix L_δ(s) play important roles. In this paper, we study the case where the Lundberg fundamental equation has multiple roots or the corresponding eigenvectors are linearly dependent in the PH (n) risk model. We show that the multiple roots of the Lundberg fundamental equation det[L_δ(s)] = 0 can be approximated by the distinct roots of the generalized Lundberg equation introduced in this paper and that the linearly dependent eigenvectors can be approximated by the corresponding linearly independent ones as well. Using this result we derive the expressions for the Gerber–Shiu penalty function. Two special cases of the generalized Erlang(n) risk model and a Coxian(3) risk model are discussed in detail, which illustrate the applicability of main results. Finally, we consider the PH(2) risk model and conclude that the roots of the Lundberg fundamental equation in the right half of the complex plane are distinct and that the corresponding eigenvectors are linearly independent. Copyright © 2011 John Wiley & Sons, Ltd.     

On a family of highly regular graphs by Brouwer,Ivanov, and Klin

Highly regular graphs for which not all regularities are explainable by symmetries are fascinating creatures. Some of them like, e.g., the line graph of W. Kantor’s non-classical $GQ(5^2,5)$, are stumbling stones for existing implementations of graph isomorphism tests. They appear to be extremely rare and even once constructed it is difficult to prove their high regularity. Yet some of them, like the McLaughlin graph on 275 vertices and Ivanov’s graph on 256 vertices are of profound beauty. This alone makes it an attractive goal to strive for their complete classification or, failing this, at least to get a deep understanding of them. Recently, one of the authors discovered new methods for proving high regularity of graphs. Using these techniques, in this paper we study a classical family of strongly regular graphs, originally discovered by A.E. Brouwer, A.V. Ivanov, and M.H. Klin in the late 80s. We analyse their symmetries and show that they are $(3,5)$-regular but not 2-homogeneous. Thus we promote these graphs to the distinguished club of highly regular graphs with few symmetries.     

一类正交空间填充设计的构造

空间填充设计在计算机试验中应用十分广泛,当拟合回归模型时,正交的空间填充设计保证了因子效应估计的独立性.基于广义正交设计,文章给出了构造二阶正交拉丁超立方体设计和列正交设计的方法,新构造的设计不仅满足任意两列之间相互正交,还能保证每一列与任一列元素平方组成的列以及任两列元素相乘组成的列都正交.当某些正交的空间填充设计不存在时,具有较小相关系数的近似正交设计可作为替代设计使用.设计构造的灵活性为计算机试验在实践中的广泛应用提供了必要的支持.