正定Hermite矩阵特征值的相对扰动界

给出了正定Hermite矩阵特征值的一个新扰动界,同以往的结论相比我们的界形式上更简洁而且新的扰动界在合同变换下保持不变。     

On Some Criteria for Estimating the Order of a Markov Chain

Tong (1975) has proposed a procedure for estimating the order of a Markov chain based on Akaike's information criterion (AIC). In this paper, the asymptotic distribution of the AIC estimator is derived and it is shown that the estimator is inconsistent. As an alternative to the AIC procedure, the Bayesian information criterion (BIC) proposed by Schwarz (1978) is shown to be consistent. These two procedures yield different estimated orders when applied to specific samples of meteorological observations. For parameters based on these meteorological examples, the AIC and BIC procedures are compared by means of simulation for finite samples. The results obtained have practical implications concerning whether, in the routine fitting of precipitation data, it is necessary to consider higher than first-order Markov chains.     

On the optimization of free resources using non-homogeneous Markov chain software rejuvenation model

Software rejuvenation is an important way to counteract the phenomenon of software aging and system failures. It is a preventive and proactive technique, which consists of periodically restarting an application at a clean internal state. Starting an application generally means that an amount of memory is captured and closing an application engenders the release of an amount of memory. In general, when an application is initiated an amount of memory is captured and when terminated an amount of memory is released. In this paper a model describing the amount of free memory on a system is presented. The modelling is formulated under a continuous time Markov chain framework. Additionally the cost of performing rejuvenation is also taken into consideration, a cost function for the model is produced and a rejuvenation policy is proposed. The contribution of this paper consists of using a cyclic non-homogeneous Markov chain in order to study the overall behaviour of the system capturing time dependence of the rejuvenation rates and deriving an optimal rejuvenation policy. Finally, a case study is presented in order to illustrate the results of the cost analysis.     

供应链拓扑结构模型研究

供应链是随着全球制造的兴起而出现的新型的管理模式。本文从企业与企业之间关系的角度提出了供应链的拓扑结构模型：链状模型、网状模型和石墨模型,相应地给出了供应链的子网、级、入点、出点等概念。本文针对不同的研究对象和研究阶段而提出的供应链概念和模型有助于对供应链的和认识和研究,对国有企业重组有启示意义。     

灰色马尔可夫链在道路交通事故预测中的应用

将灰色系统理论与马尔可夫链相结合,建立道路交通事故灰色马尔可夫链预测模型研究证明．这种模型的预测精度高于GM（1,1）模型,可用于道路交通事故预测。     

On Generating Optimal Sparse Probabilistic Boolean Networks with Maximum Entropy from a Positive Stationary Distribution

To understand a genetic regulatory network, two popular mathematical models, Boolean Networks (BNs) and its extension Probabilistic Boolean Networks (PBNs) have been proposed. Here we address the problem of constructing a sparse Probabilistic Boolean Network (PBN) from a prescribed positive stationary distribution. A sparse matrix is more preferable, as it is easier to study and identify the major components and extract the crucial information hidden in a biological network. The captured network construction problem is both ill-posed and computationally challenging. We present a novel method to construct a sparse transition probability matrix from a given stationary distribution. A series of sparse transition probability matrices can be determined once the stationary distribution is given. By controlling the number of nonzero entries in each column of the transition probability matrix, a desirable sparse transition probability matrix in the sense of maximum entropy can be uniquely constructed as a linear combination of the selected sparse transition probability matrices (a set of sparse irreducible matrices). Numerical examples are given to demonstrate both the efficiency and effectiveness of the proposed method.     

A general formulation for transition probabilities of Markov model and the application to fracture of composite materials

A generalized method for formulating unit-jump Markov chain model is presented. This method uses geometric series to determine the transition probabilities instead of using a moment generation function. Recursive equation for the transition probabilities has been derived in terms of the mean values. Present method is also compared by other method for robustness. Application of the unit-jump Markov chain model for characterizing fracture process of composites is described. By introducing a proper scaling factor, the entire probability history of the crack propagation at any loading states can be evaluated by the present model.     

An Equation of State for the Hard-Sphere Chain Fluid Based on the Thermodynamic Perturbation Theory of Sequential Polymerization

New equations of state for freely jointed hard-sphere chain fluids are developed. The equations of state are based on the thermodynamic perturbation theory. The new equations of state use the contact values of the radial distribution function (RDF) for monomer–dimer mixtures, which is derived from the multidensity Ornstein–Zernike theory. These RDFs are composed of a monomer reference term, the Carnahan–Starling or the Percus–Yevick expression, and an additional bond contribution. These equations of state are then extended to real fluids. To calculate the phase equilibrium properties of nonassociating chain fluids, a dispersion contribution is added to the repulsive hard-chain reference term. With the new equations of state of chain fluids supplemented with the dispersion term, the vapor pressures and the coexisting densities of several real fluids are calculated.     

On the Structure of Linear and Cyclic Codes over a Finite Chain Ring

We generalise structure theorems of Calderbank and Sloane for linear and cyclic codes over ℤ _pa to a finite chain ring. Our results are more detailed and do not use non-trivial results from Commutative Algebra. Received: January 25, 1999; revised version: November 17, 1999     

On Condition Numbers for the Weighted Moore-Penrose Inverse and the Weighted Least Squares Problem involving Kronecker Products

We establish some explicit expressions for norm-wise, mixed and componentwise condition numbers for the weighted Moore-Penrose inverse of a matrix $A⊗B$ and more general matrix function compositions involving Kronecker products. The condition number for the weighted least squares problem (WLS) involving a Kronecker product is also discussed.     

