we determine the infimum of the areas of the simple n-gons in the Euclidean plane, having sides of length a1,...,an (in some order). The infimum is attained (in limit) if the polygon degenerates into a certain kind of triangle, plus some
parts of zero area. We show the same result for simple polygons on the sphere (of not too great length), and for simple polygons
in the hyperbolic plane. Replacing simple n-gons by convex ones, we answer the analogous questions. The infimum is attained also here for degeneration into a certain
kind of triangle.
Authors:I. Tamáska, Z. Vértesy, A. Deák, P. Petrik, K. Kertész and László Biró
Bioinspired 1+2D nanoarchitectures inspired by the quasi-ordered structures occurring in photonic nano-architectures of biological origin, like for example butterfly scales, were produced by depositing a layer of SiO2 nanospheres (156 nm and 292 nm in diameter) on Si wafers, over which a regular multilayer composed from three alternating layers of SiO2 and TiO2 was deposited by physical vapor deposition. Flat multilayers were deposited in the same run on oxidized Si (324 nm SiO2 thickness) for comparison. Different types of disorder (in plane and out of plane) were purposefully allowed in the 1+2D nanoarchitectures. The positions of the specular reflection maxima for the flat multilayer and for the two different bioinspired nanoarchitectures were found to be similar. Additionally to this, the bioinspired nanoarchitectures exhibited angle independent diffuse reflection too, which was absent in the flat multilayer. Different model calculations were made to explain the specular and diffuse optical properties of the samples. Satisfactory agreement was obtained between experimental data and model calculations.
Authors:F. Samu, F. Kádár, G. Ónodi, M. Kertész, A. Szirányi, É. Szita, K. Fetykó, D. Neidert, E. Botos and V. Altbäcker
Recent environmental and land use changes have made wildfires more frequent in natural habitats of the Kiskunság Sand Ridge on the Hungarian Plain. In a study initiated 2.5 years after an extensive fire that destroyed half of the area of a sand grassland — juniper, poplar forest steppe habitat, we assessed the effects of fire on two generalist arthropod groups: spiders and carabid beetles, as well as on the vegetation. Utilizing the natural experiment situation, samples were taken by pitfalls and suction sampling during a 1.5 years period in four 1 ha blocks, two of which were on the burnt part of the habitat, and two in the unburnt control. At the time of the investigation, in the burnt area the vegetation in the grass layer showed a quick but not complete recovery, while the canopy layer of the juniper bushes burnt down with no sign of regeneration. Carabid beetles and spiders showed differences in recovery after fire. In the carabid assemblages of the burnt parts — compared to the unburnt control — there were over three times more beetles, out of which significantly more represented the macropterous life form and granivorous feeding strategy. There was a higher ratio of pioneer species and a simplified assemblage structure in the burnt area, which meant that the conservation value of the carabid assemblage became lower there. In contrast, for the spider assemblage quantitative changes in abundance and species numbers were not significant, and the differences in species composition did not lead to a decrease in conservation value. Spider species in the burnt plots could not be described as pioneer species, rather they had ecological characteristics that suited the changed vegetation structure. Comparing the two groups, to repopulate the burnt areas, dispersal abilities proved to be more limiting for carabids. However, in both groups a strong assemblage level adaptation could be observed to the postfire conditions. In spiders, species with a stratum preference for the grass layer prevailed, while in carabids individuals with granivore strategy gained dominance. Thus, despite the differences in their speed, basically both assemblages tracked vegetation changes. The effect of future fires will depend on their scale, as well as land-use practices, such as grazing, that interact with fire frequency and recovery. If extensive fires in the future permanently change the vegetation, then it would also lead to a fundamental change in the arthropod fauna.