Choosing a random spanning subtree: a case study

Broder⁽⁴⁾ has suggested a stochastic algorithm for generating a random spanning subtree of a graph. This paper studies this algorithm for a special class of graphs. A complete spectral decomposition of the associated Markov chain is given. The analysis available from this is compared to stopping-time techniques and purely geometric bounds on the second eigenvalue.     

On the evaluation of strategies for branching bandit processes

Glazebrook [1] has given an account of improved procedures for strategy evaluation for resource allocation in a stochastic environment. These methods are extended in the paper in such a way that they can be applied to problems which, for example, have precedence constraints and/or an arrivals process of new jobs. Theoretical results, backed up by numerical studies, show that quasi-myopic heuristics often perform well.     

Explicit optimal value for Dynkin's stopping game

Under the One-step Look Ahead rule of Dynamic Programming, an explicit game value of Dynkin's stopping problem for a Markov chain is obtained by using a potential operator. The condition on the One-step rule could be extended to the k-step and infinity-step rule. We shall also decompose the game value as the sum of two explicit functions under these rules.     

动量相关作用对两体耗散同位旋效应的重要性

利用同位旋相关的量子分子动力学,研究了中能重离子碰撞中动量相关的状态方程对原子核阻止基于两体耗散的同位旋效应的影响.计算结果表明原子核阻止对同位旋相关和同位旋无关的核子–核子碰撞截面(两体耗散)的差值强烈地依赖于动量相关势,即在有动量相关势的情况下原子核阻止对同位旋相关和同位旋无关的核子–核子碰撞截面的差值大于没有动量相关势的情况.这就意味着动量相关作用明显地提高了原子核阻止对于核子–核子碰撞截面的灵敏性.因此,在考虑动量相关势的情况下,原子核阻止可以更准确地作为提取同位旋相关的核子–核子碰撞截面的一个探针.     

停止变换的不变性

利用条件期望的表达式给出了两指标过程在停线处的停止定义,研究了停止变换下的若干不变性．给出了这种停止意义下的局部平方可积强鞅的定义,进一步研究了局部平方可积强鞅二次变差的存在性及其停止性质，得到了重要的Burkholder-Davis-Gundy型不等式及平方可积强鞅的一个充要条件。     

Interruptible Exact Sampling in the Passive Case

We establish, for various scenarios, whether or not interruptible exact stationary sampling is possible when a finite-state Markov chain can only be viewed passively. In particular, we prove that such sampling is not possible using a single copy of the chain. Such sampling is possible when enough copies of the chain are available, and we provide an algorithm that terminates with probability one.     

A Newton type iterative inverse method for heat-conduction problems

An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.     

具有缺失数据的Eichhorn模型

为了解决在Eichhorn乘法扰动模型中存在的项目无回答问题,对敏感变量总体均值在辅助变量总体均值已知与未知条件下提出了比率插补方法.理论比较和数值模拟得出的结果表明提出的插补方法比传统的方法效率更高.     

Dynamics of turbulent air-flow in droplet driven sprays

This paper presents a study of the fundamental mechanics of droplet and gas motion in sprays. Only vertical sprays are considered and our theoretical analysis identifies two main flow zones, corresponding to where the droplet velocity is much greater than or of the same order as the induced air velocity. Analytical asymptotic results for the induced air velocity for small and large downstream distances confirmed a full numerical calculation and also agreed with experimental results. The second half of the paper deals with some of the most important aspects of spray jets in a cross flow. We find that the ratio of the cross-wind speed to the induced air jet speedU ₀/V _j is a crucial factor for specifying the dynamical behaviour. We present results for an axi-symmetric spray in uniform cross flow for bothweak andstrong cross-winds.     

Additive comparisons of stopping values and supremum values for finite stage multiparameter stochastic processes

This paper concerns the optimal stopping problem for discrete time multiparameter stochastic processes with the index set Nd. In the classical optimal stopping problems, the comparisons between the expected reward of a player with complete foresight and the expected reward of a player using nonanticipating stop rules, known as prophet inequalities, have been studied by many authors. Ratio comparisons between these values in the case of multiparameter optimal stopping problems are studied by Krengel and Sucheston (1981) [9] and Tanaka (2007, 2006) [14] and [15]. In this paper an additive comparison in the case of finite stage multiparameter optimal stopping problems is given.