Polygonal Billiards with Small Obstacles

The technique of unfolding a polygonal billiard table is used to answer certain questions concerning the illumination problem. The main problem addressed is how many point obstacles would suffice to block any billiard path between two points of the polygon. The answer can then be generalized from point obstacles to small -neighborhoods of points.     

Remarks on regular (LF)-spaces

Developing ideas found in a recent paper of Gilsdorf to arbitrary topological vector spaces (tvs) one shows that a Hausdorff (LB) _tv -spaceE is regular provided every null-sequence inE has a series convergent subsequence inE. Received by the editors 1980Mathematics Subject Classification (1985 Revision) 46A12.     

一种新的自相关拓扑指数及其互补指数应用于不饱和链烃物理性质的QSPR研究

依据系统命名法的编号原则及不饱和链烃的结构特证,建立了原子的染色序数(ti),并在邻矩阵基础上由ti构建原子染色序数自相关指数(mR)及互补指数mR′,其中0R1、R、互补指数0R′1、R′,C原子个数(N)与炔烃的沸点、烯烃的热力学性质(标准生成焓、标准熵、标准熵和标准生成自由能)有良好的相关性,相关系数分别为0.999 2,0.999 4,0.999 4和0.994 1.该模型用于预测不饱和链烃的物理性质,计算简便,结果准确.     

Curvature and defects in nematic liquid crystals

ABSTRACT

The use of nematic liquid crystals for directed assembly of particles and for the creation of multistable systems depends on the ability to control the topological defects and the distortions of the director field. These are not only driven by topological constraints and by anchoring energies but also by the curvature field created by the bounding surfaces. This review explores the interaction between defects, topology, inclusions and curvature in nematics. I will introduce the relationship between curvature and the Frank elastic energy in nematics, and then I will give an overview of specific examples that show how this coupling can create unexpected behaviours, such as lock-and-key interactions, anchoring transitions on curved surfaces and memory effects.     

Azide–Alkyne Interactions: A Crucial Attractive Force for Their Preorganization for Topochemical Cycloaddition Reaction

A new class of attractive intermolecular interaction between azide and ethynyl structural entities in a wide range of molecular crystals is reported. This interaction was systematically evaluated by using 11 geometrically different structural motifs that are preorganized to direct a solid-state topochemical azide–alkyne cycloaddition (TAAC) reaction. The supramolecular features of the azide–alkyne interaction were mapped by various crystallographic and quantum chemical approaches. Topological analysis shows the noticeable participation of electron density in the azide⋅⋅⋅alkyne interactions. Interestingly, reorientation of the atomic polarizabilities in vicinal azide and alkyne groups upon interaction in crystals favors soft orbital-guided TAAC reactions. Moreover, various solid-state and gas-phase energy decomposition methods of individual azide⋅⋅⋅alkyne interactions summarize that the strength (varies from −5.7 to −30.1 kJ mol⁻¹) is primarily guided by the dispersion forces with a influencing contribution from the electrostatics.     

Topological photonic states in gyromagnetic photonic crystals: Physics,properties, and applications

Topological photonic states (TPSs) as a new type of waveguide state with one-way transport property can resist backscattering and are impervious to defects, disorders and metallic obstacles. Gyromagnetic photonic crystal (GPC) is the first artificial microstructure to implement TPSs, and it is also one of the most important platforms for generating truly one-way TPSs and exploring their novel physical properties, transport phenomena, and advanced applications. Herein, we present a brief review of the fundamental physics, novel properties, and practical applications of TPSs based on GPCs. We first examine chiral one-way edge states existing in uniformly magnetized GPCs of ordered and disordered lattices, antichiral one-way edge states in cross magnetized GPCs, and robust one-way bulk states in heterogeneously magnetized GPCs. Then, we discuss the strongly coupling effect between two co-propagating (or counter-propagating) TPSs and the resulting physical phenomena and device applications. Finally, we analyze the key issues and prospect the future development trends for TPSs in GPCs. The purpose of this brief review is to provide an overview of the main features of TPSs in GPC systems and offer a useful guidance and motivation for interested scientists and engineers working in related scientific and technological areas.     

RuX2 (X=P、As、Sb) 家族化合物中的压力诱导的超导和拓扑相变

作为热电材料 FeSb2 的姊妹材料，RuSb2 被广泛研究，但以前的工作主要集中在与 FeSb2 的比较上，尚未对 RuSb2 在压力下的性质进行深入研究。在本文中，我们研究了 RuSb2 在压力 下的性质，并探讨了其与 Ru 的磷族化合物 RuP2 和 RuAs2 之间晶体和电子结构的异同。我们 用晶体结构搜索方法结合第一性原理计算，发现该族化合物经历了一系列结构相变：（I）RuSb2： Pnnm → I4/mcm → I4/mmm；(II) RuP2：Pnnm → I41/amd → Cmcm；(III) RuAs2： Pnnm → P-62m。新发现的五个相在高压下都是热力学和动力学稳定的，并表现出金属性。RuSb2 和 RuP2 的四个高压相在泄压到零压后动力学依旧稳定。我们计算得到 RuSb2 的 I4/mcm 和 I4/mmm 相以及 RuP2 的 I41/amd 和 Cmcm 相的超导转变温度在 0 GPa 时分别约为 7.3 K、 10.9 K、13.0 K 和 10.1 K。另外，RuSb2 的 I4/mcm 和 I4/mmm 相以及 RuP2 的 I41/amd 相还具有拓扑非平庸的表面态。我们的研究表明，压力是调节 Ru 的磷族化合物结构、电子和超 导性质的有效方法。     

Existence of Solutions to a p-Laplacian Equation with Integral Initial Condition

In this paper,a class of one-dimension p-Laplacian equation with nonlocal initial value is studied.The existence of solutions to such a problem is obtained by using the topological degree method.