Book reviews

John Lawrence Tone, The Fatal Knot: The Guerrilla War in Navarre and the Defeat of Napoleon in Spain. Chapel Hill and London; The University of North Carolina Press 1994. Pp.vii + 239, 1 map, biblio., index. $34.95 (cloth). ISBN 0–8078–2169–1.

Robert Holland (ed), Emergencies and Disorder in the European Empires after 1945. London: Frank Cass, 1994. Pp.x + 256; index. £32 (cloth); £15 (paper). ISBN 0–7146–4516–8 and 4109 X

Deborah L. Norden, Military Rebellion in Argentina: Between Coups and Consolidation. Lincoln, NE: University of Nebraska Press, 1996. Pp.242, index, $35/$17.50 (paper). ISBN 0–8032–8369–5.

William M. Minter, Apartheid's Contras: An Inquiry into the Roots of War in Angola and Mozambique. London and Atlantic Highlands, NJ: Zed Books Ltd; Johannesburg: Witwatersrand University Press, 1994. Pp. xii +308, 3 maps, biblio., index. $69.95/£39.95 (cloth); $29.95/£16.95(paper). ISBN 1–85649–266–4 and 266–4.     

On the number of games played in a best of (2n – 1) series

Let p(⩾0.5) denote the probability that team A beats B in a single game. The series continues until either A or B wins n games. Assuming that these games are independent replications, we study some features of the distribution of X_n, the number of games played in the series. It is shown that X_n is unimodal, has an IFRA distribution, and is stochastically decreasing in p. Close approximations to its mode, mean, and variance are given. Finally, it is shown that the maximum-likelihood estimator of p based on X_n is unique.     

Simulation of stochastic activity networks using path control variates

This article details several procedures for using path control variates to improve the accuracy of simulation-based point and confidence-interval estimators of the mean completion time of a stochastic activity network (SAN). Because each path control variate is the duration of the corresponding directed path in the network from the source to the sink, the vector of selected path controls has both a known mean and a known covariance matrix. This information is incorporated into estimation procedures for both normal and nonnormal responses. To evaluate the performance of these procedures experimentally, we examine the bias, variance, and mean square error of the controlled point estimators as well as the average half-length and coverage probability of the corresponding confidence-interval estimators for a set of SANs in which the following characteristics are systematically varied: (a) the size of the network (number of nodes and arcs); (b) the topology of the network; (c) the percentage of activities with exponentially distributed durations; and (d) the relative dominance of the critical path. The experimental results show that although large improvements in accuracy can be achieved with some of these procedures, the confidence-interval estimators for normal responses may suffer serious loss of coverage probability in some applications.     

一类二次微分系统在三次多项式扰动下的极限环估计

计算了一类二次Hamilton微分系统的一阶Mel’nikov函数,通过此方法对该系统在三次多项式扰动下分岔的极限环个数进行了估计。