一类混合遗传算法的收敛性研究

针对遗传算法的有效性一般是通过数值实验来说明这一问题,本文在三个假设的条件下给出了一类混合遗传算法依概率收敛的证明,而且得到了在此算法的框架下通过改变子种群Ⅱ的变异算子而不改变依概率收敛特性的结论.     

Large deviations for generalized compound Poisson risk models and its bankruptcy moments

We extend the classical compound Poisson risk model to the case where the premium income process, based on a Poisson process, is no longer a linear function. For this more realistic risk model, Lundberg type limiting results on the finite time ruin probabilities are derived. Asymptotic behaviour of the tail probabilities of the claim surplus process is also investigated.     

On the survival probability of generalized nearest-particle systems

A class of spatial growth models, including reversible nearest-particle systems as special cases, is defined via the range of an underlying random walk. Lower and upper bounds for the survival probability are established under various assumptions. The proofs rely on potential theoretic results for the random walk.     

19F+93Nb耗散反应产物不重复截面的分析

完成了¹⁹F+⁹³Nb耗散反应产物激发函数的两次独立测量,入射束流的能量从102MeV到108MeV,步长250keV.实验结果在一些相同能量点两次测量的截面不能重复.分析表明:能量自关联函数的离散程度大约相当于随机计数率引起的离散程度的3倍;激发函数曲线相对于能量平均本底的几率分布,有大约21髎超出了标准高斯分布宽度的3倍;两次测量得到的截面之差的几率分布大约有18髎也超出了标准高斯分布宽度的3倍.可见,两次测量的¹⁹F+⁹³Nb耗散反应产物激发函数的截面不重复性具有明确的统计意义,其来源不是计数率的随机涨落.     

布朗马达的非均匀高斯跃迁模型

提出了布朗马达的非均匀高斯跃迁理论，用布朗粒子在多态之间的跃迁模型描述分子马达的定向运动.假定跃迁速率与位置有关，且在跃迁点附近具有高斯函数形式，将布朗粒子在x处的概率密度Pm(x,t)在跃迁点附近展开，可以进行任意阶的近似计算.这一理论涵盖了以往的定点跃迁模型和均匀跃迁模型.作为具体例子，研究了系统在两态之间的跃迁问题.假定在一个周期内有两个跃迁点，讨论了布朗粒子定向运动产生的概率流随温度、跃迁速率和 跃迁宽度的变化关系. 关键词： 布朗马达 高斯跃迁 概率流     

On the value distribution of the Matsumoto zeta-function

The Matsumoto zeta-function is defined by a polynomial Euler product and is a generalization of classical zeta-functions. In the paper a discrete limit theorem in the sense of the weak convergence of probability measures on the complex plane for the Matsumoto zeta-function is proved.     

一类公交车调度问题的数学模型及其解法

本讨论了城市公交车调度问题中的上车乘客流分布和下车概率矩阵的处理方法，建立了基于模拟公共汽车运行的公交车调度问题的数学模型，给出了解法，并对模型的应用进行了讨论。     

Computational methods in risk theory: A matrix-algorithmic approach

This paper is concerned with the numerical computation of the probability ψ(u) of ruin with initial reserve u. The basic assumption states that the claim size distribution is phase-type in the sense of Neuts. The models considered are: the classical compound Poisson risk process, the Sparre Anderse process and varying environments which are either governed by a Markov process or exhibit periodic fluctuations. The computational steps involve the iterative solution of a non-linear matrix equation Q = Ψ (Q) as well as the evaluation of matrix-exponentials e^Qu. A number of worked-out numerical examples are presented.     

Finitely additive random walks on infinitely generated free groups

We consider any purely finitely additive probability measure supported on the generators of an infinitely generated free group and the Markov strategy with stationary transition probability . As well as for the case of random walks (with countably additive transition probability) on finitely generated free groups, we prove that all bounded sets are transient. Finally, we consider any finitely additive measure (supported on the group generators) and we prove that the classification of the state space depends only on the continuous part of .     

Approximations to the birthday problem with unequal occurrence probabilities and their application to the surname problem in Japan

Let X ₁, X ₂,..., X _n be iid random variables with a discrete distribution {p _i } _i =1 ^m . We will discuss the coincidence probability R _n , i.e., the probability that there are members of {X _i } having the same value. If m=365 and p _i 1/365, this is the famous birthday problem. Also we will give two kinds of approximation to this probability. Finally we will give two applications. The first is the estimation of the coincidence probability of surnames in Japan. For this purpose, we will fit a generalized zeta distribution to a frequency data of surnames in Japan. The second is the true birthday problem, that is, we will evaluate the birthday probability in Japan using the actual (non-uniform) distribution of birthdays in Japan.This research is supported in part by Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture under the contact number 01540141 and 02640057.