A new series solution of Molodensky's problem

A complete series solution of Molodensky's boundary-value problem is derived using, instead of an integral equation, analytical continuation by means of power series. This solution is shown to be equivalent, term by term, to the Molodensky-Brovar series, but is simpler and practically more convenient.

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Zusammenfassung Eine vollst?ndige Reihenl?sung des Problems von Molodensky wird hergeleitet, wobei anstatt einer Integralgleichung die analytische Fortsetzung mittels Potenzreihen zugrunde gelegt wird. Es zeigt sich, dass diese L?sung gliedweise ?quivalent zur Reihe von Molodensky-Brovar ist, aber sie ist einfacher und praktisch brauchbarer.

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Résumé On déduit une série qui donne une solution complète du problème de Molodensky, en utilisant, au lieu d'une équation intégrale, la continuation analytique par une série de puissances. Il s'ensuit que cette solution est équivalente à la série de Molodensky-Brovar, mais elle est plus simple et plus pratique.

     

Factors Controlling Total Concentration and Aqueous Speciation of Aluminium in an Acidic Headwater Stream of the Bavarian Forest National Park: a Modelling Approach

The purpose of the present paper is to analyse factors controlling total concentration and aqueous speciation of aluminium in the Große Ohe River, using a thermodynamic equilibrium model and a mixing approach. A model compound for humic substances is derived on the basis of the relation between anion deficit and the organic carbon content in the river as well as literature data. An equilibrium speciation model for aluminium is set up, considering this model compound and relevant inorganic solutes. Although the model cannot be verified directly, its results may be viewed as qualitatively correct. Applying the model to measured stream water samples highlights that aqueous speciation of aluminium is mainly controlled by the pH value and discharge and that free aluminium concentrations reach clearly toxic levels during acidic episodes. Comparing measured concentrations of sulfate and H⁺ and calculated concentrations of Al³⁺ with solubility curves of gibbsite like minerals and jurbanite clearly shows that total aluminium concentrations are not controlled by equilibria with these mineral phases alone. The observed relationship can be better explained from a mixture of two distinct waters, representing lowflow and highflow chemistry, and the resulting equilibrium concentrations. This indicates that total aluminium concentration, in particular during high discharge events, is mainly controlled by the mixture of waters with differing chemistry and flowpaths.     

Topographic signatures of progressive glacial landscape transformation

The Pleistocene glaciations left a distinct topographic footprint in mountain ranges worldwide. The geometric signature of glacial topography has been quantified in various ways, but the temporal development of landscape metrics has not been traced in a landscape evolution model so far. However, such information is needed to interpret the degree of glacial imprint in terms of the integrated signal of temporal and spatial variations in erosion as a function of glacial occupation time. We apply a surface process model for cold-climate conditions to an initially fluvial mountain range. By exploring evolving topographic patterns in model time series, we determine locations where topographic changes reach a maximum and where the initial landscape persists. The signal of glacial erosion, expressed by the overdeepening of valleys and the steepening of valley flanks, develops first at the glacier front and migrates upstream with ongoing glacial erosion. This leads to an increase of mean channel slope and its variance. Above steep flanks and head-walls, however, the observed mean channel slope remains similar to the mean channel slope of the initial fluvial topography. This leads to a characteristic turning point in the channel slope–elevation distribution above the equilibrium line altitude, where a transition from increasing to decreasing channel slope with elevation occurs. We identify this turning point and a high channel slope variance as diagnostic features to quantify glacial imprint. Such features are abundant in glacially imprinted mid-latitude mountain ranges such as the Eastern Alps. By analysing differently glaciated parts of the mountain range, we observe a decreasing clarity of this diagnostic morphometric property with decreasing glacial occupation. However, catchments of the unglaciated eastern fringe of the Alps also feature turning points in their channel slope–elevation distributions, but in contrast to the glaciated domain, the variance of channel slope is small at all elevation levels.     

