混沌群作用

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｉｓｐａｐｅｒｉｓｔｈｅｓｅｑｕｅｌｔｏ[1 ,2 ].Ｃａｉｒｎｓｅｔａｌ.[1] ｉｎｔｒｏｄｕｃｅｄｔｈｅｎｏｔｉｏｎｏｆａｃｈａｏｔｉｃｇｒｏｕｐａｃｔｉｏｎａｓａｇｅｎｅｒａｌｉｚａｔｉｏｎｏｆｃｈａｏｔｉｃｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓ(ｓｅｅｄｅｆｉｎｉｔｉｏｎｂｅｌｏｗ) .Ｔｈｅｙｓｈｏｗｅｄｔｈａｔｔｈｅｃｉｒｃｌｅｄｏｅｓｎｏｔａｄｍｉｔａｃｈａｏｔｉｃａｃｔｉｏｎｏｆａｎｙｇｒｏｕｐ ,ａｎｄｃｏｎｓｔｒｕｃｔｅｄａｃｈａｏｔｉｃａｃｔｉｏｎｏｆＧ =Ｚ×…     

Representation of Hilbert algebras and implicative semilattices

In this paper we shall give a topological representation for Hilbert algebras that extend the topological representation given by A. Diego in [4]. For implicative semilattices this representation gives a full duality. We shall also consider the representation for Boolean ring.     

Weak Density of Smooth Maps in W 1, 1(M,N) for Non-Abelian π1(N)

We prove that smooth maps are dense in the sense of biting convergence in W ^{1, 1}(M, N) when M and Nare compact Riemannian manifolds and N is closed.     

多环涡旋光束的实验研究

涡旋光束的产生、传输与应用是当前光学领域热门的研究课题之一.本文提出的新型多环涡旋光束,包括双环涡旋及三环涡旋光束,它是由多束携带不同拓扑电荷数且束腰半径不同的拉盖尔-高斯涡旋光束共轴叠加而成,其光强分布为多环结构.从理论上研究了多环涡旋光束的形成与分布特征,基于共轭对称延拓Fourier计算全息方法生成了多环涡旋光束的计算全息图,并利用一个空间光调制器实验产生了与理论一致的高质量的多环涡旋光束.研究表明多环涡旋光束的各环携带不同的轨道角动量,空间分布保持相互独立.这种新型的多环涡旋光束相对于携带单一拓扑电荷数的涡旋光束,提供了更多的控制参数和更加多样化的结构分布,因此在光学镊子、光学捕获等微操控以及光通信领域具有潜在的应用潜力.     

A Combined Experimental and Theoretical Study on the Formation of Ag Filaments on β‐Ag2MoO4 Induced by Electron Irradiation

A combined experimental and theoretical study is presented to understand the novel observed nucleation and early evolution of Ag filaments on β‐Ag₂MoO₄ crystals, driven by an accelerated electron beam from an electronic microscope under high vacuum. The growth process, chemical composition, and the element distribution in these filaments are analyzed in depth at the nanoscale level using field‐emission scanning electron microscopy (FE‐SEM) and transmission electron microscopy (TEM) with energy‐dispersive spectroscopy (EDS) characterization. To complement experimental results, chemical stability, structural and electronic aspects have been studied systematically using first‐principles electronic structure theory within a quantum theory of atoms in molecules (QTAIM) framework. The Ag nucleation and formation on β‐Ag₂MoO₄ are a result of structural and electronic changes of the AgO₄ tetrahedral cluster as a constituent building block of β‐Ag₂MoO₄, consistent with Ag metallic formation. The formation of Ag filament transforms the β‐Ag₂MoO₄ semiconductor from n‐ to p‐type concomitant with the appearance of Ag defects.     

有叶顶间隙的涡轮弯叶栅拓扑与旋涡结构(Ⅱ)——横截面流场拓扑结构与叶栅旋涡结构

根据具有叶顶间隙的直叶栅和正、反弯叶栅壁面流动的墨迹显示以及横截面内气动参数测量,应用拓扑学原理,分析了叶栅流道横截面内的拓扑结构。与直叶栅比较,叶片正弯消除了上通道涡分离线,并使二次涡由闭式分离转变为开式分离,而叶片反弯仅影响奇点位置、旋涡强度与尺度。     

Heusler型X_2RuPb(X=Lu,Y)合金的反带结构和拓扑绝缘性

采用第一性原理的计算方法,在不同条件下对Heusler型X2RuPb(X=Lu,Y)体系的电子结构展开研究.计算结果表明,这些合金在适当晶格变形或掺杂条件下,能够具有真正的拓扑绝缘体特性.杂化作用和自旋-轨道耦合作用都对材料产生"反带"结构发挥作用.但是针对不同成分所构成的材料,它们各自所起作用的程度有所不同,二者可以相辅相成.利用替换掺杂和四角变形双重调控方式可以更理想地进行"反带"结构调控进而获得理想的拓扑绝缘体,这对于材料的实际制备具有重要意义.     

$G$核开集,$G$核邻域与$G$ 核导集

在拓扑空间中, 在$G$方法意义下以$G$壳与$G$核为基础, 引入$G$壳闭集,$G$核开集,$G$核邻域与$G$核导集的概念, 讨论其相应的一些性质. 特别的, 定义了点式$G$方法, 提供了在此方法下$G$闭集与$G$壳闭集, $G$开集与$G$核开集, $G$邻域与$G$核邻域, $G$导集与$G$核导集的一致性, 丰富了拓扑空间中关于$G$闭集, $G$开集, $G$内部, $G$邻域和$G$导集的一些结果. 同时, 提出一些问题以供进一步研究.     

Existence theorems and Hyers-Ulam stability for a class of Hybrid fractional differential equations with $p$-Laplacian operator

In this paper, we prove necessary conditions for existence and uniqueness of solution (EUS) as well Hyers-Ulam stability for a class of hybrid fractional differential equations (HFDEs) with $p$-Laplacian operator. For these aims, we take help from topological degree theory and Leray Schauder-type fixed point theorem. An example is provided to illustrate the results.     

Bulk and surface electron transport in topological insulator candidate YbB6–δ

We report the study of transport and magnetic properties of the YbB_6–δsingle crystals grown by inductive zone melting. A strong disparity in the low temperature resistivity, Seebeck and Hall coefficients is established for the samples with the different level of boron deficiency. The effective parameters of the charge transport in YbB_6–δ are shown to depend on the concentration of intrinsic defects, which is estimated to range from 0.09% to 0.6%. The pronounced variation of Hall mobility μ_H found for bulk holes is induced by the decrease of transport relaxation time from τ ≈ 7.7 fs for YbB_5.994 to τ ≈ 2.2 fs for YbB_5.96. An extra contribution to conductivity from electrons with μ_H≈ –1000 cm² V^–1 s^–1 and the very low concentration n /n_Yb≈ 10^–6 discovered below 20 K for all the single crystals under investigation is suggested to arise from the surface electron states appeared in the inversion layer due to the band bending. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)