Book reviews

Reappraisal of a Road Project in Iran. By Herman G. Van Der Tak and Jan de Weille. (world Bank Staff Occasional Papers, No. 7). Baltimore, Maryland: The Johns Hopkins University Press, 1969. 127 pp. $3.00.

The Economic History of the Middle East, 1800–1914: A Book of Readings. Edited by Charles Issawi. Chicago: University of Chicago Press, 1967. xv + 543 pp. $12.50     

Some Spatial Representation Problems in Disease Modeling

The paper examines the applicability of spatial representation ideas to the determination of equilibrium solutions for multiregion disease models. In particular, alternatives to the standard specification of regionally variable infectivity rates are devised and their impact on the space-time behavior of a carrier model for Hodgkin's disease is assessed using data for Greater Manchester.     

Inca builders at Machu Picchu National Archaeological Park

Knowledge about the Inca measurement system is based on information from the colonial chronicles and modern studies of the 16th-century Quechua dictionaries. Based on those texts, we can presume that the Incas used an anthropometric system of measurement adopted from the proportions of the human body. Using cosine quantogram analysis and statistical verification, it is possible to verify the existence of the measurement system used by the Inca architects. For this purpose, a measurement series of architectural and water infrastructure elements were collected from 3D point cloud of the Chachabamba and Machu Picchu settlements in Machupicchu National Archaeological Park.     

CENTER POINTS, EQUILIBRIUM POSITIONS, AND THE OBNOXIOUS LOCATION PROBLEM

ABSTRACT. Real variable analysis has een used to great benefit in a variety of classical problems in location theory. In this paper we explore basic complex variable techniques in one formulation of the obnoxious location problem. A general definition of center points is first given and used to formulate several alternate versions of the obnoxious location problem. A logarithmic transformation is then used to demonstrate some equivalences between these families of distinct location problems (defined via center points). A prototype logarithmic potential function which results from this formulation is then investigated, and it is demonstrated that the extremal solutions with this objective reside on the boundary of its domain of definition. An application using zero- and one-dimensional centers is discussed, and a generalization to the spatial obnoxious problem is also briefly examined. We define a zero-dimensional center as a critical point of the logarithmic potential function, and it is shown that these centers are equivalent to the solutions of the Complex Moment Problem.