Hadron resonances generated from the dynamics of the lightest scalar ones

We have studied the interactions of the scalar resonances f_0(980) and a_0(980) with the vector resonance \phi(1020) and with the lightest pseudoscalars \pi, K, \eta and \eta'. We first obtain the interaction kernels without including any new free parameter. Afterwards, the interaction kernels are unitarized and the final S-wave amplitudes result. We find that these interactions are very rich and generate a large amount of pseudoscalar resonances including the K(1460), \pi(1300), \pi(1800), \eta(1475) and X(1835) resonances. The f_0(980)\phi(1020) self-interactions give rise to the \phi(2170) resonance. For realistic choices of the parameters we also obtain an isovector companion in the same mass region from the a_0(980) \phi(1020) interactions.Comment: 4 pafes, 4 figures. Invited talk at QCD 10 (25th anniversary), 15th International QCD Conference, 28th June - 3rd July 2010 Montpellier (France). To be published in Nucl. Phys. B (Proc. Suppl.

Conceptions about mathematics, its teaching and learning in Compendio Mathematico (1707) written by the Spanish Thomas Vicente Tosca (1651-1723)

The preface of a book is one of the main examples of paratexts, defined by Gérard Genette as those devices and conventions that enable a text to become a book. It can provide information about aspects such as the author''s motivation and intention, the origin of the presented ideas, the potential readers, etc. In the particular case of a mathematical text devoted to some extent to teaching, the preface can provide information about the author''s conceptions and beliefs about mathematics, its teaching and learning. In this work, we analyze the preface of Compendio Mathematico written by Thomas Vicente Tosca in 1707. This approach will allow us to have a view of how the teaching and learning of mathematics as well as mathematics itself were conceived during Spanish pre-enlightenment. O prólogo de um livro é um dos múltiplos exemplos de paratextos, definidos por Gérard Genette como esses elementos e convenções que fazem um texto tornar-se um livro. Isso pode fornecer informações sobre aspectos como a motivação e a intenção do autor, a origem das ideias apresentadas, potenciais leitores etc. No caso particular de textos matemáticos dedicados em certa medida ao ensino, o prólogo pode informar as concepções e crenças do autor sobre a matemática, seu ensino e sua aprendizagem. Neste trabalho, analisamos o prólogo do Compendio Mathematico, escrito por Thomas Vicente Tosca em 1707. Essa abordagem nos permitirá obter uma visão sobre como a matemática, seu ensino e sua aprendizagem foi concebida durante a pré-ilustração na Espanha

On the diameter of the commuting graph of the full matrix ring over the real numbers

In a recent paper C. Miguel proved that the diameter of the commuting graph of the matrix ring Mn(R) is equal to 4 if either n = 3 or n = 5. But the case n = 4 remained open, since the diameter could be 4 or 5. In this work we close the problem showing that also in this case the diameter is 4

Characterization of behavior of correctors when grading mathematics tests

In this work, we present some results obtained from the analysis of the behavior of 91 mathematics teachers (prospective, secondary education and university) when they grade three different types of correct answers to a classical high school problem through a questionnaire. In addition to a descriptive analysis that studies the variability and the interrater reliability, we analyze the role of experience and training as well as the influence of the different solving methods. Furthermore, we try to identify profiles of correctors among secondary education teachers using both quantitative (cluster analysis) and qualitative (content analysis) methods. In particular, we observe a great variability on the assigned grades as well as a low interrater reliability. The belonging to a particular group has impact over the assigned rates while experience has no significant influence. The grades are higher when methods closer to the corrector are used. Finally, we have been able to identify three different clusters, which are determined by the comments and actions regarding three aspects of the students’ answers: argumentation, correctness and method

Relativistic chiral representation of the πN\pi N scattering amplitude I: The Goldberger-Treiman relation

In this work we study the $\pi N$ scattering process within the Baryon Chiral Perturbation Theory framework in the covariant scheme of Extended-On-Mass-Shell (EOMS). We compare the description obtained in this scheme with the previously obtained using the Infrared Regularization scheme and show that EOMS accomplishes the best convergence, being able to extract from partial wave analyses reliable values of important quantities as the Goldberger-Treiman deviation. In regard to the latter, we solve the long-standing problem concerning to the extraction of the Goldberger-Treiman deviation with covariant ChPT that jeopardized the applicability of ChPT to the $\pi N$ system. We also show the potential of the unitarization techniques applied to the perturbative calculation in the EOMS scheme, that allow us to increase the range of validity of our description up to $\approx 200$ MeV in $\sqrt{s}$.Comment: PROCEEDINGS to the 33rd International School of Nuclear Physics "From Quarks and Gluons to Hadrons and Nuclei"- 7 Pag,, 1 Table, 4 Figures. Erice-Sicily: 16 - 24 September 201

