Solitons for the cubic-quintic nonlinear Schrödinger equation with Raman effect in nonlinear optics

Considering the ultrashort optical soliton propagation in the non-Kerr media, the cubic-quintic nonlinear Schrödinger equation with Raman effect is studied through the dependent variable transformation and Hirota method. Based on symbolic computation, the bilinear form, the explicit one- and two-soliton solutions for the equation are presented. The constraint parametric condition for the existence of soliton solutions is also derived. Propagation characteristics and interaction behaviors of the solitons are graphically shown and discussed: (1) Overtaking elastic interactions of the two solitons; (2) periodic attraction and repulsion of the bounded states of two solitons; (3) propagation in parallel of the two solitons.     

锥形光纤激发盘腔光学模式互易性研究

光学谐振腔由于其高Q值特性,作为谐振式陀螺的核心元件,有望实现谐振式陀螺的小型化、集成化,但是非互易性噪声成为制约其精度提高的不利因素. 介绍了采用传统半导体工艺制备的盘型腔与熔融法拉制的锥形光纤组成的耦合系统. 当盘型腔在光纤锥区的不同位置进行耦合谐振时,将输入输出正/反对调,观察到输出透射谱发生偏差,谐振频率、耦合效率以及Q值均发生变化,即存在非互易性现象. 用Rsoft软件对锥形光纤倏逝场分布特性进行仿真,理论分析了非互易性产生的原因. 以此可抑制谐振式光学陀螺应用中由锥形光纤与谐振腔组成的耦合系统产生的非互易性噪声. 关键词： 光学谐振腔 锥形光纤 非互易性 谐振式陀螺     

Cation distributions estimated using the magnetic moments of the spinel ferrites Co_(1-x)Cr_xFe_2O_4 at 10K

（A）[B]2O4 ferrite samples with the composition COl_xCrxFe204 （0.0 ≤ x ≤1.0） are prepared using a hydrothermal method, and subjected to calcining in a tube furnace with an argon-flow at 1673 K for 2 h. X-ray diffraction patterns indicate that each of all the samples has a single phase cubic spinel structure with a space group of Fd3m. Magnetic measurements show that the saturation magnetization decreases with as the Cr content x increases. The cation distribution of the samples is estimated by fitting the dependence of the magnetic moments on x at l 0 K, using the quantum mechanical model previously proposed by our group. The calculated sum of the content values of the Cr3＋ and Cr2＋ cations occupying the （A） sites increases as the value of x increases. In the fitting process, the magnetic moment directions of the Cr3＋ and Cr2＋ cations are assumed to be antiparallel to those of the Fe and Co cations, respectively, which is in accordance with Hund＇s rules.     

Damage evaluation of reinforced concrete frame based on a combined fiber beam model

In order to analyze and simulate the impact collapse or seismic response of the reinforced concrete(RC)structures,a combined fiber beam model is proposed by dividing the cross section of RC beam into concrete fiber and steel fiber.The stress-strain relationship of concrete fiber is based on a model proposed by concrete codes for concrete structures.The stress-strain behavior of steel fiber is based on a model suggested by others.These constitutive models are implemented into a general finite element program ABAQUS through the user defined subroutines to provide effective computational tools for the inelastic analysis of RC frame structures.The fiber model proposed in this paper is validated by comparing with experiment data of the RC column under cyclical lateral loading.The damage evolution of a three-dimension frame subjected to impact loading is also investigated.     

Imbalance-oriented SVM methods for financial distress prediction: a comparative study among the new SB-SVM-ensemble method and traditional methods

Previous studies on financial distress prediction (FDP) almost construct FDP models based on a balanced data set, or only use traditional classification methods for FDP modelling based on an imbalanced data set, which often results in an overestimation of an FDP model’s recognition ability for distressed companies. Our study focuses on support vector machine (SVM) methods for FDP based on imbalanced data sets. We propose a new imbalance-oriented SVM method that combines the synthetic minority over-sampling technique (SMOTE) with the Bagging ensemble learning algorithm and uses SVM as the base classifier. It is named as SMOTE-Bagging-based SVM-ensemble (SB-SVM-ensemble), which is theoretically more effective for FDP modelling based on imbalanced data sets with limited number of samples. For comparative study, the traditional SVM method as well as three classical imbalance-oriented SVM methods such as cost-sensitive SVM, SMOTE-SVM, and data-set-partition-based SVM-ensemble are also introduced. We collect an imbalanced data set for FDP from the Chinese publicly traded companies, and carry out 100 experiments to empirically test its effectiveness. The experimental results indicate that the new SB-SVM-ensemble method outperforms the traditional methods and is a useful tool for imbalanced FDP modelling.     

