WEBER'S PROBLEM WITH ATTRACTION AND REPULSION*

ABSTRACT. Weber's problem consists of locating a facility in the plane in such a way that the weighted sum of Euclidean distances to n given points be minimum. The case where some weights are positive and some are negative is shown to be a d.-c. program (i.e., a global optimization problem with both the objective function and constraint functions written as differences of convex functions), reducible to a problem of concave minimization over a convex set. The reduced problem is then solved by outer-approximation and vertex enumeration. Moreover, locational constraints can be taken into account by combining the previous algorithm with an enumerative procedure on the set of feasible regions. Finally, the algorithm is extended to solve the case where obnoxiousness of the facility is assumed to have exponential decay. Computational experience with n up to 1000 is described.     

Paleo-Eskimo kitchen midden preservation in permafrost under future climate conditions at Qajaa,West Greenland

Remains from Paleo-Eskimo cultures are well-documented, but complete preservation is rare. Two kitchen middens in Greenland are known to hold extremely well-preserved organic artefacts. Here, we assess the fate of the Qajaa site in Western Greenland under future climate conditions based on site characteristics measured in situ and from permafrost cores. Measurements of thermal properties, heat generation, oxygen consumption and CO₂ production show that the kitchen midden can be characterized as peat but produces 4–7 times more heat than natural sediment. An analytical model from permafrost research has been applied to assess future thawing of the midden. Results show that the preservation conditions are controlled by freezing temperatures and a high water/ice content limiting the subsurface oxygen availability. Threats to the future preservation are related to thawing followed by drainage and increasing subsurface oxygen availability and heat generation. The model predicts that the unique 4000-year-old Saqqaq layer below more than 1 m of peat is adequately protected against thawing for the next 70 years.     

Early agrarian landscapes in Finland

Cadastral maps from the 17th and 18th centuries of villages in southwest Finland and Ostrobothnia have been used in this study to map the variations in land organisation that existed before the first enclosure ( storskiftet ). Settlement structure and land division in particular were found to vary regionally, a fact that can be explained by topographical circumstances but also by the different historical background of the historical provinces. The aim was to distinguish between the cultural influences on the use and ownership of land from Sweden (the west) and Finland (the east) respectively. Through the Swedish colonisation of Finland a feudal social organisation was introduced which affected village organisation all over the investigated area but to a varying degree, resulting in several types of settlements from planned villages with regular strip parcelling to villages developed through piecemeal colonisation and with an unsystematic division of the land.     

Reviews

Bente Magnus: Krosshaugfunnet. Et fors?k på kronologisk og stilhistorisk plassering i 5. årh. (The Krosshaug find. An attempt at a chronological and stylistic placing within the 5th century). Stavanger Museums Skrifter 9. Stavanger 1975. 159 Pages, 68 Figs. English summary.