基于串联两阶段网络DEA模型的供应链规模收益分析

数据包络分析(DEA)是评价供应链系统(Supply chain system)间相对有效性的一种重要的工具,但是传统的DEA不考虑供应链的内部结构,对系统效率评价偏高;而本文所研究两阶段串联供应链系统,考虑把部分中间产品作为最终产品输出,增加额外中间投入的情形.基于所提出的供应链系统结构,本文建立相应的串联结构下的网络DEA模型,并针对所建立模型进行相关理论的研究,给出了串联结构下的生产可能集和规模收益情况判定方法.最后,进行数值实验,以验证我们提出的结论.     

Kalman filtering of a space-time Markov random field

In this paper, finite-dimensional recursive filters for space-time Markov random fields are derived. These filters can be used with the expectation maximization (EM) algorithm to yield maximum likelihood estimates of the parameters of the model.     

Intramolecular photocycloaddition of β-stilbazoles tethered by silyl chains

Intramolecular (2+2) photocycloaddition of β-stilbazoles tethered by silyl chains took place with high efficiency. Complexation with dicarboxylic acid or catechol further enhanced both the efficiency and stereoselectivity.     

Modelling recruitment training in mathematical human resource planning

This paper deals with mathematical human resource planning; more specifically, it suggests a new model for a manpower‐planning system. In general, we study a k‐classed hierarchical system where the workforce demand at each time period is satisfied through internal mobility and recruitment. The motivation for this work is based on various European Union incentives, which promote regional or local government assistance programs that could be exploited by firms not only for hiring and training newcomers, but also to improve the skills and knowledge of their existing personnel. In this respect, in our augmented mobility model we establish a new ‘training/standby’ class, which serves as a manpower inventory position for potential recruits. This class, which may very well be internal or external to the system, is incorporated into the framework of a non‐homogeneous Markov chain model. Furthermore, cost objectives are employed using the goal‐programming approach, under different operating assumptions, in order to minimize the operational cost in the presence of system's constraints and regulations. Copyright © 2002 John Wiley & Sons, Ltd.     

Likelihood Ratio Processes for Markovian Particle Systems with Killing and Jumps

We consider Markov processes built from pasting together pieces of strong Markov processes which are killed at a position dependent rate and connected via a transition kernel. We give necessary and sufficient conditions for local absolute continuity of probability laws for such processes on a suitable path space and derive an explicit formula for the corresponding likelihood ratio process. The main tool is the consideration of the process between successive jumps – what we call ‘elementary experiments’ – and criteria for absolute continuity of laws of the process there. We apply our results to systems of branching diffusions with interactions and immigrations. This revised version was published online in June 2006 with corrections to the Cover Date.     

Projection of Markov Measures May Be Gibbsian

We study the induced measure obtained from a 1-step Markov measure, supported by a topological Markov chain, after the mapping of the original alphabet onto another one. We give sufficient conditions for the induced measure to be a Gibbs measure (in the sense of Bowen) when the factor system is again a topological Markov chain. This amounts to constructing, when it does exist, the induced potential and proving its Hölder continuity. This is achieved through a matrix method. We provide examples and counterexamples to illustrate our results.     

Estimation in the continuous time mover‐stayer model with an application to bond ratings migration

The usual tool for modelling bond ratings migration is a discrete, time‐homogeneous Markov chain. Such model assumes that all bonds are homogeneous with respect to their movement behaviour among rating categories and that the movement behaviour does not change over time. However, among recognized sources of heterogeneity in ratings migration is age of a bond (time elapsed since issuance). It has been observed that young bonds have a lower propensity to change ratings, and thus to default, than more seasoned bonds. The aim of this paper is to introduce a continuous, time‐non‐homogeneous model for bond ratings migration, which also incorporates a simple form of population heterogeneity. The specific form of heterogeneity postulated by the proposed model appears to be suitable for modelling the effect of age of a bond on its propensity to change ratings. This model, called a mover–stayer model, is an extension of a Markov chain. This paper derives the maximum likelihood estimators for the parameters of a continuous time mover–stayer model based on a sample of independent continuously monitored histories of the process, and develops the likelihood ratio statistic for discriminating between the Markov chain and the mover–stayer model. The methods are illustrated using a sample of rating histories of young corporate issuers. For these issuers the default probabilities predicted by the Markov chain and mover–stayer models are different. In particular for 1–4 years old bonds the mover–stayer model estimates substantially lower default probabilities from rating C than a Markov chain. Copyright © 2004 John Wiley & Sons, Ltd.     

基于MMD算法的HMM参数重估计的矩阵表示

本文提出的MMD算法用于提高模型区别错误信息和正确信息的能力．利用该算法在对模型的参数进行重估计时．涉及到复杂的目标函数的梯度运算．击运用矩阵运算使得梯度运算变得简单明了，因此本文给出了MMD算法下的HMM参数重估计的矩阵表示形式并给出了证明．     

NCD系统的数学理论

无索赔折扣系统(No Claim Discount system,简记为NCD系统)是世界各国机动车辆险中广泛采用的一种经验费率厘定机制.本文尝试建立了NCD系统严谨的数学理论, 重点讨论了NCD系统的数学建模和稳态分析.此外,作为本文必要的数学前提,首先在第2节着重探讨了随机矩阵间的随机优序关系,并将所得结论运用至齐次不可约且遍历的马尔科夫链的研究中,这些内容也有其独立的数学上的兴趣.