Weighted Sobolev spaces of radially symmetric functions

We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best constants.Comment: 38 page

Laser-induced etching of few-layer graphene synthesized by Rapid-Chemical Vapour Deposition on Cu thin films

The outstanding electrical and mechanical properties of graphene make it very attractive for several applications, Nanoelectronics above all. However a reproducible and non destructive way to produce high quality, large-scale area, single layer graphene sheets is still lacking. Chemical Vapour Deposition of graphene on Cu catalytic thin films represents a promising method to reach this goal, because of the low temperatures (T < 900 Celsius degrees) involved during the process and of the theoretically expected monolayer self-limiting growth. On the contrary such self-limiting growth is not commonly observed in experiments, thus making the development of techniques allowing for a better control of graphene growth highly desirable. Here we report about the local ablation effect, arising in Raman analysis, due to the heat transfer induced by the laser incident beam onto the graphene sample.Comment: v1:9 pages, 8 figures, submitted to SpringerPlus; v2: 11 pages, PDFLaTeX, 9 figures, revised peer-reviewed version resubmitted to SpringerPlus; 1 figure added, figure 1 and 4 replaced,typos corrected, "Results and discussion" section significantly extended to better explain etching mechanism and features of Raman spectra, references adde

Probing the close environment of young stellar objects with interferometry

The study of Young Stellar Objects (YSOs) is one of the most exciting topics that can be undertaken by long baseline optical interferometry. The magnitudes of these objects are at the edge of capabilities of current optical interferometers, limiting the studies to a few dozen, but are well within the capability of coming large aperture interferometers like the VLT Interferometer, the Keck Interferometer, the Large Binocular Telescope or 'OHANA. The milli-arcsecond spatial resolution reached by interferometry probes the very close environment of young stars, down to a tenth of an astronomical unit. In this paper, I review the different aspects of star formation that can be tackled by interferometry: circumstellar disks, multiplicity, jets. I present recent observations performed with operational infrared interferometers, IOTA, PTI and ISI, and I show why in the next future one will extend these studies with large aperture interferometers.Comment: Review to be published in JENAM'2002 proceedings "The Very Large Telescope Interferometer Challenges for the future

Direct generation of intense extreme ultraviolet supercontinuum with 35 fs, 11 mJ pulses from a femtosecond laser amplifier

We report on the generation of intense extreme ultraviolet (EUV) supercontinuum with photon energies spanning from 35 eV to 50 eV (i. e., supporting an isolated attosecond pulse with a duration of ~271 as) by loosely focusing 35 fs, 11 mJ pulses from a femtosecond laser amplifier into a 10-mm long gas cell filled with krypton gas. The dramatic change of spectral and temporal properties of the driver pulses after passing through the gas cell indicates that propagation effects play a significant role in promoting the generation of the EUV supercontinuum.Comment: 14 pages, 4 figure

Direct magnetic field detection in the innermost regions of an accretion disc

Models predict that magnetic fields play a crucial role in the physics of astrophysical accretion disks and their associated winds and jets. For example, the rotation of the disk twists around the rotation axis the initially vertical magnetic field, which responds by slowing down the plasma in the disk and by causing it to fall towards the central star. The magnetic energy flux produced in this process points away from the disk, pushing the surface plasma outwards, leading to a wind from the disk and sometimes a collimated jet. But these predictions have hitherto not been supported by observations. Here we report the direct detection of the magnetic field in the core of the protostellar accretion disk FU Orionis. The surface field reaches strengths of about 1 kG close to the centre of the disk, and it includes a significant azimuthal component, in good agreement with recent models. But we find that the field is very filamentary and slows down the disk plasma much more than models predict, which may explain why FU Ori fails to collimate its wind into a jet.Comment: 11 pages, 3 figure

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

Symmetric Sensorimotor Somatotopy

BACKGROUND: Functional imaging has recently been used to investigate detailed somatosensory organization in human cortex. Such studies frequently assume that human cortical areas are only identifiable insofar as they resemble those measured invasively in monkeys. This is true despite the electrophysiological basis of the latter recordings, which are typically extracellular recordings of action potentials from a restricted sample of cells. METHODOLOGY/PRINCIPAL FINDINGS: Using high-resolution functional magnetic resonance imaging in human subjects, we found a widely distributed cortical response in both primary somatosensory and motor cortex upon pneumatic stimulation of the hairless surface of the thumb, index and ring fingers. Though not organized in a discrete somatotopic fashion, the population activity in response to thumb and index finger stimulation indicated a disproportionate response to fingertip stimulation, and one that was modulated by stimulation direction. Furthermore, the activation was structured with a line of symmetry through the central sulcus reflecting inputs both to primary somatosensory cortex and, precentrally, to primary motor cortex. CONCLUSIONS/SIGNIFICANCE: In considering functional activation that is not somatotopically or anatomically restricted as in monkey electrophysiology studies, our methodology reveals finger-related activation that is not organized in a simple somatotopic manner but is nevertheless as structured as it is widespread. Our findings suggest a striking functional mirroring in cortical areas conventionally ascribed either an input or an output somatotopic function

Dynamical Boson Stars

The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called {\em geons}, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name {\em boson stars}. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.Comment: 79 pages, 25 figures, invited review for Living Reviews in Relativity; major revision in 201

Blockade of advanced glycation end product formation attenuates bleomycin-induced pulmonary fibrosis in rats

<p>Abstract</p> <p>Background</p> <p>Advanced glycation end products (AGEs) have been proposed to be involved in pulmonary fibrosis, but its role in this process has not been fully understood. To investigate the role of AGE formation in pulmonary fibrosis, we used a bleomycin (BLM)-stimulated rat model treated with aminoguanidine (AG), a crosslink inhibitor of AGE formation.</p> <p>Methods</p> <p>Rats were intratracheally instilled with BLM (5 mg/kg) and orally administered with AG (40, 80, 120 mg/kg) once daily for two weeks. AGEs level in lung tissue was determined by ELISA and pulmonary fibrosis was evaluated by Ashcroft score and hydroxyproline assay. The expression of heat shock protein 47 (HSP47), a collagen specific molecular chaperone, was measured with RT-PCR and Western blot. Moreover, TGFβ1 and its downstream Smad proteins were analyzed by Western blot.</p> <p>Results</p> <p>AGEs level in rat lungs, as well as lung hydroxyproline content and Ashcroft score, was significantly enhanced by BLM stimulation, which was abrogated by AG treatment. BLM significantly increased the expression of HSP47 mRNA and protein in lung tissues, and AG treatment markedly decreased BLM-induced HSP47 expression in a dose-dependent manner (p < 0.05). In addition, AG dose-dependently downregulated BLM-stimulated overexpressions of TGFβ1, phosphorylated (p)-Smad2 and p-Smad3 protein in lung tissues.</p> <p>Conclusion</p> <p>These findings suggest AGE formation may participate in the process of BLM-induced pulmonary fibrosis, and blockade of AGE formation by AG treatment attenuates BLM-induced pulmonary fibrosis in rats, which is implicated in inhibition of HSP47 expression and TGFβ/Smads signaling.</p