从Fermat大定理看数学问题在数学发展中的作用

回顾费马大定理的解决过程,从一个侧面论述了数学问题对数学发展的推动作用.     

三阶线性齐次微分方程解的Sturm比较定理

研究了一类三阶线性齐次微分方程解的Sturm比较定理的理论,在三阶线性齐次微分方程的Sturm基本定理的基础上得出了Sturm比较定理,所得结论推广了现有文献的相应结果。     

基于适度财务指标和遗传算法的财务危机预测模型研究

以往进行财务危机预测主要使用统计方法建模,迄今尚未见到因考虑财务指标的适度性而建立遗传算法模型的中外文献。适度财务指标是指该指标在某个区间内公司才是健康的,过大或过小则公司发生财务危机的可能性都较大。故以中国上市公司数据为样本,建立了基于适度财务指标和遗传算法的创新型财务危机预测模型,结果显示该类模型具有较高的预测准确率。     

Functional Estimation of a Density Under a New Weak Dependence Condition

The purpose of this paper is to prove, through the analysis of the behaviour of a standard kernel density estimator, that the notion of weak dependence defined in a previous paper (cf. Doukhan & Louhichi, 1999) has sufficiently sharp properties to be used in various situations. More precisely we investigate the asymptotics of high order losses, asymptotic distributions and uniform almost sure behaviour of kernel density estimates. We prove that they are the same as for independent samples (with some restrictions for a.s. behaviours). Recall finally that this weak dependence condition extends on the previously defined ones such as mixing, association and it allows considerations of new classes such as weak shifts processes based on independent sequences as well as some non-mixing Markov processes.     

Boosting with Bayesian stumps

Boosting is a new, powerful method for classification. It is an iterative procedure which successively classifies a weighted version of the sample, and then reweights this sample dependent on how successful the classification was. In this paper we review some of the commonly used methods for performing boosting and show how they can be fit into a Bayesian setup at each iteration of the algorithm. We demonstrate how this formulation gives rise to a new splitting criterion when using a domain-partitioning classification method such as a decision tree. Further we can improve the predictive performance of simple decision trees, known as stumps, by using a posterior weighted average of them to classify at each step of the algorithm, rather than just a single stump. The main advantage of this approach is to reduce the number of boosting iterations required to produce a good classifier with only a minimal increase in the computational complexity of the algorithm.     

高阶拟线性时滞差分方程非振动解的存在性与渐近性

考虑一类高阶拟线性时滞差分方程给出了存在无界非振动解的充要条件。     

Combinatorial Optimization in Real-Time Scheduling: Theory and Algorithms

Real-time computer systems are essential for many applications, such as robot control, avionics, medical instrumentation, manufacturing, etc. The correctness of the system depends on the temporal correctness as well as the functional correctness of the task executions. In order to assure temporal correctness it is necessary that the resources be scheduled to meet the temporal requirements of applications. When we consider the problem of nonpreemptive scheduling of a set of tasks in a processor for which no feasible solution exists, some tasks may have to be rejected so that a schedule can be generated for the rest. In this paper, we consider the problem of generating an optimal schedule such that the number of rejected tasks is minimized, and then the finish time is minimized for the accepted tasks. We propose to use an analytic approach to solve this problem. We first discuss the super sequence based technique which was originally proposed for reducing the search space in testing the feasibility of a task set. Then we show by the Conformation theorem that the super sequence constructed from the task set also provides a valid and reduced search space for the optimization problem. While the complexity of our scheduling algorithm in the worst case remains exponential, our simulation results show that the cost is reasonable for the average case.     

计算机与智力:推理过程的机械化

在概述几何定理机器证明近期成果的基础上,提出了推理过程机械化的一个关键问题,即对计算机推理产生的那些不能用人工检验的结论如何看待的问题。     

数列极限比较理论

给出数列极限比较式定义 ,由此简明地导出极限理论 .证明了该定义等价于原定义(ε-N) ,以及单调子列定理、单调归结原则等 .该理论不仅便于教学 ,而且揭示了数列极限可归结到单调数列 ,最终归结到自然数列     

模态系统T的Herbrand定理

模态Herbrand定理研究是模态逻辑领域的重要开放问题.不含Barcan公式的模态系统T的Herbrand定理的获得必须完成两个方向的证明工作:首先是证明相对简单的从右到左方向;而对于相对复杂的从左到右方向,则可以通过在加标公式表列系统K的基础上增加特殊规则获得加标公式表列系统T,证明T的可靠性和完全性,并在此基础上完成从左到右方向的证明.同样的方法还可以用来证明模态系统D、K4、s4的Herbrand定理.