SEM-EDS characterization of western Mediterranean obsidians and the Neolithic site of A Fuata (Corsica)

During the Neolithic, obsidians of the Monte Arci (Sardinia) volcanic complex were by far more used in the northern Tyrrhenian area than those of the three other source-islands (Lipari, Palmarola, Pantelleria) in the western Mediterranean. It is shown that merely determinations of content for six major elements with a scanning electron microscope by energy dispersion spectrometry (SEM-EDS) are sufficient to distinguish the four types of Monte Arci obsidians. Because of the compositional similarities between these obsidian types, a multivariate analysis is recommended in provenance studies. Although SEM-EDS, electron microprobe-wavelength dispersion spectrometry (EMP-WDS) and particle induced X-ray emission (PIXE) give essentially concordant results in the determination of these six element contents, subtle technique-related biases prevent the combination of SEM-EDS, EMP-WDS and PIXE data on source samples for provenance purposes. An SEM-EDS test-study reveals the first occurrence of obsidians of Lipari for the A Fuata Middle to Late Neolithic site of NW Corsica (north of Sardinia), in addition to the usual Monte Arci obsidians. Similar to EMP-WDS, the SEM-EDS technique requires only millimeter-sized fragments.     

Advances in the Theory of Market Areas

The purpose of the paper is to state general properties of theoretical market areas of cities. We consider two centers on the Euclidean plane, several models describing the spatial influence of a center, and a general, continuous, and strictly increasing transportation cost function. Derived properties of market areas concern area measure, topological bounds, emptiness, boundedness, connectedness, convexity, and the membership of a city to its own market area. In particular, it is shown how the shape of market areas changes with the transportation cost function. Finally, prospects for further research are presented.     

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.