Spike swapping in basis reinversion

During basis reinversion of either a product form or elimination form linear programming system, it may become necessary to swap spike columns to effect the reinversion and maintain the desired sparsity characteristics. This note shows that the only spikes which need be examined when an interchange is required are those not yet processed in the current external bump.     

The search for an intelligent evader concealed in one of an arbitrary number of regions

This paper considers the search for an evader concealed in one of an arbitrary number of regions, each of which is characterized by its detection probability. We shall be concerned here with the double-sided problem in which the evader chooses this probability secretly, although he may not subsequently move; his aim is to maximize the expected time to detection, while the searcher attempts to minimize it. The situation where two regions are involved has been studied previously and reported on recently. This paper represents a continuation of this analysis. It is normally true that as the number of regions increases, optimal strategies for both searcher and evader are progressively more difficult to determine precisely. However it will be shown that, generally, satisfactory approximations to each are almost as easily derived as in the two region problem, and that the accuracy of such approximations is essentially independent of the number of regions. This means that so far as the evader is concerned, characteristics of the two-region problem may be used to assess the accuracy of such approximate strategies for problems of more than two regions.     

Stochastic duels with round-dependent hit probabilities

The effect of round dependent hit probabilities in the fundamental stochastic duel are examined. The general solution and several specific examples are derived where one side's hit probabilities are improved from round to round. For these specific cases the advantages of round to round improvement are explicitly displayed.     

Stock control in a many depot system

The chief problems considered are: (1) In a parallel set of warehouses, how should stocks be allocated? (2) In a system consisting of a central warehouse and several subsidiary warehouses, how much stock should be carried in each? The demands may have known, or unknown, distribution functions. For problem (1), the i-th stock n_i should usually be allocated in proportion to the i-th demand m_i; in special cases, a significant improvement is embodied in the formula (N = total allocable stock)

     

A simple Markov model for the analysis of multiple air combat

It is proposed to describe multiple air-to-air combat having a moderate number of participants with the aid of a stochastic process based on end-game duels. A simple model describing the dominant features of air combat leads to a continuous time discrete-state Markov process. Solution of the forward Kolmogorov equations enables one to investigate the influence of initial force levels and performance parameters on the outcome probabilities of the multiple engagement. As is illustrated, such results may be useful in the decision-making process for aircraft and weapon system development planning. Some comparisons are made with Lanchester models as well as with a semi-Markov model.     

Mexico: a model for success

In Mexico, a 40 year period of political stability and economic advancement, hailed for its high rates of growth in income per capita, rapid urbanization, and impressive gains in indicators of health and education, seemed to come to a halt in the early 1980s. Since the early 1970s, fertility has declined sharply in chronological association with a new population policy and the implementation of a national family planning program. If in 1940 there was no apparent reason for the Mexican state to have much interest in limiting fertility, such was no longer the case by 1970. The General Law of Population that had been passed in 1947 was laced with the expansionist ideology that dominated demographic issues for more that a century; its pro-natalism had been reinforced by health regulations prohibiting the sale and use of contraceptives and by a penal code that made abortion a crime. Between 1970 and 1981 the total fertility rate fell by about 39%. Since 1975, change in contraceptive practice accounts for the bulk of the measured fertility decline. Between 1976 and 1982 there was a 66% increase in contraceptive prevalence. The government's involvement in family planning activities helped to: 1) develop an effective contraceptive distribution system; 2) circulate extensive information, education, and communication publicizing fertility and images of the small family; and 3) mobilize health practitioners in public institutions to counsel and persuade their clients to accept and practice contraception. The emerging debate over population policy in Brazil may well prefigure debates in other Latin American countries; the recent democratization in Brazil is the vocalization of a demand from women's groups and the left for government provided family planning services. Overall, Mexico's willingness to take the long view tackle the birth rate issue head on is likely to remain an exception in Latin America.     

Initiatives in Africa

Since the 1st oil crisis in 1973, the economies of sub-Saharan Africa have barely kept pace with their burgeoning populations. Women in Sub-Saharan Africa give birth more often than women in any other region of the world, with an average of more than 6.5 live births each. The region's natural increase average 2.5% a year in the 1960s, 2.7% in the 1970s, and in the mid-1980s, it is 3.1% per annum--a rate that will double the regions population in 22 years. National leaders in Sub-Saharan Africa were slow to consider population policy as a key component of the social and economic development effort. The neglect of population issues is reflected in the limited scope of public or private family planning programs in the sub-continent. Donor countries and institutions play an important role in developing the information base by providing technical training to government staff, supporting research, and disseminating information to a broad spectrum of political actors. Some examples of policy reconsiderations in Nigeria, Zambia, Liberia, and Niger are given. These countries are starting to give active consideration to population policies to reduce fertility and high rates of population growth by expanding family planning services, raising the age of marriage, improving the status of women, providing family-life education, and incorporating economic incentives for smaller families into the provision of social services. The highly centralized nature of African governments dictates that the acquiescence of the governmental elite must be obtained before any policy can take hold. Overall, high population growth rates in combination with a stagnating social and economic development effort throughout the region have provided the catalyst for a new look at Sub-Saharan Africa population policy. The ability of African nations to implement policies that reduce fertility is more open to question; no African nation has as yet done so, and the socioeconomics factors contributing to high fertility remain strong.