随机事元的关联性与条件传导概率

讨论了随机事元的关联性和独立性,给出了条件随机事元的概念.在对随机事元的传导概率和条件随机事元研究的基础上,建立了条件传导概率的概念.最后举例讨论了传导概率和条件传导概率在解决矛盾问题中的应用.     

基于传导变换的马尔可夫链平稳分布的研究

利用可拓学中的参变量事元描述随机过程,引入了随机过程元的概念,建立了随机过程的可拓模型.利用随机事元刻画随机过程的状态,引入了随机状态元和随机状态元集的概念,给出了马尔可夫事元链模型.利用随机状态元的可拓性以及传导变换对马尔可夫链及其平稳分布进行了初步的拓展研究.     

基元的算术运算

以提升可扩分析的有效性为目的,分别从物元、事元和关系元从发,讨论基元的和、差、积、商等基本算术运算及其实际涵义,为客观世界中物、事和关系组分方式的形式化表达提供新的方法,进而可为可拓策略生成的计算机实现奠定基础.     

关于B-值迭对数律的一些结论

本文讨论小球条件在B－值独立同分布随机元迭对数律中的应用，并给出了B－值随机元迭对数律的一些结论。     

在通常矩条件下B—值随机元配重迭对数律不成立的一个反例

本文讨论B－值随机元配重迭对数律,给出了在通常矩条件下B－值随机元配重迭对数律不成立的一个反例,文中还指出,当随机元范数矩的条件弱于二阶矩时,配重迭对数律不成立。     

B值独立随机元重对数律收敛速度的一般形式

本文讨论了Ｂ值独立同分布（ｉｉｄ）随机元重对数律收敛速度的一般形式,使得Ｄａｖｉｓ＾「１」及Ｇｕｔ＾「２,３」中的一些结果成为特款,同时减弱了Ｄａｖｉｓ结果中的矩条件,并且得到了Ｂ值ｉｉｄ随机元满足有界重对数律的一个充分性条件。作为应用,我们给出了随机足标和的相应结果。     

关于B值随机元随机指标和的矩的讨论

在本文中,我们研究停止时间N的矩、B值随机元X_n的矩以及{X_n,n≥1}的随机指标和S_N的矩之间的关系。特别,在赋予Banach空间以某些特定的几何性质,例如假设B为p-阶光滑空间、q-凸空间及Hilbert空间的情形下,讨论了上述各种矩之间的关系。     

随机事件与随机变量概率分布的拓展研究

给出了随机事元的拓展概率以及随机事元可拓集的概念.运用可拓集合、可拓变换与可拓推理等可拓学的理论与方法,对随机事件发生的概率与随机变量概率分布的变化作了初步的拓展研究.     

一类独立B值随机元的完全收敛性

本文讨论 B 值随机元的完全收敛性,将有关独立同分布随机元的完全收敛性的研究拓广到独立不同分布情形,同时将随机元单纯的矩条件过渡到选定的函数类 S 上.     

B值行独立随机元阵列的矩完全收敛性

本文研究了B值行独立的随机元阵列的矩完全收敛性.利用B值行独立的随机元阵列的概率不等式,在随机元阵列随机有界于某非负随机变量的条件下,获得了B值行独立的随机元阵列的矩完全收敛性的一些充分条件,并完善了Chow关于实值独立同分布随机变量列的矩完全收敛性的结果.     

一类抽球模型中两两(或相互)独立的条件及其模型构建

以一类抽球模型中由两两独立不能推出相互独立为基础,导出只由单色球和全色球构成的抽球模型中,抽到的球上的颜色两两独立的充要条件;然后得到并为必然事件的n个随机事件相互独立一个必要条件,并构建抽球模型中抽到的球上的颜色相互独立的球色彩结构.     

基于失效分析的独立均匀随机变量和的分布及应用初探

数学模型是基于材料失效分析提出来的,同时结合了BS模型的方法理论背景.材料样品在周期性应力作用下,主因裂纹的扩大量是一个随机变量.对于均匀材料,主因裂纹的扩大量可看作是均匀随机变量与一个大于零的实数的乘积,材料主因裂纹的总的扩大量可表示为这些独立均匀随机变量的和,或称为加权随机和.实际上,本文给出一类新的随机模型及其概率分布函数,并初步讨论了该模型分布的一些基本特征,通过数值模拟还讨论了其独特的分布特征,如与正态分布的关系与区别,以及该模型分布收敛于正态分布的速度等.这些工作可为材料失效分析提供新的模型与方法.     