基于FANP方法的供应链配送中心评价选择

供应链配送中心的评价选择是供应链管理的重要课题.层次分析法(AHP)只能分析经过大量简化处理的树状结构或者其他理想结构.因此,采用解释结构模型(ISM)建立配送中心评价选择指标体系,用模糊网络分析法(FANP)进行计算分析,对以制造业为主导的供应链配送中心进行评价和选择,不仅考虑了指标的层次关系,也考虑到各层中因素之间的相互关系,解决了对具有网络关系的混合型结构评价指标体系的评价选择问题,克服了层次分析法(AHP)等传统算法的局限,在实际应用中具有很好的效果.     

On the Uniformity of Distribution of the ElGamal Signature

 We show that, under some natural conditions,the pairs (r,s) produced by the ElGamal signature scheme are uniformly distributed. In particular this implies that values of r and s are not correlated. The result is based on some new estimates of exponential sums. Received: May 17, 2000; revised version: August 23, 2001     

商品钢筋供应链渠道长度设计研究

立足于商品钢筋经销商,以避免与渠道中下游客户的冲突和提升竞争力为目的,研究商品钢筋供应链渠道长度优化选择方法。将双层规划模型应用于商品钢筋供应链渠道长度设计之中,通过对模型解的分析,给出了商品钢材经销商在渠道长度选择中应采取的策略。结合实例,验证双层规划方法可有效地用于供应链渠道长度选择。     

Bayesian Inference and Life Testing Plan for the Weibull Distribution in Presence of Progressive Censoring

This article deals with the Bayesian inference of unknown parameters of the progressively censored Weibull distribution. It is well known that for a Weibull distribution, while computing the Bayes estimates, the continuous conjugate joint prior distribution of the shape and scale parameters does not exist. In this article it is assumed that the shape parameter has a log-concave prior density function, and for the given shape parameter, the scale parameter has a conjugate prior distribution. As expected, when the shape parameter is unknown, the closed-form expressions of the Bayes estimators cannot be obtained. We use Lindley's approximation to compute the Bayes estimates and the Gibbs sampling procedure to calculate the credible intervals. For given priors, we also provide a methodology to compare two different censoring schemes and thus find the optimal Bayesian censoring scheme. Monte Carlo simulations are performed to observe the behavior of the proposed methods, and a data analysis is onducted for illustrative purposes.     

A semiparametric model for compositional data analysis in presence of covariates on the simplex

Compositional data occur as natural realizations of multivariate observations comprising element proportions of some whole quantity. Such observations predominate in disciplines like geology, biology, ecology, economics and chemistry. Due to unit sum constraint on compositional data, specialized statistical methods are required for analyzing these data. Dirichlet distributions were originally used to study compositional data even though this family of distribution is not appropriate (see Aitchison, 1986) because of their extreme independence properties. Aitchison (1982) endeavored to provide a viable alternative to existing methods by employing Logistic Normal distribution to analyze such constrained data. However this family does not include the Dirichlet class and is therefore unable to address the issue of extreme independence. In this paper generalized Liouville family is investigated to model compositional data which includes covariates. This class permits distributions that admit negative or mixed correlation and also contains non-Dirichlet distributions with non-positive correlation and overcomes deficits in the Dirichlet class. Semiparametric Bayesian methods are proposed to estimate the probability density. Predictive distributions are used to assess performance of the model. The methods are illustrated on a real data set.     

A method to account for outliers in the development of safety performance functions

Accident data sets can include some unusual data points that are not typical of the rest of the data. The presence of these data points (usually termed outliers) can have a significant impact on the estimates of the parameters of safety performance functions (SPFs). Few studies have considered outliers analysis in the development of SPFs. In these studies, the practice has been to identify and then exclude outliers from further analysis. This paper introduces alternative mixture models based on the multivariate Poisson lognormal (MVPLN) regression. The proposed approach presents outlier resistance modeling techniques that provide robust safety inferences by down-weighting the outlying observations rather than rejecting them. The first proposed model is a scale-mixture model that is obtained by replacing the normal distribution in the Poisson-lognormal hierarchy by the Student t distribution, which has heavier tails. The second model is a two-component mixture (contaminated normal model) where it is assumed that most of the observations come from a basic distribution, whereas the remaining few outliers arise from an alternative distribution that has a larger variance. The results indicate that the estimates of the extra-Poisson variation parameters were considerably smaller under the mixture models leading to higher precision. Also, both mixture models have identified the same set of outliers. In terms of goodness-of-fit, both mixture models have outperformed the MVPLN. The outlier rejecting MVPLN model provided a superior fit in terms of a much smaller DIC and standard deviations for the parameter estimates. However, this approach tends to underestimate uncertainty by producing too small standard deviations for the parameter estimates, which may lead to incorrect conclusions. It is recommended that the proposed outlier resistance modeling techniques be used unless the exclusion of the outlying observations can be justified because of data related reasons (e.g., data collection errors).     

焊接接头断裂韧度J_(ⅠC)统计分布函数的蒙特卡罗模拟

建立了用于确定焊接接头断裂韧度ＪⅠＣ统计分析函数的蒙特卡罗模拟方法。对３１６Ｌ奥氏体不锈钢焊接接头ＪⅠＣ的统计分布函数进行了统计模拟，结果表明，ＪⅠＣ的最佳拟合分布为威布尔分布。分析了样本数量对蒙特卡罗模拟结果的影响。