A trace theorem for Dirichlet forms on fractals

We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on Sierpinski gaskets and Sierpinski carpets to their boundaries, where the boundaries are represented by triangles and squares that confine the gaskets and the carpets. As an application, we construct diffusion processes on a collection of fractals called fractal fields. These processes behave as an appropriate fractal diffusion within each fractal component of the field.     

The effect of HCP on the formation of twin boundaries and dislocations in Ni–Co alloys

In this study, molecular dynamics (MD) was used to simulate the rapid solidification process of Ni₄₇Co₅₃ and Ni₄₈Co₅₂ alloys at a cooling rate of 10¹² K/s. The effects of HCP on the formation of twin boundaries and dislocations in two Ni–Co alloys are studied. It is found that the difference of HCP clusters is the main effect that producing discrepancies on microstructure of two alloys. The number of HCP clusters accounted for 9.23% in Ni₄₇Co₅₃ alloy. They are regularly arranged to form the number of single-layer twin boundaries, and each twin boundary ends in a dislocation. The FCC and HCP structures coexist in the same atomic layers, which is easy to create dislocations. The relatively standard FCC crystal and only 0.32% HCP clusters are formed in Ni₄₈Co₅₂ alloy at 300 K. That small amount of HCP clusters are dispersed on the surface, and cause the formation of dislocation in the border with FCC clusters.     

Synthesis and characterization of 2D transition metal dichalcogenides: Recent progress from a vacuum surface science perspective

Layered transition metal dichalcogenides (TMDs) are a diverse group of materials whose properties vary from semiconducting to metallic with a variety of many body phenomena, ranging from charge density wave (CDW), superconductivity, to Mott-insulators. Recent interest in topologically protected states revealed also that some TMDs host bulk Dirac- or Wyle-semimetallic states and their corresponding surface states. In this review, we focus on the synthesis of TMDs by vacuum processes, such as molecular beam epitaxy (MBE). After an introduction of these preparation methods and categorize the basic electronic properties of TMDs, we address the characterization of vacuum synthesized materials in their ultrathin limit-mainly as a single monolayer material. Scanning tunneling microscopy and angle resolved photoemission spectroscopy has revealed detailed information on how monolayers differ in their properties from multi-layer and bulk materials. The status of monolayer properties is given for the TMDs, where data are available. Distinct modifications of monolayer properties compared to their bulk counterparts are highlighted. This includes the well-known transition from indirect to direct band gap in semiconducting group VI-B TMDs as the material-thickness is reduced to a single molecular layer. In addition, we discuss the new or modified CDW states in monolayer VSe₂ and TiTe₂, a Mott-insulating state in monolayer 1T-TaSe₂, and the monolayer specific 2D topological insulator 1T′-WTe₂, which gives rise to a quantum spin Hall insulator. New structural phases, that do not exist in the bulk, may be synthesized in the monolayer by MBE. These phases have special properties, including the Mott insulator 1T-NbSe₂, the 2D topological insulators of 1T′-MoTe₂, and the CDW material 1T-VTe₂. After discussing the pure TMDs, we report the properties of nanostructured or modified TMDs. Edges and mirror twin grain boundaries (MTBs) in 2D materials are 1D structures. In group VI-B semiconductors, these 1D structures may be metallic and their properties obey Tomonaga Luttinger quantum liquid behavior. Formation of Mo-rich MTBs in Mo-dichalcogenides and self-intercalation in between TMD-layers are discussed as potential compositional variants that may occur during MBE synthesis of TMDs or may be induced intentionally during post-growth modifications. In addition to compositional modifications, phase switching and control, in particular between the 1H and 1T (or 1T′) phases, is a recurring theme in TMDs. Methods of phase control by tuning growth conditions or by post-growth modifications, e.g. by electron doping, are discussed. The properties of heterostructures of TMD monolayers are also introduced, with a focus on lateral electronic modifications in the moiré-structures of group VI-B TMDs. The lateral potential induced in the moiré structures forms the basis of the currently debated moiré-excitons. Finally, we review a few cases of molecular adsorption on nanostructured monolayer TMDs. This review is intended to present a comprehensive overview of vacuum studies of fundamental materials' properties of TMDs and should complement the investigations on TMDs prepared by exfoliation or chemical vapor deposition and their applications.     

