Subresultants in multiple roots: an extremal case

We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x-\alpha)^m and (x-\beta)^n with respect to the set of Bernstein polynomials \{(x-\alpha)^j(x-\beta)^{d-j}, \, 0\le j\le d\}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.Comment: 18 pages, uses elsart. Revised version accepted for publication at Linear Algebra and its Application

Modellare lo scavo archeologico: esperienze e tecniche a confronto

By examining the potential offered by the digital survey, the article aims at encourag¬ing archaeologists to undertake a more rational approach towards three-dimensional data acquisition and management. Data was derived from excavations at Aveia (AQ - Italy) and Seglamen (Ethiopia). The 3D data-capture was achieved with the laser scanner and structure from motion techniques that make it possible to obtain a point cloud of an object from a sequence of photographic images, which are neither ordered nor calibrated. The conclusions reflect the role of digital technologies in the field of stratigraphic survey. Independence from scale and the ability to extract profiles and contours of stratigraphic units are factors of great importance for a virtual reconstruction of archaeological excavations

Polariton-polariton scattering in microcavities: A microscopic theory

We apply the fermion commutation technique for composite bosons to polariton-polariton scattering in semiconductor planar microcavities. Derivations are presented in a simple and physically transparent fashion. A procedure of orthogonolization of the initial and final two-exciton state wavefunctions is used to calculate the effective scattering matrix elements and the scattering rates. We show how the bosonic stimulation of the scattering appears in this full fermionic approach whose equivalence to the bosonization method is thus demonstrated in the regime of low exciton density. We find an additional contribution to polariton-polariton scattering due to the exciton oscillator strength saturation, which we analyze as well. We present a theory of the polariton-polariton scattering with opposite spin orientations and show that this scattering process takes place mainly via dark excitonic states. Analytical estimations of the effective scattering amplitudes are given.Comment: Theoretical paper on polariton-polariton scattering in planar microcavities. The new version contains a slightly modified abstract and a revised introduction. Typos have been corrected wherever spotted. 16 page

Excitonic Effects in Quantum Wires

We review the effects of Coulomb correlation on the linear and non-linear optical properties of semiconductor quantum wires, with emphasis on recent results for the bound excitonic states. Our theoretical approach is based on generalized semiconductor Bloch equations, and allows full three-dimensional multisubband description of electron-hole correlation for arbitrary confinement profiles. In particular, we consider V- and T-shaped structures for which significant experimental advances were obtained recently. Above band gap, a very general result obtained by this approach is that electron-hole Coulomb correlation removes the inverse-square-root single-particle singularity in the optical spectra at band edge, in agreement with previous reports from purely one-dimensional models. Strong correlation effects on transitions in the continuum are found to persist also at high densities of photoexcited carriers. Below bandgap, we find that the same potential- (Coulomb) to kinetic-energy ratio holds for quite different wire cross sections and compositions. As a consequence, we identify a shape- and barrier-independent parameter that governs a universal scaling law for exciton binding energy with size. Previous indications that the shape of the wire cross-section may have important effects on exciton binding are discussed in the light of the present results.Comment: Proc. OECS-5 Conference, G\"ottingen, 1997 (To appear in Phys. Stat. Sol. (b)

Bidimensional ray tracing model for the underwater noise propagation prediction

An increasing attention has recently been paid to the effect of the underwater noise field generated by ship activities on the marine environment. Although this problem is widely discussed in international treaties and conventions, it has not yet found a consolidated technical-scientific treatment capable of quantifying the level of underwater noise emissions produced by naval systems. As part of a national research collaboration, a novel code has been developed to predict noise propagation according to the Ray Tracing approach. Such optical geometry-based technique allows for calculating the Transmission Loss (TL) trend in its respective contributions: geometrical loss (due to the distance between the source and receiver), dissipation loss (due to the characteristics of the propagation environment), and reflection loss (due to the surfaces that delimit the field). The simulation requires as input parameters the source info as spatial position, frequency, and sound pressure level (SPL) as well as the sea properties like seabed depth, the speed of sound profile, the layers thickness the water column is divided into, the sea salinity, temperature, and pH. The simulation code provides the SPL spatial distribution useful as a fast industrial tool in the future studies addressed to identify the emission limits for the protection of marine wildlife