THE MAXIMUM CAPTURE OR “SPHERE OF INFLUENCE” LOCATION PROBLEM: HOTELLING REVISITED ON A NETWORK*

ABSTRACT. The problem of the ice cream vendor on the beach is extended to the siting of multiple entering servers into the midst of existing servers which are already in place at multiple sites on a network. The network of population nodes, joining arcs, and eligible sites for servers provides the underlying matrix of the problem. The goal of the single firm which is siting the multiple entering servers is the capture of the maximum population from existing servers. This combinatorial problem can be described as a linear integer program for which solutions can easily be derived. Computational experience and insights derived therefrom are reported.     

Das Werden des Kosmos Von der Erfahrung der zeitlichen Dimension astronomischer Objekte im 18. Jahrhundert

The Permanent ‘Becoming’ of the Cosmos: On Experiencing the Time Dimension of Astronomical Entities in the 18th Century. - This paper deals with two of the initial stages through which the dimension of time, in the sense of an irreversible development, found its way into astronomical-cosmological thinking. The one resulted from the first consequental application of Newtonian principles and laws to cosmic entities outside of our solar system found in the General Natural History or Theory of the Heavens of Immanuel Kant (1755): Endeavoring to explain through natural causes first the peculiarities of the solar system, no longer naturally explainable through the celestial mechanics of Isaac Newton (such as the common orbital plane and rotational direction of all the members of the solar system and the distribution of the masses) - which, however, had been deducible in Johannes Keplers Weltharmonik -, and endeavoring secondly to explain above all the beginning of the inertial movement of all discrete heavenly bodies - which, however, could have been derived from René Descartes's vortex theory - without using arbitrary acts of God as Newton had done, Kant had to introduce an initial state in which matter in the form of atoms was equally and almost homogeneously distributed over the whole space (similar to the permanent state in Descartes's theory). Thereupon, according to Kant, the initial movements of the slowly growing masses resulted from the effect of gravitational forces. The parameters within the solar system which had to be explained, could then be easily deduced from the process of mass concentration at different points and from the resulting vortex movements. - The other initial stage is found in the classification of ‘nebulae’ by William Herschel who introduced the historical time factor, in the above-mentioned sense, as a principle of order in addition to the outward shape, which had become common for all the different elements in natural history during the second half of the 18th century. Thereupon the different shapes of the nebulae could be interpreted as stages of development from the primordial nebular state to multiple or single stars. (Herschel had not yet considered them to be accumulations of stars for lack of a suitable telescope.) Both initial stages, which arose out of the thinking of the second half of the 18th century, were still premature for astronomy and cosmology; they have only been taken up again since the end of the 19th century as a result of the emergence of astrophysics, which provided the empirical data for the earlier speculations and conclusions from analogy.     

ALTERNATIVE MEDICINE IN WESTERN INDUSTRIALIZED COUNTRIES: AN AGENDA FOR MEDICAL GEOGRAPHY

The range of health and health care topics amenable to geographical analyses in Western industralized countries has increased tremendously in the past two decades. These studies of health care systems have focused on the health organization, delivery, and utilization of biomed-ical services, however, to the virtual exclusion of analyses of a wide variety of alternative approaches to health and healing in these countries. This lacuna is regrettable in view of the fact that people's health care behaviour suggests that medical pluralism is a persisting reality in the industrialized countries. There is indeed a coexistence of biomedicine with several alternative therapies and, in recent years, there has been resurgence in the popularity and use of alternative medicine.