On Hopf's Lemma and the Strong Maximum Principle

In this paper we consider Hopf's Lemma and the Strong Maximum Principle for supersolutions to a class of non elliptic equations. In particular we prove a sufficient condition for the validity of Hopf's Lemma and of the Strong Maximum Principle and we give a condition which is at once necessary for the validity of Hopf's Lemma and sufficient for the validity of the Strong Maximum Principle.Comment: 27 pages,4 figure

Global attractors for nonlinear viscoelastic equations with memory

We study the asymptotic properties of the semigroup S(t) arising from a nonlinear viscoelastic equation with hereditary memory on a bounded three-dimensional domain written in the past history framework of Dafermos. We establish the existence of the global attractor of optimal regularity for S(t) for a wide class of nonlinearities as well as within the most general condition on the memory kernel

On the behavior of solutions to Schr\"odinger equations with dipole-type potentials near the singularity

Asymptotics of solutions to Schroedinger equations with singular dipole-type potentials is investigated. We evaluate the exact behavior near the singularity of solutions to elliptic equations with potentials which are purely angular multiples of radial inverse-square functions. Both the linear and the semilinear (critical and subcritical) cases are considered

Unit cell of graphene on Ru(0001): a 25 x 25 supercell with 1250 carbon atoms

The structure of a single layer of graphene on Ru(0001) has been studied using surface x-ray diffraction. A surprising superstructure has been determined, whereby 25 x 25 graphene unit cells lie on 23 x 23 unit cells of Ru. Each supercell contains 2 x 2 crystallographically inequivalent subcells caused by corrugation. Strong intensity oscillations in the superstructure rods demonstrate that the Ru substrate is also significantly corrugated down to several monolayers, and that the bonding between graphene and Ru is strong and cannot be caused by van der Waals bonds. Charge transfer from the Ru substrate to the graphene expands and weakens the C-C bonds, which helps accommodate the in-plane tensile stress. The elucidation of this superstructure provides important information in the potential application of graphene as a template for nanocluster arrays.Comment: 9 pages, 3 figures, paper submitted to peer reviewed journa

Ultrastructural and spectrophotometric study on the effects of putative triggers on aortic valve interstitial cells in in vitro models simulating metastatic calcification.

Metastatic calcification of cardiac valves is a common complication in patients affected by chronic renal failure. In this study, primary bovine aortic valve interstitial cells (AVICs) were subjected to pro-calcific treatments consisting in cell stimulation with (i) elevated inorganic phosphate (Pi = 3mM), in order to simulate hyperphosphatemic conditions; (ii) bacterial endotoxin lipopolysaccharide (LPS), simulating direct effects by microbial agents; and (iii) conditioned media (CM) derived from cultures of either LPS-stimulated heterogenic macrophages (commercial murine RAW264.7 cells) or LPS-stimulated fresh allogeneic monocytes/macrophages (bCM), simulating consequent inflammatory responses, alone or combined. Compared to control cultures, spectrophotometric assays revealed shared treatment-dependent higher values of both calcium amounts and alkaline phosphatase activity for cultures involving the presence of elevated Pi. Ultrastructurally, shared peculiar pro-calcific degeneration patterns were exhibited by AVICs from the same cultures irrespectively of the applied treatment. Disappearance of all cytomembranes and concurrent formation of material showing positivity to Cuprolinic Blue and co-localizing with silver precipitation were followed by the outcropping of such a material, which transformed in layers outlining the dead cells. Subsequent budding of these layers resulted in the formation of bubbling bodies and concentrically laminated calcospherulae mirroring those in actual soft tissue calcification. In conclusion, the in vitro models employed appear to be reliable tools for simulating metastatic calcification and indicate that hyperphosphatemic-like conditions could trigger valve calcification per se, with LPS and allogeneic macrophage-derived secretory products acting as possible calcific enhancers via inflammatory responses

The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity

The implications of the SU(2) gauge fixing associated with the choice of invariant triads in Loop Quantum Cosmology are discussed for a Bianchi I model. In particular, via the analysis of Dirac brackets, it is outlined how the holonomy-flux algebra coincides with the one of Loop Quantum Gravity if paths are parallel to fiducial vectors only. This way the quantization procedure for the Bianchi I model is performed by applying the techniques developed in Loop Quantum Gravity but restricting the admissible paths. Furthermore, the local character retained by the reduced variables provides a relic diffeomorphisms constraint, whose imposition implies homogeneity on a quantum level. The resulting picture for the fundamental spatial manifold is that of a cubical knot with attached SU(2) irreducible representations. The discretization of geometric operators is outlined and a new perspective for the super-Hamiltonian regularization in Loop Quantum Cosmology is proposed.Comment: 6 page

Survival-related autophagic activity versus procalcific death in cultured aortic valve interstitial cells treated with critical normophosphatemic-like phosphate concentrations

Valve dystrophic calcification is a common disorder affecting normophosphatemic subjects. Here, cultured aortic valve interstitial cells (AVICs) were treated 3 to 28 days with phosphate (Pi) concentrations spanning the normal range in humans (0.8, 1.3, and 2.0 mM) alone or supplemented with proinflammatory stimuli to assess possible priming of dystrophic-like calcification. Compared with controls, spectrophotometric analyses revealed marked increases in calcium amounts and alkaline phosphatase activity for 2.0-mM-Pi-containing cultures, with enhancing by proinflammatory mediators. Ultrastructurally, AVICs treated with low/middle Pi concentrations showed an enormous endoplasmic reticulum (ER) enclosing organelle debris, so apparently executing a survival-related atypical macroautophagocytosis, consistently with ultracytochemical demonstration of ER-associated acid phosphatase activity and decreases in autophagosomes and immunodetectable MAP1LC3. In contrast, AVICs cultured at 2.0-mM Pi underwent mineralization due to intracellular release and peripheral layering of phospholipid-rich material acting as hydroxyapatite nucleator, as revealed by Cuprolinic Blue and von Kossa ultracytochemical reactions. Lack of immunoblotted caspase-3 cleaved form indicated apoptosis absence for all cultures. In conclusion, fates of cultured AVICs were crucially driven by Pi concentration, suggesting that serum Pi levels just below the upper limit of normophosphatemia in humans may represent a critical watershed between macroautophagy-associated cell restoring and procalcific cell death

Characterization of nanometer-sized, mechanically exfoliated graphene on the H-passivated Si(100) surface using scanning tunnelling microscopy

We have developed a method for depositing graphene monolayers and bilayers with minimum lateral dimensions of 2-10 nm by the mechanical exfoliation of graphite onto the Si(100)-2x1:H surface. Room temperature, ultra-high vacuum (UHV) tunnelling spectroscopy measurements of nanometer-sized single-layer graphene reveal a size dependent energy gap ranging from 0.1-1 eV. Furthermore, the number of graphene layers can be directly determined from scanning tunnelling microscopy (STM) topographic contours. This atomistic study provides an experimental basis for probing the electronic structure of nanometer-sized graphene which can assist the development of graphene-based nanoelectronics.Comment: Accepted for publication in Nanotechnolog

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