不交树:对网络系统和故障树进行定量分析的新方法

本文提出了一个对事件集建造不交树的方法。这个方法中通过分离独立项和提取公因子使割集(路集)的项数和阶次迅速下降。所建成的不交树中所有分支互不相交,因此可由直接计算求得顶事件的发生概率。给出了应用例子。讨论了向多态系统的推广以及近似计算方法。     

Criterion for a chain of σ-processes to be the composition of triangular chains

The purpose of this paper is to establish a topological criterion for a chain of spheres in a two-dimensional complex manifold to be a composition of so-called triangular chains. Explicit formulas are given for the relevant topological characteristics of chains. Certain corollaries of this criterion related to the Jacobian conjecture are discussed. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 643–653, May, 1999.     

约束最小生成树问题研究

本文对约束最小生成树问题提出一个算法,它的计算复杂性是O(n3)．然后把约束最小生成树作为约束Steiner最小树的一个近似解,则近似解的性能比为3?/2．     

树上马氏链场的若干极限性质

该文引进广义Ｂｅｔｈｅ树和广义Ｃａｙｌｅｙ树的概念,并研究其上马氏链场关于状态和状态序偶出现频率的强极限定理,作为主要结果的推论,得到Ｂｅｔｈｅ树和Ｃａｙｌｅｙ树上马氏链场的ＳｈａｎｎｏｎＭｃＭｉｌｌａｎ定理．证明中采用了研究概率论强极限定理的一种新的方法．     

树映射有异状点的一个充要条件

讨论了树上连续自映射的拓扑熵与非稳定流形之间的关系． 证明了：树上连续自映射有异状点的充要条件是其拓扑熵大于零． 因而推广了区间上连续自映射的一个结果．     

计算最小支撑出树的一种简便算法

本文通过对网络中有向支撑出树性质的研究,提出了在有向网络图中寻找以某一定点为根的最小有向支撑出树一种较简便的计算方法,并给出了应用该算法进行实际操作的一个算例．     

Recurrence Times in Quasi-Periodic Motion: Statistical Properties,Role of Cell Size,Parameter Dependence

We investigate the probabilistic properties of recurrence times for the simplest form of aperiodic deterministic dynamics, quasi-periodic motion. Previous results using number theory techniques predict two fundamental recurrence times for uniform quasi-periodic motion on a two-dimensional torus, while no analogous analytic result seems to exist for higher dimensional tori. The two-dimensional uniform case is reanalyzed from a more geometric point of view and new, workable expressions are derived that enable us fully to understand and predict the recurrence phenomenon and to analyze its parameter dependence. Emphasis is placed on the statistical properties and, in particular, on the variability of recurrence times around their mean, in relation to local Farey tree structure. Higher-dimensional tori are considered, and seen to also display a high variability in their finite-time recurrence behavior. The results are finally extended to the non-uniform quasi-periodic case.     

一个一维CI相变模型的进一步研究

对一个一维CI相变模型进行进一步研究。外势周期D具有一个临界值Dc。D < c时的相图与D > c时的相图非常地不同。当D < c时,相图随D而变化,且在D的大部分区域显示出Farey树结构。当D > c时,相图不再变化,且不满足Farey树结构。通过有效势F(u)研究了相变过程。     

Splitting Choice and Computational Complexity Analysis of Decision Trees

Some theories are explored in this research about decision trees which give theoretical support to the applications based on decision trees. The first is that there are many splitting criteria to choose in the tree growing process. The splitting bias that influences the criterion chosen due to missing values and variables with many possible values has been studied. Results show that the Gini index is superior to entropy information as it has less bias regarding influences. The second is that noise variables with more missing values have a better chance to be chosen while informative variables do not. The third is that when there are many noise variables involved in the tree building process, it influences the corresponding computational complexity. Results show that the computational complexity increase is linear to the number of noise variables. So methods that decompose more information from the original data but increase the variable dimension can also be considered in real applications.     

船舶海上交通事故人因致因因素分析方法研究

为克服模糊故障树分析模型计算过程专家人员需求量大,参评专家众多时,定量量化过程复杂及缺少随机性的问题,采用蒙特卡罗法建立模糊故障树分析模型,使用计算机运作生成随机数,并以船舶海上交通事故调查报告中的3个基本事故最小割集进行定量分析.结果表明,蒙特卡罗模型法结合使用计算机生成随机数可以解决模糊故障树分析模型对事故随机性分析结果不准确的问题,实现了在参评专家人员众多情形下简化计算过程的目标.最后通过案例验证了该模型法具有很强的针对性和实用性.