Curvature and distance function from a manifold

This paper is concerned with the relations between the differential invariants of a smooth manifold embedded in the Euclidean space and the square of the distance function from the manifold. In particular, we are interested in curvature invariants like the mean curvature vector and the second fundamental form. We find that these invariants can be computed in a very simple way using the third order derivatives of the squared distance function. Moreover, we study a general class of functionals depending on the derivatives up to a given order γ of the squared distance function and we find an algorithm for the computation of the Euler equation. Our class of functionals includes as particular cases the well-known area functional (γ = 2), the integral of the square of the quadratic norm of the second fundamental form (γ = 3), and the Willmore functional.     

High-resolution 2-DE for resolving proteins, protein adducts and complexes in plasma

A 2-DE system has been devised in which proteins are first separated in their native state followed by separation according to mass under denaturing conditions (Nat/SDS-PAGE). Hydrophilic properties of the gel and the presence of dihydroxybisacrylamide in the first dimension allowed a good resolution for high-molecular-weight proteins and maintained interactions. With this method 252 plasma spots have been resolved and 140 have been characterized by MS as isoforms of 60 proteins, a relevant part of which (12) were not detected by traditional 2-D gels or by other nondenaturing 2-D techniques. The list includes complement factors (C4d, C7), coagulation factors (coagulation factor II, fibrin beta), apolipoproteins (apolipoprotein B) and cell debris (vinculin, gelsolin, tropomyosin, dystrobrevin beta, fibrinectin I). Nat/SDS PAGE also allowed separation of nicked forms of albumin, Apo B100 and alpha2-macroglobulin and showed the presence of atypical albumin adducts corresponding to post-translational and oxidation products. Our system provides therefore new tools for resolving proteins, protein aggregates and complexes and amplifies the potentiality of traditional electrophoretic analysis.     

Amperometric Detection of Ethanol Vapors by Screen Printed Electrodes Modified by Paper Crowns Soaked with Room Temperature Ionic Liquids

A convenient assembly recently proposed for screen printed gold electrodes (SPEs) suitable for measurements in gaseous samples is here tested for the analysis of the ethanol content in alcoholic drinks. This assembly involves the use of a circular crown of filter paper, soaked in the room temperature ionic liquid (RTIL) 1-butyl-3-methylimidazolium hydrogen sulfate, which is simply placed upon a disposable screen printed cell, so as to contact the outer edge of the gold disc working electrode, as well as peripheral counter and reference electrodes. The electrical contact between the paper crown soaked in RTIL and the SPE electrode is assured by a gasket and all components are installed in a polylactic acid holder. This assembly provides a portable and disposable electrochemical platform, assembled by the easy immobilization onto a porous and inexpensive supporting material such as paper of a RTIL characterized by profitable electrical conductivity and negligible vapor pressure. The electroanalytical performance of this device was assayed for the flow injection analysis of the ethanol concentration in some real samples of wine and beer and the results obtained are compared with the alcoholic degree reported in the relevant bottle-labels, thus highlighting a substantially satisfactory agreement. Repeatable sharp peaks (RSD=6–8 %) were detected for ethanol over a wide linear range (1–20 % v/v in water) and a detection and quantitation limit of 0.55 % v/v and 1.60 % v/v were inferred for a signal-to-noise ratio of 3 and 10, respectively.     

On the regularity of the pressure field of Brenier’s weak solutions to incompressible Euler equations

In this paper we improve the regularity in time of the gradient of the pressure field arising in Brenier’s variational weak solutions (Comm Pure Appl Math 52:411–452, 1999) to incompressible Euler equations. This improvement is necessary to obtain that the pressure field is not only a measure, but a function in . In turn, this is a fundamental ingredient in the analysis made by Ambrosio and Figalli (2007, preprint) of the necessary and sufficient optimality conditions for the variational problem by Brenier (J Am Mat Soc 2:225–255, 1989; Comm Pure Appl Math 52:411–452, 1999).     

