关于线性回归的若干补充

线性回归分析在传统的数理统计教材中，编写的科学性和体系等许多方面尽管非常好，但也存在知识单调、材料陈旧、不能反映现代的前沿等问题。在教学中应补充介绍前沿的应用背景，全面地介绍回归模型，将法则循序渐进地推广，并运用多媒体教学演示回归的实例。     

广义线性模型(六)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 :建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的 :《MultivariateStatisticalModel ingBasedonGeneralizedLinearModles》。     

Well-posedness of the time-varying linear electro-magnetic initial-boundary value problem

The well-posedness of the initial-boundary value problem of the time-varying linear electromagnetic field in a multi-medium region is investigated. Function spaces are defined, with Faraday's law of electromagnetic induction and the initial-boundary conditions considered as constraints. Gauss's formula applied to a multi-medium region is used to derive the energy-estimating inequality. After converting the initial-boundary conditions into homogeneous ones and analysing the characteristics of an operator introduced according to the total current law, the existence, uniqueness and stability of the weak solution to the initial-boundary value problem of the time-varying linear electromagnetic field are proved.     

磁场对非对称量子点中极化子性质的影响

采用线性组合算符和幺正变换方法研究磁场对非对称量子点中弱耦合磁极化子性质的影响.导出了非对称量子点中弱耦合磁极化子的振动频率、基态能量和基态结合能随量子点的横向和纵向有效受限长度、磁场和电子-声子耦合强度的变化关系.数值计算结果表明:非对称量子点中弱耦合磁极化子的基态能量和基态结合能随量子点的横向和纵向有效受限长度的增加而迅速增大.随回旋频率的增加而增大,随电子-声子耦合强度的增加而减小.     

Manipulation of Particles with Counter-Propagating Evanescent Waves

Two counter-propagating evanescent beams are used to align and manipulate polystyrene particles on a prism surface. Since the radiation pressure transferred laterally from the evanescent wave is negated on both sides, particles can be stably aligned. By projecting a circular and a linear beam spot onto the interface, both multiple and single arrays of particles are achieved. Arrays of particles trapped on the interface can be easily moved adjusting the intensity of incident beams on either side. We also simulate electromagnetic distribution of scattering light that is converted from the evanescent wave using the FDTD method. The results show that scattering light converts from an evanescent wave propagating through a particle array and has a distance longer than that propagating from a normal evanescent wave.     

Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems

We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional(2D) systems.The mathematical model of the discrete-time 2D system is established upon the well-known Roesser model,and the uncertainty phenomenon,which appears typically in practical environments,is modeled by a convex bounded(polytope type) uncertain domain.The stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability theory.In the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed techniques.Moreover,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,numerical examples are given to demonstrate the effectiveness of the obtained results.     

Efficient three-step entanglement concentration for an arbitrary four-photon cluster state

We propose an entanglement concentration protocol to concentrate an arbitrary partially-entangled four-photon cluster state.As a pioneering three-step entanglement concentration scheme,our protocol only needs a single-photon resource to assist the concentration in each step,which makes this protocol more economical.With the help of the linear optical elements and weak cross-Kerr nonlinearity,one can obtain a maximally-entangled cluster state via local operations and classical communication.Moreover,the protocol can be iterated to obtain a higher success probability and is feasible under current experimental conditions.     

Impacts of higher-order dispersions and saturable nonlinearities on modulation instability in negative-refractive metamaterials

On the basis of the standard linear stability analysis and Drude electromagnetic model,the impacts of higher-order dispersions and three kinds of typical saturable nonlinearities on modulation instability(MI) have been analyzed and calculated for negative-refractive metamaterials(MMs).Our results show that the MI gain spectra consist of only one spectral region instead of one or two regions in ordinary materials,which may be close to or far from the zero point.Particularly,the spectrum far from the zero point has a high cut-off frequency but a narrow spectral width,which is obviously beneficial to the generation of high-repetition-rate pulse trains.Moreover,MI characteristics here will vary with the normalized angular frequency which can be modified by adjusting the structures of negative-refractive MMs,signifying the controllability of bistable solitons and MI based applications.The effects of saturable nonlinearities are similar to those in ordinary materials.     

量子阱中强耦合束缚极化子的温度效应

采用线性组合算符与变分相结合的方法讨论了无限深量子阱中强耦合束缚极化子的温度效应.给出了无限深量子阱中束缚极化子的基态能量和振动频率随温度和阱宽的变化关系.对RbCl晶体进行了数值计算,结果表明：当温度升高时,量子阱中强耦合束缚极化子的振动频率增大,基态能量的绝对值增大;并且基态能量的绝对值随阱宽增大而增大.