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

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

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

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)

Prognostic significance of primary-tumor extension, stage and grade of nuclear differentiation in patients with renal cell carcinoma

Surgery remains the preferred therapy for renal cell carcinoma. The various adjunctive or complementary therapies currently yield disappointing results. Identifying reliable prognostic factors could help in selecting patients most likely to benefit from postoperative adjuvant therapies. We reviewed the surgical records of 78 patients who had undergone radical nephrectomy with lymphadenectomy for renal cell carcinoma, matched for type of operation and histology. According to staging (TNM), 5.1% of the patients were classified as stage I, 51.3% as stage II, 29.5% as stage III and 14.5% as stage IV. Of the 78 patients 40 were T2N0 and 21 T3aN0. Tumor grading showed that 39.7% of the patients had well-differentiated tumors(G1), 41.1% moderately-differentiated (G2), and 19.2% poorly-differentiated tumors (G3). Overall actuarial survival at 5 and 10 years was 100% for stage 1; 91.3% at 5 years and 83.1% at 10 years for stage II; 45.5% and 34.1% for stage III; and 29.1% and nil for stage IV (stage II vs stage III p = 0.0001). Patients with tumors confined to the kidney (pT2N0) had better 5- and 10-year survival rates than patients with tumors infiltrating the perirenal fat (pT3aN0) (p = 0.000006). Survival differed according to nuclear grading (G1 vs G3 ; p = 0.000005; G2 vs G3; p = 0.0009). In conclusion our review identified tumor stage, primary-tumor extension, and the grade of nuclear differentiation as reliable prognostic factors in patients with renal cell carcinomas