Late Cretaceous porphyry Cu and epithermal Cu–Au association in the Southern Panagyurishte District,Bulgaria: the paired Vlaykov Vruh and Elshitsa deposits

Vlaykov Vruh–Elshitsa represents the best example of paired porphyry Cu and epithermal Cu–Au deposits within the Late Cretaceous Apuseni–Banat–Timok–Srednogorie magmatic and metallogenic belt of Eastern Europe. The two deposits are part of the NW trending Panagyurishte magmato-tectonic corridor of central Bulgaria. The deposits were formed along the SW flank of the Elshitsa volcano-intrusive complex and are spatially associated with N110-120-trending hypabyssal and subvolcanic bodies of granodioritic composition. At Elshitsa, more than ten lenticular to columnar massive ore bodies are discordant with respect to the host rock and are structurally controlled. A particular feature of the mineralization is the overprinting of an early stage high-sulfidation mineral assemblage (pyrite ± enargite ± covellite ± goldfieldite) by an intermediate-sulfidation paragenesis with a characteristic Cu–Bi–Te–Pb–Zn signature forming the main economic parts of the ore bodies. The two stages of mineralization produced two compositionally different types of ores—massive pyrite and copper–pyrite bodies. Vlaykov Vruh shares features with typical porphyry Cu systems. Their common geological and structural setting, ore-forming processes, and paragenesis, as well as the observed alteration and geochemical lateral and vertical zonation, allow us to interpret the Elshitsa and Vlaykov Vruh deposits as the deep part of a high-sulfidation epithermal system and its spatially and genetically related porphyry Cu counterpart, respectively. The magmatic–hydrothermal system at Vlaykov Vruh–Elshitsa produced much smaller deposits than similar complexes in the northern part of the Panagyurishte district (Chelopech, Elatsite, Assarel). Magma chemistry and isotopic signature are some of the main differences between the northern and southern parts of the district. Major and trace element geochemistry of the Elshitsa magmatic complex are indicative for the medium- to high-K calc-alkaline character of the magmas. ⁸⁷Sr/⁸⁶Sr_(i) ratios of igneous rocks in the range of 0.70464 to 0.70612 and ¹⁴³Nd/¹⁴⁴Nd_(i) ratios in the range of 0.51241 to 0.51255 indicate mixed crustal–mantle components of the magmas dominated by mantellic signatures. The epsilon Hf composition of magmatic zircons (+6.2 to +9.6) also suggests mixed mantellic–crustal sources of the magmas. However, Pb isotopic signatures of whole rocks (²⁰⁶Pb/²⁰⁴Pb = 18.13–18.64, ²⁰⁷Pb/²⁰⁴Pb = 15.58–15.64, and ²⁰⁸Pb/²⁰⁴Pb = 37.69–38.56) along with common inheritance component detected in magmatic zircons also imply assimilation processes of pre-Variscan and Variscan basement at various scales. U–Pb zircon and rutile dating allowed determination of the timing of porphyry ore formation at Vlaykov Vruh (85.6 ± 0.9 Ma), which immediately followed the crystallization of the subvolcanic dacitic bodies at Elshitsa (86.11 ± 0.23 Ma) and the Elshitsa granite (86.62 ± 0.02 Ma). Strontium isotope analyses of hydrothermal sulfates and carbonates (⁸⁷Sr/⁸⁶Sr = 0.70581–0.70729) suggest large-scale interaction between mineralizing fluids and basement lithologies at Elshitsa–Vlaykov Vruh. Lead isotope compositions of hydrothermal sulfides (²⁰⁶Pb/²⁰⁴Pb = 18.432–18.534, ²⁰⁷Pb/²⁰⁴Pb = 15.608–15.647, and ²⁰⁸Pb/²⁰⁴Pb = 37.497–38.630) allow attribution of ore-formation in the porphyry and epithermal deposits in the Southern Panagyurishte district to a single metallogenic event with a common source of metals.     

Revisiting gateway cities: connecting hubs in global networks to their hinterlands

Gateway cities have received much attention from urban geographers. In spite of outstanding contributions being made, we think that the concept needs to be revisited with regard to regional development implications. Bringing together research on global production networks (GPNs) and world cities, this article shows that gateway cities are critical for development in networks, generating impulses for peripheral locations by engaging them in processes of “strategic coupling.” Yet, gateway cities also concentrate segments of GPNs to the detriment of their hinterlands. We conceptualize gateway cities with the aid of five features: logistics and transport, industrial processing, corporate control, service provision and knowledge generation. Our concept allows for an understanding of cities in global and regional economic processes beyond corporate headquarters, corporate services and governance – that is, beyond the boundaries of existing research. It unsettles traditional understandings of strategic coupling and world cities, filling a lacuna on city–hinterland connections.