Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

Snow and ice surfaces on King George Island (Antarctic Peninsula) with high-resolution TerraSAR-X time series, with links to shapfiles and GeoTIFFs

Changes of glaciers and snow cover in polar regions affect a wide range of physical and ecosystem processes on land and in the adjacent marine environment. In this study, we investigate the potential of 11-day repeat high-resolution satellite image time series from the TerraSAR-X mission to derive glaciological and hydrological parameters on King George Island, Antarctica during the period Oct/25/2010 to Apr/19/2011. The spatial pattern and temporal evolution of snow cover extent on ice-free areas can be monitored using multi-temporal coherence images. SAR coherence is used to map glacier extent of land terminating glaciers with an average accuracy of 25 m. Multi-temporal SAR color composites identify the position of the late summer snow line at about 220 m above sea level. Glacier surface velocities are obtained from intensity feature-tracking. Surface velocities near the calving front of Fourcade Glacier were up to 1.8 ± 0.01 m/d. Using an intercept theorem based on fundamental geometric principles together with differential GPS field measurements, the ice discharge of Fourcade Glacier was estimated to 20700 ± 5500 m**3/d (corresponding to ~19 ± 5 kt/d). The rapidly changing surface conditions on King George Island and the lack of high-resolution digital elevation models for the region remain restrictions for the applicability of SAR data and the precision of derived products.

Equivalent dose, dose rate and age determination of cobble surfaces in the Antarctic

Most current methods of reconstructing past sea levels within Antarctica rely on radiocarbon dating. However, radiocarbon dating is limited by the availability of material for dating and problems inherent with radiocarbon reservoirs in Antarctic marine systems. Here we report on the success of a new approach to dating raised beach deposits in Antarctica for the purpose of reconstructing past sea levels. This new approach is the use of optically stimulated luminescence (OSL) on quartz-grains obtained from the underside of cobbles within raised beaches and boulder pavements. We obtained eight OSL dates from three sites along the shores of Maxwell Bay in the South Shetland Islands of the Antarctic Peninsula. These dates are internally consistent and fit well with previously published radiocarbon ages obtained from the same deposits. In addition, when the technique was applied to a modern beach, it resulted in an age of zero. Our results suggest that this method will provide a valuable tool in the reconstruction of past sea levels in Antarctica and other coarse-grained beach deposits across the globe.

Holomorphic Automorphisms of Danielewski Surfaces II: Structure of the Overshear Group

We apply Nevanlinna theory for algebraic varieties to Danielewski surfaces and investigate their group of holomorphic automorphisms. Our main result states that the overshear group, which is known to be dense in the identity component of the holomorphic automorphism group, is a free product.

Fast Correction of Tiled Display Systems on Planar Surfaces

A method for fast colour and geometric correction of a tiled display system is presented in this paper. Such kind of displays are a common choice for virtual reality applications and simulators, where a high resolution image is required. They are the cheapest and more flexible alternative for large image generation but they require a precise geometric and colour correction. The purpose of the proposed method is to correct the projection system as fast as possible so in case the system needs to be recalibrated it doesn’t interfere with the normal operation of the simulator or virtual reality application. This technique makes use of a single conventional webcam for both geometric and photometric correction. Some previous assumptions are made, like planar projection surface and negligibleintra-projector colour variation and black-offset levels. If these assumptions hold true, geometric and photometric seamlessness can be achievedfor this kind of display systems. The method described in this paper is scalable for an undefined number of projectors and completely automatic.

Estimation of the solubility parameters of model plant surfaces and agrochemicals: a valuable tool for understanding plant surface interactions

Background Most aerial plant parts are covered with a hydrophobic lipid-rich cuticle, which is the interface between the plant organs and the surrounding environment. Plant surfaces may have a high degree of hydrophobicity because of the combined effects of surface chemistry and roughness. The physical and chemical complexity of the plant cuticle limits the development of models that explain its internal structure and interactions with surface-applied agrochemicals. In this article we introduce a thermodynamic method for estimating the solubilities of model plant surface constituents and relating them to the effects of agrochemicals. Results Following the van Krevelen and Hoftyzer method, we calculated the solubility parameters of three model plant species and eight compounds that differ in hydrophobicity and polarity. In addition, intact tissues were examined by scanning electron microscopy and the surface free energy, polarity, solubility parameter and work of adhesion of each were calculated from contact angle measurements of three liquids with different polarities. By comparing the affinities between plant surface constituents and agrochemicals derived from (a) theoretical calculations and (b) contact angle measurements we were able to distinguish the physical effect of surface roughness from the effect of the chemical nature of the epicuticular waxes. A solubility parameter model for plant surfaces is proposed on the basis of an increasing gradient from the cuticular surface towards the underlying cell wall. Conclusions The procedure enabled us to predict the interactions among agrochemicals, plant surfaces, and cuticular and cell wall components, and promises to be a useful tool for improving our understanding of biological surface interactions.

Estimation of the solubility parameters of model plant surfaces and agrochemicals: a valuable tool for understanding plant surface interactions

Background Most aerial plant parts are covered with a hydrophobic lipid-rich cuticle, which is the interface between the plant organs and the surrounding environment. Plant surfaces may have a high degree of hydrophobicity because of the combined effects of surface chemistry and roughness. The physical and chemical complexity of the plant cuticle limits the development of models that explain its internal structure and interactions with surface-applied agrochemicals. In this article we introduce a thermodynamic method for estimating the solubilities of model plant surface constituents and relating them to the effects of agrochemicals. Results Following the van Krevelen and Hoftyzer method, we calculated the solubility parameters of three model plant species and eight compounds that differ in hydrophobicity and polarity. In addition, intact tissues were examined by scanning electron microscopy and the surface free energy, polarity, solubility parameter and work of adhesion of each were calculated from contact angle measurements of three liquids with different polarities. By comparing the affinities between plant surface constituents and agrochemicals derived from (a) theoretical calculations and (b) contact angle measurements we were able to distinguish the physical effect of surface roughness from the effect of the chemical nature of the epicuticular waxes. A solubility parameter model for plant surfaces is proposed on the basis of an increasing gradient from the cuticular surface towards the underlying cell wall. Conclusions The procedure enabled us to predict the interactions among agrochemicals, plant surfaces, and cuticular and cell wall components, and promises to be a useful tool for improving our understanding of biological surface interactions.