Quantum Pairing Time Orders

The concept of the time-independent correlators for the even- and odd-frequency pairing states that can be defined for both bosonic and fermionic quasiparticles is proposed. These correlators explicitly capture the existence of two distinct classes of pairing states and provide a direct probe of the hidden Berezinskii order. This concept is illustrated in the cases of pairings for Majorana fermions and quasiparticles in Dirac semimetals. It is shown that the time-independent correlator is able to effectively capture the energy scale relevant for pairing.     

Self-Assembly Behavior of Diacetylenic Acid Molecules upon Vapor Deposition: Odd–Even Effect on the Film Morphology

A series of linear carboxylic acids containing diacetylenic units at different positions along the chain (C₁₂H₂₅(C≡C)₂(CH₂)_nCOOH, n=7–11) were vacuum-deposited on clean silica substrates. The morphologies of the initial films after UV irradiation were studied. A clear odd–even effect on the morphology of the initial film was observed in that, depending on the spacer length between the diacetylenic unit and carboxyl head group, rings or dendrites of acid dimer layers were obtained. A molecular dynamic simulation of the aggregation process suggests that two competing intermolecular interactions and thus aggregation directions are involved and modulated by the odd or even carbon chain length. Further modulation of the interaction by substitution of a phenyl group at the terminus of the chain or by changing the carboxyl head group to an amidobenzoic acid head group led to a similar odd–even effect but with different dimensions or trends, which can be rationalized similarly. These results give the opportunity to create aligned conjugated polymer chains of different dimensions through self-assembly for applications in molecular/organic electronics.     

Weierstrass逼近定理的应用

讨论 Weierstrass逼近定理的应用 .运用 Weierstrass逼近定理 ,我们对于连续偶函数和连续奇函数的性质进行了进一步的刻划 .     

偶奇q相干态的振幅立方压缩性质

研究结果表明,偶q相干态呈现振幅立方压缩性质;奇q相干态不呈现振幅立方压缩性质。     

不饱和链烃分子结构与沸点的关系

在分子图的基本结构要素的基础上，提出了三个新的拓扑指数：顶点度-距离 指数（VDI），边度-距离指数（EDI）和奇偶指数（OEI），并用这些指数对C2- C20的150个不饱和链烃（包括烯烃、炔烃及烯炔）的沸点（bp)进行相关分析，得 到如下回归方程：ln(795-bp)=6.935044-0.373392EDI^1/5-3.900564×10^- 2OEI+6.396343×10^-3VDI（F=10539.14,r=0.9977,s=6.24)，该回归模型对不饱和 链烃的沸点具有较好的估算和预测能力，表明本文所提出的三个拓扑指数具有良好 的结构-性质相关性。     

Odd‐even effect during layer‐by‐layer assembly of polyelectrolytes inspired by marine mussel

Biomimetic polyelectrolyte of Dopa modified poly(acrylic acid) (PAADopa) was synthesized taking advantage of Dopa, the major unit of marine adhesive proteins. Zinc crosslinked PAADopa (PAADopa‐Zn) were formed at acidic pH for more compact structure and assembled with the positively charged polyethylenimine (PEI) to build robust polyelectrolyte multilayers at high salt concentration. Effects of pH, crosslinking degree, and salt concentration on polymer structure, film building process, and morphology were investigated, respectively. An “odd‐even” effect was observed by quartz crystal microbalance with dissipation and AFM in the presence of zinc ion, which becomes more obvious with an optimum crosslinking degree (Zn/Dopa = 2.0) under high salt concentration (0.6 M NaCl). It indicates the different swollen properties of PEI chain and PAADopa‐Zn complexes during the layer‐by‐layer building process under optimum crosslinking degree of PAADopa‐Zn at high salt concentration. Such odd‐even phenomenon of the biocompatible system is of critical importance for understanding the mechanism of layer formation and film structures. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 245–255     

The homomorphism threshold of -free graphs

We determine the structure of -free graphs with n vertices and minimum degree larger than : such graphs are homomorphic to the graph obtained from a -cycle by adding all chords of length , for some k. This answers a question of Messuti and Schacht. We deduce that the homomorphism threshold of -free graphs is 1/5, thus answering a question of Oberkampf and Schacht.     

Liquid crystal dimers and the twist-bend nematic phase. The preparation and characterisation of the α,ω-bis(4-cyanobiphenyl-4′-yl) alkanedioates

Eleven members of the homologous series of liquid crystal dimers, the α,ω-bis(4-cyanobiphenyl-4′-yl) alkanedioates, have been synthesised and their transitional properties characterised. These dimers consist of two cyanobiphenyl units connected by an alkyl spacer attached via ester linkages. All eleven members exhibit exclusively nematic behaviour. The nematic–isotropic transition temperatures, T_NI, and associated entropy changes, ?S_NI/R, exhibit pronounced alternations as the length and parity of the spacer is varied; this is characteristic behaviour of liquid crystal dimers. The transitional properties of the ester-linked dimers are compared with the corresponding materials having either ether, methylene or carbonate linkages between the spacer and mesogenic units. For short spacer lengths and both odd- and even-membered dimers, the ester-linked materials show the highest values of T_NI and the methylene-linked the lowest. For longer spacer lengths, T_NI of the carbonate-linked dimers fall between those of the corresponding ester- and ether-linked dimers. The ether-linked materials show the largest alternation in ?S_NI/R on varying spacer length and the carbonate-linked dimers the lowest. This behaviour is interpreted in terms of the molecular geometry and it is suggested that the ether- and ester-linked odd-membered dimers have rather similar shapes. A phase diagram constructed using binary mixtures of the pentyl member of this ester-linked series and the known twist-bend nematogen, 1,7-bis(4-cyanobiphenyl-4′-yl)heptane (CB7CB), is presented. The twist-bend nematic–nematic transition temperature of the mixtures shows a striking convex curvature as the concentration of CB7CB is decreased, and so it is not possible to estimate a virtual twist-bend nematic–nematic transition temperature for the ester-linked material.     

High-spin states in 128I

The high-spin states in 128I have been studied by using in-beam γ-ray spectroscopy with the 124Sn(7Li,3n)128I reaction at beam energies of 25, 28 and 42 MeV. A new level scheme including 20 new levels and 27 new γ-transitions for 128I has been established preliminarily.