First-passage times in a critical stochastic model

Average first-passage times for a single-variable stochastic model with a critical fixed point at the origin are computed by exact enumeration. The numerical measurements show excellent agreement with analytical results. The scaling function approaches the predicted asymptotic dependence.     

一类随机环境中的随机游动

在Solomn的模型的基础上对一类随机环境中随机游动进行了讨论，并得出了一个常返性准则和一些极限性质。     

触销式双障碍买权价值过程鞅性

主要证明了在不存在交易成本的完全市场条件下连续时间欧式触销式双障碍买权贴现到0时刻的价值过程为鞅,并且给出了对应单障碍买权价值过程的鞅性质.同时还讨论了执行价格为随机的触销式双障碍买权的鞅性质,给出了任意时刻 t(0≤ t≤T)其内在价值的表达式.     

Dynamics of Random One-Dimensional ±J Systems

Finite chains of a two-state random Potts spin model with periodic boundary conditions are studied within Glauber dynamics. The spin exchange is assumed random with frustration between ferro and antiferromagnetic values (±J). Time-dependent fluctuations are induced by periodic temperature oscillations. Master type differential equations for spin correlation functions are solved within linear response theory. The spectrum of relaxation times are calculated at different temperatures. The ±J Potts glass chains undergo a zero temperature phase transition. The barriers against inversion of the spin chain take only two values; 0 and 2|J|. The temperature behaviour of specific heat is characterized by rounded peaks. The frequency dependence displays two plateaus for the real part of specific heat and two corresponding peaks for the imaginary part. The dynamic specific heat is not affected by the longest relaxing mode like susceptibility. The time separation of the modes is demonstrated by the Cole-Cole plots.     

Analysis of a Multiserver Queue with Setup Times

This paper deals with the analysis of an M/M/c queueing system with setup times. This queueing model captures the major characteristics of phenomena occurring in production when the system consists in a set of machines monitored by a single operator. We carry out an extensive analysis of the system including limiting distribution of the system state, waiting time analysis, busy period and maximum queue length. AMS subject classification: 90B22, 60K25     

SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES AND COMPRESSION COSTS （PART I：EQUAL TIMES AND COSTS）

Most papers in scheduling research have treated individual job processing times as fixed parameters. However, in many practical situations, a manager may control processing time by realloeating resources. In this paper, authors consider a machine scheduling problemwith controllable processing times. In the first part of this paper, a special case where the pro-cessing times and compression costs are uniform among jobs is discussed. Theoretical results are derived that aid in developing an O（n^2) algorithm to slove the problem optimally. In the second part of this paper, authors generalize the discussion to general case, An effective heuristic to the genera/ problem will be presented.     

Intégalités de Sobolev et Temps d'Atteinte

We investigate the links between Sobolev and Nash inequalities, capacity and hitting times estimates and ultracontractive semigroups, in a non-symmetric setting.     

Rotational Motion of a Solute Molecule in a Highly Viscous Liquid Studied byC NMR: 1,3-Dibromoadamantane in Polymeric Chlorotrifluoroethene

The viscosity-dependent retarding effect of a polymeric solvent on the rotation of small solute molecules is investigated by¹³C NMR relaxation measurements. It is found that the relaxation data of 1,3-dibromoadamantane in highly viscous polymeric chlorotrifluoroethene can be explained neither by isotropic nor by realistic anisotropic tumbling in a single environment. The experimental data are rationalized in terms of fast exchange between at least two environments with correlation times differing by up to two orders of magnitude. The study shows that a uniform retardation of molecular tumbling by a polymeric solvent, desirable for shifting the NMR observation window in studies of intramolecular mobility, is not always feasible.     

On the cover time of random walks on graphs

This article deals with random walks on arbitrary graphs. We consider the cover time of finite graphs. That is, we study the expected time needed for a random walk on a finite graph to visit every vertex at least once. We establish an upper bound ofO(n ²) for the expectation of the cover time for regular (or nearly regular) graphs. We prove a lower bound of (n logn) for the expected cover time for trees. We present examples showing all our bounds to be tight.Mike Saks was supported by NSF-DMS87-03541 and by AFOSR-0271. Jeff Kahn was supported by MCS-83-01867 and by AFOSR-0271.     

Small random perturbations of finite- and infinite-dimensional dynamical systems: Unpredictability of exit times

We apply previous results on the pathwise exponential loss of memory of the initial condition for stochastic differential equations with small diffusion to the problem of the asymptotic distribution of the first exit times from an attracted domain. We show under general hypotheses that the suitably rescaled exit time converges in the zero-noise limit to an exponential random variable. Then we extend the results to an infinite-dimensional case obtained by adding a small random perturbation to a nonlinear heat equation.