高阶非线性对双折射光纤中亮孤子成形的影响

本文采用拉格朗日近似方法讨论了高阶非线性对双折射光纤中亮孤子传输特性的影响,给出了计入五阶非线性时入射到双折射光纤中的光脉冲演化成束缚亮孤子对的阈值条件。研究结果表明,与不计入高阶非线性的情形相比,正的高阶非线性减小入射脉冲演化成束缚亮孤子对的振幅阈值;负的高阶非线性的存在,不仅提高了入射脉冲演化成束缚亮孤子对的振幅阈值,而且还存在着入射脉冲演化成束缚亮弧子对的振幅上界。     

基于温度变量的四维荧光光谱的石油类污染物测定

三维荧光光谱结合多元校正分析对石油类污染物复杂多组分体系测定方法多谱图混叠,且易受到空白荧光和干扰物荧光影响降低了测定准确性。提出在三维荧光光谱中增加一维温度信息构造激发波长-发射波长-温度-样品（EEM-temperature data array）的四维荧光光谱数据阵列,应用四线性成分模型建立高维荧光光谱定性定量分析的方法。实验证明在15～25 ℃温度范围内,矿物油荧光光谱轮廓形状不随温度变化,而其强度随温度线性变化,满足四线性要求,这为构建四维荧光光谱发展高维数据的三阶校正提取更丰富的有效信息提供了可能。三阶校正不仅可以在干扰物共存的情况下对感兴趣组份进行定量测定,即具有“二阶优势”,还具有更高的选择性和灵敏性,可以对高共线性和背景干扰的重叠光谱表现更好的解析能力,即“三阶优势”。对0#柴油、97#汽油和机油为混合油待测组分,腐殖酸为水体干扰组分组成的复杂体系污染油样品为进行实验,得到的三维荧光光谱利用平行因子（PARAFAC）算法和交替惩罚三线性分解（APTLD）算法进行二阶校正分析,将三维荧光光谱在温度方向上堆叠构成增加温度维度的四维荧光光谱数阵,并将其利用四维平行因子算法（4-PARAFAC）和交替惩罚四线性分解（APQLD）算法进行三阶校正分析,比较,0#柴油、97#汽油和机油的预测结果表明增加了影响荧光光谱的温度因素构造的四维荧光光谱提高了有效信息提取能力,四维荧光光谱结合高阶校正算法能提高油种光谱识别和浓度精确检测,较传统的三维荧光光谱分析提高了回收率（recovery rate）和预测均方根误差（root mean square error of prediction,RMSEP）,有利于石油类污染物的有效,准确,实时,绿色环保检测。同时指出了4-PARAFAC和APQLD算法各自的特点及其不同适用环境,为油类污染物检测具体情况提供算法选择依据。引入温度参量的四维荧光光谱结合三阶校正算法的检测技术较三维荧光光谱技术,在组分光谱定性分辨和浓度定量检测方面能对复杂体系油类污染物实现快速有效,绿色无污染地检测,实现“数学分离”更有效代替“化学分离”。     

高阶贝塞尔脉冲光束通过色散光阑透镜的传输特性*

研究了高阶贝塞尔脉冲光束通过色散光阑透镜的光谱和时间空间特性.结果表明:脉冲光束在几何焦面上会出现光谱开关,透镜色散使产生光谱开关的临界位置向z轴移动|透镜一阶色散使几何焦面上峰值光强减小,并使脉冲波形产生显著时间移动和展宽,而二阶和高阶色散的影响较小.此外,光束阶数n和空间参量α也会影响横向光强分布.     

The higher-order differential operator for the generalized Jacobi polynomials — new representation and symmetry

For a long time it has been a challenging goal to identify all orthogonal polynomial systems that occur as eigenfunctions of a linear differential equation. One of the widest classes of such eigenfunctions known so far, is given by Koornwinder’s generalized Jacobi polynomials with four parameters $\alpha ,\beta \in {\mathbb{N}}_0$ and $M,N\ge 0$ determining the orthogonality measure on the interval $?1\le x\le 1$. The corresponding differential equation of order $2\alpha +2\beta +6$ is presented here as a linear combination of four elementary components which make the corresponding differential operator widely accessible for applications. In particular, we show that this operator is symmetric with respect to the underlying scalar product and thus verify the orthogonality of the eigenfunctions.     

