Regularity results for positive solutions of a semilinear elliptic system

Let , N≧3 be an open set. In this paper we study weak positive solutions of the following semilinear system where p≧1, q≧1, with pq>1, and u∈L^q(Ω), v∈L^p(Ω), and we give in particular some regularity results. Furthermore, we give some applications to the biharmonic equation. Entrata in Redazione il 25 febbraio 1999.     

Gaussian Limiting Behavior of the Rescaled Solution to the Linear Korteweg–de Vries Equation with Random Initial Conditions

We analyze the asymptotic behavior of the rescaled solution to the linear Korteweg–de Vries equation when the initial conditions are supposed to be random and weakly dependent. By means of the method of moments we prove the Gaussianity of the limiting process and we present its correlation function. The same technique is applied to the analysis of another third-order heat-type equation.     

Hardy inequalities with optimal constants and remainder terms

We show that the classical Hardy inequalities with optimal constants in the Sobolev spaces and in higher-order Sobolev spaces on a bounded domain can be refined by adding remainder terms which involve norms. In the higher-order case further norms with lower-order singular weights arise. The case being more involved requires a different technique and is developed only in the space .

     

Speciation of metal(loid)s in environmental samples by X-ray absorption spectroscopy: A critical review

Element specificity is one of the key factors underlying the widespread use and acceptance of X-ray absorption spectroscopy (XAS) as a research tool in the environmental and geo-sciences. Independent of physical state (solid, liquid, gas), XAS analyses of metal(loid)s in complex environmental matrices over the past two decades have provided important information about speciation at environmentally relevant interfaces (e.g. solid–liquid) as well as in different media: plant tissues, rhizosphere, soils, sediments, ores, mineral process tailings, etc. Limited sample preparation requirements, the concomitant ability to preserve original physical and chemical states, and independence from crystallinity add to the advantages of using XAS in environmental investigations. Interpretations of XAS data are founded on sound physical and statistical models that can be applied to spectra of reference materials and mixed phases, respectively. For spectra collected directly from environmental matrices, abstract factor analysis and linear combination fitting provide the means to ascertain chemical, bonding, and crystalline states, and to extract quantitative information about their distribution within the data set. Through advances in optics, detectors, and data processing, X-ray fluorescence microprobes capable of focusing X-rays to micro- and nano-meter size have become competitive research venues for resolving the complexity of environmental samples at their inherent scale. The application of μ-XANES imaging, a new combinatorial approach of X-ray fluorescence spectrometry and XANES spectroscopy at the micron scale, is one of the latest technological advances allowing for lateral resolution of chemical states over wide areas due to vastly improved data processing and detector technology.     

Measurement of labile Cu in soil using stable isotope dilution and isotope ratio analysis by ICP-MS

Isotope dilution is a useful technique to measure the labile metal pool, which is the amount of metal in soil in rapid equilibrium (<7 days) with the soil solution. This is normally performed by equilibrating soil with a metal isotope, and sampling the labile metal pool by using an extraction (E value), or by growing plants (L value). For Cu, this procedure is problematic for E values, and impossible for L values, due to the short half-life of the ⁶⁴Cu radioisotope (12.4 h), which makes access and handling very difficult. We therefore developed a technique using enriched ⁶⁵Cu stable isotope and measurement of ⁶³Cu/⁶⁵Cu ratios by quadrupole inductively coupled plasma mass spectrometry (ICP-MS) to measure labile pools of Cu in soils using E value techniques. Mass spectral interferences in detection of ⁶³Cu/⁶⁵Cu ratios in soil extracts were found to be minimal. Isotope ratios determined by quadrupole ICP-MS compared well to those determined by high-resolution (magnetic sector) ICP-MS. E values determined using the stable isotope technique compared well to those determined using the radioisotope for both uncontaminated and Cu-contaminated soils.     

Characterisation of different clones of Picea abies (L.) Karst using head-space sampling of cortical tissues combined with enantioselective capillary gas chromatography for the separation of chiral and non-chiral monoterpenes

Head-space sampling (HS) has been combined with enantioselective gas chromatography (GC) for the analysis of chiral and non-chiral monoterpenes present in the cortical tissues of five different Norway spruce clones. (1S)-(-)-alpha-Pinene, (1S,5S)-(-)sabinene, (1S)-(-)-beta-pinene, and (4S)-(-)limonene dominated over (1R)-(+)-alpha-pinene, (1R,5R)-(+)-sabinene, (1R)-(+)-beta-pinene, and (4R)-(+)-limonene. Results showed a large variation in the enantiomeric composition of cortical tissues between different clones. The development of HS-GC greatly increased the speed of precise analyses of chiral monoterpenes in small samples and therefore offer excellent opportunities in studies on the ecophysiological and chemotaxomic roles of these chiral components.     

Mechanochemical synthesis and electrochemical properties of nanostructured electrode materials for Li ion batteries

We focus on the synthesis by ball milling and on the electrochemical characterization of nanocrystalline bimetallic and composite materials to be employed as anodes in Li ion batteries. Ni₃Sn₄ and Ni₃Sn₂ based compounds were obtained by ball milling of three different Ni–Sn mixtures. The properties of the resulting anodes for Li ion batteries were evaluated as a function of composition. Moreover, a biphasic system is presented, with CoSn₂ and CoSn type structures, arising from the synthesis of the Sn₃₁Co₂₈C₄₁ composition. When cycled in a Li cell, this material showed a high reversible specific capacity, about 450 mA h g⁻¹, and a very good electrochemical and structural stability, making it of interest for application purposes. Contribution to the Fall Meeting of the European Materials Research Society, Symposium D: 9th International Symposium on Electrochemical–Chemical Reactivity of Metastable Materials, Warsaw, 17th–21st September, 2007.     

Chemical waves and pattern formation in the 1,2-dipalmitoyl-sn-glycero-3-phosphocholine/water lamellar system

The present work deals with the spatially extended oscillatory Belousov Zhabotinsky reaction-diffusion system carried out in an anisotropic environment of phosphatidylcholines/water binary system, which presents layered aqueous domains separated by lipid bilayers. We report the occurrence of stable Turing patterns, spiral waves, and other exotic structures in phospholipids bilayers that are generally used as a models for cell plasma membranes.