Two-Centered Magical Charge Orbits

We determine the two-centered generic charge orbits of magical N = 2 and maximal N = 8 supergravity theories in four dimensions. These orbits are classified by seven U-duality invariant polynomials, which group together into four invariants under the horizontal symmetry group SL(2,R). These latter are expected to disentangle different physical properties of the two-centered black-hole system. The invariant with the lowest degree in charges is the symplectic product (Q1,Q2), known to control the mutual non-locality of the two centers.Comment: 1+17 pages, 1 Table; v2: Eq. (3.23) corrected; v3: various refinements in text and formulae, caption of Table 1 expanded, Footnote and Refs. added. To appear on JHE

On Black Attractors in 8D and Heterotic/Type IIA Duality

Motivated by the study of black attractors in 8D supergravity with 16 supersymmetries, we use the field theory approach and 8D supersymmetry with non trivial central charges to shed light on the exact duality between heterotic string on T^2 and type IIA on real connected and compact surfaces {\Sigma}2. We investigate the two constraints that should be obeyed by {\Sigma}2 and give their solutions in terms of intersecting 2-cycles as well their classification using Dynkin diagrams of affine Kac-Moody algebras. It is shown as well that the moduli space of these dual theories is given by SO(1,1)x((SO(2,r+2))/(SO(2)xSO(r+2))) where r stands for the rank of the gauge symmetry G_{r} of the 10D heterotic string on T^2. The remarkable cases r=-2,-1,0 as well as other features are also investigated.Comment: LaTex, 18 pages, 2 figures, To appear in JHE

University students at work with mathematical machines to trace conics

This paper aims to investigate the way past experience with some tools to draw conics becomes part of the experience of designing a new drawer. In particular, it centres on the thinking processes of a group of university students who have the following task: to design a hyperbola drawer. The analysis is carried out using the perspectives of transfer of learning and instrumental approach, and focuses on utilization schemes and the interplay between scientific and technological aspects

Are mathematics students thinking as Kepler? Conics and mathematical machines

Our interest is the analysis of the thinking processes of some university students who worked on the design of a machine that uses a tightened thread to draw a hyperbola. Previously, the students worked with other machines for conics. We focus on the way past experience becomes part of a new experience, in which making of the machine is the end point of the task. This implies the presence of technological and scientific aspects, whose interplay is fundamental to shape thinking

FOLLOW-UP AFTER PEDIATRIC MYRINGOPLASTY: OUTCOME AT 5 YEARS

Aim. The aim of this paper was to evaluate anatomical and functional outcomes 5 years after myringoplasty in children affected by perforated eardrum. To analyze the main differences in the frequency of postoperative complications between patients under and over 9 years of age. Methods. One hundred and thirty-two children, aged from 4 to 15 years, who underwent myringoplasty with or without mastoidectomy, were followed for a five-year period after surgery. The cohort was divided in two groups: children from 4 to 9 years old (G1) and patients older than 9 years (G2); all subjects underwent a pre- and post-operatively clinical exam and were evaluated through audiometry and impedenzometry. Adenoidectomy, if necessary, was performed three months before myringoplasty. Results. Of the total 132 children of our cohort, the 32.58% were from 4 to 9 years old (G1) and the 67.42% were older than 9 years (G2). Twenty-five (58.13%) G1 and 2 (2.24%) G2 patients underwent adenoidectomy before myringoplasty (P<0.0001); in 18 (41.86%) G1 and 23 (25.84%) G2 subjects a mastoidetomy was associated to myringoplasty (P=0.062). The main postoperative complications observed were respectively retraction pockets (9.3%) and recurrent seromucous otitis (9.3%) in G1 group and myringosclerosis (4.4%) in G2 group. The GAP index (IG) resulted >2 (good-excellent degree) in the 89.36% of G1 and 91% of G2 children (P>0.5). Conclusion. Nevertheless good audiologic outcomes in patients under and over 9 years of age, our study evidenced a different percentages of success after myringoplasty in G1 and G2 groups (P=0.0024). Thus, considering the higher percentage of postoperative complications in children with less than 9 years of age, myringoplasty should be considered cautiously due to the risk of reperforation and/or cholesteatoma