A full wave model of high-harmonic EMIC wave propagation in sheared magnetic fields

ABSTRACT

A new dispersion relation, with finite Larmor orbit effects, for oblique propagating electromagnetic ion cyclotron (EMIC) waves in a magnetized plasma medium, is derived including the magnetic shear effect. The approximate, yet accurate, dispersion relation is used to implement the ray tracing model. A parabolic magnetic field is considered to model the geomagnetic field in the magnetosphere. Energetic protons are also considered as resonant particles. The propagation characteristics of EMIC waves in the vicinity of the ion cyclotron resonances are investigated in some detail. The results reveal adiabatic oscillating motion for wave and magnetic field fluctuations where high harmonics limit the wave damping and confines the magnetic fluctuations. For inward propagating EMIC waves we find (1) turning points which depend on the wave launch position, and (2) wave trapped areas playing a role in quasi-coherent wave-particle interaction in agreement with the observational and theoretical studies. This wave trapping is an effective process for particle acceleration in the context of space plasmas.     

Stability of peakons for the generalized modified Camassa–Holm equation

In this paper, we study orbital stability of peakons for the generalized modified Camassa–Holm (gmCH) equation, which is a natural higher-order generalization of the modified Camassa–Holm (mCH) equation, and admits Hamiltonian form and single peakons. We first show that the single peakon is the usual weak solution of the PDEs. Some sign invariant properties and conserved densities are presented. Next, by constructing the corresponding auxiliary function $h(t,x)$ and establishing a delicate polynomial inequality relating to the two conserved densities with the maximal value of approximate solutions, the orbital stability of single peakon of the gmCH equation is verified. We introduce a new approach to prove the key inequality, which is different from that used for the mCH equation. This extends the result on the stability of peakons for the mCH equation (Qu et al. 2013) [36] successfully to the higher-order case, and is helpful to understand how higher-order nonlinearities affect the dispersion dynamics.     

Differential-geometric Newton method for the best rank-(R1, R2, R3) approximation of tensors

An increasing number of applications are based on the manipulation of higher-order tensors. In this paper, we derive a differential-geometric Newton method for computing the best rank-(R ₁, R ₂, R ₃) approximation of a third-order tensor. The generalization to tensors of order higher than three is straightforward. We illustrate the fast quadratic convergence of the algorithm in a neighborhood of the solution and compare it with the known higher-order orthogonal iteration (De Lathauwer et al., SIAM J Matrix Anal Appl 21(4):1324–1342, 2000). This kind of algorithms are useful for many problems. This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The scientific responsibility rests with its authors. Research supported by: (1) Research Council K.U.Leuven: GOA-Ambiorics, CoE EF/05/006 Optimization in Engineering (OPTEC), (2) F.W.O.: (a) project G.0321.06, (b) Research Communities ICCoS, ANMMM and MLDM, (3) the Belgian Federal Science Policy Office: IUAP P6/04 (DYSCO, “Dynamical systems, control and optimization”, 2007–2011), (4) EU: ERNSI. M. Ishteva is supported by a K.U.Leuven doctoral scholarship (OE/06/25, OE/07/17, OE/08/007), L. De Lathauwer is supported by “Impulsfinanciering Campus Kortrijk (2007–2012)(CIF1)” and STRT1/08/023.     

Existence of homoclinic solutions for higher-order periodic difference equations with p-Laplacian

Using the critical point theory in combination with periodic approximations, we establish sufficient conditions on the existence of homoclinic solutions for higher-order periodic difference equations with p-Laplacian. Our results provide rather weaker conditions to guarantee the existence of homoclinic solutions and considerably improve some existing ones even for some special cases.     

Deflection in higher-order gravitational lensing

The deflection of light rays by rotating gravitational lens is considered in the framework of higher-order gravitational theory. The bending angle of light is derived. The effect of the massive scalar and tensor components of higher-order gravitational field as well as the gravito-magnetic on light deflection are discussed.