El Grup de Concurrència i Temps Real col·labora amb la branca d'estudiants de l'IEEE

Peer Reviewe

Diseño e implementación de tareas de alta demanda cognitiva basadas en la sucesión look and say

Pese a que su tratamiento escolar usual se centra en aspectos principalmente de cálculo, las sucesiones son un tópico matemático con el potencial para desarrollar en los alumnos aspectos del razonamiento matemático. En este trabajo se diseña una secuencia de tareas de alta demanda cognitiva basadas en la sucesión ‘look and say’ y se implementa en un grupo de secundaria con especial interés por las matemáticas durante una sesión del Taller de Talento Matemático en la Universidad de Zaragoza. La metodología es exploratoria y descriptiva con análisis mixto de datos cualitativos. Los alumnos participantes resolvieron las tareas con un alto grado de éxito y surgieron bastantes respuestas de gran riqueza conceptual. Estas tareas pueden ser útiles para trabajar aspectos transversales del currículo e identificar alumnos con altas capacidades matemáticas. Even though their school treatment is mainly based on calculations, numerical sequences are a mathematical topic with the potential to develop aspects of mathematical reasoning amongststudents.In this work, we design a sequence of tasksofcognitive high-demandbased on the ‘look and say’se-quence andimplement them with a group of secondary schoolstudents particularly interested in math-ematics during a session of the Workshop of Mathematical Talent at the University of Zaragoza.The methodology is exploratory and descriptive with mixedanalysis of qualitative data.Participants solved the taskswith a high rate of success and several answers were ofhigh conceptual richness. Thesetasksmight be useful to work transversal curricular aspectsand to identifythosemathematically gifted

Sliding window multi-curve resolution: application to gas chromatography - ion mobility spectrometry

Blind source separation (BSS) techniques aim to extract a set of source signals from a measured mixture in an unsupervised manner. In the chemical instrumentation domain source signals typically refer to time-varying analyte concentrations, while the measured mixture is the set of observed spectra. Several techniques exist to perform BSS on ion mobility spectrometry, being simple-to-use interactive self-modelling mixture analysis (SIMPLISMA) and multivariate curve resolution (MCR) the most commonly used. The addition of a multi-capillary gas chromatography column using the ion mobility spectrometer as detector has been proposed in the past to increase chemical resolution. Short chromatography times lead to high levels of co-elution, and ion mobility spectra are key to resolve them. For the first time, BSS techniques are used to deconvolve samples of the gas chromatography-ion mobility spectrometry tandem. We propose a method to extract spectra and concentration profiles based on the application of MCR in a sliding window. Our results provide clear concentration profiles and pure spectra, resolving peaks that were not detected by the conventional use of MCR. The proposed technique could also be applied to other hyphenated instruments with similar strong co-elutions

Rescattering and chiral dynamics in B\to \rho\pi decay

We examine the role of B^0(\bar B^0) \to \sigma \pi^0 \to \pi^+\pi^- \pi^0 decay in the Dalitz plot analysis of B^0 (\bar B^0) \to \rho\pi \to \pi^+\pi^-\pi^0 decays, employed to extract the CKM parameter \alpha. The \sigma \pi channel is significant because it can break the relationship between the penguin contributions in B\to\rho^0\pi^0, B\to\rho^+\pi^-, and B\to\rho^-\pi^+ decays consequent to an assumption of isospin symmetry. Its presence thus mimics the effect of isospin violation. The \sigma\pi^0 state is of definite CP, however; we demonstrate that the B\to\rho\pi analysis can be generalized to include this channel without difficulty. The \sigma or f_0(400-1200) ``meson'' is a broad I=J=0 enhancement driven by strong \pi\pi rescattering; a suitable scalar form factor is constrained by the chiral dynamics of low-energy hadron-hadron interactions - it is rather different from the relativistic Breit-Wigner form adopted in earlier B\to\sigma\pi and D\to\sigma\pi analyses. We show that the use of this scalar form factor leads to an improved theoretical understanding of the measured ratio Br(\bar B^0 \to \rho^\mp \pi^\pm) / Br(B^-\to \rho^0 \pi^-).Comment: 26 pages, 8 figs, published version. typos fixed, minor change