Arithmétique fonctorielle des topologies de Grothendieck

Riassunto Il punto di partenza di questo lavoro è l'interpretazione delle topologie di Grothendieck nel linguaggio dei sistemi relazionali (cfr. [5]); ciò permette uno studio aritmetico di tali topologie. Attraverso nuove tecniche, qui introdotte, si ottengono risultati non privi di interesse, tra i quali una caratterizzazione degli spazi topologici noetheriani, ed ulteriori strutture topologiche di tipo locale (siti tangenti), per le quali vengono dimostrate numerose proprietà. Vengono, infine, date alcune applicazioni alla teoria degli schemi, utilizzando il funtore inviluppo affine.

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Summary The starting point of this paper is the interpretation of Grothendieck's topologies in the language of relational systems (cfr. [5]); this permits an arithmetical study of these topologies. By applying new techniques introduced here, we have achieved interesting results. These include a new characterization of Noetherian topological spaces, and further topological structures of local type (tangent sites) for which we have shown numerous properties. Finally, we have used the affine-envelope functor to illustrate some applications to the theory of schemes.

     

WKB-type approximations for second-order differential equations in -algebras

Rigorous asymptotic approximations of the WKB (or Liouville-Green) type are obtained for a basis of solutions to in the framework of -algebras. Both cases and are included, thus generalizing the classical theory for scalar equations developed by F.W.J. Olver to matrix as well as to infinite-dimensional equations.

     

Methods for correlating T1ρ and FID components in wideline H NMR studies of motionally heterogeneous polymer systems

We address the problem of correlating the observed FID and T_1ρ components in wideline ¹H relaxation measurements of motionally heterogeneous polymers, and show that different methods of data treatment can highlight different aspects of the correlations present. For a sample of polypropylene we find that the T_1ρ relaxation behaviour is driven by relaxation associated with the intermediate FID component, which strongly suggests a motionally inhomogeneous amorphous region in the sample.     

Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space.¶ II. Construction of the Navier-Stokes Solution

This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, which were constructed in the first paper, plus an error term. This shows that the Navier-Stokes solution goes to an Euler solution outside a boundary layer and to a solution of the Prandtl equations within the boundary layer. The error term is written as a sum of first order Euler and Prandtl corrections plus a further error term. The equation for the error term is weakly nonlinear; its linear part is the time dependent Stokes equation. This error equation is solved by inversion of the Stokes equation, through expressing the solution as a regular (Euler-like) part plus a boundary layer (Prandtl-like) part. The main technical tool in this analysis is the Abstract Cauchy-Kowalewski Theorem. Received: 5 September 1996 / Accepted: 14 July 1997     

CEMS of nitride coatings in agressive environments

The corrosion properties of single layered TiN and CrN films have been compared to bi-layered and multi-layered Ti/TiN films. XPS has showed that in humid SO₂ atmosphere the best corrosion properties have been achieved by a multi-layered Ti/TiN coating. Cyclic voltammetry in acetate buffer has been applied to measure the porousity and corrosion resistance of coatings. The best results have been achieved by multi-layered Ti/TiN and CrN films. Conversion electron Mössbauer spectroscopy has been used to study the changes in the interface Fe/TiN during thermal treatment in UHV. It has been shown that the amount of iron nitrides in the interface increases with increasing temperature.     

Hadron masses and matrix elements from the QCD Schrödinger functional

We explain how masses and matrix elements can be computed in lattice QCD using Schrödinger functional boundary conditions. Numerical results in the quenched approximation demonstrate that good precision can be achieved. For a statistical sample of the same size, our hadron masses have a precision similar to what is achieved with standard methods, but for the computation of matrix elements such as the pseudoscalar decay constant the Schrödinger functional technique turns out to be much more efficient than the known alternatives.     

The corrosion of weathering steel by SO2 polluted atmospheres at its very early stages

CEMS was used in conjunction with AES to study the protective film formed on a weathering steel by exposure to a highly SO₂-polluted atmosphere. Ferrous species (sulphite) and ferric oxyhydroxides (ferrihydrite and α-FeOOH) were identified as corrosion products. From the correlation of CEMS and AES results the evolution with time of the different compounds is obtained, and a possible reaction sequence is outlined.     

Lateral IBIC characterization of single crystal synthetic diamond detectors

In order to evaluate the charge collection efficiency (CCE) profile of single‐crystal diamond devices based on a p‐type/intrinsic/metal configuration, a lateral Ion Beam Induced Charge (IBIC) analysis was performed over their cleaved cross sections using a 2 MeV proton microbeam. CCE profiles in the depth direction were extracted from the cross‐sectional maps at variable bias voltage. IBIC spectra relevant to the depletion region extending beneath the frontal Schottky electrode show a 100% CCE, with a spectral resolution of about 1.5%. The dependence of the width of the high efficiency region from applied bias voltage allows the constant residual doping concentration of the active region to be evaluated. The region where the electric field is absent shows an exponentially decreasing CCE profile, from which it is possible to estimate the diffusion length of the minority carriers by means of a drift–diffusion model. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)