Decomposability index of tournaments

Given a tournament $T$, a module of $T$ is a subset $X$ of $V\left(T\right)$ such that for $x,y\in X$ and $v\in V\left(T\right)?X$, $(x,v)\in A\left(T\right)$ if and only if $(y,v)\in A\left(T\right)$. The trivial modules of $T$ are $?$, $\left\{u\right\}$ $(u\in V\left(T\right))$ and $V\left(T\right)$. The tournament $T$ is indecomposable if all its modules are trivial; otherwise it is decomposable. The decomposability index of $T$, denoted by $\delta \left(T\right)$, is the smallest number of arcs of $T$ that must be reversed to make $T$ indecomposable. For $n\ge 5$, let $\delta \left(n\right)$ be the maximum of $\delta \left(T\right)$ over the tournaments $T$ with $n$ vertices. We prove that $?\frac{n+1}{4}?\le \delta \left(n\right)\le ?\frac{n?1}{3}?$ and that the lower bound is reached by the transitive tournaments.     

A Photo- and Thermo-Driven Azoarene-Based Circularly Polarized Luminescence Molecular Switch in a Liquid Crystal Host

The development of chiral optical active materials with switchable circularly polarized luminescence (CPL) signals remains a challenge. Here an azoarene-based circularly polarized luminescence molecular switch, (S, R, S)-switch 1 and (R, R, R)-switch 2 , are designed and prepared with an (R)-binaphthyl azo group as a chiral photosensitive moiety and two (S)- or (R)-binaphthyl fluorescent molecules with opposite or the same handedness as chiral fluorescent moieties. Both switches exhibit reversible trans/cis isomerization when irradiated by 365 nm UV light and 520 nm green light in solvent and liquid crystal (LC) media. In contrast with the control (R, R, R)-switch 2 , when switch 1 is doped into nematic LCs, polarization inversion and switching-off of the CPL signals are achieved in the resultant helical superstructure upon irradiation with 365 nm UV and 520 nm green light, respectively. Meanwhile, the fluorescence intensity of the system is basically unchanged during this switching process. In particular, these variations of the CPL signals could be recovered after heating, realizing the true sense of CPL reversible switching. Taking advantage of the unique CPL switching, the proof-of-concept for “a dual-optical information encryption system” based on the above CPL active material is demonstrated.     

A new approach to the synthesis of lactams of muramic,isomuramic and normuramic acids via intramolecular O-alkylation: Stereochemical features of the intramolecular nucleophilic substitution

The title compounds were synthesized from the selectively protected N-acylated d-glucosamine derivatives, containing α-halo carboxylic acid moieties, via intramolecular 3-O-alkylation. It was found that if the starting compound contains asymmetric electrophilic center, isomuramic acid derivatives were mainly formed, regardless of the configuration of the electrophilic carbon atom. An explanation for the observed stereochemical results was proposed on the basis of the analysis of steric interactions in the molecules of the starting compounds, as well as using the concept of anchimeric assistance. It was shown that N-acetylation of the obtained lactam derivatives and subsequent methanolysis under mild conditions led to the selective cleavage of δ-lactam ring resulting in the formation of the corresponding ester derivatives of N-acetylmuramic acid or its analogues in high yields.     

On the two dimensional effective electron mass in quantum wells,inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures.     

基于多孔径闪烁的湍流强度廓线反演方法研究

以多孔径闪烁方法的理论为基础,分别讨论了孔径滤波函数和光谱响应函数对权重函数的影响.根据包括边界层项的Hufnagel-Valley 5/7模型得到的闪烁指数,采用奇异值分解法反演了垂直方向的湍流强度廓线,结果的量级介于10~(-15)~10~(-17)之间,并随高度的增加不断减小,在量级和趋势上与理论模型基本一致;同时结合Shack-Hartman的实际测量结果,反演了水平方向1 km传输路径上的湍流强度分布状况.水平方向反演结果的量级在10~(-14)~10~(-15)之间,随传播距离的变化趋势与实验场地的实际情况较为符合,随时间的变化趋势与合肥地区同期的统计结果基本一致.     

Calculating particle pair potentials from fluid‐state pair correlations: Iterative ornstein–zernike inversion

An iterative Monte Carlo inversion method for the calculation of particle pair potentials from given particle pair correlations is proposed in this article. The new method, which is best referred to as Iterative Ornstein–Zernike Inversion, represents a generalization and an improvement of the established Iterative Boltzmann Inversion technique (Reith, Pütz and Müller‐Plathe, J. Comput. Chem. 2003, 24, 1624). Our modification of Iterative Boltzmann Inversion consists of replacing the potential of mean force as an approximant for the pair potential with another, generally more accurate approximant that is based on a trial bridge function in the Ornstein–Zernike integral equation formalism. As an input, the new method requires the particle pair correlations both in real space and in the Fourier conjugate wavenumber space. An accelerated iteration method is included in the discussion, by which the required number of iterations can be greatly reduced below that of the simple Picard iteration that underlies most common implementations of Iterative Boltzmann Inversion. Comprehensive tests with various pair potentials show that the new method generally surpasses the Iterative Boltzmann Inversion method in terms of reliability of the numerical solution for the particle pair potential. © 2018 Wiley Periodicals, Inc.     

Kinetic Studies of the Thermal cis-to-trans Isomerization of Dioxaphospholanes

By following a previously reported method,¹ the synthesis of r-2-alkoxy-cis-4-cis-5-dimethyl-1,3,2-λ³-dioxaphospholanes ligands (1 and 3) was carried out. The purpose of this work is the kinetic study of the inversion barrier at phosphorus for 1 and 3 and the comparison with the already informed dioxaphospholane 2. The kinetic measurements of the thermal isomerization cis-to-trans were performed by ³¹P NMR spectroscopy, observing a first order kinetics for both compounds. The energy of activation (E_a) for the epimerization of compounds cis-1 and cis-3 was calculated to be 16.0 ± 0.6 and 11.8 ± 0.8 kcal/mol, respectively. The values of the thermodynamic parameters of the transition state (Δ H^≠, Δ S^≠, Δ G^≠) suggest that the inversion at phosphorus not only depends on the spatial requirements of the alkoxy substituent but also on entropic effects. The thermodynamic parameters Δ H°, Δ S°, and Δ G° were also evaluated and they show that the cis isomers are preferred from enthalpic point of view, but entropic effects dominate the equilibrium trans ? cis leading to the entropically favored trans isomers. Furthermore, the results are supported by density functional theory calculations of 1–4 at the B3LYP/6-31G** level.     

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根据反向积分原理编写了流场反演程序,并开展了程序验证计算。在反演区域内,由临界面速度反演出与辐射流体力学程序MULTI计算结果几乎一致的结果;由Saturn加速器上实验测试的单个样品后自由面速度反演出了加载压强历史、多种厚度样品后自由面粒子速度历史等信息,与文献对比发现,反演结果与由加速器工作电流推出结果、WONDY程序计算结果、实验测试结果相吻合。本工作为即将开展的激光驱动准等熵压缩实验奠定了技术基础。