“矩阵有理插值及其误差公式”一文的注

本文对文[1]中所给出的错误的误差公式做了修订,并给出了相应的证明。     

The Ring of Invariants of Three (3 × 3)-Matrices over a Field of Prime Characteristic

We find a minimal system of generators and a homogeneous system of parameters for the algebra of invariants of three matrices of third order over a field of an arbitrary characteristic.     

无穷矩阵环上的导子

讨论无穷矩阵环上的导子,证明了环R上有限个元素不为零的无穷矩阵坏的每个导子均可表示为两个特殊导子之和。     

有消费或投资的华氏宏观经济模型

本文对华罗庚教授的宏观经济模型进行了推广 ,在原来模型的基础上 ,分别增加了消费、投资 ,得到两种不同的模型 ,并对模型具有经济意义的解进行了研究     

Axisymmetric frictionless contact of functionally graded materials

The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at     

Sequential Estimation of the Parameters in a Trigonometric Regression Model with the Gaussian Coloured Noise

This paper considers the estimation problem for a trigonometric regression model with the noise specified by the Ornstein–Uhlenbeck process with unknown parameter. We propose a sequential procedure which ensures a prescribed mean square precision uniformly in the nuisance parameter. The asymptotic behaviour of the procedure duration mean has been studied. This revised version was published online in August 2006 with corrections to the Cover Date.     

有向全图的幂敛指数和周期

设G是有向图,T(G)表示G的有向全图.本文得到了它们的幂敛指数k(G)和k(T)之间的关系:对任何有向图G,周期p(T(G))=1;当G是本原图时,k(T)≤k(G)+1,文中给出了取得k(G)+1的两类图;当G是无圈图时,k(T)=2k(G)-1,当G是有向圈时,k(T)=2|V(G)|-1,当G是强连通时得到了k(T)的一些估计.     

面阵探测器的像点亚像素定位研究

面阵探测器可直接探测点目标图像的位置，但其定位精度受到探测器分辨率的限制。因此，亚像元精度技术得到了发展。它是利用目标像点的灰度分布特性，通过内插细分算法，确定出像点位置。可将定位精度提高1—2个数量级。本文介绍了几种实现目标像点亚像素定位的内插细分算法。对它们的计算公式、特点进行了分析，并进行了实验验证。     

Novel optical film sensor design based on p-polarized reflectance

A new scheme of optical film sensor is presented. The sensor is based on p-polarized reflectance, consisting of a sensing coated substrate, is easily optimized for maximum sensitivity in different applications. The resolutions of refractive index n_f, extinction coefficient k_f and thickness h_f of the sensitive films are predicted to be 10⁻⁷, 10⁻⁵ and 10⁻³ nm, respectively. Experimentally, we selected the sol–gel derived SnO₂ films as gas-sensitive films and conducted preliminary gas-sensing test. The results indicate that novel optical film sensor scheme has higher sensitivity, and the detection sensitivity is available to 10⁻¹ ppm on the condition of optimum optical parameters and incident angle.