New exact solution structures and nonlinear dispersion in the coupled nonlinear wave systems

In this Letter, to further understand the role of nonlinear dispersion in coupled nonlinear wave systems in both real and complex fields, we study the coupled Klein–Gordon equations with nonlinear dispersion in real field (called CKG(m,n,k)$\mathrm{CKG}(m,n,k)$ equation) and (2+1)$(2+1)$-dimensional generalization of coupled nonlinear Schrödinger equation with nonlinear dispersion in complex field (called GCNLS(m,n,k)$\mathrm{GCNLS}(m,n,k)$ equation) via some transformations. As a consequence, some types of solutions are obtained, which contain compactons, solitary pattern solutions, envelope compacton solutions, envelope solitary pattern solutions, solitary wave solutions and rational solutions.     

On the spurious eigenvalues for a concentric sphere in BIEM

In this paper, the null-field integral equation method is employed to study the occurring mechanism of spurious eigenvalues for a concentric sphere. By expanding the fundamental solution into degenerate kernels and expressing the boundary density in terms of spherical harmonics, all boundary integrals can be analytically determined. It is noted that our null-field integral formulation can locate the collocation point on the real boundary thanks to the degenerate kernel. In addition, the spurious eigenvalues are parasitized in the formulations while true eigensolutions are dependent on the boundary condition such as the Dirichlet or Neumann problem. By using the updating term and updating document of singular value decomposition (SVD) technique, true and spurious eigenvalues can be extracted out, respectively. Besides, true and spurious boundary eigenvectors are obtained in the right and left unitary vectors in the SVD structure of the influence matrices. This finding agrees with that of 2D cases.     

A nonextensive approach to the dynamics of financial observables

We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy . More precisely, we present stochastic dynamical mechanisms which mimic probability density functions empirically observed. These mechanisms provide possible interpretations for the emergence of the entropic indices q in the time evolution of the corresponding observables. In addition to this, through multi-fractal analysis of return time series, we verify that the dual relation q_stat+q_sens=2 is numerically satisfied, q_stat and q_sens being associated to the probability density function and to the sensitivity to initial conditions respectively. This type of simple relation, whose understanding remains ellusive, has been empirically verified in various other systems.     

Effect of pH value on the structural and magnetic properties of nanocrystalline strontium hexaferrite thin films

Strontium hexaferrite SrFe₁₂O₁₉ thin films have been synthesized at different pH, adjusted by NH₄OH, on the Si (1 0 0) substrate using a spin coating sol-gel process. Fourier transform infrared spectroscopy analysis and theoretical calculations were conducted for determination and controlling metal citrates in solution precursors. X-ray diffraction, scanning electron microscopy and vibrating sample magnetometer were applied to evaluate the composition, microstructure, crystallite size and magnetic properties of the SrFe₁₂O₁₉ thin films. Using the solution with pH 7, the approximately single phase strontium hexaferrite thin films with optimum physical properties can be obtained at calcination temperature of 800 °C. The SrFe₁₂O₁₉ thin films derived from the solution with pH 7 after calcination at 800 °C exhibited crystallite size of 42 nm and magnetic properties of M_s=267 emu/cm³ (at 10 kOe), M_r=134 emu/cm³ and H_c=4290 Oe.     

The N-soliton solution of a two-component modified nonlinear Schrödinger equation

The N-soliton solution is presented for a two-component modified nonlinear Schrödinger equation which describes the propagation of short pulses in birefringent optical fibers. The solution is found to be expressed in terms of determinants. The proof of the solution is carried out by means of an elementary theory of determinants. The generalization of the 2-component system to the multi-component system is discussed as well as a (2+1)-dimensional nonlocal equation arising from its continuum limit.     

亚酞菁:一种新的信息光子学材料

亚酞菁是一种可望在信息光子学技术中获得重要应用的新型染料,其优良的非红性光学性质源于它特有非中心对称三维近平面锥形结构以及较大的共轭体和丰富的π电子,此外,基于它的短波长光学特性,这类材料也可能在高密度光存储中得到应用,文章综述了亚酞菁的一般结构和性能及其在非红性光学和光存储等方面的应用。     

局部方差在图像质量评价中的应用

将灰度图像的局部方差分布（QLS）作为表征图像结构信息的一个重要特征,对局部方差分布矩阵进行奇异值分解,计算得到相应的奇异值特征向量;通过计算降质图像与原参考图像局部方差矩阵奇异值特征向量的夹角大小度量两图像的结构相似度,实现了对降质图像的质量评价。实验结果表明：局部方差分布更能突出图像的结构特征,评价结果优于传统的均方误差（MSE）、峰值信噪比（PSNR）、结构相似度（SSIM）以及直接评价图像像素分布的奇异值分析（SVD）等方法,与人眼视觉感知效果的一致性较好。     

Surface solitons at the interface between semi-infinite linear and thermal nonlinear optical media

We investigate numerically surface-wave solitons occurring at the interface between semi-infinite linear and thermal nonlinear optical media, with the refractive index of the linear medium being greater than that of the nonlinear medium (in the absence of light). We find that the threshold energy flows of the existence of the surface solitons depend on the linear refractive index difference of the two media. Their fitting empirical formula has been obtained. Furthermore, we elucidate that the optical beams propagating in thermal nonlinear optical media, either as a single surface soliton or as a dipole surface soliton, can be attracted to the surface, even when launched from far away.     

Observability analysis of navigation system using point-based visual and inertial sensors

A matrix Kalman filter (MKF) has been implemented for a navigation system using point-based visual and inertial sensors. The observability conditions have been proved by the observability rank criterion based on Lie derivatives. The conditions are: (a) at least one degree of rotational freedom is excited and (b) at least three observed points are not collinear where any two points are linearly independent. Experimental results have demonstrated that the proposed algorithm obtains the same accurate as the line-based algorithm.     

Nonlinear spectral-like schemes for hybrid schemes

In spectral-like resolution-WENO hybrid schemes,if the switch function takes more grid points as discontinuity points,the WENO scheme is often turned on,and the numerical solutions may be too dissipative.Conversely,if the switch function takes less grid points as discontinuity points,the hybrid schemes usually are found to produce oscillatory solutions or just to be unstable.Even if the switch function takes less grid points as discontinuity points,the final hybrid scheme is inclined to be more stable,provided the spectral-like resolution scheme in the hybrid scheme has moderate shock-capturing capability.Following this idea,we propose nonlinear spectral-like schemes named weighted group velocity control(WGVC)schemes.These schemes show not only high-resolution for short waves but also moderate shock capturing capability.Then a new class of hybrid schemes is designed in which the WGVC scheme is used in smooth regions and the WENO scheme is used to capture discontinuities.These hybrid schemes show good resolution for small-scales structures and fine shock-capturing capabilities while the switch function takes less grid points as discontinuity points.The seven-order WGVC-WENO scheme has also been applied successfully to the direct numerical simulation of oblique shock wave-turbulent boundary layer interaction.