On the stability of circular orbits in galactic dynamics: Newtonian thin disks

The study of off-equatorial orbits in razor-thin disks is still in its beginnings. Contrary to what was presented in the literature in recent publications, the vertical stability criterion for equatorial circular orbits cannot be based on the vertical epicyclic frequency, because of the discontinuity in the gravitational field on the equatorial plane. We present a rigorous criterion for the vertical stability of circular orbits in systems composed by a razor-thin disk surrounded by a smooth axially symmetric distribution of matter, the latter representing additional structures such as thick disk, bulge and (dark matter) halo. This criterion is satisfied once the mass surface density of the thin disk is positive. Qualitative and quantitative analyses of nearly equatorial orbits are presented. In particular, the analysis of nearly equatorial orbits allows us to construct an approximate analytical third integral of motion in this region of phase-space, which describes the shape of these orbits in the meridional plane.Comment: 3 pages, 1 figure. In Proceedings of the MG13 Meeting on General Relativity, Stockholm University, Sweden, 1-7 July 2012. World Scientific, Singapore. Based on arXiv:1206.6501. in The Thirteenth Marcel Grossmann Meeting: On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories (In 3 Volumes), chap. 438, pages 2346-2348 (2015

Vertical stability of circular orbits in relativistic razor-thin disks

During the last few decades, there has been a growing interest in exact solutions of Einstein equations describing razor-thin disks. Despite the progress in the area, the analytical study of geodesic motion crossing the disk plane in these systems is not yet so developed. In the present work, we propose a definite vertical stability criterion for circular equatorial timelike geodesics in static, axially symmetric thin disks, possibly surrounded by other structures preserving axial symmetry. It turns out that the strong energy condition for the disk stress-energy content is sufficient for vertical stability of these orbits. Moreover, adiabatic invariance of the vertical action variable gives us an approximate third integral of motion for oblique orbits which deviate slightly from the equatorial plane. Such new approximate third integral certainly points to a better understanding of the analytical properties of these orbits. The results presented here, derived for static spacetimes, may be a starting point to study the motion around rotating, stationary razor-thin disks. Our results also allow us to conjecture that the strong energy condition should be sufficient to assure transversal stability of periodic orbits for any singular timelike hypersurface, provided it is invariant under the geodesic flow.Comment: 13 pages, 4 figures; Accepted for publication in Physical Review

Enhancing web supported learning in higher education by adding a management layer to LMSs

There are many situations in the e-Learning experiences that can compromise the success of the courses. Many times simple reasons are great enough to motivate people to abandon them. For example, if someone does not execute a programmed activity inside the defined window of time, it can compromise the rest of the course to that person. In such situations it would be important that the teacher knew about the situation in useful time, to be able to take any corrective action. Another example could be presented, involving the professor and the learners. Let us assume that an activity A2 is programmed to be executed by the learners and that it depends on the previous knowledge of the result of the evaluation of a work submitted by the learners to the teacher (activity A1). If the teacher doesn’t inform the learners about their classification in useful time, that can compromise the execution of the activity A2. It seems to be necessary to use mechanisms of automatic management, in real time, of the envolvement of each participant in a distance learning course using LMS (Learning Management System). Such a functionality allows the detection of deviations to the scheduled activities planned for each actor. If it is the case, the referred mechanism can initiate the process of sending notifications to the relevant entities, enabling the correction of these deviations. Several organizations and consortiuns, involving the industry, governmental institutions and universities, are developing projects of standardization. It seemed important to us to see how the referred aspects were covered by those projects, and to perceive how it could be possible to articulate our work with the ones that are available from these organizations and consortiuns. This article describes the work that the authors are developing towards the specification of a layer for real-time management of user interactions with LMSs, during the operationalization of a course, and also includes a management meta-data model, related to that management layer

Fuzzy Sets Across the Natural Language Generation Pipeline

We explore the implications of using fuzzy techniques (mainly those commonly used in the linguistic description/summarization of data discipline) from a natural language generation perspective. For this, we provide an extensive discussion of some general convergence points and an exploration of the relationship between the different tasks involved in the standard NLG system pipeline architecture and the most common fuzzy approaches used in linguistic summarization/description of data, such as fuzzy quantified statements, evaluation criteria or aggregation operators. Each individual discussion is illustrated with a related use case. Recent work made in the context of cross-fertilization of both research fields is also referenced. This paper encompasses general ideas that emerged as part of the PhD thesis "Application of fuzzy sets in data-to-text systems". It does not present a specific application or a formal approach, but rather discusses current high-level issues and potential usages of fuzzy sets (focused on linguistic summarization of data) in natural language generation.Comment: Paper features: 16 pages, 2 tables, 13 figure