Age and sedimentological features of fluvial series in the Toruń Basin and the Drwęca Valley (Poland)

The deposits of the Toruń Basin are dominated by a few-metre thick sand series which fill up buried valley-like depressions. In many cases they underlie the Weichselian till which builds up the ice marginal streamway (pradolina) terraces or they are exposed at the basin slopes. As the results of the geological and sedimentological studies, as well as of the dating of the deposits at the sites in the Toruń Basin indicate, the deposits include two fluvial series accumulated before the advancement of the Leszno Phase ice sheet, i.e. in Middle Weichselian and at the beginning of Late Weichselian. The oldest fluvial series connected with the Saalian Glaciation was found at the mouth section of the Drwęca Valley. The fluvial system of the Toruń Basin during Middle Weichselian and at the beginning of Late Weichselian developed in two phases of the sand-bed braided river. During the first one the river channel were dominated by large mid-riverbed sandbars, while during the second phase the water flow was smaller and, as a result, low transverse sandbars and two-dimensional dunes developed. Other active river channel also showed low-energy flows, more intensive meandering than in the case of the braided rivers, as well as sandy side-bars. Analysis of the rounding and frosting of the quartz grains indicate that the studied series of the Weichselian sandy deposits represent alluvia of a river which were fed from two diverse sources. The first one might have represented the alluvia of a warm river which transformed its load, while the other one might have mainly carried the underlying Quaternary deposits.     

A PROPERTY OF THE RANK-SIZE DISTRIBUTION AND ITS USE IN AN URBAN HIERARCHY CONTEXT

This paper proves the symmetry of the classical rank-size distribution with respect to any city according to a criterion of relative population difference. This property is used to characterize the distribution of city sizes around the median center of their hierarchical level by the existence of symmetry, of an upper bound to dispersion, and of a regular spacing. An interpretation is suggested.     

Urban Hierarchy and the Rank-Size Distribution

The paper analyzes some connections between the rank-size distribution of cities and central place population models. Compatibility conditions with the rank-size distribution are determined for the models considered. The values for two specific parameters under these conditions are determined, and additional interpretations of the rank-size distribution are suggested.     

Provenance of Early Bronze Age metal artefacts in Western Switzerland using elemental and lead isotopic compositions and their possible relation with copper minerals of the nearby Valais

Ten Early Bronze Age (BzA1, 2200–2000 BC) copper artefacts from the central Valais region from Switzerland were studied for their elemental composition and lead isotope ratios. In order to answer the archaeological question of a local copper supply, a database for copper minerals across the Valais (Switzerland) has been established. This database contains 69 data on lead isotope ratios as well as additional information on the minerals and geochemical associations for copper minerals from 38 locations in the Valais. Comparisons of the artefacts were also made with data pertaining to minerals from various deposits from Europe and Anatolia taken from the literature. The provenance of the materials is very diverse. Some of the data are compatible with the data from the copper mineral deposits of the Valais region. Moreover, three copper lunulae were identified as possibly Tuscan, which suggests contacts between Italy and the Valais region. This pattern also establishes a multiplicity of provenances for the metal and cultural influences in the Alpine environment of the Rhone Valley of Switzerland at the beginning of the Early Bronze Age.     

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.