Ergodicity for Stochastic Porous Media Equations with Multiplicative Noise

The long time behavior of solutions to stochastic porous media equations with nonlinear multiplicative noise on bounded domains with Dirichlet boundary data is studied. Based on weighted $L^{1}$-estimates, the existence and uniqueness of invariant measures with optimal bounds on the rate of mixing are proved. Along the way, the existence and uniqueness of entropy solutions are shown

Random attractors for degenerate stochastic partial differential equations

We prove the existence of random attractors for a large class of degenerate stochastic partial differential equations (SPDE) perturbed by joint additive Wiener noise and real, linear multiplicative Brownian noise, assuming only the standard assumptions of the variational approach to SPDE with compact embeddings in the associated Gelfand triple. This allows spatially much rougher noise than in known results. The approach is based on a construction of strictly stationary solutions to related strongly monotone SPDE. Applications include stochastic generalized porous media equations, stochastic generalized degenerate p-Laplace equations and stochastic reaction diffusion equations. For perturbed, degenerate p-Laplace equations we prove that the deterministic, infinite dimensional attractor collapses to a single random point if enough noise is added.Comment: 34 pages; The final publication is available at http://link.springer.com/article/10.1007%2Fs10884-013-9294-

From teaching physics to teaching children : beginning teachers learning from pupils

This paper discusses the development of beginning physics teachers' pedagogical content knowledge (PCK) in the context of teaching basic electricity during a one-year Professional Graduate Diploma in Education course (PGDE) and beyond. This longitudinal study used repeated semi-structured interviews over a period of four-and-a-half years. The interview schedule followed a line of development through the secondary school electrical syllabus in Scotland. Fifteen student teachers were interviewed during the PGDE year. Six of them were followed up at the end of the Induction Year (their first year as a newly qualified teacher), and again two-and-a-half years later. Thematic analysis of the interviews showed that before the beginning teachers had taught any classes, their initial focus was on how to transform their own subject matter knowledge (SMK) about electricity into forms that were accessible to pupils. As the beginning teachers gained experience working with classes, they gave vivid descriptions of interacting with particular pupils when teaching electricity which showed the development of their pedagogical knowledge. This played a significant role in the teachers' change of focus from teaching physics to teaching children as they transformed their SMK into forms that were accessible to pupils and developed their general pedagogical knowledge

Rinistachya hilleri gen. et sp. nov.(Sphenophyllales), from the upper Devonian of South Africa

A rich and diverse plant assemblage has been excavated from latest Devonian (Famennian) black shales of the Witpoort Formation (Witteberg Group) at Waterloo Farm, close to the city of Grahamstown (South Africa). Several specimens of a new sphenopsid have been collected. The description of this as a new taxon, here named Rinistachya hilleri, gen. et sp. nov., provides an important addition to the scarce early record of the group. Rinistachya hilleri presents a novel architecture that include apparently plesiomorphic characters, reminiscent of the organisation of the Iridopteridales (including the production of two types of laterals at one node, the location of fertile parts in loose whorls on lateral branches and an organisation of the fertile parts in which they branch several times before bearing distally elongate sporangia). Other characters unambiguously nest Rinistachya within the Sphenopsida (including presence of planate and slightly webbed ultimate appendages and lateral strobili made of successive whorls of fertile leaves with fertile parts located at their axil). This provides strong support for a close relationship between Sphenopsida and Iridopteridales. Rinistachya furthermore represents the first record of a Devonian sphenopsid from Gondwana and extends the known distribution of the Sphenopsida from the tropics to very high palaeolatitudes. It is a new sphenopsid with a peculiar organisation. The new taxon allows better characterization of the initial evolutionary radiation at the base of the group

New morphological information on, and species of placoderm fish Africanaspis (Arthrodira, Placodermi) from the Late Devonian of South Africa

Here we present a new species of placoderm fish, Africanaspis edmountaini sp. nov., and redescribe Africanaspis doryssa on the basis of new material collected from the type locality of Africanaspis. The new material includes the first head shields of Africanaspis doryssa in addition to soft anatomy for both taxa. Hitherto Africanaspis was entirely described from trunk armour and no record of body and fin outlines had been recorded. In addition the first record of embryonic and juvenile specimens of Africanaspis doryssa is presented and provides a growth series from presumed hatchlings to presumed adults. The presence of a greater number of juveniles compared to adults indicates that the Waterloo Farm fossil site in South Africa represents the first nursery site of arthrodire placoderms known from a cold water environment. The preservation of an ontogenetic series demonstrates that variation within the earlier known sample, initially considered to have resulted from ontogenetic change, instead indicates the presence of a second, less common species Africanaspis edmountaini sp. nov. There is some faunal overlap between the Waterloo Farm fossil site and faunas described from Strud in Belgium and Red Hill, Pennsylvania, in north America, supporting the concept of a more cosmopolitan vertebrate fauna in the Famennian than earlier in the Devonian

Sodium-Dependent Vitamin C Transporter 2 (SVCT2) Expression and Activity in Brain Capillary Endothelial Cells after Transient Ischemia in Mice

Expression and transport activity of Sodium-dependent Vitamin C Transporter 2 (SVCT2) was shown in various tissues and organs. Vitamin C was shown to be cerebroprotective in several animal models of stroke. Data on expression, localization and transport activity of SVCT2 after cerebral ischemia, however, has been scarce so far. Thus, we studied the expression of SVCT2 after middle cerebral artery occlusion (MCAO) in mice by immunohistochemistry. We found an upregulation of SVCT2 after stroke. Co-stainings with Occludin, Von-Willebrand Factor and CD34 demonstrated localization of SVCT2 in brain capillary endothelial cells in the ischemic area after stroke. Time-course analyses of SVCT2 expression by immunohistochemistry and western blots showed upregulation in the subacute phase of 2–5 days. Radioactive uptake assays using 14C-labelled ascorbic acid showed a significant increase of ascorbic acid uptake into the brain after stroke. Taken together, these results provide evidence for the expression and transport activity of SVCT2 in brain capillary endothelial cells after transient ischemia in mice. These results may lead to the development of novel neuroprotective strategies in stroke therapy

Monitoring frequency influences the analysis of resting behaviour in a forest carnivore

Resting sites are key structures for many mammalian species, which can affect reproduction, survival, population density, and even species persistence in human-modified landscapes. As a consequence, an increasing number of studies has estimated patterns of resting site use by mammals, as well as the processes underlying these patterns, though the impact of sampling design on such estimates remain poorly understood. Here we address this issue empirically, based on data from 21 common genets radiotracked during 28 months in Mediterranean forest landscapes. Daily radiotracking data was thinned to simulate every other day and weekly monitoring frequencies, and then used to evaluate the impact of sampling regime on estimates of resting site use. Results showed that lower monitoring frequencies were associated with major underestimates of the average number of resting sites per animal, and of site reuse rates and sharing frequency, though no effect was detected on the percentage use of resting site types. Monitoring frequency also had a major impact on estimates of environmental effects on resting site selection, with decreasing monitoring frequencies resulting in higher model uncertainty and reduced power to identify significant explanatory variables. Our results suggest that variation in monitoring frequency may have had a strong impact on intra- and interspecific differences in resting site use patterns detected in previous studies. Given the errors and uncertainties associated with low monitoring frequencies, we recommend that daily or at least every other day monitoring should be used whenever possible in studies estimating resting site use patterns by mammals