Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.     

First principles study on the structural,electronic and phonon properties of monolayer B2Si

Using first principles density functional theory, we predict a monolayer B₂Si structure with space group Pmm2 in the present work. This structure is confirmed to be dynamically stable. Based on the plane wave pseudopotential approach, the charge density, electron localization function, density of states, energy band, phonon property and thermal conductivity of Pmm2-B₂Si are systematically studied. It is interesting that the sp² hybridization and coordination bond of Si are found in Pmm2-B₂Si, which is the most important factor for its structural stability. The density of states and energy band analysis reveals that Pmm2-B₂Si is metallic because of the partial occupied Si 3pz and B 2pz states. Moreover, the acoustic-optical coupling is important for phonon transport in Pmm2-B₂Si, and the contribution of optical modes to the lattice thermal conductivity along the [100] and [010] directions is 13% and 12%, respectively. This study gives a fundamental understanding of the structural, electronic and phonon properties in Pmm2-B₂Si.     

双模随机交错晶场中最近邻弱交换相互作用对重入现象的影响

利用有效场理论研究了双模随机交错晶场中混合自旋 Blume-Capel 模型纳米管系统的重入现象, 发现了系统的重入现象与晶场取值概率、 晶场强度和外壳层与内壳层格点间最近邻交换相互作用的关系. 结果表明: 取值概率、 交换相互作用、 晶场强度和温度等诸多因素相互竞争, 使系统表现出丰富的磁化现象: 正( 负) 晶场较弱时, 系统只发生二级相变; 随着正( 负) 晶场增强, 系统的二级相变消失, 呈现一级相变; 一定条件下, 系统会出现重入现象.     

Coherent electron transport in a helical nanotube

The quantum dynamics of carriers bound to helical tube surfaces is investigated in a thin-layer quantization scheme. By numerically solving the open-boundary Schrödinger equation in curvilinear coordinates, geometric effect on the coherent transmission spectra is analysed in the case of single propagating mode as well as multimode. It is shown that, the coiling endows the helical nanotube with different transport properties from a bent cylindrical surface. Fano resonance appears as a purely geometric effect in the conductance, the corresponding energy of quasibound state is obviously influenced by the torsion and length of the nanotube. We also find new plateaus in the conductance. The transport of double-degenerate mode in this geometry is reminiscent of the Zeeman coupling between the magnetic field and spin angular momentum in quasi-one-dimensional structure.     

The a posteriori error estimates of Chebyshev–Petrov–Galerkin methods for second-order equations

In this paper, the a posteriori error estimates of Chebyshev–Petrov–Galerkin approximations are investigated. For simplicity, we choose the Poisson equation with Dirichlet boundary conditions to discuss the a posteriori error estimators, and deduce their efficient and reliable properties. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error estimators.     

Enhanced Peroxidase‐Like Properties of Graphene–Hemin‐Composite Decorated with Au Nanoflowers as Electrochemical Aptamer Biosensor for the Detection of K562 Leukemia Cancer Cells

Graphene composites with hemin and gold nanoparticles show a better performance for hydrogen peroxide decomposition compared to that of the three components alone or duplex/hybrid complexes. Our previous studies showed that the morphology of the Au nanoparticles may greatly influence the catalytic activity of graphene‐family peroxidase mimics. Recently, we found that Au nanoflowers could grow in situ and form on the surface of hemin/RGO (reduced graphene oxide). The prickly morphology of this Au nanoflower brought a higher catalytic ability with enhanced kinetic parameters than traditional Au nanoparticles that showed a smooth surface. Therefore, based on this discovery, a smart electrochemical aptamer biosensor for K562 leukemia cancer cells was further presented with good performance in selectivity and sensitivity attributed to the excellent mimetic peroxidase catalytic activity of this newly synthesized Au nanoflower decorated graphene–hemin composite (H‐RGO‐Au NFs).     

17.1%-Efficiency organic photovoltaic cell enabled with two higher-LUMO-level acceptor guests as the quaternary strategy

Quaternary blended organic solar cells utilize four blended material components(one donor plus three acceptors, two donors and two acceptors, or three donors plus one acceptor) as the active layer materials. The use of four material components allows us to have more material selections and more mechanism choices to improve the photon-to-electron conversion efficiency. In this contribution, we present a new case of quaternary material system, that shows 17.1% efficiency obtained by adding IDIC and PC_(71)BM as the guest acceptors of the host binary of PM6:Y6. The lowest unoccupied molecular orbital(LUMO) levels of IDIC and PC_(71)BM are both higher than that of Y6, which is one reason to obtain increased open-circuit voltage(V_(oc)) in the quaternary device. Upon introduction of IDIC and PC_(71)BM as the acceptor guests, the hole and electron mobilities are both increased, which contributes to the increased short-circuit current-density(J_(sc)). Effects of the weight ratios of the three acceptor components are investigated, which demonstrates that the increased hole and electron mobilities, the accelerated hole-transfer, and the reduced monomolecular recombination are the factors contributing to the increased J_(sc)and fill-factor. This case of quaternary device demonstrates the applicability of the quaternary strategy in increasing the device functions and hence the efficiencies in the field of organic photovoltaic cells.     

Rapid microwave-assisted synthesis and electrochemical characterization of gold/carbon nanotube composites

Hybrid nanostructures composed of gold nanoparticles (NPs) and carbon nanotubes (CNTs) have been prepared by a microwave-assisted method in the mixed solvents of oleylamine and oleic. The morphology, structure and composition of as-obtained Au/CNT composites are characterized by transmission electron microscopy (TEM), energy dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD). The composites show characteristic plasmon absorption of Au NPs in the Ultraviolet–visual spectrum. Fourier transform infrared spectrum shows the successful introduction of functional groups on the surface of CNTs, which are crucial factors to assist the nucleation in situ of Au NPs on the surface of CNTs. Electrochemical measurements show the enhancement electrochemical response for the gold electrode modified with Au/CNT composites.     

Global Error Bound for the Generalized Linear Complementarity Problem over a Polyhedral Cone

In this paper, the global error bound estimation for the generalized linear complementarity problem over a polyhedral cone (GLCP) is considered. To obtain a global error bound for the GLCP, we first develop some equivalent reformulations of the problem under milder conditions and then characterize the solution set of the GLCP. Based on this, an easily computable global error bound for the GLCP is established. The results obtained in this paper can be taken as an extension of the existing global error bound for the classical linear complementarity problems. This work was supported by the Research Grant Council of Hong Kong, a Chair Professor Fund of The Hong Kong Polytechnic University, the Natural Science Foundation of China (Grant No. 10771120) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.