Some variant of Newton’s method with third-order convergence

We present a new modification of the Newton’s method which produces iterative methods with order of convergence three. A general error analysis providing the higher order of convergence is given, and the best efficiency, in term of function evaluations, of two of this new methods is provided.     

Denumerable controlled Markov chains with average reward criterion: Sample path optimality

We consider discrete-time nonlinear controlled stochastic systems, modeled by controlled Makov chains with denumerable state space and compact action space. The corresponding stochastic control problem of maximizing average rewards in the long-run is studied. Departing from the most common position which usesexpected values of rewards, we focus on a sample path analysis of the stream of states/rewards. Under a Lyapunov function condition, we show that stationary policies obtained from the average reward optimality equation are not only average reward optimal, but indeed sample path average reward optimal, for almost all sample paths.Research supported by a U.S.-México Collaborative Research Program funded by the National Science Foundation under grant NSF-INT 9201430, and by CONACyT-MEXICO.Partially supported by the MAXTOR Foundation for applied Probability and Statistics, under grant No. 01-01-56/04-93.Research partially supported by the Engineering Foundation under grant RI-A-93-10, and by a grant from the AT&T Foundation.     

André-Quillen cohomology and rational homotopy of function spaces

We develop a simple theory of André-Quillen cohomology for commutative differential graded algebras over a field of characteristic zero. We then relate it to the homotopy groups of function spaces and spaces of homotopy self-equivalences of rational nilpotent CW-complexes. This puts certain results of Sullivan in a more conceptual framework.     

Parallel radial basis function methods for the global optimization of expensive functions

We introduce a master–worker framework for parallel global optimization of computationally expensive functions using response surface models. In particular, we parallelize two radial basis function (RBF) methods for global optimization, namely, the RBF method by Gutmann [Gutmann, H.M., 2001a. A radial basis function method for global optimization. Journal of Global Optimization 19(3), 201–227] (Gutmann-RBF) and the RBF method by Regis and Shoemaker [Regis, R.G., Shoemaker, C.A., 2005. Constrained global optimization of expensive black box functions using radial basis functions, Journal of Global Optimization 31, 153–171] (CORS-RBF). We modify these algorithms so that they can generate multiple points for simultaneous evaluation in parallel. We compare the performance of the two parallel RBF methods with a parallel multistart derivative-based algorithm, a parallel multistart derivative-free trust-region algorithm, and a parallel evolutionary algorithm on eleven test problems and on a 6-dimensional groundwater bioremediation application. The results indicate that the two parallel RBF algorithms are generally better than the other three alternatives on most of the test problems. Moreover, the two parallel RBF algorithms have comparable performances on the test problems considered. Finally, we report good speedups for both parallel RBF algorithms when using a small number of processors.     

Infrared Image Series Automatic Registration and a History & Tendency Analysis

Infrared camera has been widely used in electrical power systems for predictive and preventive thermal fault diagnosis. Without historical IR images being considered, most thermograph analysis used at present are concerned with static image. The dynamic history and tendency analysis which compares the newly taken image with historical images is particularly attractive. Conclusions can be drawn from temperature variations rather than just from anomalous thermal pattern. However the spatial distortions prevent such dynamic analysis from being practicable. So the need to register infrared images arises. This paper proposes an automatic registration algorithm based on closed temperature contour matching for infrared image series of a target equipment taken at different times. Centroid Distance Function is used in image registration for the first time. The algorithm can remove spatial distortions, bring temperature variations into prominence and endow infrared camera with dynamic analysis ability. Experiment shows that the algorithm is simple, effective and extensible.     

非齐次线性差分方程的Cm解[英文]

设c0,c1,…,cn均为实的常数，F（x)是个从R到R的C^m映射。本文讨论了非齐次线性差分方程∑i=1ncif(x i)=F(x)的C^m(m≥0）的存在性和唯一性。     

The Interpolation Problem on the Maximal Ideal Space of H~∞

ＴｈｅＩｎｔｅｒｐｏｌａｔｉｏｎＰｒｏｂｌｅｍｏｎｔｈｅＭａｘｉｍａｌＩｄｅａｌＳｐａｃｅｏｆＨ~∞￥ＧｕｏＫｕｎｇｕ（郭坤宇）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｉｃｈｕａｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈｅｎｇｄｕ，６１００６４）Ａｂｓ?..     

带时滞观测线性离散系统的递推滤波

本文讨论带时滞观测线性离散系统的滤波问题,提出利用联合分布函数,得到滤波递推格式.这种方法还适用于一般的带有状态时滞的线性离散系统.     

INVARIANCE PRINCIPLE FOR THE INTEGRAL PERIODOGRAM OF A MULTIPLE TIME SERIES

Many authers have studied the asymptotic behavior of the integral periodogram of a Gaussian stationary series. In this paper, the invariance principle for the integral periodogram of a multiple time series is investigated. We have obtained the following theorem:Let X, be a real M -dimensional stationary time series with spectral density matrix f(λ) which satis-fies the conditions:M,and X, can be represented in theform: Xn =whereξ, is the M-dimensional fourth order moment existedstationary martingale series, thenweakly converges to a Gauss process η(λ) withEη(λ) = 0,where V and Q are the second and fourth moment of the martingale seriesξ , respectively.From this theorem, two corollaries have been given, which cover some results of [2][5][6].     

基于集值统计的模糊神经网络专家系统及其应用

建立基于集值统计的模糊神经网络专家评审系统，并应用于科研项目评审工作，实际应用表明该系统是可行的。