The system of generalized vector equilibrium problems with applications

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a solution of these systems. As an application, we derive existence results for a solution of a more general Nash equilibrium problem for vector-valued functions.     

Wave theory of light leading to the generalized vectorial laws of reflection and refraction

This paper deals with the application of Huygens’ wave theory of light for the derivation of the generalized vectorial laws of reflection and refraction discovered by the author in 2005. The long-running literature falls short of such a theoretical proof of the generalized vectorial laws of reflection and refraction on the basis of wave theory. As such the present work is novel and original. At the same time it also enhances the theoretical foundation of the discovery of the generalized vectorial laws of reflection and refraction there by proving the efficiency and increasing the range of applicability of the wave theory of light as well.     

(1+2)维强非局域空间光孤子的相互作用

强非局域空间光孤子是指满足强非局域条件的空间孤子.在Snyder和Mitchell工作的基础上，获得了不共面对称斜入射(1+2)维强非局域空间光孤子对相互作用问题的精确解析解.结果表明，光束初始中心距离在大范围尺度内变化时，双孤子的演化都能形成类似DNA结构的稳定缠绕，这种稳定缠绕的结构与双孤子的初始相位差无关；光束中心在横截面上的投影轨迹一般是一个斜椭圆，通过改变两光束的初始中心距离和倾斜度可以控制该椭圆轨迹的变化.指出了利用(1+2)维强非局域空间光孤子的相互作用特性实现平面全光开关和全光互联的潜在可能性. 关键词： (1+2)维非局域非线性介质 空间光孤子的相互作用 全光开关 全光互联     

A system of coupled partial differential equations exhibiting both elevation and depression rogue wave modes

Analytical solutions are obtained for a coupled system of partial differential equations involving hyperbolic differential operators. Oscillatory states are calculated by the Hirota bilinear transformation. Algebraically localized modes are derived by taking a Taylor expansion. Physically these equations will model the dynamics of water waves, where the dependent variable (typically the displacement of the free surface) can exhibit a sudden deviation from an otherwise tranquil background. Such modes are termed ‘rogue waves’ and are associated with ‘extreme and rare events in physics’. Furthermore, elevations, depressions and ‘four-petal’ rogue waves can all be obtained by modifying the input parameters.     

Parametric Study of Nonplanar Dust Acoustic Solitons in Two‐Dimensional Superthermal Dusty Plasmas

The nonlinear properties of two dimensional low‐frequency electrostatic excitations of charged dust particles (or defects) are studied in a collisionless, unmagnetized dusty plasma. A fully ionized three‐component model plasma consisting of kappa distributed electrons, Maxwellian ions, and negatively charged massive dust grains is considered. In this regard, the well known reductive perturbation technique is used to the hydrodynamical equations and the Poisson equation, obtaining the cylindrical Kadomtsev–Petviashvili (CKP) equation. A parametric investigation indicates that the structural characteristics of these nonlinear excitations (width, amplitude) are significantly affected by the plasma nonthermality as well as by the relevant plasma parameters, such as dust concentration and dust temperature. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Symmetry Reductions,Group‐Invariant Solutions,and Conservation Laws of a (2+1)‐Dimensional Nonlinear Schrödinger Equation in a Heisenberg Ferromagnetic Spin Chain

Nonlinear spin excitations in ferromagnetic spin chains are studied for spintronic and magnetic devices including magnetic‐field sensors and for high‐density data storage. Here, (2+1)‐dimensional nonlinear Schrödinger equation is investigated, which describes the nonlinear spin dynamics for a Heisenberg ferromagnetic spin chain. Lie point symmetry generators and Lie symmetry groups of that equation are derived. Lie symmetry groups are related to the time, space, scale, rotation transformations, and Galilean boosts of that equation. Certain solutions, which are associated with the known solutions, are constructed. Based on the Lie symmetry generators, the reduced systems of such an equation are obtained. Based on the polynomial expansion and through one of the reduced systems, group‐invariant solutions are constructed. Soliton‐type group‐invariant solutions are graphically investigated and effects of the magnetic coupling coefficients, that is, α₁, α₂, α₃, and α₄, on the soliton's amplitude, width, and velocity are discussed. It is seen that α₁, α₂, α₃, and α₄ have no influence on the soliton's amplitude, but can affect the soliton's velocity and width. Lax pair and conservation laws of such an equation are derived.     

偏心和倾斜光学系统的像差特性

运用一种新的分析偏心和倾斜光学系统初级像差特性的方法—矢量像差理论,分析了具有较大交叉倾斜角的平行平板光学系统和具有较大倾斜角的光楔光学系统的像差特性.通过ZEMAX光学设计软件像差分析功能中的垂轴像差曲线、场曲曲线和点列图加以比较,两者非常吻合,证明该理论可以对具有较大倾斜元件的非共轴光学系统设计起指导作用.     

用单个矢量水听器基于DEMON线谱的双目标分辨

不同目标的解调线谱频率是不同的。本文提出了一种在DEMON谱域内对双目标测向的方法,它具有较好的抗相干及非相干干扰能力,表明单个矢量水听器也能分辨多目标。文中叙述了利用DEMON线谱测向的原理,给出了轴频提取及双目标DEMON线谱分离的方法,对DEMON线谱区分双目标的能力做了仿真分析。     

支持向量机(SVM)在傅里叶变换近红外光谱分析中的应用研究

支持向量机(SVM)用于两类问题的识别研究,它是统计学习理论中最年轻的分支,所建分析模型有严格的数学基础。同时介绍了SVM学习的基本原理和方法,并将该方法引入化学计量学,以103个中药大黄样品为实验材料,通过SVM近红外光谱法建立了大黄样品真伪识别模型。对学习集中33个样品模型识别准确率为100％;对70个预测样品的识别准确率为96.77％, 为中药大黄的快速识别提供了参考。研究结果表明了SVM近红外光谱法建立生物样品识别模型的可行性。通过旨在介绍SVM学习方法的基本思想,以引起化学计量学工作者的进一步关注。     

离散的五次非线性薛定谔方程的精确孤子解

利用推广的双曲函数法，我们研究了离散的五次非线性薛定谔方程。当方程的系数满足某种约束关系时，我们得到了新的局域解。这些解包括亮孤子解，暗孤子解，相位交替变化的亮孤子解和相位交替变化的暗孤子解。