A diagram approach to the strong coupling in the single-impurity Anderson model

We propose a diagram theory around the atomic limit for the single-impurity Anderson model in which the strongly correlated impurity electrons hybridize with free (uncorrelated) conduction electrons. Using this diagram approach, we prove a linked-cluster theorem for the vacuum diagrams and derive Dyson-type equations for localized and conduction electrons and the corresponding equations for mixed propagators. The system of equations can be closed by summing an infinite series of ladder diagrams containing irreducible Green’s functions. The result allows discussing resonances associated with quantum transitions at the impurity site. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 474–497, June, 2008.     

g-循环矩阵的谱分解和Jordan块结构

首先证明了n级非奇异g-循环矩阵必定可以对角化，并且给出了它的谱分解。其次，当（n,g）=1时，给出了n级奇异g-循环矩阵相似于某些对角阵和某些幂零Jordan块的直和，进一步给出了其中幂零Jordan块的幂零指数的计算法。     

多缝衍射光谱技术

本文从重叠干涉强度分布和重叠光谱强度分布的概念出发,论证和推导了多缝衍射光谱技术中复原光谱的极限理论分辨率的公式。讨论了稳定求解的条件。并对多缝衍射光谱技术和经典的衍射光谱技术两者的光谱分辨本领作了比较,同时给出了几个计算机实验的结果。     

一种指纹宏观曲率特征提取算法

在自动指纹识别系统中,如何有效的利用大量的指纹脊线弯曲信息是个重要问题.本文提出了一种新算法,通过综合邻近几条指纹脊线的信息,求出了一种能反映指纹宏观弯曲规律的特征.实验结果表明,该算法提取出的特征清楚地描述了指纹脊线的弯曲规律,同时对噪声不敏感,可作为指纹识别的辅助特征.     

QAM调制分析与其SystemView仿真实现

正交振幅调制OAM(Ouadrature Amplitude Modulation)是一种频谱利用率很高的调制方式.文章在介绍OAM调制、解调原理的基础上,深入探讨了OAM的频谱利用率和误码率性能.并在SystemView下对该系统进行了完整仿真.通过仿真观察到调制与解调信号的波形,星座图以及OAM信号功率谱密度曲线,并对仿真结果进行了分析.由分析结果可知,OAM调制系统具有很高的频谱利用率以及较好的误码率性能,因此可增大系统容量,同时也保证了系统的可靠性.     

Estimation of prediction error variance

This note considers an estimate of the variance of the prediction error for a normal stationary time series based on the periodogram. It is shown that as T → ∞, the estimate converges almost surely to σ², the variance of the prediction error for the best linear predictor. By applying a result of Hannan [2] it thus follows that if in fitting an autoregression to the data x(1),…,x(T) the order k is greatly overstated, then the resultant estimate σ²_k of σ² will be biased downward.     

Generalizations of P. Lévy's inversion theorem

We extend the Lévy inversion formula for the recovery of a bounded measure over $\text{R}$ from its Fourier-Stieltjes transform to bounded complex-valued, orthogonally scattered Hilbert space-valued, and spectral projection operator-valued measures over any first countable locally compact Abelian group. All our results are direct generalizations of known inversions for $\text{R}$.     

Asymptotic expansions of the distributions of some test statistics for Gaussian ARMA processes

Let {X_t} be a Gaussian ARMA process with spectral density f_θ(λ), where θ is an unknown parameter. The problem considered is that of testing a simple hypothesis H:θ = θ₀ against the alternative A:θ ≠ θ₀. For this problem we propose a class of tests , which contains the likelihood ratio (LR), Wald (W), modified Wald (MW) and Rao (R) tests as special cases. Then we derive the χ² type asymptotic expansion of the distribution of T up to order n⁻¹, where n is the sample size. Also we derive the χ² type asymptotic expansion of the distribution of T under the sequence of alternatives A_n: θ = θ₀ + /√n, ε > 0. Then we compare the local powers of the LR, W, MW, and R tests on the basis of their asymptotic expansions.     

Estimation of second-order properties from jittered time series

This paper considers spectral and autocovariance estimation for a zero-mean, band-limited, stationary process that has been sampled at time points jittered from a regular, equi-interval, sampling scheme. The case of interest is where the sampling scheme is near regular so that the jitter standard deviation is small compared to the sampling interval. Such situations occur with many time series collected in the physical sciences including, in particular, oceanographic profiles.Spectral estimation procedures are developed for the case of independent jitter and autocovariance estimation procedures for both independent and dependent jitter. These are typically modifications of general estimation procedures proposed elsewhere, but tailored to the particular jittered sampling scheme considered. The theoretical properties of these estimators are developed and their relative efficiencies compared.The properties of the jittered sampling point process are also developed. These lead to a better understanding, in this situation, of more general techniques available for processes sampled by stationary point processes.