The group of pythagorean triples in Number fields

Sunto Generalizzando precedenti definizioni, si introduce il gruppo delle terne pitagoriche nell'anello di interi R di una fissata estensione finita K di Q. Sia S l'anello degli interi di K(i): si dà una descrizione esplicita di tali gruppi in termini delle unità di S, del suo gruppo di classi di ideali e di opportuni ideali primi di S.

---

---

Lavoro eseguito con il contribute del M.P.I.     

Crystal-chemical features of monoclinic lanthanide oxobromotungstates of composition LnWO4Br (Ln = Eu, Gd, Dy, Er, Yb)

The crystal-chemical properties of lanthanide oxobromotungstates of composition LnWO₄Br (Ln = Eu, Gd, Dy, Er, Yb) are studied. The crystal system and space group for the oxobromotungstates are determined. The unit cell parameters are refined. The parameters a, b, c, and V of the LnWO₄Br compounds are studied as functions of the atomic number of the lanthanide. Analytical equations are derived to predict unit cell parameters for unsynthesized lanthanide oxobromotungstates of the class in question.     

Local control of electric current driven shell etching of multiwalled carbon nanotubes

We report on a novel method for local control of shell engineering in multiwalled carbon nanotubes (MWNTs) using Joule-heating induced electric breakdown. By modulating the heat dissipation along a nanotube, we can confine its thinning and shell breakdown to occur within localized regions of peak temperatures, which are distributed over one-half of the NT length. The modulation is achieved by using suitably designed nanomachined heat sinks with different degrees of thermal coupling at different parts of a current-carrying nanotube. The location of electric breakdown occurs precisely at the regions of high temperatures predicted by the classical finite-element model of Joule heating in the MWNT. The experiments herein provide new insight into the electric breakdown mechanism and prove unambiguously that shell removal occurs due to thermal stress, underpinning the diffusive nature of MWNTs. The method demonstrated here has the potential to be a powerful tool in realizing MWNT bearings with complex architectures for use in integrated nanoelectromechanical systems (NEMS). In addition, the breakdown current and power in the nanotubes are significantly higher than those observed in nanotubes without heat removal via additional heat sinks. This indicates future avenues for enhancing the performance of MWNTs in electrical interconnect and nanoelectronic applications. PACS  73.63.Fg; 65.80.+n     

Deep trench etching in macroporous silicon

We present a method to create at the same time trenches and ordered macropore arrays during photo-electrochemical etching of n-type silicon. This novel method allows in situ separation of single devices with a submicrometer precision. It also enables new device structures in macroporous silicon in the areas of photonics, sensing and electronics. The limits of this new process are simulated using electrostatic models and are verified experimentally. PACS 82.45.Yz; 81.16.-c     

Optical and photoelectric properties of pure and cadmium-and lead-doped neodymium sesquisulfide thin films

A technique for preparing γ-Nd₂S₃ crystalline thin films through discrete vacuum thermal evaporation of a presynthesized bulk material is developed. The films deposited are doped with cadmium and lead. The reflectance and transmittance spectra of the films are measured in the photon energy range 0.2–3.0 eV at a temperature of 300 K. The frequency analysis of the absorption coefficient demonstrates that the γ-Nd₂S₃ films are characterized by an exponential absorption edge. The photoconductivity spectra and temperature dependences of the photoconductivity for the γ-Nd₂S₃ films doped with cadmium and lead are measured in the photon energy range 0.2–3.3 eV at temperatures varying from 115 to 380 K. The experimental data obtained are interpreted under the assumption that the acceptor levels formed by vacancies in the cation sublattice and compensated for by cadmium and lead donor dopants play a crucial role in the photoconduction. The ionization energy at the lead donor level is determined.     

On the Asymptotics of Fekete-Type Points for Univariate Radial Basis Interpolation

Suppose that K ^d is compact and that we are given a function fC(K) together with distinct points x_iK, 1in. Radial basis interpolation consists of choosing a fixed (basis) function g : ⁺→ and looking for a linear combination of the translates g(|x−x_j|) which interpolates f at the given points. Specifically, we look for coefficients c_j such that has the property that F(x_i)=f(x_i), 1in. The Fekete-type points of this process are those for which the associated interpolation matrix [g(|x_i−x_j|)]_1i,jn has determinant as large as possible (in absolute value). In this work, we show that, in the univariate case, for a broad class of functions g, among all point sequences which are (strongly) asymptotically distributed according to a weight function, the equally spaced points give the asymptotically largest determinant. This gives strong evidence that the Fekete points themselves are indeed asymptotically equally spaced.     

Investigation by ellipsometry of the damage in GaAs bombarded with low-energy Ar ions

The crystalline-amorphous transition in GaAs induced by Ar ions (energy 1–3 keV) has been investigated using single-wavelength ellipsometry. The experiments have been performed in-situ at room temperature. Ion damage straggling, amorphization threshold and critical energy density have been derived by means of a simple analytical model for the growth of the amorphous layer. This model is discussed and the corresponding calculations are found to be in satisfactory agreement with experimental data.