Book reviews

Red Banner: the Soviet Military System in Peace and War. By Christopher Donnelly. Jane's Information Group, Coulsdon, UK (1988), 288 pp., £35.00

Images of T. E. Lawrence. By S. E. Tabachnick and C. Matheson. Jonathan Cape, London (1988); The Letters of T. E. Lawrence. Edited by Malcolm Brown. Dent, London (1988); T. E. Lawrence. By J. Wilson. National Portrait Gallery Publications, London (1988); Lawrence and the Arab Revolts. By D. Nicolle. Osprey, London (1989)

Liddell Hart and the Weight of History. By John Mearsheimer. Brassey's, London (1989), £15.95

Science and Mythology in the Making of Defence Policy. Edited by Margaret Blunden and Owen Greene. Brassey's, London (1989), £27.50/$44.00

Warfare in the Twentieth Century. Edited by Colin McInnes and G. D. Sheffield. Unwin Hyman, London (1988), 239 pp., £25.00     

On finding spanning eulerian subgraphs

In this article, we examine the problem of producing a spanning Eulerian subgraph in an undirected graph. After the ?-completeness of the general problem is established, we present polynomial-time algorithms for both the maximization and minimization versions where instances are defined on a restricted class of graphs referred to as series-parallel. Some novelties in the minimization case are discussed, as are heuristic ideas.     

The politics of population

This article suggests some of the principal factors behind the decisions by an increasing number of countries deciding that the achievement of their national objectives required a policy for population, and the way that they are likely to work out. By 1983, 35 developing countries had an official policy to reduce their population growth rate, and in 34 others, the government supported family planning activities--usually for reasons of health or as a human right. The number is remarkable given the many compelling reasons that governments have for not attempting anything so difficult as to modify demographic trends. The future results of population programs, in social and economic terms, are very difficult to quantify, thus defying cost-benefit analysis of the desirability of investing resources in this area, rather than in something else. There are also powerful political reasons why a government might well hesitate before embarking on a policy to reduce the nation's fertility. At the very least, it implies government interference in the most private and personal of human relations, an invasion of human rights, and a disturbance of the traditional patterns of society and behavior. For many countries that are pursuing a policy to limit population growth, the decision has been taken only after the grievous consequences of not having such a policy have already become manifest. The critical question is how soon a government will make the connection among political disobedience, economic and social distress, and the population explosion, and adopt a population policy. Although the number of developing countries that have officially proclaimed a strongly pro-natalist population policy is relatively small, many have Marxist governments. Overall, governments have several strategies at their disposal: 1) improving the accessability and the quality of the service; 2) promoting population education and family planning motivation (with the assistance of the media, folk art, and personal persuasion); and 3) applying a judicious mixture of incentives and disincentives.     

Quadratic forms in spherical random variables: Generalized noncentral x2 distribution

Let X denote a random vector with a spherically symmetric distribution. The density of U = X'X, called a “generalized chi-square,” is derived for the noncentral case, when μ = E(X) ≠ 0. Explicit series representations are found in certain special cases including the “generalized spherical gamma,” the “generalized” Laplace and the Pearson type VII distributions. A simple geometrical representation of U is shown to be useful in generating random U variates. Expressions for moments and characteristic functions are also given. These densities occur in offset hitting probabilities.     

A characterization of the wald distribution

Suppose X is a random variable having an absolutely continuous distribution function F(x). We assume that F(x) has the Wald distribution. A relation between the probability density function of X⁻¹ with that of X is used to characterize the Wald distribution.     

A class of inventory models with customer impatience

Classical inventory models generally assume either no backlogging of demands or unlimited backlogging. This paper treats the case wherein backlogged customers are willing to wait for a random period of time for service. A broad class of such models is discussed, with a more complete analysis performed on a simple subclass. Steady state equations are derived and solved assuming exponentially distributed interarrival times of customers, order delivery lead times, and customer patience.     

An open expanding economy model

The authors extend the generalized von Neumann model they developed (with J. G. Kemeny) in 1956 to an open model by assuming that there are exogeneously determined export and import prices and that any amount can be exported or imported at these prices. The open model is then characterized by means of seven axioms. It is shown, by applying the theory of linear programming, that if four economically reasonable assumptions hold, the open model has at least one solution in which at least one good with positive export price is exported and at least one good with positive import price is imported. It is also shown that, in general, a continuum of expansion rates can be achieved by varying certain control variables. The choice of these expansion rates gives indirectly the choice of a suitable sub-economy and also determines the exports and imports of the economy. Other results and examples are discussed.