Banach空间值鞅不等式与弱大数定律

本文证明了Ｂａｎａｃｈ空间值鞅的一些不等式，讨论了Ｂａｎａｃｈ空间的凸性及光滑性与某些鞅不等的式的联系，给出了Ｈｉｌｂｅｒｔ空间的一个鞅不等式刻划，同时还讨论了一致Ｐ光滑空间中鞅的弱大数定律，本文的结论推广与改进了很多熟知的定理。     

学生成绩分布与一种简便的评估试卷命题质量的方法

利用统计分析方法，对辽宁师范大理科学生成绩分布情况进行了分析；给出了一种评估试卷命题质量的简便易行的方法一用正态曲线拟合的方法，实际证明，效果很好。     

The application of spectral distribution of product of two random matrices in the factor analysis

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.     

Optimisation of fault-tolerant fabric-cutting schedules using genetic algorithms and fuzzy set theory

In apparel industry, manufacturers developed standard allowed minutes (SAMs) databases on various manufacturing operations in order to facilitate better scheduling, while effective production schedules ensure smoothness of downstream operations. As apparel manufacturing environment is fuzzy and dynamic, rigid production schedules based on SAMs become futile in the presence of any uncertainty. In this paper, a fuzzification scheme is proposed to fuzzify the static standard time so as to incorporate some uncertainties, in terms of both job-specific and human related factors, into the fabric-cutting scheduling problem. A genetic optimisation procedure is also proposed to search for fault-tolerant schedules using genetic algorithms, such that makespan and scheduling uncertainties are minimised. Two sets of real production data were collected to validate the proposed method. Experimental results indicate that the genetically optimised fault-tolerant schedules not only improve the operation performance but also minimise the scheduling risks.     

Asymptotics in the Baum—Katz formula for random fields

In 1996, D. Deng established an analog of the Baum—Katz theorem on the convergence rate in the law of large numbers for multi-indexed random variables. The series describing the convergence rate depends, in a natural way, on the parameter characterizing the excess of the normalized sums over some level. In this paper, we find the precise asymptotics of the sum of this series with respect to the above-mentioned parameter. Thus, a generalization of a recent result due to A. Gut and A. Spataru is obtained.     

Colliding stacks: A large deviations analysis

We analyze the performance of a prototypical scheme for shared storage allocation: two initially empty stacks evolving in a contiguous block of memory of size m. We treat the case in which the stacks are more likely to shrink than grow, but with the probabilities of insertion and deletion allowed to depend arbitrarily on stack height as a fraction of m. New results are obtained on the m → ∞ asymptotics of the stack collision time, and of the final stack heights. The results of Wentzell and Freidlin on the large deviations of Markov chains are used, and the relation of their formalism to the Hamiltonian formulation of classical mechanics is emphasized. Certain results on higher-order asymptotics follow from WKB expansions.     

基于机器视觉的离散傅里叶变换目标识别方法

提出了一种基于机器视觉与离散傅里叶变换的目标特征识别方法。利用计算机图像技术采集和处理图像信号;利用离散的傅里叶变换对图像数据提取特征,能够更好的辨别数据细节,从而可通过图像的比对来实现目标的识别。该方法在对实际的静止图像进行处理与计算后,能够很好的对图像的细节变化进行识别。     

基于SVM局部后验概率融合方法研究

研究了基于支持向量机的后验概率的应用,提出了对样本集进行分解,以产生局部后验概率,根据模式的稳健性对局部后验概率进行凸组合融合的方法.     

Computing Aviation Sparing Policies: Solving a Large Nonlinear Integer Program

Deployed US Navy aircraft carriers must stock a large number of spare parts to support the various types of aircraft embarked on the ship. The sparing policy determines the spares that will be stocked on the ship to keep the embarked aircraft ready to fly. Given a fleet of ten or more aircraft carriers and a cost of approximately 50 million dollars per carrier plus the cost of spares maintained in warehouses in the United States, the sparing problem constitutes a significant portion of the Navy’s resources. The objective of this work is to find a minimum-cost sparing policy that meets the readiness requirements of the embarked aircraft. This is a very large, nonlinear, integer optimization problem. The cost function is piecewise linear and convex while the constraint mapping is highly nonlinear. The distinguishing characteristics of this problem from an optimization viewpoint are that a large number of decision variables are required to be integer and that the nonlinear constraint functions are essentially “black box” functions; that is, they are very difficult (and expensive) to evaluate and their derivatives are not available. Moreover, they are not convex. Integer programming problems with a large number of variables are difficult to solve in general and most successful approaches to solving nonlinear integer problems have involved linear approximation and relaxation techniques that, because of the complexity of the constraint functions, are inappropriate for attacking this problem. We instead employ a pattern search method to each iteration of an interior point-type algorithm to solve the relaxed version of the problem. From the solution found by the pattern search on each interior point iteration, we begin another pattern search on the integer lattice to find a good integer solution. The best integer solution found across all interations is returned as the optimal solution. The pattern searches are distributed across a local area network of non-dedicated, heterogeneous computers in an office environment, thus, drastically reducing the time required to find the solution.     

A simple proof of Sanov’s theorem*

A simple self-contained proof of Sanov's theorem in τ-topology is given, well suited for a first course on large deviations. *This work was supported by the Hungarian National Foundation for Scientific Research under Grant T046376