A Lanchester-type model of combat with stochastic rates

The effects of environmental stochasticity in a Lanchester-type model of combat are investigated. The methodology is based on a study of stochastic differential equations with random parameters characterized by dichotomous Markov processes. Exact expressions for the Laplace transforms of the time evolution of the first- and second-order moments of the system are obtained. A special case when the fluctuations in the parameters occur with great rapidity in comparison with the natural time scale of the system is also analyzed. The stochastic stability in the mean-square sense is discussed by using the Routh–Hurwitz criterion and it is found that the stochastic perturbations tend to destabilize the system.     

Heterogeneous discrete expenditure for diminishing returns

A probabilistic model is developed that applies to military bombardment, advertising for a mass audience, and other kinds of situations in which striking a target means that less of it is left to strike. The model provides the basis for decision analysis based on marginal gain in such circumstances. Heterogneous resources are considered as well as composite targets. All expenditures are quantized. The model has been developed as part of a computer-based military expert system, to replace a large complex set of expert opinions. In that application it sharply improves efficiency, yet conforms to major tenets of tactical doctrine.     

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.