多重网格法在地球物理正反演应用研究中的进展

现阶段地球物理三维勘探面临越来越复杂的问题,其要求更精细的三维网格剖分,现有的一些方法随着网格节点的增加其收敛速度相应减慢。对于应用中更复杂实际模型、更细密网格剖分以及更快收敛速度要求,难于有进一步提高。要有所突破,需借助计算数学最新进展,引入新的高效算法。多重网格法是近二十年迅速发展的一种求解微分方程近乎最优的新算法。本文首先简单介绍了多重网格法基本原理和运算格式,着重介绍了当前国内外多重网格法在地球物理正反演中的应用成果和发展现状。此外,对多重网格法在地球物理正反演中的应用前景及发展趋势进行了展望。     

Discovering patterns in interarrival data

It is suggested that students collect interarrival data for customers arriving at a queue. Two common features will often occur across these various datasets. Some data collection hints, some problems for students to pursue and a few pointers to the literature are given.     

Introducing perception and modelling of spatial randomness in classroom

A strategy to facilitate understanding of spatial randomness is described, using student activities developed in sequence: looking at spatial patterns, simulating approximate spatial randomness using a grid of equally‐likely squares, using binomial probabilities for approximations and predictions and then comparing with given Poisson probabilities. Key questions are discussed with students on concepts needed to understand the approximate models and to generate predictions based on the approximations. The sequence is structured to be interactive to encourage student's interest and curiosity.     

强度函数为sum from i=0 to l λ_it~i的非时齐Poisson过程最大值概率分布

本文讨论一类强度函数的非时齐P0isson过程样本函数在设计基准期[O,T]内最大值概率分 布。分别给出滤过非时齐Poisson过程和单调非时齐Poisson过程样本函数在设计基准期[O,T]内最大值概率分布表述式。     

两类风险过程调节系数的近似

考虑了含两个类的风险过程,首先介绍了复合Poisson分布的一些性质,在此基础上给出了含两个类的风险过程调节系数的近似。     

DVD在线租赁的数学模型

运用概率统计的有关原理和方法,研究了DVD在线租赁的数学模型.利用LINGO软件求得了模型的最优解,给出了最优解相应的DVD在线分配方案.     

带Poisson跳随机微分方程解的存在与唯一性

讨论了一类带Poisson跳的随机微分方程解的存在唯一性问题,在局部Lipschitz条件下给出了带跳随机微分方程解的存在与唯一性的充分条件.     

随机需求下垄断厂商二级价格歧视的研究

在随机需求——总需求为齐次Poisson过程下,分别研究了垄断厂商二段、三段定价执行二级价格歧视的情形,并给出了需求区间的最优分段点.     

随机过程在寿险精算中的一些应用

介绍了在复合泊松过程下保险公司保费的厘定问题,假定在[0,t]时间内投保人随机进入、随机死亡,利用泊松过程的分解模型,抛开复杂的n重积分计算,利用一些假定和数学定理,求得保险公司的期望支出和期望收入,确定保费.并可以把模型推广到更广泛的情况.     

Some optimal dividend problems for a surplus process with interest

We derive some results on the dividend payments prior to ruin in the classical surplus process with interest. An integro-differential equation with a boundary conditions satisfied by the expected present value of dividend payments is derived and solved. Furthermore, we derive an integro-differential equation for the moment generating function, through which we analyze the higher moment of the present value of dividend payments. Finally, closed-form expressions for exponential claims are given.