Actitudes hacia las matemáticas y el trabajo con resolución de problemas de profesores que asistieron el curso “pró-letramento”

El objetivo de este trabajo es investigar cómo las actitudes hacia las matemáticas influyen en la práctica pedagógica en el trabajo con resolución de problemas de los profesores que asistieron al curso de formación continua del "Pró-Letramento". La investigación se basa, principalmente, en estudios de Brito (1996, 2006) que abordan temas tales como la resolución de problemas y actitudes hacia las matemáticas. El “Pró-Letramento” fue un programa de formación continua, en Brazil, para profesores en los primeros años de la escuela primaria interesados en mejorar la calidad del aprendizaje en la lectura/escritura de la Lengua Portuguesa y de las Matemáticas

Brill-Noether loci for divisors on irregular varieties

WetakeupthestudyoftheBrill–NoetherlociWr(L,X):={η∈Pic0(X)|h0(L⊗η) ≥ r + 1}, where X is a smooth projective variety of dimension > 1, L ∈ Pic(X), and r ≥ 0 is an integer. By studying the infinitesimal structure of these loci and the Petri map (defined in analogy with the case of curves), we obtain lower bounds for h0(KD), where D is a divisor that moves linearly on a smooth projective variety X of maximal Albanese dimension. In this way we sharpen the results of [Xi] and we generalize them to dimension > 2. In the 2-dimensional case we prove an existence theorem: we define a Brill–Noether number ρ(C, r) for a curve C on a smooth surface X of maximal Albanese dimension and we prove, under some mild additional assumptions, that if ρ(C,r) ≥ 0 then Wr(C,X) is nonempty of dimension ≥ ρ(C,r). Inequalities for the numerical invariants of curves that do not move linearly on a surface of maximal Albanese dimension are obtained as an application of the previous results

On the dimension of Voisin sets in the moduli space of abelian varieties

We study the subsets $V_k(A)$ of a complex abelian variety $A$ consisting in the collection of points $x\in A$ such that the zero-cycle $\{x\}-\{0_A\}$ is $k$-nilpotent with respect to the Pontryagin product in the Chow group. These sets were introduced recently by Voisin and she showed that $\dim V_k(A) \leq k-1$ and $V_k(A)$ is countable for a very general abelian variety of dimension at least $2k-1$. We study in particular the locus $\mathcal V_{g,2}$ in the moduli space of abelian varieties of dimension $g$ with a fixed polarization, where $V_2(A)$ is positive dimensional. We prove that an irreducible subvariety $\mathcal Y \subset \mathcal V_{g,2}$, $g\ge 3$, such that for a very general $y \in \mathcal Y$ there is a curve in $V_2(A_y)$ generating $A$ satisfies $\dim \mathcal Y \le 2g - 1.$ The hyperelliptic locus shows that this bound is sharp.Comment: Final version to appear in Mathematische Annale

Hyperelliptic Jacobians and isogenies

In this note we mainly consider abelian varieties isogenous to hyperelliptic Jacobians. In the first part we prove that a very general hyperelliptic Jacobian of genus is not isogenous to a non-hyperelliptic Jacobian. As a consequence we obtain that the intermediate Jacobian of a very general cubic threefold is not isogenous to a Jacobian. Another corollary tells that the Jacobian of a very general d-gonal curve of genus is not isogenous to a different Jacobian. In the second part we consider a closed subvariety of the moduli space of principally polarized varieties of dimension . We show that if a very general element of is dominated by the Jacobian of a curve C and , then C is not hyperelliptic. In particular, if the general element in is simple, its Kummer variety does not contain rational curves. Finally we show that a closed subvariety of dimension such that the Jacobian of a very general element of is dominated by a hyperelliptic Jacobian is contained either in the hyperelliptic or in the trigonal locus

On the canonical map of surfaces with q>=6

We carry out an analysis of the canonical system of a minimal complex surface of general type with irregularity q>0. Using this analysis we are able to sharpen in the case q>0 the well known Castelnuovo inequality K^2>=3p_g+q-7. Then we turn to the study of surfaces with p_g=2q-3 and no fibration onto a curve of genus >1. We prove that for q>=6 the canonical map is birational. Combining this result with the analysis of the canonical system, we also prove the inequality: K^2>=7\chi+2. This improves an earlier result of the first and second author [M.Mendes Lopes and R.Pardini, On surfaces with p_g=2q-3, Adv. in Geom. 10 (3) (2010), 549-555].Comment: Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in the special issue of Science of China Ser.A: Mathematics dedicated to him. V2:some typos have been correcte

Parameterized Complexity of the k-anonymity Problem

The problem of publishing personal data without giving up privacy is becoming increasingly important. An interesting formalization that has been recently proposed is the $k$-anonymity. This approach requires that the rows of a table are partitioned in clusters of size at least $k$ and that all the rows in a cluster become the same tuple, after the suppression of some entries. The natural optimization problem, where the goal is to minimize the number of suppressed entries, is known to be APX-hard even when the records values are over a binary alphabet and $k=3$, and when the records have length at most 8 and $k=4$ . In this paper we study how the complexity of the problem is influenced by different parameters. In this paper we follow this direction of research, first showing that the problem is W[1]-hard when parameterized by the size of the solution (and the value $k$). Then we exhibit a fixed parameter algorithm, when the problem is parameterized by the size of the alphabet and the number of columns. Finally, we investigate the computational (and approximation) complexity of the $k$-anonymity problem, when restricting the instance to records having length bounded by 3 and $k=3$. We show that such a restriction is APX-hard.Comment: 22 pages, 2 figure

System Level Analysis of Millimetre-wave GaN-based MIMO Radar for Detection of Micro Unmanned Aerial Vehicles

The detection of Unmanned Aerial Vehicles (UAVs) of micro/nano dimensions, is becoming a hot topic, due to their large diffusion, and represents a challenging task from both the system architecture and components point of view. The Frequency Modulated Continuous Wave (FMCW) radar architecture in a Multi-Input Multi-Output configuration has been identified as the most suitable solution for this purpose, due to both its inherent short-range detection capability and compact implementation. This paper describes the operation and technology challenges inherent to the development of a millimeter-wave FMCW MIMO radar for small UAVs detection. In particular it analyzes the sub-systems specifications and the expected system performance with respect to a chip set designed and developed in GaN at 37.5 GHz applications