Strong limit-point classification of singular Hamiltonian expressions

Strong limit-point criteria for singular Hamiltonian differential expressions with complex coefficients are obtained. The main results are extensions of the previous results due to Everitt, Giertz, and Weidmann for scalar differential expressions.

     

Classical Limit of Expectation Values in a Wave Packet Involving Few Stationary States

Expectation values of physical quantities in a wave packet involving few stationary states in an infinite square well are calculated. Explicit results show that the expectation values in the classical limit go over to the corresponding classical quantity in the form of the arithmetic mean (in mathematical term, the Fejér's average) of the partial Fourier series converging to the classical quantity. The number of the stationary states is that of the partial Fourer series in the Fejér's average. The quantum uncertainty is then demonstrated to have a classical counterpart.     

Nonparametric estimation of distributions with categorical and continuous data

In this paper we consider the problem of estimating an unknown joint distribution which is defined over mixed discrete and continuous variables. A nonparametric kernel approach is proposed with smoothing parameters obtained from the cross-validated minimization of the estimator's integrated squared error. We derive the rate of convergence of the cross-validated smoothing parameters to their ‘benchmark’ optimal values, and we also establish the asymptotic normality of the resulting nonparametric kernel density estimator. Monte Carlo simulations illustrate that the proposed estimator performs substantially better than the conventional nonparametric frequency estimator in a range of settings. The simulations also demonstrate that the proposed approach does not suffer from known limitations of the likelihood cross-validation method which breaks down with commonly used kernels when the continuous variables are drawn from fat-tailed distributions. An empirical application demonstrates that the proposed method can yield superior predictions relative to commonly used parametric models.     

Study on a Distributed Wavelength Routing Algorithm in WDM Optical Transport Networks

A new design scheme for a distributed algorithm for routing and wavelength assignment (RWA) is developed in this paper, and the communication rules between the nodes to exchange signaling packets are discussed. The Adaptive-Alternate-Routing-Least-Load (AARLL) algorithm is implemented in the distributed scheme for the first time. Under dynamic traffic circumstances, the influence of the race condition, which does not exist in centralized scheme, on the network performance is analyzed and the analyzed results show that the race condition has a major impact on network performance only under light traffic load, while under medium and heavy traffic load the impact is very small. To analyze the performance loss caused by adopting the distributed algorithm for RWA, the capacity loss factor (CLF) is introduced and the calculated results show that CLF does not exceed 6% under medium traffic load.     

基于径向矢量的不变性形状分类方法

介绍一种利用径向矢量提取形状特征的方法，着重于分析二维图形的不变性，提出一种带有方向因子的径向矢量描述，该矢量以图形边界弧长为自变量，完整地刻画了图形特点，克服了非凸图形识别中存在的多义性，以归一化的特征矢量的输入，采用三层神经网络为分类器，在字符及军事目标不变性识别中取得了令人满意的结果。     

Synthesis and transition temperatures of liquid crystals incorporating a 1,4-tetrafluorophenylene unit

Two homologous series of mesogenic materials which incorporate a 1,4-tetrafluorophenylene moiety and a terminal cyano- or nitro-substituent have been synthesized by using palladiumcatalysed coupling procedures. The compounds exhibit nematic and/or smectic A phases.     

Robinson-Trautman equations and Chandrasekhar's special perturbation of the Schwarzschild metric

A perturbation wave solution of the Robinson-Trautman equations is proved to be a perturbation of the Schwarzschild black hole which describes an outgoing axial gravitational wave and corresponds to a special case of Chandrasekhar's algebraically special perturbation of the Schwarzschild metric.     

A problem in extremal quasiconformal extensions

A constantK ₀ ^(m) (h) is introduced for every quasisymmetric mappingh of the unit circle and every integerm≥4 which contains the constantK ₀(h) (indicated by the change in module of the quadrilaterals with vertices on the circle) as a special case. A necessary and sufficient condition is established forK ₀ ^(m) (h) =K ₁(h). It is shown that there are infinitely many quasisymmetric mappings of the unit circle having the property thatK ₀ ^(m) (h)<K ₁(h), wherek ₁(h) is the maximal dilatation ofh.     

宽带被动导引头天线系统性能分析

详细讨论了宽带被动导引头中的关键部件－超宽频带天线的性能，并在此基础上分析了三种具备大视角特性的被动测角方法。由于宽带天线没有确定的相位中心，因此不能采用通常的振幅和差式单脉冲法进行宽频带测角。本文提出的波束运算网络可用于一个宽带螺旋天线同时得到两个交叉波束的振幅－振幅式单脉冲系统中。此外，对比幅相干测向法中的测角模糊问题也进行了研究。