一类圆周自映射拓扑熵的计算

本文讨论了一类新的圆周自映射 ,证明了它是拓扑熵为零的圆周自映射 ,从而推广了 [1][2 ]的一个结果 .     

G相对乘积空间中的Ti(i=-1,0,1,2)及次T0分离性

讨论了G相对乘积空间中的Ti(i=-1,O,l,2)与次T0分离性质．     

饱和链烷烃沸点的拓扑研究

本文从距离矩阵和邻接矩阵出发,结合矩阵的数学知识,提出了一种新的拓扑指数Qx=(W×V)1/8,用最小二乘法拟合b.p.(℃),得到线性回归方程为:b.p.(℃)=-277.814+165.248Qx(r=0.993)     

拓扑指数mP在价电子轨道能量中的相关性研究

本文提出了一种新的键参数拓扑指数^mP.用其零、一阶指数0p、1p分别与20种碱金属卤化物的晶格能U、生成焓△Hf,m,离子水化能△Gh,m和核间距R0以及16种碱金属卤化物的熔点Tm、磁化率xm和键长Bd的相关联,采用最小二乘法,拟合的回归方程的相关系数分别为0.995、0.988、0.996、0.995、0.964、0.988、0.964,满足优级标准,预测结果良好.     

Subdivision surface modeling system based on arbitrary topological curves network and combined subdivision

Arbitrary topological curve network has no restriction in topology structure,so it has more powerful representing ability in defining complex surfaces.A complex surface modeling system is presented based on arbitrary topological curve network and the improved combined subdivision method,its functions including creating and editing curve network,and generating and modifying curve network's interpolated surface.This modeling system can be used to the process of products'concept design,and its applications is ...     

一类保序压缩变换半群的Green关系

设Xn={1,2,…,n},Q（Xn）={A1,A2,…,Ar}为Xn上任意一个划分,令OCT（Xn）={α∈On：Ai,Aj∈Xn,d（Aiα,Ajα）≤d（Ai,Aj）},则OCT（Xn）是一个半群。本文刻划了该半群的Green关系及一些相关的性质。     

Surface superconductivity in the type II Weyl semimetal TaIrTe4

The search for unconventional superconductivity in Weyl semimetal materials is currently an exciting pursuit, since such superconducting phases could potentially be topologically non-trivial and host exotic Majorana modes. The layered material TaIrTe₄ is a newly predicted time-reversal invariant type II Weyl semimetal with the minimum number of Weyl points. Here, we report the discovery of surface superconductivity in Weyl semimetal TaIrTe₄. Our scanning tunneling microscopy/spectroscopy (STM/STS) visualizes Fermi arc surface states of TaIrTe₄ that are consistent with the previous angle-resolved photoemission spectroscopy results. By a systematic study based on STS at ultralow temperature, we observe uniform superconducting gaps on the sample surface. The superconductivity is further confirmed by electrical transport measurements at ultralow temperature, with an onset transition temperature (T_c) up to 1.54 K being observed. The normalized upper critical field h*(T/T_c) behavior and the stability of the superconductivity against the ferromagnet indicate that the discovered superconductivity is unconventional with the p-wave pairing. The systematic STS, and thickness- and angular-dependent transport measurements reveal that the detected superconductivity is quasi-1D and occurs in the surface states. The discovery of the surface superconductivity in TaIrTe₄ provides a new novel platform to explore topological superconductivity and Majorana modes.     

High-Tc superconductor Fe(Se,Te) monolayer: an intrinsic,scalable and electrically tunable Majorana platform

Iron-based superconductors have been identified as a novel platform for realizing Majorana zero modes (MZMs) without heterostructures, due to their intrinsic topological properties and high-T_c superconductivity. In the two-dimensional limit, the FeTe_1−xSe_x monolayer, a topological band inversion has recently been experimentally observed. Here, we propose to create MZMs by applying an in-plane magnetic field to the FeTe_1−xSe_x monolayer and tuning the local chemical potential via electric gating. Owing to the anisotropic magnetic couplings on edges, an in-plane magnetic field drives the system into an intrinsic high-order topological superconductor phase with Majorana corner modes. Furthermore, MZMs can occur at the domain wall of chemical potentials at either one edge or certain type of tri-junction in the two-dimensional bulk. Our study not only reveals the FeTe_1−xSe_x monolayer as a promising Majorana platform with scalability and electrical tunability and within reach of contemporary experimental capability, but also provides a general principle to search for realistic realization of high-order topological superconductivity.     

拓扑空间中的截口定理及其应用

将KyFan截口定理推广到具有性质（H）的拓扑空间．作为应用,在具有性质（H）的拓扑空间上进一步推广了Browder不动点定理,并利用所得结果在具有性质（H）的拓扑空间中证明了极大极小不等式定理和鞍点定理．     

光调控的Shastry-Sutherland格子上电子的体态-边缘态对应

在Shastry-Sutherland格子上运动的电子具有丰富的性质。利用Floquet 方法证明在上述系统中高频圆偏振光产生包括Dirac fermion,semi-Dirac fermion,quadratic band touch,SO（3）fermion和具有能隙的多种物相。在考虑自旋轨道耦合作用后,发现4种无能隙激发的相之间是拓扑等价的。通过计算纳米带的边缘态,按照体态-边缘态对应原则,发现这4种无能隙激发相在打开能隙之后都变成拓扑绝缘体。此外,还发现semi-Dirac fermion体态的各向异性色散关系和沿不同方向裁剪的纳米带边缘态之间也同样存在体态-边缘态对应。