The Collaboration of a Principal and a Mathematics Specialist

This article describes the importance of the collaboration between the principal, Patty Granada, and the Mathematics Specialist, Susan Garthwaite, in fostering a highly functioning mathematics program. While many aspects of the collaboration as facilitators for a mathematics program are logical, the messy aspects provide greater challenges. Through continued collaboration, they have come to embrace the messiness which has contributed to an awareness of similar belief systems in their roles. These beliefs include openness to learning and a sincere commitment to bringing out the best in students and teachers. The principal and the Mathematics Specialist share their continued journey in this collaborative relationship that is essential to the success of the mathematics program

The evolution of single B-type stars with a large angular momentum content

The database of intermediate mass rotating stellar models presented in the past years by the Geneva Stellar Evolution Group can be used to build synthetic stellar populations that fully account for the effects of stellar rotation. However, up to now we still lacked stellar evolutionary tracks that rotate close to the critical limit during the whole MS phase. This occurs because the flat internal profile of rotation imposed at the Zero-Age MS (ZAMS) is modified by the action of meridional currents immediately after the ZAMS, causing the surface rotational velocity to decrease abruptly until it reaches a quasi-stationary state. We compute stellar models with non-solid rotation at the ZAMS to obtain stellar evolutionary tracks with a larger content of angular momentum, that attain rotational equatorial velocities close to the critical limit throughout their MS phase. These models have a longer MS lifetime and a higher surface chemical enrichment already at the end of the MS, particularly at Z=0.002. Stellar models with solid rotation at the ZAMS adequately represent the overall characteristics and evolution of differentially rotating models of identical angular momentum content, but with a lower initial surface rotational velocity. For these models we recommend to use as the initial rotational rate the values derived once the quasi-stationary state is reached, after the abrupt decrease in surface velocity. Interestingly, the initial equatorial rotational velocities are virtually metallicity independent for the stellar models we computed with the same mass and angular momentum content at the ZAMS. If, as some observational evidence indicates, B-type stars at Z=0.002 rotate with a higher equatorial velocity at the ZAMS than stars with Z=0.014, our finding would indicate that the angular momentum content of B-type stars in the SMC is higher than their Galactic counterparts.Comment: 15 pages, Accepted for publication in A&

Infrared studies of the Be star X Per

Photometric and spectroscopic results are presented for the Be star X Per/HD 24534 from near-infrared monitoring in 2010-2011. The star is one of a sample of selected Be/X-ray binaries being monitored by us in the near-IR to study correlations between their X ray and near-IR behaviour. Comparison of the star's present near-IR magnitudes with earlier records shows the star to be currently in a prominently bright state with mean J, H, K magnitudes of 5.49, 5.33 and 5.06 respectively. The JHK spectra are dominated by emission lines of HeI and Paschen and Brackett lines of HI. Lines of OI 1.1287 and 1.3165 micron are also present and their relative strength indicates, since OI 1.1287 is stronger among the two lines, that Lyman beta fluorescence plays an important role in their excitation. Recombination analysis of the HI lines is done which shows that the Paschen and Brackett line strengths deviate considerably from case B predictions. These deviations are attributed to the lines being optically thick and this supposition is verified by calculating the line center optical depths predicted by recombination theory. Similar calculations indicate that the Pfund and Humphrey series lines should also be expected to be optically thick which is found to be consistent with observations reported in other studies. The spectral energy distribution of the star is constructed and shown to have an infrared excess. Based on the magnitude of the IR excess, which is modeled using a free-free contribution from the disc, the electron density in the disc is estimated and shown to be within the range of values expected in Be star discs.Comment: Accepted for publication in MNRAS, 7 pages, 6 figure

Guarding the border: watchtowers of the Nasrid Kingdom of Granada. Characterization and vulnerability assessment

RUIZ-JARAMILLO, J. y GARCÍA-PULIDO, L.J., 2018. Guarding the border: watchtowers of the Nasrid Kingdom of Granada. Characterization and vulnerability assessment. Heritage 2018: 6th International Conference on Heritage and Sustainable Development. Granada: Green Lines Institute for Sustainable Development, pp. 1511-1518The Islamic Nasrid kingdom of Granada occupied the mountainous areas of the south-eastern of the Iberian Peninsula. The frontier between the Nasrid kingdom and the Christian kingdom of Castile from 1232 to 1492 was controlled by an extensive network of watchtowers built by Nasrid through the provinces of Granada, Malaga, Almeria and the eastern parts of Jaen, Cordoba and Cadiz. They allowed controlling this frontier stablishing visual communication between them and the Nasrid centre at the Alhambra citadel. Even protected by Spanish Heritage law, many of these medieval towers and their cultural landscapes are in severe risk be-cause of anthropic action as well as natural deterioration. Within the framework of the R&D project called ‘Las atalayas que defendieron el reino nazarí de Granada. Análisis y docu-mentación científica (Nazalaya)”, the towers are being studied. As a complement of planimetry obtained by procedures as photogrammetry or terrestrial laser scanning (TLS), complete architectural surveys using non-destructive techniques are being performed as part of the analysis to obtain a global description of construction systems used.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Globalized justice - fragmented justice. Human rights violations by "private" transnational actors

Plenarvortrag Weltkongress der Rechtsphilosophie und Sozialphilosophie, 24.-29. Mai, Granada 2005. S.a. die deutsche Fassung: "Die anonyme Matrix: Menschenrechtsverletzungen durch "private" transnationale Akteure". Spanische Fassung: Sociedad global, justicia fragmentada: sobre la violatión de los derechos humanos por actores transnacionales 'privados'. In: Manuel Escamilla and Modesto Saavedra (eds.), Law and Justice in a global society, International Association for philosophy of law and social philosophy, Granada 2005, S. 529-546

Sociophysics Simulations II: Opinion Dynamics

Individuals have opinions but can change them under the influence of others. The recent models of Sznajd (missionaries), of Deffuant et al. (negotiators), and of Krause and Hegselmann (opportunists) are reviewed here, while the voter and Ising models, Galam's majority rule and the Axelrod multicultural model were dealt with by other lecturers at this 8th Granada Seminar.Comment: 18 pages including 9 figs., for 8th Granada seminar (AIP Conf.Proc.

Predictive dynamical and stochastic systems

We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how far ahead in time to make them. We also report that noise can induce oscillatory behavior, which we call "predictive stochastic resonance".Comment: Presented and To appear in the Proc. of 9th Granada Seminar, (Granada, Spain, September 11-15, 2006