拓扑线性空间中的Drop定理与Drop性质

给出了拓扑线性空间中的一个Drop定理.利用此Drop定理,证明了拓扑线性空间中的每个序列紧凸集具有Drop性质;每个可数紧闭凸集具有拟Drop性质.而且结出了拓扑线性空间中Drop性质和拟Drop性质的序列流特征.也讨论了Drop性质和拟Drop性质与泛函取极值之间的联系.     

关于Barge和Toledo的几个问题

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｃｈａｉｎａｂｌｅｃｏｎｔｉｎｕａｈａｖｅｂｅｅｎｅｘｔｅｎｓｉｖｅｌｙｓｔｕｄｉｅｄｆｏｒｍａｎｙｙｅａｒｓａｎｄｈａｖｅｇｅｎｅｒａｔｅｄｎｅｗｉｎｔｅｒｅｓｔｉｎｔｈｅｒｅｃｅｎｔｙｅａｒｓａｓｔｈｅｃｈａｉｎａｂｌｅｃｏｎｔｉｎｕｕｍｗｈｉｃｈｉｓｔｈｅｉｎｖｅｒｓｅｌｉｍｉｔｓｐａｃｅｏｆａｃｏｎｔｉｎｕｏｕｓｍａｐｆｒｏｍａｃｌｏｓｅｄｉｎｔｅｒｖａｌｉｎｔｏｉｔｓｅｌｆｃａｎｂｅｒｅａｌｉｚｅｄａｓａｇｌｏｂａｌａｔｔｒａｃｔｏｒｏｆｓｏｍｅｐｌａｎ…     

局部熵高维重分形谱的上界估计

We discuss the problem of higher-dimensional multifractal spectrum of local entropy for arbitrary invariant measures. By utilizing characteristics of a dynamical system, namely, higher-dimensional entropy capacities and higher-dimensional correlation entropies, we obtain three upper estimates on the hlgher-dimensional multifractal spectrum of local entropies. We also study the domain of higher-dimensional multifractai spetrum of entropies.     

On the moduli space of deformations of bihamiltonian hierarchies of hydrodynamic type

We investigate the deformation theory of the simplest bihamiltonian structure of hydrodynamic type, that of the dispersionless KdV hierarchy. We prove that all of its deformations are quasi-trivial in the sense of B. Dubrovin and Y. Zhang, that is, trivial after allowing transformations where the first partial derivative ∂u of the field is inverted. We reformulate the question about deformations as a question about the cohomology of a certain double complex, and calculate the appropriate cohomology group.     

Floquet bands and photon-induced topological edge states of graphene nanoribbons

Floquet theorem is widely used in the light-driven systems. But many 2 D-materials models under the radiation are investigated with the high-frequency approximation, which may not be suitable for the practical experiment. In this work,we employ the non-perturbative Floquet method to strictly investigate the photo-induced topological phase transitions and edge states properties of graphene nanoribbons under the light irradiation of different frequencies(including both low and high frequencies). By analyzing the Floquet energy bands of ribbon and bulk graphene, we find the cause of the phase transitions and its relation with edge states. Besides, we also find the size effect of the graphene nanoribbon on the band gap and edge states in the presence of the light.     

Effects of post-annealing on crystalline and transport properties of Bi_2Te_3 thin films

A well-established method is highly desirable for growing topological insulator thin films with low carrier density on a wafer-level scale. Here, we present a simple, scalable method based on magnetron sputtering to obtain high-quality Bi_2 Te_3 films with the carrier density down to 4.0 × 10~(13) cm~(-2). In contrast to the most-used method of high substrate temperature growth, we firstly sputtered Bi_2 Te_3 thin films at room temperature and then applied post-annealing. It enables the growth of highly-oriented Bi_2 Te_3 thin films with larger grain size and smoother interface. The results of electrical transport show that it has a lower carrier density as well as a larger coherent length(～ 228 nm, 2 K). Our studies pave the way toward large-scale, cost-effective production of Bi_2 Te_3 thin films to be integrated with other materials in wafer-level scale for electronic and spintronic applications.     

Nematodynamics and structures in junctions of cylindrical micropores

ABSTRACT

We explore equilibrium structures and flow-driven deformations of nematic liquid crystals confined to 3D junctions of cylindrical micropores with homeotropic surface anchoring. The topological state of the nematic ordering field in such basic unit of porous networks is controlled by nematic orientation profiles in individual pores, anchoring frustration along the edges of joining pores and coupling to the material flow field. We numerically investigate formation of the flow-aligned configurations in single cylindrical pores and pore junctions. Depending on the arrangement of inlet and outlet flows in the junction, we demonstrate existence of numerous stationary nematic configurations, characterised by specific bulk defects and surface disclinations along joining edges. Observed bulk defects are nonsingular escaped structures, disclinations in the form of loops or disclination lines pinned to the joining edges of the pores. Furthermore, we show examples of defect dynamics during the flow-induced topological transformations.     

类升力体外形高超声速粘性绕流拓扑结构分析

采用交替方向隐式分解的隐式NND格式求解全N-S方程模拟“类升力体”外形在高超声速下的大攻角流动,给出了“类升力体”外形表面极限流线随攻角变化的拓扑结构及40°攻角下垂直于体轴的横截面流线拓扑结构。结果表明:类升力体外形三维流场结构十分复杂,攻角从0°～40°变化时,背风面表面极限流线依次由不分离、开式分离向起始于鞍、结点组合的高阶奇点的分离方式转化,翼面横向分离亦随攻角增大而增大;垂直于体轴的横截面流动拓扑结构与文献[2]给出的理论分析一致。