Vector NLS solitons interacting with a boundary

We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions (BCs): the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs. The construction is based on the so-called dressing the boundary, which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process. Under the Robin BCs, examples, including boundary-bound solitons, are explicitly derived; under the mixed Neumann/Dirichlet BCs, the boundary can act as a polarizer that tunes different components of the vector solitons. Connection of our construction to the inverse scattering transform is also provided.     

信息化课堂教学设计--以“刚体定轴转动的角动量及角动量守恒定律”为例

遵循“学生主体、教师主导”的教育教学理念,借助信息化教学工具,合理有效地设计好每一个教学环节.采用演示、体验、探究、问题导向和分组讨论等教学手段和方法,让学生在课堂中自主发现问题、分析问题并解决问题,实现“学生做中学、教师做中教”,大大提升教学效果.     

Acid/base controllable self-complexes that mimic flapping butterfly

A new type of self-complexed bis-crown ether containing two bis(p-phenylene)-34-crown-10 (BPP34C10) ether rings and two secondary ammoniums has been synthesized and characterized. The formation of these bis-self-complexes has been identified by NMR spectroscopy, mass spectrometry and X-ray analysis. The acid/base controlled movement of these bis–crown ethers can mimic a flapping butterfly.     

Synthesis and characterization of a biphenyl-linked hemicryptophane and an endohedral cobalt(II) complex

Hemicryptophanes are covalent molecular cages, constructed from a cyclotriveratrylene-based host unit and a functional unit linked by covalent spacers, which have been designed to accommodate endohedral functionalities in the cavity. In this study, the synthesis and characterization of the rigid, biphenyl-linked hemicryptophane 1 were investigated by NMR, ESI-MS, and X-ray crystallography. The structure of the inclusion complex, in which a dichloromethane molecule was constructed encapsulated within 1, was characterized by X-ray crystallography. An endohedral, cobalt(II) hemicryptophane complex 2 was also synthesized and characterized ESI-MS and X-ray crystallography. The X-ray crystal structure of 2 showed that the biphenyl-linked hemicryptophane had three components—a molecule each of chloroform and acetonitrile, and a cobalt(II) ion—within its cavity.     

Specific and Direct Amplified Detection of MicroRNA with MicroRNA:Argonaute‐2 Cleavage (miRACle) Beacons

MicroRNA detection is a valuable method for determining cell identity. Molecular beacons are elegant sensors that can transform intracellular microRNA concentration into a fluorescence intensity. While target binding enhances beacon fluorescence, the degree of enhancement is insufficient for demanding applications. The addition of specialty nucleases can enable target recycling and signal amplification, but this process complicates the assay. We have developed and characterized a class of beacons that are susceptible to the endogenous nuclease Argonaute‐2 (Ago2). After purification of the complex by co‐immunoprecipitation, microRNA:Ago2 cleavage (miRACle) beacons undergo site‐ and sequence‐specific cleavage, and show a 13‐fold fluorescence enhancement over traditional beacons. The system can be adapted to any microRNA sequence, and can cleave nuclease‐resistant, non‐RNA bases, potentially allowing miRACle beacons to be designed for cells without interference from non‐specific nucleases.     

Synthesis,characterization and heterogeneous catalytic application of a nickel(II) Schiff base complex immobilized on MWCNTs for the Hantzsch four-component condensation

A nickel(II) Schiff base complex immobilized on multi-wall carbon nanotubes (MWCNTs) surface as a highly efficient heterogeneous catalyst was synthesized and characterized by IR, X-ray diffraction patterns, scanning electron microscopy, energy-dispersive X-ray spectroscopy, inductively coupled plasma, elemental analysis, and thermal gravimetric analysis. Then a facile and environmentally benign procedure was developed for synthesis of polyhydroquinoline derivatives via Hantzsch one-pot condensation reaction of aromatic aldehydes, 1,3-diones, ethyl acetoacetate, and ammonium acetate in the presence of above synthesized catalyst under solvent-free conditions. This protocol has the advantages of stability, easy availability, recyclability and eco-friendly nature of catalyst, simple experimental and work-up procedure, and also high to excellent yields. Considering the solvent-free condition and also temperature, time, and yield of the model reaction, the nanocatalyst reported here is among the best catalysts reported so far for synthesis of polyhydroquinolines.