Uniform nonsquareness and locally uniform nonsquareness in Orlicz–Bochner function spaces and applications

In this paper, criteria for uniform nonsquareness and locally uniform nonsquareness of Orlicz–Bochner function spaces equipped with the Orlicz norm are given. Although, criteria for uniform nonsquareness and locally uniform nonsquareness in Orlicz function spaces were known, we can easily deduce them from our main results. Moreover, we give a sufficient condition for an Orlicz–Bochner function space to have the fixed point property.     

Minimal Zero Norm Solutions of Linear Complementarity Problems

In this paper, we study minimal zero norm solutions of the linear complementarity problems, defined as the solutions with smallest cardinality. Minimal zero norm solutions are often desired in some real applications such as bimatrix game and portfolio selection. We first show the uniqueness of the minimal zero norm solution for Z-matrix linear complementarity problems. To find minimal zero norm solutions is equivalent to solve a difficult zero norm minimization problem with linear complementarity constraints. We then propose a p norm regularized minimization model with p in the open interval from zero to one, and show that it can approximate minimal zero norm solutions very well by sequentially decreasing the regularization parameter. We establish a threshold lower bound for any nonzero entry in its local minimizers, that can be used to identify zero entries precisely in computed solutions. We also consider the choice of regularization parameter to get desired sparsity. Based on the theoretical results, we design a sequential smoothing gradient method to solve the model. Numerical results demonstrate that the sequential smoothing gradient method can effectively solve the regularized model and get minimal zero norm solutions of linear complementarity problems.     

Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density

In the context of semi-functional partial linear regression model, we study the problem of error density estimation. The unknown error density is approximated by a mixture of Gaussian densities with means being the individual residuals, and variance a constant parameter. This mixture error density has a form of a kernel density estimator of residuals, where the regression function, consisting of parametric and nonparametric components, is estimated by the ordinary least squares and functional Nadaraya–Watson estimators. The estimation accuracy of the ordinary least squares and functional Nadaraya–Watson estimators jointly depends on the same bandwidth parameter. A Bayesian approach is proposed to simultaneously estimate the bandwidths in the kernel-form error density and in the regression function. Under the kernel-form error density, we derive a kernel likelihood and posterior for the bandwidth parameters. For estimating the regression function and error density, a series of simulation studies show that the Bayesian approach yields better accuracy than the benchmark functional cross validation. Illustrated by a spectroscopy data set, we found that the Bayesian approach gives better point forecast accuracy of the regression function than the functional cross validation, and it is capable of producing prediction intervals nonparametrically.     

Optical ammonia gas sensor based on a porous silicon rugate filter coated with polymer-supported dye

An ammonia gas sensor chip was prepared by coating an electrochemically-etched porous Si rugate filter with a chitosan film that is crosslinked by glycidoxypropyltrimethoxysilane (GPTMS). The bromothylmol blue (BTB), a pH indicator, was loaded in the film as ammonia-sensing molecules. White light reflected from the porous Si has a narrow bandwidth spectrum with a peak at 610 nm. Monitoring reflective optical intensity at the peak position allows for direct, real-time observation of changes in the concentration of ammonia gas in air samples. The reflective optical intensity decreased linearly with increasing concentrations of ammonia gas over the range of 0–100 ppm. The lowest detection limit was 0.5 ppm for ammonia gas. At optimum conditions, the full response time of the ammonia gas sensor was less than 15 s. The sensor chip also exhibited a good long-term stability over 1 year. Therefore, the simple sensor design has potential application in miniaturized optical measurement for online ammonia gas detection.     

Dissociative double ionization of 1-bromo-2-chloroethane irradiated by an intense femtosecond laser field

The dissociative double ionization and multi-photon ionization of 1-bromo-2-chloroethane (BCE) irradiated by the 800 nm femtosecond laser field have been investigated by dc-slice imaging technology. The charged parent ion ratio [BCE(2+)]/[BCE(+)] was measured, and the corresponding ionization process including non-sequential double ionization and sequential double ionization was analyzed. The sliced images of different photo-dissociated ions were detected, and the corresponding kinetic energy release (KER) distributions were calculated and extracted. Furthermore, the dissociative double ionization channels, attributed to the cleavage of the C-C, C-Br, and C-Cl bonds by the Coulombic repulsive forces, were discussed, and the revised equilibrium distance R(e)*, the energy ratio E(exp)/E(coul), and the value a=√(R(e)*)/(E(exp)/E(coul)) were calculated.