High‐Order Soliton Solution of Landau–Lifshitz Equation

The Landau–Lifshitz equation is analyzed via the inverse scattering method. First, we give the well‐posedness theory for Landau–Lifshitz equation with the frame of inverse scattering method. The generalized Darboux transformation is rigorous considered in the frame of inverse scattering transformation. Finally, we give the high‐order soliton solution formula of Landau–Lifshitz equation and vortex filament equation.     

Cauchy-type integral formula and Plemelj formula of hypermonogenic functions on unbounded domains

In this paper, we discuss the Cauchy-type integral formula of hypermonogenic functions on unbounded domains in real Clifford analysis, then we extend the Plemelj formula and Cauchy–Pompeiu formula of hypermonogenic functions on bounded domains to unbounded domains. We also deal with the Green-type formula on unbounded domains and get several important corollaries.     

Some results on fractionaln-factor-critical graphs

A simple graphG is said to be fractionaln-factor-critical if after deleting anyn vertices the remaining subgraph still has a fractional perfect matching. For fractionaln-factor-criticality, in this paper, one necessary and sufficient condition, and three sufficient conditions related to maximum matching, complete closure are given.     

关于二维光滑线性方程无解的注记

Abstract. A smooth linear complex partial differential equation in two variables which is without solutions is found.     

The optimal execution strategy of employee stock options

In this paper, we develop an optimal execution strategy for employee stock options by means of the fluid model, in which a voluntary turnover is considered. We show that the value function is the viscosity solution of the Hamilton-Jacobi-Bellman variational inequality and prove the uniqueness of the viscosity solution. Finally, we present numerical illustrative examples and numerical solutions of optimal strategies which are computed by the finite difference method.     

Optimal Decision for Selling an Illiquid Stock

This paper is concerned with liquidation of an illiquid stock. The stock price follows a fluid model which is dictated by the rates of selling and buying over time. The objective is to maximize the expected overall return. The method of constrained viscosity solution is used to characterize the dynamics governing the optimal reward function and the associated boundary conditions. Numerical examples are given to illustrate the results.     

3D coordinate measurement based on inverse photogrammetry and fringe analysis

A method based on inverse photogrammetry and fringe analysis is presented for 3D coordinate measurement. Measurement system mainly consists of a micro-camera fixed on one end of a measuring rod, a measuring probe on the other end and a liquid crystal display screen for displaying 2D fringe pattern in the measurement. In the measurement process, the probe contacts the surface of the measured object, and the CCD camera captures the stripes image on displays screen. The coordinates of camera principal point in the world coordinate system may be determined by the phase information carried in the fringe pattern. The coordinate relations between the principal point of the camera and the measuring probe can be determined with a least square optimization technique in camera coordinate system. This method has the advantage of large measurement range, good flexibility, and portable, which is suitable for field measurement. A result of our method is compared with that of the Coordinate Measuring Machine (CMM), which shows that the measurement accuracy of this method can meet accuracy requirement of the field measurement in large dimension.     

Au-Nanoparticle-Array/Aligned-Ag-Nanowire-Based Flexible Dual Plasmonic Substrate for Sensitive Surface-Enhanced Raman Scattering Detection

The fabrication of flexible surface-enhanced Raman scattering (SERS) substrates for sensitive detection on uneven or irregular surfaces is challenging. In this study, a flexible dual plasmonic SERS (FDPS) substrate rationally constructed using Au nanoparticle (AuNP) arrays/aligned Ag nanowires (AgNWs) and elastic polyurethane (PU) is demonstrated. It exhibits high sensitivity (detection limit of 10⁻⁸ m for melamine and 10⁻¹⁰ m for malachite green) and excellent reproducibility. The well-designed structure of AuNP arrays/aligned AgNWs fabricated using block copolymer self-assembly and oil–water–air interfacial self-assembly successfully enhances the electromagnetic field through plasmonic coupling. In addition, the FDPS substrate retains a high SERS sensitivity after exposure to air at room temperature for 30 days because of the high stability of AuNP arrays and antioxidation characteristic of the PU covered on the aligned AgNWs. Even after undergoing stretching, bending, and twisting for 100 cycles, the FDPS substrate maintains a stable SERS activity owing to the introduction of the elastic PU. This study demonstrates a potential application of SERS detection under practical conditions for irregular surfaces and may be helpful in the development of flexible sensors.     

低速~(84)Kr~(15+,17+)离子轰击GaAs单晶

用345 keV的Kr15+和340 keV的Kr17+离子以45fi角入射n型GaAs单晶(100)面,测量了表面形貌的变化和发射的375—500 nm Ga I和Kr II的特征光谱线.Krq+(q=15,17)离子轰击后表面形貌的变化主要取决于入射离子的电荷态q.离子沉积到靶表面的能量引起Ga原子激发,其辐射光谱为Ga I 403.2 nm和Ga I 417.0 nm.入射离子中性化过程中俘获GaAs导带电子形成高激发态原子,通过级联退激填充3p,4d等空穴,P壳层电子跃迁发射谱线为Kr II 410.0 nm,Kr II 430.4 nm,Kr II 434.0 nm和Kr II 486.0 nm,Kr II486.0 nm为较强谱线.实验结果表明,入射离子与GaAs单晶相互作用发射的可见光产额与入射离子的电荷态密切相关,较高电荷态Kr17+离子入射产生的光辐射产额大约为Kr15+离子的两倍.     

Superthermostability of nanoscale TIC-reinforced copper alloys manufactured by a two-step ball-milling process

A Cu-TiC alloy, with nanoscale TiC particles highly dispersed in the submicron-grained Cu matrix, was manufactured by a self-developed two-step ball-milling process on Cu, Ti and C powders. The thermostability of the composite was evaluated by high-temperature isothermal annealing treatments, with temperatures ranging from 727 to 1273 K. The semicoherent nanoscale TiC particles with Cu matrix, mainly located along the grain boundaries, were found to exhibit the promising trait of blocking grain boundary migrations, which leads to a super-stabilized microstructures up to approximately the melting point of copper (1223 K). Furthermore, the Cu-TiC alloys after annealing at 1323 K showed a slight decrease in Vickers hardness as well as the duplex microstructure due to selective grain growth, which were discussed in terms of hardness contributions from various mechanisms.