Covariance operator estimation of a functional autoregressive process with random coefficients

We deal with the covariance and cross covariance operators estimation of a Hilbert space valued autoregressive process with random coefficients. We establish bounds for empirical estimators in mean square error and almost sure convergence in Hilbert–Schmidt norm. Consistent estimators of the eigenvalues are also derived.     

全空间上一类非齐次椭圆方程正解的衰减

本文研究了非齐次椭圆方程不同衰减正解的存在性和衰减问题.利用上下解方法,得到了两个有着不同衰减的正解的存在性,推广了文献[2]中非齐次方程正解的存在性.     

Geometry of quasilinear hyperbolic systems with characteristic fields of constant multiplicity

In this paper, we study the regularity of the eigenvalues and eigenvectors and the existence of normalized coordinates for quasilinear hyperbolic systems with characteristic fields of constant multiplicity. We prove that the eigenvalues and eigenvectors of the system have the same regularity as the coefficients of the system. On the other hand, we show that, for the quasilinear hyperbolic system of conservation laws with characteristic fields of constant multiplicity, the normalized coordinates exist on the domain under consideration.     

Radiative transfer in absorbing, emitting and linearly anisotropic-scattering inhomogeneous cylindrical medium

Radiative integral transfer equations for one-dimensional solid cylinder with absorbing, emitting and linearly anisotropic-scattering inhomogeneous medium were derived by Abulwafa et al. (JQSRT 62 (1999) 755). The anisotropic terms in the integral equations and their results for anisotropic benchmark problems (JQSRT 66 (2000) 487) are inaccurate. In this study, the integral equations for absorbing, emitting and linearly anisotropic-scattering medium are rederived, and the integral equations for one-dimensional solid cylindrical medium are solved. The results are compared with selected cases using the discrete ordinates S₁₆ and the exact solutions available in the literature.     

Analyzing integrated-optical inhomogeneous planar waveguides by Galerkin's method: A detailed comparison of two different basis functions

The trigonometric and Hermite-Gaussian basis functions for determining the modal characteristics of inhomogeneous optical waveguides by means of the Galerkin's method are presented and analyzed. The results obtained with each set of basis functions for mode spectra and field distributions are compared with other exact and approximate methods. The merits and problems arising with each set of basis functions are discussed.     

Banach空间中余弦算子函数生成元的有界性

A是Banach空间X中余弦算子函数C（t),t∈R，和正弦算子函数S（t),t∈R，的生成元。本证明了，对每个f∈C（[0,T];X)，连续函数u,u(t)=∫-tS(t-s)f(s)ds,f∈[0,T]是二阶非齐次0初值问题，u″=Au f的强解的充要条件是：A是空间X中的有界算子。     

The finite capacity multi-server queue with inhomogeneous arrival rate and discrete service time distribution — and its application to continuous service time problems

The finite capacity multi-server queueing model with inhomogeneous arrival rate and discrete service time distribution is developed. The system is formulated as an inhomogeneous Markov chain in discrete time. An algorithm is described to solve the model numerically. A method is then proposed for using this model to approximate the time dependent behaviour of multi-server queues with inhomogeneous arrival rate and continuous service time distribution. Empirical results are presented to show that this approximation will produce results that are accurate enough for most practical purposes.     

Spread‐out percolation in ℝd

Fix d ≥ 2, and let X be either ℤ^d or the points of a Poisson process in ℝ^d of intensity 1. Given parameters r and p, join each pair of points of X within distance r independently with probability p. This is the simplest case of a “spread‐out” percolation model studied by Penrose [Ann Appl Probab 3 (1993) 253–276], who showed that, as r → ∞, the average degree of the corresponding random graph at the percolation threshold tends to 1, i.e., the percolation threshold and the threshold for criticality of the naturally associated branching process approach one another. Here we show that this result follows immediately from of a general result of [3] on inhomogeneous random graphs. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007     

An explicitly solvable kinetic model for semiconductors

We consider a simple model for the electron Boltzmann equation in a semiconductor and show that specific boundary value problems can be explicitly solved. Cases of both homogeneous and inhomogeneous electric fields are considered.