Near-Infrared Time-Series Photometry in the Field of Cygnus OB2 Association I - Rotational Scenario For Candidate Members

In the last decades, the early pre main sequence stellar rotational evolution picture has been constrained by studies targeting different young regions at a variety of ages. Observational studies suggest a mass-rotation dependence, and for some mass ranges a connection between rotation and the presence of a circumstellar disk. Not still fully explored, though, is the role of environmental conditions on the rotational regulation. We investigate the rotational properties of candidate members of the young massive association Cygnus OB2. The Stetson variability index, Lomb-Scargle periodogram, Saunders statistics, string/rope length method, and visual verification of folded light curves were applied to select 1224 periodic variable stars. Completeness and contamination of the periodic sample was derived from Monte Carlo simulations, out of which 894 periods were considered reliable. Our study was considered reasonably complete for periods from 2 to 30 days. The general rotational scenario seen in other young regions is confirmed by Cygnus OB2 period distributions, with disked stars rotating on average slower than non-disked stars. A mass-rotation dependence was also verified, but as in NGC 6530, lower mass stars are rotating on average slower than higher mass stars, with an excess of slow rotators among the lower mass population. The effect of the environment on the rotational properties of the association was investigated by re-analysing the results while taking into account the incident UV radiation arising from O stars in the association. Results compatible with the disk-locking scenario were verified for stars with low UV incidence, but no statistical significant relation between rotation and disk presence was verified for stars with high UV incidence suggesting that massive stars can have an important role on regulating the rotation of nearby low mass stars.Comment: Submitted on December 23, 201

Near-infrared time-series photometry in the field of Cygnus OB2 association II. Mapping the variability of candidate members

We present the results of a J, H, and K photometric variability survey of the central 0.78 square degrees of the young OB association Cygnus OB2. We used data observed with the Wide-Field CAMera at the United Kingdom Infrared Telescope in 2007 (spanning 217 days) to investigate the light curves of 5083 low mass candidate members in the association and explore the occurrence and main characteristics of their near-infrared variability. We identified 2529 stars ($\sim$50$\%$ of the sample) with significant variability with time-scales ranging from days to months. We classified the variable stars into the following three groups according to their light curve morphology: periodic variability (1697 stars), occultation variability (124 stars), and other types of variability (726 stars). We verified that the disk-bearing stars in our sample are significantly more variable in the near-infrared than diskless stars, with a steep increase in the disk-fraction among stars with higher variability amplitude. We investigated the trajectories described by variable stars in the color-space and measured slopes for 335 stars describing linear trajectories. Based on the trajectories in the color-space, we inferred that the sample analyzed is composed of a mix of young stars presenting variability due to hot and cold spots, extinction by circumstellar material, and changes in the disk emission in the near-infrared. We contemplated using the use of near-infrared variability to identify disk-bearing stars and verified that 53.4$\%$ of the known disk-bearing stars in our sample could have been identified as such based solely on their variability. We present 18 newly identified disk-bearing stars and 14 eclipsing binary candidates among CygOB2 lower-mass members.Comment: 19 pages, 21 Figure

A Cauchy-Dirac delta function

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201

Stevin numbers and reality

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420

The VVV Templates Project. Towards an Automated Classification of VVV Light-Curves. I. Building a database of stellar variability in the near-infrared

Context. The Vista Variables in the V\'ia L\'actea (VVV) ESO Public Survey is a variability survey of the Milky Way bulge and an adjacent section of the disk carried out from 2010 on ESO Visible and Infrared Survey Telescope for Astronomy (VISTA). VVV will eventually deliver a deep near-IR atlas with photometry and positions in five passbands (ZYJHK_S) and a catalogue of 1-10 million variable point sources - mostly unknown - which require classifications. Aims. The main goal of the VVV Templates Project, that we introduce in this work, is to develop and test the machine-learning algorithms for the automated classification of the VVV light-curves. As VVV is the first massive, multi-epoch survey of stellar variability in the near-infrared, the template light-curves that are required for training the classification algorithms are not available. In the first paper of the series we describe the construction of this comprehensive database of infrared stellar variability. Methods. First we performed a systematic search in the literature and public data archives, second, we coordinated a worldwide observational campaign, and third we exploited the VVV variability database itself on (optically) well-known stars to gather high-quality infrared light-curves of several hundreds of variable stars. Results. We have now collected a significant (and still increasing) number of infrared template light-curves. This database will be used as a training-set for the machine-learning algorithms that will automatically classify the light-curves produced by VVV. The results of such an automated classification will be covered in forthcoming papers of the series.Comment: 12 pages, 16 figures, 3 tables, accepted for publication in A&A. Most of the data are now accessible through http://www.vvvtemplates.org

A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's foundational work associated with the work of Boyer and Grabiner; and to Bishop's constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint

Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond

Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley's criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz's infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz's defense of infinitesimals is more firmly grounded than Berkeley's criticism thereof. We show, moreover, that Leibniz's system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz's strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity.Comment: 69 pages, 3 figure

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

Open Problems on Central Simple Algebras

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered, compared to v