A framework for classification with single feature kernel matrix

In this paper, we propose a novel classification framework using single feature kernel matrix. Different from the traditional kernel matrices which make use of the whole features of samples to build the kernel matrix, this research uses features of the same dimension of any two samples to build a sub-kernel matrix and sums up all the sub-kernel matrices to get the single feature kernel matrix. We also use single feature kernel matrix to build a new SVM classifier, and adapt SMO (Sequential Minimal Optimization) algorithm to solve the problem of SVM classifier. The results of the experiments on several artificial datasets and some challenging public cancer datasets display the classification performance of the algorithm. The comparisons between our algorithm and L₂-norm SVM on the cancer datasets demonstrate that the accuracy of our algorithm is higher, and the number of support vectors selected is fewer, indicating that our proposed framework is a more practical approach.     

Two matrix algorithms for eigenmodes of a Bessel-Gauss resonator

A Bessel-Gauss resonator (BGR) was proposed to produce the Bessel Gauss beams. In this paper transverse profiles and their corresponding losses of the BGR are computed by use of the entire matrix formalism and the transfer matrix method, and the computation results from two algorithms are compared. The computation results show that for the BGR there is no inconsistence in the mode fields yielded by two methods, and the transfer matrix methods are more accurate in the mode losses than the entire matrix formalism, which lead to a believable conclusion that the BGR with a convex-spherical mirror easily produces the fundamental Bessel-Gauss mode of good quality.     

Closed-form Analysis of Lossy Cosine-Squared Tapered Nonuniform Transmission Lines

The rigorous analytical solutions and the ABCD matrix of the lossy Cosine-Squared tapered nonuniform transmission lines (CSTNTL) are presented in this paper. According to different boundary conditions, the unique solution is obtained mathematically. Through the numerical calculations based on analytical solutions, the distributed voltages and currents in different terminated cases are shown to explain the transmission characteristics of CSTNTL. Especially in the lossy case the distributed power values are simulated to show the attenuation phenomenon.     

Theoretical studies on the optical absorption coefficients and refractive index changes in parabolic quantum dots in the presence of electric and magnetic fields

The optical absorption coefficients and the changes in the refractive index in GaAs/AlGaAs parabolic quantum dots(QDs) with applied electric and magnetic fields are studied in detail. Analytical expressions for the linear and nonlinear intersubband absorption coefficients and refractive index changes are obtained by using a compact density matrix approach and an iterative procedure. Finally, the calculated results show the incident optical intensity, the frequencies of the confined potential of the QDs and the applied electric and magnetic fields have a great influence on the optical absorption coefficients and refractive index changes in this system.     

一个新的三维混沌系统

构造了一个新的三维连续自治混沌系统.该系统含有两个参数、一个反正切函数形式的非线性项.基于线性矩阵不等式方法研究了系统的稳定性.通过理论分析、数值仿真、Lyapunov指数谱、分岔图以及Poincaré截面图分别研究了系统的复杂动力学特性. 关键词： 混沌系统 稳定性 线性矩阵不等式 Lyapunov指数谱     

磁共振成像谱仪梯度波形分析

梯度是磁共振成像（MRI）的关键环节.通过采集谱仪梯度波形信号并进行分析,提取出各通道波形的特征点,从而有助于快速准确地判断谱仪梯度硬件电路或脉冲序列编写是否存在问题.采用虚拟仪器LabVIEW软件控制高速采集卡DAQ-2005设计实现多路采集系统,对谱仪的梯度输出进行采集.通过对波形数据进行直方图统计、滤波、差分计算等分析,提取出波形的特征点,这些特征点包含时间与幅度信息.使用实验室自主研发的谱仪进行了多次实验,对该方法进行验证,证明了该方法的有效性,也为谱仪研制和脉冲序列开发提供了一种辅助测试方法.     

一维光子晶体缺陷模的偏振特性研究

利用周期结构的布洛赫定理推导了一维无限光子晶体缺陷模方程,研究了缺陷模的偏振特性,以及在不同入射角和缺陷层厚度下缺陷模位置的变化.利用传输矩阵方法对有限周期数光子晶体也进行了研究,分别对应一维无限光子晶体和有限周期数光子晶体给出了数值计算结果.通过比较这两者的数值结果得出了缺陷模随入射角和缺陷层厚度变化的一般规律.     

光梯度力与激光捕获

从电偶极子在非均匀电磁场中所受梯度力出发,用光的电磁理论和电解质小球的电偶极子模型,论述了介质小球在光场中所受光梯度力与光强梯度成正比,并以此来定量说明激光对介质小球的捕获原理.     

The multicomponent （2＋1）-dimensional Glachette-Johnson （GJ） equation hierarchy and its super-integrable coupling system

This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent （2＋1）-dimensional Glachette-Johnson （G J） hierarchy is given. Finally, the super-integrable coupling system of multicomponent （2＋1）-dimensional GJ hierarchy is established through enlarging the spectral problem.