Representation Formulae for Solutions to Some Classes of Higher Order Systems and Related Liouville Theorems

Let m ≥ 1 be an integer and N > 2m. Let μ be a positive Radon measure on . We study necessary and sufficient conditions on possible distributional solutions of , that guarantee the validity of the representation formula a.e. on , where and c(2m) is a positive constant depending on m and N. Several consequences are derived. In particular we prove Liouville theorems for systems of higher order elliptic inequalities and weighted form of Hardy-Littlewood-Sobolev systems of integral equations. Received: March 2008     

A biomimetic approach to the chemical inactivation of chrysotile fibres by lichen metabolites

Some lichens were recently reported to modify the surface state of asbestos. Here we report some new insight on the physico-chemical modifications induced by natural chelators (lichen metabolites) on two asbestos samples collected in two different locations. A biomimetic approach was followed by reproducing in the laboratory the weathering effect of lichen metabolites. Norstictic, pulvinic and oxalic acid (0.005, 0.5 and 50 mM) were put in contact with chrysotile fibres, either in pure form (A) or intergrown with balangeroite, an iron-rich asbestiform phase (B). Mg and Si removal, measured by inductively coupled plasma atomic emission spectrometry (ICP-AES) and scanning electron microscopy-energy dispersive X-ray spectroscopy (SEM-EDS), reveals an incongruent dissolution for pure chrysotile (A), with Mg removal always exceeding that of Si, while chrysotile-balangeroite (B) follows a congruent dissolution pattern in all cases except in the presence of 50 mM oxalic acid. A much larger removal of Mg than Si in the solutions of 0.5 and 50 mM oxalic acid with chrysotile (A) suggests a structural collapse, which in the case of chrysotile-balangeroite (B) only occurs with 50 mM oxalic acid; in these cases both samples are converted into amorphous silica (as detected by X-ray diffraction (XRD)). Subsequent to incubation, some new phases (Fe(2)O(3), CaMg(CO(3))(2), Ca(C(2)O(4)) x H(2)O and Mg(C(2)O(4))2 x H(2)O), similar to those observed in the field, were detected by XRD and micro-Raman spectroscopy. The leaching effect of lichen metabolites also modifies the Fenton activity, a process widely correlated with asbestos pathogenicity: pure chrysotile (A) activity is reduced by 50 mM oxalic acid, while all lichen metabolites reduce the activity of chrysotile-balangeroite (B). The selective removal of poorly coordinated, highly reactive iron ions, evidenced by NO adsorption, accounts for the loss in Fenton activity. Such fibres were chemically close to the ones observed in the field. Chrysotile-rich rocks, colonised by lichens, could be exposed to a natural bioattenuation and considered as a transient environmental hazard.     

The occurrence of phenyl propanoid glycosides in endemic Teucrium species

The phenyl propanoid fraction of Teucrium subspinosum Pourrette ex Willd. (Lamiaceae) from Baleari Island, was examined together with the same fraction of T. subspinosum from Sardinia. In T. subspinosum, besides verbascoside as main component, a new phenyl-propanoid-glycoside was isolated and identified by (1)H- and (13)C-NMR spectra analysis. Comparison with molecular composition of T. marum confirmed the differences between these species and evidenced their endemic character.     

Multiple Solutions for a Class of Nonhomogeneous Fractional Schrödinger Equations in $$\mathbb {R}^{N}$$

This paper is concerned with the following fractional Schrödinger equation

$$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s} u+u= k(x)f(u)+h(x) \text{ in } \mathbb {R}^{N}\\ u\in H^{s}(\mathbb {R}^{N}), \, u>0 \text{ in } \mathbb {R}^{N}, \end{array} \right. \end{aligned}$$

where \(s\in (0,1),N> 2s, (-\Delta )^{s}\) is the fractional Laplacian, k is a bounded positive function, \(h\in L^{2}(\mathbb {R}^{N}), h\not \equiv 0\) is nonnegative and f is either asymptotically linear or superlinear at infinity. By using the s-harmonic extension technique and suitable variational methods, we prove the existence of at least two positive solutions for the problem under consideration, provided that \(|h|_{2}\) is sufficiently small.

     

Photoconductivity of multiwalled CNT deposited by CVD

Structural, optical and electrical properties of multiwalled carbon nanotubes deposited by chemical vapour deposition at 750 °C on sapphire substrate have been investigated. The main results concern the photoconductivity measurements. The photocurrent induced by white light illumination is a linear function of either the bias voltage or the optical power density in wide ranges. The photoresponse increases from the near infrared to the ultraviolet region with decreasing the wavelength of the monochromatic incident radiation in the 325–850 nm range. The photoresponse is strongly correlated to the optical absorbance. The optical and photoconductivity properties explored in multiwalled carbon nanotube samples with relatively large area appear very interesting for the development of light sensors.     

Metric differentiability of Lipschitz maps defined on Wiener spaces

This note is devoted to the differentiability properties of -Lipschitz maps defined on abstract Wiener spaces and with values in metric spaces (Y,d _Y ). We prove the existence γ-a.e. of local seminorms in the Cameron-Martin space which allow to compute the metric derivative of the map. Second Author partially supported by DGES (Spain) MTM2006-03531.