B值随机元和的完全收敛性

在B值随机元随机有界于一非负随机变量的情况下．讨论了B值独立随机元序列非随机足标和的完全收敛性，作为应用，得到了随机足标和完全收敛性的相应结果，将[5]中的一些结果推广到B值独立随机无情形，同时使[3]（d=1），[4]，[6]的相应结果成为特例．     

The branching chain with drift in space-time random environment (I): Model,Markov property,moments

There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment (BCDSTRE), i.e., the coupling of branching chain and random walk. In Section 2, we prove that any BCDSTRE must be a Markov chain in time random environment when we consider the distribution of the particles in space as a random element. In Section 3, we calculate the first-order moments and the second-order moments of BCDSTRE.     

Structure of random 312‐avoiding permutations

We evaluate the probabilities of various events under the uniform distribution on the set of 312‐avoiding permutations of . We derive exact formulas for the probability that the i^th element of a random permutation is a specific value less than i, and for joint probabilities of two such events. In addition, we obtain asymptotic approximations to these probabilities for large N when the elements are not close to the boundaries or to each other. We also evaluate the probability that the graph of a random 312‐avoiding permutation has k specified decreasing points, and we show that for large N the points below the diagonal look like trajectories of a random walk. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 49, 599–631, 2016     

THE BRANCHING CHAIN WITH DRIFT IN SPACE-TIME RANDOM ENVIRONMENT （I）： MODEL,MARKOV PROPERTY,MOMENTS

There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment （BCDSTRE）, i.e., the coupling of branching chain and random walk. In Section 2, we prove that any BCDSTRE must be a Markov chain in time random environment when we consider the distribution of the particles in space as a random element. In Section 3, we calculate the first-order moments and the second-order moments of BCDSTRE.     

应用随机数渐近线分布法评估飞机飞行安全

严重纵向人机耦合事件是公认的危及飞行安全问题 ,出现概率一般为 10 -6.若采用传统的频率统计法进行趋势预测 ,需要的样本数大于 10 7个 ,工程实际中是无法实现的 .为此 ,文中提出了有效的随机数渐近线分布法对其进行评估 .     

CME on March 16, 2001, electron pulsation event and solar-terrestrial phenomena related with CMEs

The electron pulsation event is defined in the paper. Firstly, a slow Halo CME on March 16, 2001 that led to low-energetic solar proton event, electron pulsation event and major geomagnetic storm was analyzed. And then, dozens of events are collected. The interrelations among the solar flare, CME, solar proton event, electron pulsation event and geomagnetic storm are studied. The results show that: (ⅰ) Solar proton events can be regarded as the indication that CMEs get to the earth and the electron pulsation events can be regarded as the indication of solar proton flux. (ⅱ) Not only can fast CMEs strongly influence the earth, but also slow CMEs can influence the earth, and its influences are more frequent and cannot be neglected. (ⅲ) Most of high-energetic solar proton events with E≥10 MeV can lead to geomagnetic storms, but most of the medium and weak geomagnetic storms result from low-energetic solar proton events that are caused by CMEs. (ⅳ) Both the electron pulsation events and geomagnetic storms are the link effects of high- and low-energetic solar proton events, but the occurrence of electron pulsation event are generally prior to the geomagnetic storm. So in the circumstance where the near real-time observing data of the low-energetic solar proton event cannot be obtained, we can regard electron pulsation event as the indication of the low-energetic solar proton flux reaching the earth, which can be used as one of the important 参考文献 of short-term prediction and alert of the geomagnetic storm.     

Large‐deviations/thermodynamic approach to percolation on the complete graph

We present a large‐deviations/thermodynamic approach to the classic problem of percolation on the complete graph. Specifically, we determine the large‐deviation rate function for the probability that the giant component occupies a fixed fraction of the graph while all other components are “small.” One consequence is an immediate derivation of the “cavity” formula for the fraction of vertices in the giant component. As a byproduct of our analysis we compute the large‐deviation rate functions for the probability of the event that the random graph is connected, the event that it contains no cycles and the event that it contains only small components. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2007