Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces

We prove optimal integrability results for solutions of the p(x)-Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials map L1 to variable exponent weak Lebesgue spaces

New insights on the interaction between thiophene derivatives and Au surfaces: the case of 3,4-ethylenedioxythiophene and the relevant polymer.

The nature of the interface between electrogenerated poly(3,4-ethylenedioxythiophene) and the Au substrate is studied in detail. In particular, the adsorption of the relevant monomer, namely, 3,4-ethylenedioxythiophene, is investigated and compared with that of other thiophene derivatives. Different deposition procedures have been adopted: very thin films of the thiophene derivatives have been obtained through chemisorption processes from vapor and liquid phases, on Au polycrystalline substrates, Au nano particles possessing different size, and a Au(111) single crystal. Different techniques, operating both in situ and ex situ, have been employed for the characterization of these deposits, that is, X-ray photoemission and surface enhanced Raman spectroscopy. The results show that the poly(3,4-ethylenedioxythiophene)/metal interface is far from being simply constituted by unreacted molecules in contact with the substrate; rather, the formation of oligothiophene species and sulfur atoms at the interface has been ascertained

Spatial Structure and Coherent Motion in Dense Planetary Rings Induced by Self-Gravitational Instability

We investigate the formation of spatial structure in dense, self-gravitating particle systems such as Saturn's B-ring through local $N$-body simulations to clarify the intrinsic physics based on individual particle motion. In such a system, Salo (1995) showed that the formation of spatial structure such as wake-like structure and particle grouping (clump) arises spontaneously due to gravitational instability and the radial velocity dispersion increases as the formation of the wake structure. However, intrinsic physics of the phenomena has not been clarified. We performed local $N$-body simulations including mutual gravitational forces between ring particles as well as direct (inelastic) collisions with identical (up to $N\sim40000$) particles. In the wake structure particles no longer move randomly but coherently. We found that particle motion was similar to Keplerian motion even in the wake structure and that the coherent motion was produced since the particles in a clump had similar eccentricity and longitude of perihelion. This coherent motion causes the increase and oscillation in the radial velocity dispersion. The mean velocity dispersion is rather larger in a more dissipative case with a smaller restitution coefficient and/or a larger surface density since the coherence is stronger in the more dissipative case. Our simulations showed that the wavelength of the wake structure was approximately given by the longest wavelength \hs{\lambda}{cr} = 4\pi^2 G\Sigma/\kappa^2 in the linear theory of axisymmetric gravitational instability in a thin disk, where $G$, $\Sigma$, and $\kappa$ are the gravitational constant, surface density, and a epicyclic frequency.Comment: Accepted by Earth, Planets, and Space. 39 pages, 20 figures. PostScript files also available from http://www.geo.titech.ac.jp/nakazawalab/hdaisaka/works

Avoidance, biomass and survival response of soil dwelling (endogeic) earthworms to OECD artificial soil: potential implications for earthworm ecotoxicology

Soil dwelling earthworms are now adopted more widely in ecotoxicology, so it is vital to establish if standardised test parameters remain applicable. The main aim of this study was to determine the influence of OECD artificial soil on selected soil-dwelling, endogeic earthworm species. In an initial experiment, biomass change in mature Allolobophora chlorotica was recorded in Standard OECD Artificial Soil (AS) and also in Kettering Loam (KL). In a second experiment, avoidance behaviour was recorded in a linear gradient with varying proportions of AS and KL (100% AS, 75% AS + 25% KL, 50% KS + 50% KL, 25% AS + 75% KL, 100% KL) with either A. chlorotica or Octolasion cyaneum. Results showed a significant decrease in A. chlorotica biomass in AS relative to KL, and in the linear gradient, both earthworm species preferentially occupied sections containing higher proportions of KL over AS. Soil texture and specifically % composition and particle size of sand are proposed as key factors that influenced observed results. This research suggests that more suitable substrates are required for ecotoxicology tests with soil dwelling earthworms

Theoretical study on the electronic, structural, properties and reactivity of a series of mono-, di-, tri- and tetrachlorothiophenes as well as corresponding radical cation forms as monomers for conducting polymers

In this paper, electrical and structural properties of mono-, di-, tri- and tetrachlorothiophenes and their radical cations have been studied using the density functional theory and B3LYP method with 6-311++G** basis set. The effects of the number and position of the substituent of chlorine atoms on the properties of the thiophene ring for all chlorothiophenes and their radical cations have been studied. Vibrational frequencies, nuclear chemical shielding constants, spin-density distribution, size and direction of dipole moment vector, ionization potential, electric polarizabilities and NICS values of these compounds have been calculated as well. The analysis of these data showed that double bonds in 3-chlorothiophene are more delocalized and it is the best possible candidate monomer among all chlorothiophenes for the synthesis of corresponding conducting polymers with modified characteristics

Compact Polyelectrolyte Complexes: “Saloplastic” Candidates for Biomaterials

Precipitates of polyelectrolyte complexes were transformed into rugged shapes suitable for bioimplants by ultracentrifugation in the presence of high salt concentration. Salt ions dope the complex, creating a softer material with viscous fluid-like properties. Complexes that were compacted under the centrifugal field (CoPECs) were made from poly(diallyldimethyl ammonium), PDADMA, as polycation, and poly(styrene sulfonate), PSS, or poly(methacrylic acid), PMAA, as polyanion. Dynamic mechanical testing revealed a rubbery plateau at lower frequencies for PSS/PDADMA with moduli that decreased with increasing salt concentration, as internal ion pair cross-links were broken. CoPECs had significantly lower modulii compared to similar polyelectrolyte complexes prepared by the “multilayering ” method. The difference in mechanical properties was ascribed to higher water content (located in micropores) for the former and, more importantly, to their nonstoichiometric polymer composition. The modulus of PMAA/PDADMA CoPECs, under physiological conditions, demonstrated dynamic mechanical properties that were close to those of the nucleus pulposus in an intervertebral disk

Biodiversity and structure of spider communities along a metal pollution gradient

The objective of the study was to determine whether long-term metal pollution affects communities of epigeal spiders (Aranea), studied at three taxonomic levels: species, genera, and families. Biodiversity was defined by three indices: the Hierarchical Richness Index (HRI), Margalef index (DM) and Pielou evenness index (J). In different ways the indices describe taxa richness and the distribution of individuals among taxa. The dominance pattern of the communities was described with four measures: number of dominant species at a site, percentage of dominant species at a site, average dominant species abundance at a site, and the share of the most numerous species (Alopecosa cuneata) at a site. Spiders were collected along a metal pollution gradient in southern Poland, extending ca. 33 km from zinc and lead smelter to an uncontaminated area. The zinc concentration in soil was used as the pollution index.The study revealed a significant effect of metal pollution on spider biodiversity as described by HRI for species (p = 0.039), genera (p = 0.0041) and families (p = 0.0147), and by DM for genera (p = 0.0259) and families (p = 0.0028). HRI correlated negatively with pollution level, while DM correlated positively. This means that although broadly described HRI diversity decreased with increasing pollution level, species richness increased with increasing contamination. Mesophilic meadows were generally richer. Pielou (J) did not show any significant correlations. There were a few evidences for the intermediate disturbance hypothesis: certain indices reached their highest values at moderate pollution levels rather than at the cleanest or most polluted sites