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.     

A tale of two towns: Buntingford and Standon in the later middle ages

The controversy over the fortunes of English towns in the later middle ages has tended to generate more heat than light. Much of the evidence employed in this debate has been drawn from the larger English towns, but this essay suggests a widening of the research agenda to include a more systematic assessment of small towns and village markets. Although weakened by the reduced demand for grain after the Black Death, these places competed for the growing local trade in basic consumer goods. Evidence from northeast Hertfordshire reveals that this competition resulted in a significant restructuring of the hierarchy of local marketing centres, and a decline in the ability of seigneurial and urban authorities to regulate trading activity.     

POLICY IMPLICATIONS OF ALTERNATIVE AGRICULTURE

This paper suggests that there has been a small shift in American agricultural practices, and more importantly in policy making in this area, toward what can be called organic or alternative agriculture. These policy changes are partially due to triggering devices, exogenous forces that have led to changes in the policy agenda. Two major exogenous factors are reviewed–the energy “crisis” and environmental factors. Both sets of forces have resulted in farmers beginning to turn to alternative agricultural techniques, in government officials changing their attitudes about alternative agriculture, and new research activities in this direction being undertaken by various government bodies.     

Computer analysis of an inconsistent data source: the case of probate inventories

Computers are becoming increasingly popular for analysing data in historical geography and are being applied to an extending range and variety of historical sources. The methods described in most computer texts for geographers and historians, using the langueage allied to punched cards, are only suitable for numeric data which are in a standardized and consistent form. Rather than attempting to apply these methods to sources not organized in this way, it is more sensible to tailor a technique to a particular class of data.This paper considers some advantages of computer analysis, using English probate inventories as an example. Limitations of conventional methods are discussed and a technique is described for dealing with sources whose information is inconsistent between records. The method relates the logical structure of inventories to the storage and use of data by the computer, and considers the forms data can take for input to the machine. An example from the analysis of inventory data prepared by this method is briefly presented, describing two aspects of agricultural change in East Anglia between 1580 and 1740.     

The weight of nineteenth century Mexicans in the Western United States

When traditional methods for measuring economic welfare are scarce or unreliable, heights and BMIs are now well-accepted measurements that represent biological conditions during economic development. Weight, after controlling for height, is an additional measure for current net nutrition. Little is known about how weights varied among Mexicans living in the nineteenth century American West. Between 1870 and 1920, average Mexican weight was low and remained constant. Mexican farmers had the heaviest weights, and unskilled worker weights were low. Weight of Mexican-born individuals were higher than Mexicans born in the United States at low weights but lower at high weights. For combined characteristics, weight varied the most with age, an uncontrollable characteristic, indicating that nineteenth century Mexican current net nutrition varied the most with factors over which they had no control.