Subset representations and eigenvalues of the universal intertwining matrix

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation.     

复杂势场量子弹球中疤痕态的量子化条件

量子疤痕是波函数在经典不稳定周期轨道周围反常凝聚的一种量子或波动现象.人们对疤痕态的量子化条件进行了大量研究,对深入理解半经典量子化起到了一定的促进作用.之前大部分研究工作主要集中在硬墙量子弹球上,即给定边界形状的无穷深量子势阱系统.本文研究具有光滑复杂势场的二维量子弹球系统,考察疤痕态的量子化条件及其重复出现的规律,得到了与硬墙弹球不一样的结果,对理解这类现象是一个有益的补充.这些结果将有助于理解具有无规长程杂质分布的二维电子系统的态密度谱和输运行为.     

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。     

Probabilism,entropies and strictly proper scoring rules

Accuracy arguments are the en vogue route in epistemic justifications of probabilism and further norms governing rational belief. These arguments often depend on the fact that the employed inaccuracy measure is strictly proper. I argue controversially that it is ill-advised to assume that the employed inaccuracy measures are strictly proper and that strictly proper statistical scoring rules are a more natural class of measures of inaccuracy. Building on work in belief elicitation I show how strictly proper statistical scoring rules can be used to give an epistemic justification of probabilism.An agent's evidence does not play any role in these justifications of probabilism. Principles demanding the maximisation of a generalised entropy depend on the agent's evidence. In the second part of the paper I show how to simultaneously justify probabilism and such a principle. I also investigate scoring rules which have traditionally been linked with entropies.     

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.     

Chebyshev spectral variational integrator and applications

The Chebyshev spectral variational integrator(CSVI) is presented in this paper. Spectral methods have aroused great interest in approximating numerically a smooth problem for their attractive geometric convergence rates. The geometric numerical methods are praised for their excellent long-time geometric structure-preserving properties.According to the generalized Galerkin framework, we combine two methods together to construct a variational integrator, which captures the merits of both methods. Since the interpolating points of the variational integrator are chosen as the Chebyshev points,the integration of Lagrangian can be approximated by the Clenshaw-Curtis quadrature rule, and the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of configuration variables and the corresponding derivatives. The numerical float errors of the first-order spectral differentiation matrix can be alleviated by using a trigonometric identity especially when the number of Chebyshev points is large. Furthermore, the spectral variational integrator(SVI) constructed by the Gauss-Legendre quadrature rule and the multi-interval spectral method are carried out to compare with the CSVI, and the interesting kink phenomena for the Clenshaw-Curtis quadrature rule are discovered. The numerical results reveal that the CSVI has an advantage on the computing time over the whole progress and a higher accuracy than the SVI before the kink position. The effectiveness of the proposed method is demonstrated and verified perfectly through the numerical simulations for several classical mechanics examples and the orbital propagation for the planet systems and the Solar system.     

Quantum fractionalism: The Born rule as a consequence of the complex Pythagorean theorem

Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in orthogonal projections from the complex line of a quantum state to eigenspaces of an observable. Unit total probability corresponds to a complex Pythagorean theorem: the measure of a subset of the complex line is the sum of the measures of its projections on all eigenspaces.Postulating the existence of a continuum infinity of identical quantum universes, all with the same quasi-classical worlds, we show that projection factors give relative amounts of worlds. These appear as relative frequencies of results in quantum experiments, and play the role of probabilities in decisions and inference. This solves the probability problem of Everett's theory, allowing its preferred basis problem to be solved as well, and may help settle questions about the nature of probability.     

Persistent Room Temperature Phosphorescence from Triarylboranes: A Combined Experimental and Theoretical Study

Achieving highly efficient phosphorescence in purely organic luminophors at room temperature remains a major challenge due to slow intersystem crossing (ISC) rates in combination with effective non‐radiative processes in those systems. Most room temperature phosphorescent (RTP) organic materials have O‐ or N‐lone pairs leading to low lying (n, π*) and (π, π*) excited states which accelerate k_isc through El‐Sayed's rule. Herein, we report the first persistent RTP with lifetimes up to 0.5 s from simple triarylboranes which have no lone pairs. RTP is only observed in the crystalline state and in highly doped PMMA films which are indicative of aggregation induced emission (AIE). Detailed crystal structure analysis suggested that intermolecular interactions are important for efficient RTP. Furthermore, photophysical studies of the isolated molecules in a frozen glass, in combination with DFT/MRCI calculations, show that (σ, B p)→(π, B p) transitions accelerate the ISC process. This work provides a new approach for the design of RTP materials without (n, π*) transitions.     

Study of semileptonic decay of ${\bar{B}}_{s}^{0} \rightarrow \phi {l}^{+}{l}^{-}$ in QCD sum rule

In this work we study the semileptonic decay of ${\bar{B}}_{s}^{0}\to \phi {l}^{+}{l}^{-}$ (l=e, μ, τ) with the QCD sum rule method. We calculate the ${\bar{B}}_{s}^{0}\to \phi $ translation form factors relevant to this semileptonic decay, then the branching ratios of ${\bar{B}}_{s}^{0}\to \phi {l}^{+}{l}^{-}$ (l=e, μ, τ) decays are calculated with the form factors obtained here. Our result for the branching ratio of ${\bar{B}}_{s}^{0}\to \phi {\mu }^{+}{\mu }^{-}$ agree very well with the recent experimental data. For the unmeasured decay modes such as ${\bar{B}}_{s}^{0}\to \phi {e}^{+}{e}^{-}$ and ${\bar{B}}_{s}^{0}\to \phi {\tau }^{+}{\tau }^{-}$, we give theoretical predictions.