A model for semiconductor quantum dot molecule based on the current spin density functional theory

Based on the current spin density functional theory, a theoretical model of three vertically aligned semiconductor quantum dots is proposed and numerically studied. This quantum dot molecule (QDM) model is treated with realistic hard-wall confinement potential and external magnetic field in three-dimensional setting. Using the effective-mass approximation with band nonparabolicity, the many-body Hamiltonian results in a cubic eigenvalue problem from a finite difference discretization. A self-consistent algorithm for solving the Schrödinger-Poisson system by using the Jacobi-Davidson method and GMRES is given to illustrate the Kohn-Sham orbitals and energies of six electrons in the molecule with some magnetic fields. It is shown that the six electrons residing in the central dot at zero magnetic field can be changed to such that each dot contains two electrons with some feasible magnetic field. The Förster-Dexter resonant energy transfer may therefore be generated by two individual QDMs. This may motivate a new paradigm of Fermionic qubits for quantum computing in solid-state systems.     

Bandpass filters using periodically loaded combline resonators

A novel combline filter is proposed for cellular‐radio base stations. The Q‐factor is significantly improved. The eigenvalue equation is expressed with the single‐team approximation in the gap region of the combline resonator. A two‐pole combline filter is designed. The calculation, simulation, and experiment results are presented and are in good agreement. © 2005 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.     

An analytical and numerical study of the two-dimensional Bratu equation

Bratu's problem, which is the nonlinear eigenvalue equationu+ exp(u)=0 withu=0 on the walls of the unit square and as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance ofsymmetry: because of invariance under the C₄ rotation group and parity in bothx andy, one can slash the size of the basis set by a factor of eight and reduce the CPU time by three orders of magnitude. Second, the pseudospectral method is ananalytical as well as a numerical tool: the simple approximation3.2A exp(–0.64A), whereA is the maximum value ofu(x, y), is derived via collocation with but a single interpolation point, but is quantitatively accurate for small and moderateA. Third, the Newton-Kantorovich/Chebyshev pseudospectral algorithm is so efficient that it is possible to compute good numerical solutions—five decimal places—on amicrocomputer inbasic. Fourth, asymptotic estimates of the Chebyshev coefficients can be very misleading: the coefficients for moderately or strongly nonlinear solutions to Bratu's equations fall off exponentially rather than algebraically withv untilv is so large that one has already obtained several decimal places of accuracy. The corner singularities, which dominate the behavior of the Chebyshev coefficients in thelimit v, are so weak as to be irrelevant, and replacing Bratu's problem by a more complicated and realistic equation would merely exaggerate the unimportance of the corner branch points even more.     

基于主成分分析中的几类问题的计算公式及结论

讨论了主成分分析中的几类问题的计算方法,重点揭示在协方差矩阵中对角元素相同时的第一主成分及贡献率和对角元素不同时的主成分贡献率．经讨论后给出有关计算公式,并说明这些计算公式在多元统计分析中的实际作用     

复矩阵Hermitian部分的2~n次幂等性

针对J.Gross所研究的复矩阵A的Hermitian部分的幂等性问题,将其扩展到复矩阵A的Hermitian部分的2~n次幂等性,得到了复矩阵A的Hermitian部分是2~n次幂等的充分必要条件;同时也得到了复矩阵A的Hermitian部分是2~n次幂等与A的正规性和特征值之间的关系-由任意2个性质可以推出第3个性质.最后,J.Gross得到的结果成为本文的推论.     

基于图变换的图像压缩采样与分类

提出一种基于图论表示的正交变换基,并在此基础上对图像进行压缩采样与压缩域直接分类.首先,充分利用图像的边缘特性和像素关系,给出一种图像的图论表示方法;然后,通过图Laplacian矩阵的特征值分解得到其特征向量矩阵作为正交变换基,由此得到图像的图变换域稀疏表示;最后,利用随机投影后的压缩采样特征向量直接对分类器进行训练和测试,不仅保持了与原空间相当的分类精度,还大量地减少了训练和测试时间以及计算/存储代价.     

基于PANDA框架的并行有限元模态分析程序开发和应用

为提高大型结构振动分析的规模、精度和效率,基于面向对象有限元并行计算框架PANDA和高性能矩阵特征问题并行求解算法,开发出适用于大规模结构振动问题计算的并行有限元模态分析程序;在超级计算机银河YH和曙光5000A上,通过不同算例验证该程序的正确性和可靠性.以某靶室结构为研究对象演示该程序的应用,指出实际应用时需注意加速...     

A new algorithm for sparse interpolation of multivariate polynomials

To reconstruct a black box multivariate sparse polynomial from its floating point evaluations, the existing algorithms need to know upper bounds for both the number of terms in the polynomial and the partial degree in each of the variables. Here we present a new technique, based on Rutishauser’s qd$qd$-algorithm, in which we overcome both drawbacks.     

基于主次原型超平面最接近支持向量机

基于广义特征值的最接近支持向量机GEPSVM是一种新的具有与SVM性能相当的两类分类方法,通过求解广义特征值来获得两个彼此不平行的拟合两类样本的超平面,其决策规则是将测试样本归为距其最近的超平面所在的类。然而,该规则在某些情形会导致较差的分类结果。对此,本文提出了在利用GEPSVM产生一个主原型超平面的基础上,再利用主原型超平面及它类样本的信息构造一个次原型超平面,形成一个由主次原型超平面共同决策的最接近支持向量机。该方法不仅简单且易于实现,而且具有较GEPSVM更优的分类性能。在UCI数据集上的实验验证了它的有效性。     

拓扑距离特征指数对多氯联苯的QSPR研究

根据分子拓扑理论,提出1种新的多氯联苯(PCBs)化合物分子中,顶点原子(基团)点价值δ_i的计算方法,据以构建分子的结构参数——拓扑距离特征指数(TDEI);同时考虑分子体积以及氯原子在苯环上的位置和数目对PCBs性质的影响,引入分子体积参数(V_R)和基团定位指数(D),然后,采用多元线性回归法,分别建立了PCBs的正辛醇-水分配系数(lgK_(OW))和水溶解度(-lgS_w)的定量结构-性质相关模型,其相关系数分别达到0.9972和0.9730,均优于前人的工作。利用模型预测另外7个PCBs分子的lgK_(OW)和-lgS_W,预测值与实验值的一致性令人满意。