Quasiconformal mappings that highly distort dimensions of many parallel lines

We construct a quasiconformal mapping of $n$-dimensional Euclidean space, $n \geq 2$, that simultaneously distorts the Hausdorff dimension of a nearly maximal collection of parallel lines by a given amount. This answers a question of Balogh, Monti, and Tyson.Comment: 12 page

Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group

We use a Riemannnian approximation scheme to define a notion of intrinsic Gaussian curvature for a Euclidean C2 -smooth surface in the Heisenberg group H away from characteristic points, and a notion of intrinsic signed geodesic curvature for Euclidean C2 -smooth curves on surfaces. These results are then used to prove a Heisenberg version of the Gauss–Bonnet theorem. An application to Steiner’s formula for the Carnot–Carathéodory distance in H is provided

A comparative study: Methods for the determination of ascorbic acid in small and middle sized food analytic laboratories

Although vitamin C is essential as an antioxidant and as a cofactor in a series of enzymatic reactions, the ability for ascorbate biosynthesis was lost in humans. Thus, horticultural products and derived fruit drinks or commercial vitamin C products are considered to be important sources for the ascorbic acid intake in the human diet. These facts underline the importance of analytical methods for ascorbic acid determination in different food products. In our study two spectrophotometric and a fluorometric ascorbic acid determination methods have been compared with each other and with the so-called etalon HPLC method to find the best for small or middle sized food analytic laboratories with a sample number of up to several hundreds. As a result of our experiments we could establish that the OPDA-fluorometric method can be suggested for the determination of samples containing ascorbate at low concentrations. Unfortunately, the analytical properties of the OPDA method with spectrophotometric detection have been lagging far behind the others. The 2,2′-bipyridyl method could give a balanced performance for all tests. Furthermore, the results gained by this method are the closest to the results of the reference HPLC method in the case of fruit and vegetable samples

Sorption behaviours and transport potentials for selected pharmaceuticals and triclosan in two sterilised soils

Purpose: Pharmaceuticals and personal care products (PPCPs) are emerging environmental pollutants, which in addition to direct deposition processes, can find their way into surface soils through the agricultural application of sewage sludge and irrigation practices using contaminated wastewater. Therefore, it is important to assess the extent to which soils are able to retain PPCPs and to prevent their downward migration towards groundwaters. Materials and methods: To further our understanding in this area, batch sorption experiments and artificial rainwater leaching experiments have been performed using five compounds (bezafibrate, carbamazepine, chloramphenicol, diclofenac and triclosan) possessing a range of physicochemical properties in two soils with differing acidities and organic carbon contents. Results and discussion: The determined Koc values for triclosan and diclofenac consistently demonstrated their lower potential mobilities in both soils. The predicted high mobility of chloramphenicol is supported by its efficient leaching potential (89-100%) in both soils whereas bezafibrate, diclofenac and carbamazepine demonstrate slightly lower affinities for the leachate (61-96%) for soil A and are strongly retained (>99%) by soil B. The amount of PPCP in the leachate, the rate of leaching and the depth of soil penetration are explained in terms of the soil characteristics and the properties of the individual PPCPs (such as solubility and pKa) with soil organic content being shown to be a critical factor controlling the ability of a soil to retain a PPCP in the surface layers. Conclusions: The findings contribute to the scientific knowledge required by practitioners and regulators as they consider future sub-soil contamination by PPCPs and subsequent possible threats to groundwater resources and surface water habitats

Soil mobility of surface applied polyaromatic hydrocarbons in response to simulated rainfall

Polyaromatic hydrocarbons (PAHs) are emitted from a variety of sources and can accumulate on and within surface soil layers. To investigate the level of potential risk posed by surface contaminated soils, vertical soil column experiments were conducted to assess the mobility, when leached with simulated rainwater, of six selected PAHs (naphthalene, phenanthrene, fluoranthene, pyrene, benzo(e)pyrene and benzo(ghi)perylene) with contrasting hydrophobic characteristics and molecular weights/sizes. The only PAH found in the leachate within the experimental period of 26 days was naphthalene. The lack of migration of the other applied PAHs were consistent with their low mobilities within the soil columns which generally parallelled their log Koc values. Thus only 2.3% of fluoranthene, 1.8% of pyrene, 0.2% of benzo(e)pyrene and 0.4% of benzo(ghi)perylene were translocated below the surface layer. The PAH distributions in the soil columns followed decreasing power relationships with 90% reductions in the starting levels being shown to occur within a maximum average depth of 0.94 cm compared to an average starting depth of 0.5 cm. A simple predictive model identifies the extensive time periods, in excess of 10 years, required to mobilise 50% of the benzo(e)pyrene and benzo(ghi)perylene from the surface soil layer. Although this reduces to between 2 and 7 years for fluoranthene and pyrene, it is concluded that the possibility of surface applied PAHs reaching and contaminating a groundwater aquifer is unlikely

Influence of sintering temperature and pressure on crystallite size and lattice defect structure in nanocrystalline SiC

Microstructure of sintered nanocrystalline SiC is studied by x-ray line profile analysis and transmission electron microscopy. The lattice defect structure and the crystallite size are determined as a function of pressure between 2 and 5.5 GPa for different sintering temperatures in the range from 1400 to 1800 degrees C. At a constant sintering temperature, the increase of pressure promotes crystallite growth. At 1800 degrees C when the pressure reaches 8 GPa, the increase of the crystallite size is impeded. The grain growth during sintering is accompanied by a decrease in the population of planar faults and an increase in the density of dislocations. A critical crystallite size above which dislocations are more abundant than planar defects is suggested