Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals

In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals.     

一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.     

Construction of long MDS self-dual codes from short codes

In this paper, we propose a mechanism on how to construct long MDS self-dual codes from short ones. These codes are special types of generalized Reed-Solomon (GRS) codes or extended generalized Reed-Solomon codes. The main tool is utilizing additive structure or multiplicative structure on finite fields. By applying this method, more MDS self-dual codes can be constructed.     

A Generalization of Lappan’s Theorem to Higher Dimensional Complex Projective Space

In this paper, the authors discuss a generalization of Lappan’s theorem to higher dimensional complex projective space and get the following result: Let f be a holomorphic mapping of ? into Pⁿ(C), and let H₁, · · · , H_q be hyperplanes in general position in Pⁿ(C).Assume that sup {(1 ? |z|²)f^?(z) : z ∈ q[ j=1 f^?1(H_j )o < ∞,if q ≥ 2n² + 3, then f is normal.     

Probing Adsorption Configurations of Small Molecules on Surfaces by Single-Molecule Tip-Enhanced Raman Spectroscopy

Determining the adsorption configurations of organic molecules on surfaces, especially for relatively small molecules, is a key issue for understanding the microscopic physical and chemical processes in surface science. In this work, we have applied low-temperature ultrahigh-vacuum tip-enhanced Raman scattering (TERS) technique to distinguish the configurations of small 4,4′-bipyridine (44BPY) molecules adsorbed on the Ag(111) surface. The observed Raman spectra exhibit notable differences in the spectral features which can be assigned to three different molecular orientations, each featuring a specific fingerprint pattern based on the TERS selection rule that determines the distribution of the relative intensities of different vibrational peaks. Furthermore, such a small molecule can in turn act as a local probe to provide information on the local electric field distribution at the tip apex. Our work showcases the capability of TERS technique for obtaining information on adsorption configurations of small molecules on surfaces down to the single-molecule level, which is of fundamental importance for many applications in the fields of molecular science and surface chemistry.     

Assembling hydrodynamic cloaks to conceal complex objects from drag

Transformation hydrodynamics and the corresponding metamaterials have been proposed as a means to exclude the drag force acting on an object. Here, we report a strategy to deploy the hydrodynamic cloaks in a more practical manner by assembling different-shaped cloaking parts. Our strategy is to first model a square-shaped cloak and a carpet cloak and then combine them to conceal a more complex-shaped space in the three-dimensional hydrodynamic flow. With the derivation of transformation hydrodynamics, the coordinate transformations for each hydrodynamic cloaking are demonstrated with the calculated viscosity tensors. The pressure and velocity fields of the square, triangular (carpet), and exemplary three-dimensional house-shaped cloaks are numerically simulated, thus showing a cloaking effect and reduced drag. This study suggests an efficient way of cloaking complex architectures from fluid-dynamic forces.