A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space—time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained.     

Rogue Wave Solutions for Nonlinear Schrödinger Equation with Variable Coefficients in Nonlinear Optical Systems

In this paper, the generalized Darboux transformation is constructed to variable coefficient nonlinear Schrödinger (NLS) equation. The N-th order rogue wave solution of this variable coefficient NLS equation is obtained by determinant expression form. In particular, we present rogue waves from first to third-order through some figures and analyze their dynamics.     

New Solutions of Three Nonlinear Space- and Time-Fractional Partial Differential Equations in Mathematical Physics

Motivated by the widely used ansätz method and starting from the modified Riemann-Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.     

Classification of discrete equations linearizable by point transformation on a square lattice

We provide a complete set of linearizability conditions for nonlinear partial difference equations defined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to a Möbious transformation.     

远距离多源图像融合系统实时配准设计

为了实现全天候多波段远距离实时图像监控,设计了具有微光、红外和可见光融合的光学前端,对多源图像进行实时配准研究。在平行光轴的基础上,通过计算不同视场图像的成像视差,计算仿射变换需要的参数,采用双线性内插算法弥补红外在成像方面与可见光图像的差别,将红外图像的变换制作成查找表存储在图像处理器DM642中,系统通过硬件查找表可以快速实现不同图像的配准变换,实现同步视频的实时配准与融合。实验表明:该设计能够准确地实现多源图像的实时配准,系统经过图像配准、图像融合和伪彩变换处理后的时间约为24.3 ms,系统探测距离大于3 km。     

Oliver–Pharr indentation method in determining elastic moduli of shape memory alloys—A phase transformable material

Instrumented indentation test has been extensively applied to study the mechanical properties such as elastic modulus of different materials. The Oliver–Pharr method to measure the elastic modulus from an indentation test was originally developed for single phase materials. During a spherical indentation test on shape memory alloys (SMAs), both austenite and martensite phases exist and evolve in the specimen due to stress-induced phase transformation. The question, “What is the measured indentation modulus by using the Oliver–Pharr method from a spherical indentation test on SMAs?” is answered in this paper. The finite element method, combined with dimensional analysis, was applied to simulate a series of spherical indentation tests on SMAs. Our numerical results indicate that the measured indentation modulus strongly depends on the elastic moduli of the two phases, the indentation depth, the forward transformation stress, the transformation hardening coefficient and the maximum transformation strain. Furthermore, a method based on theoretical analysis and numerical simulation was established to determine the elastic moduli of austenite and martensite by using the spherical indentation test and the Oliver–Pharr method. Our numerical experiments confirmed that the proposed method can be applied in practice with satisfactory accuracy. The research approach and findings can also be applied to the indentation of other types of phase transformable materials.     

Generating a New Higher-Dimensional Coupled Integrable Dispersionless System: Algebraic Structures,Bäcklund Transformation and Hidden Structural Symmetries

The prolongation structure methodologies of Wahlquist-Estabrook [H.D. Wahlquist and F.B. Estabrook, {J. Math. Phys.} 16 (1975) 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system. Based on the obtained prolongation structure, a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed. A Lie-Algebra representation of some hidden structural symmetries of the previous system, its Bäcklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived. In the wake of the previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new (2+1)-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation, which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention.     

Constructing infinite sequence exact solutions of nonlinear evolution equations

To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding Bäcklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.     

多环麝香(PCMs)的环境行为及毒性效应

多环麝香(PCMs)作为重要的人工合成麝香广泛应用于日用品中,目前在各种环境介质中都能检测到PCMs的存在。由于其持续不断地进入环境并能够在生物体内积累,其效应类似于持久性污染物。作为一类新型污染物,PCMs所引起的环境问题受到了广泛重视。本文介绍了PCMs的物理化学性质、来源以及在不同环境介质中的分析方法和污染现状,概述了其在环境中的降解转化、生物富集行为,并总结了其能产生的急性毒性效应、亚慢性毒性效应、内分泌干扰效应和其他潜在的毒性效应,最后讨论了目前研究中存在的问题,并对未来研究进行了展望。今后,应该建立有效的、可比对的标准分析方法,更加系统地进行环境污染现状、迁移转化规律和生物降解代谢途径的研究;重视暴露途径和生物有效性的研究,并与风险评价结合;结合环境中PCMs的污染现状,探讨低剂量长期暴露和复合暴露对生物的影响。