This paper is devoted to the asymptotic analysis of the spectrum of a mathematical model that describes the vibrations of a coupled fluid–solid periodic structure. In a previous work [Arch. Rational Mech. Anal., 135 (1996), pp. 197–257] we proved by means of a Bloch wave homogenization method that, in the limit as the period goes to zero, the spectrum is made of three parts: the macroscopic or ...

This work addresses the influence of point spectrum on large sample statistics of the autoregressive spectral estimator. In particular, the asymptotic distributions of the AR coefficients, the innovations variance, and the spectral density estimator of a finite order AR(p) model for a mixed spectrum process are presented. Numerical simulations are performed to verify the analytical results.

We study the power spectrum and, more generally, the spectral covariance of weighted stationary processes. It is found that if the power spectrum of the underlying stationary process is suitably well behaved and properly matched to the weight function, then the highfrequency behavior of the power spectriom and spectral covariance is especially simple. Asymptotic theorems describing this behavio...

One of the principal themes of information theory is to establish a link between two different kinds of quantities: one is an operational quantity which is defined through the asymptotic optimality on some concrete concept such as code length, compression rate, error probability, etc., while the other is an abstract information quantity such as the entropy, divergence, mutual information, etc. ...

We show that the spectrum of linear delay differential equations with large delay splits into two different parts. One part, called the strong spectrum, converges to isolated points when the delay parameter tends to infinity. The other part, called the pseudocontinuous spectrum, accumulates near criticality and converges after rescaling to a set of spectral curves, called the asymptotic continu...

Toeplitz matrices occur in many mathematical as well as scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations ...

The covariance ordering, for discrete and continuous time Markov chains, is defined and studied. This partial ordering gives a necessary and sufficient condition for MCMC estimators to have small asymptotic variance. Connections between this ordering, eigenvalues, and suprema of the spectrum of the Markov transition kernel, are provided. A representation of the asymptotic variance of MCMC estim...

The propagation of low frequency or long wavelength disturbances in periodically layered media is considered. An asymptotic series is derived for the frequency of the first branch of the Bloch wave spectrum. The expansion is in dimensionless wavenumber and is developed explicitly for SH waves traveling obliquely through layerings with arbitrary periodic stratification. The first dispersive term...

We present an asymptotic study on the phase diagram of two-dimensional nematic liquid crystal polymer monolayers with the Onsager intermolcular potential. In contrast to the case of MaierSaupe interaction potential where there is only one nematic branch, our analysis reveals that there are infinite many nematic branches in the case of the Onsager interaction potential. An asymptotic expression ...

We derive a new formula for the asymptotic eigenvalue distribution of stiffness matrices obtained by applying P1 Finite Elements with standard mesh refinement to the semi elliptic PDE of second order in divergence form −∇(K∇Tu) = f on Ω, u = g on ∂Ω. Here Ω ⊂ R and K is supposed to be piecewise continuous and pointwise symmetric semi positive definite. The symbol describing this asymptotic eige...