Vanishings for the cohomology of certain families of stable rank two vector bundles onP 3

Sunto Si analizzano delle condizioni per l'annullamento della coomologia di fibrati stabili di rango 2su P ³.Dopo i primi risultati di annullamento dovuti principalmente ad Hartshorne, Chang congetturò che alcune disuguaglianze sulle, classi di Chern fossero sufficienti per l'annullamento del primo gruppo di coomologia. La congettura finora è provata solo in alcuni casi particolari. Nel lavoro si dimostra la congettura in molti altri casi. In particolare si completano alcuni risultati recenti dovuti ad Ellia affrontando il caso in cui la prima classe di Chern è dispari.     

Finding the contour of a union of iso-oriented rectangies

Let R₁,…,R_m be rectangles on the plane with sides parallel to the coordinate axes. An algorithm is described for finding the contour of F = R₁ ∪ … ∪ R_m in $\text{O(m}\text{log}\text{m + p}\text{log}\text{(}\text{2m}{}^2\text{p}\text{))}$ time, where p is the number of edges in the contour. This is O(m²) in the general case, and O(m log m) when F is without holes (then p ≤ 8m ? 4); both of these performances are optimal.     

Dynamics of TMMC at low temperature: A new approach to the N-pole approximation

In this paper we study the conditions to be satisfied in order to use a N-pole truncation to the continued-frac$\text{t}$ ion expansion. We show the correct way to do the cut off and apply the result to analyse experimental data for the one-dimensional antiferromagnet TMMC, at low temperatures.     

Synthesis of alpha,beta-unsaturated 4,5-disubstituted gamma-lactones via ring-closing metathesis catalyzed by the first-generation Grubbs' catalyst

[reaction: see text] 4-Methyl-5-alkyl-2(5H)-furanones have been prepared by ruthenium-catalyzed ring-closing metathesis of the suitable methallyl acrylates. Despite the electron deficiency of the conjugated double bond and of the gem-disubstitution of the allylic alkene moiety in the starting acrylates, the first-generation Grubbs' catalyst I proved to be an effective promoter for the ring closure, affording the expected butenolides in good to high yields.     

Complete single-photon counting and timing module in a microchip

A complete module for single-photon counting and timing is demonstrated in a single chip. Features comparable with or better than commercially available macroscopic modules are obtained by integration of an active-quenching and active-reset circuit in complementary metal-oxide semiconductor technology together with a single-photon avalanche diode (SPAD). The integrated SPAD has a 12-microm-diameter sensitive area and operates with an overvoltage above breakdown adjustable up to 20 V. With a 5-V overvoltage the photon detection efficiency peaks above 40% around 500 nm, and the dark-counting rate is lower than 600 counts/s at room temperature. The overall counting dead time is 33 ns.     

Surface Josephson plasma waves in layered superconductors

We predict the existence of surface waves in layered superconductors in the THz frequency range, below the Josephson plasma frequency omega J. This wave propagates along the vacuum-superconductor interface and dampens in both transverse directions out of the surface (i.e., towards the superconductor and towards the vacuum). This is the first prediction of propagating surface waves in any superconductor. These predicted surface Josephson plasma waves are important for different phenomena, including the complete suppression of the specular reflection from a sample (Wood's anomalies) and a huge enhancement of the wave absorption (which can be used as a THz detector).     

Deterministic controlled-NOT gate for single-photon two-qubit quantum logic

We demonstrate a robust implementation of a deterministic linear-optical controlled-not gate for single-photon two-qubit quantum logic. A polarization Sagnac interferometer with an embedded 45 degrees -oriented dove prism is used to enable the polarization control qubit to act on the momentum (spatial) target qubit of the same photon. The optical controlled-not gate requires no active stabilization because the two spatial modes share a common path, and it is used to entangle the polarization and momentum qubits.     

Controlling the motion of magnetic flux quanta

We study the transport of vortices in superconductors with triangular arrays of boomerang- or V-shaped asymmetric pinning wells, when applying an alternating electrical current. The asymmetry of the pinning landscape induces a very efficient "diode" effect, that allows the sculpting at will of the magnetic field profile inside the sample. We present the first quantitative study of magnetic "lensing" of fluxons inside superconductors. Our proposed vortex lens provides a near threefold increase of the vortex density at its "focus" regions. The main numerical features have been derived analytically.