Time properties of the the rho-class burst of the microquasar GRS 1915+105 observed with BeppoSAX in April 1999

We present a temporal analysis of a BeppoSAX observation of GRS 1915+105 performed on April 13, 1999 when the source was in the rho class, which is characterised by quasi-regular bursting activity. The aim of the present work is to confirm and extend the validity of the results obtained with a BeppoSAX observation performed on October 2000 on the recurrence time of the burst and on the hard X-ray delay. We divided the entire data set into several series, each corresponding to a satellite orbit, and performed the Fourier and wavelet analysis and the limit cycle mapping technique using the count rate and the average energy as independent variables. We found that the count rates correlate with the recurrence time of bursts and with hard X-ray delay, confirming the results previously obtained. In this observation, however, the recurrence times are distributed along two parallel branches with a constant difference of 5.2+/-0.5 s.Comment: Accepted for publication in Section 7. Stellar structure and evolution of Astronomy and Astrophysic

Optical radiation background from 40^{40} K decays in undersea neutrino telescopes

The photon flux produced by light sources uniformly distributed in an infinite homogeneous medium is calculated on the basis of a known property of light propagation, taking into account the contribution of both absorption and scattering processes. The results are applied to the issue of the decays of $^{40}$ K content in sea salt and then to the rates detected by photomultipliers deployed in the deep sea. Numerical calculations are in agreement with the recent measurements performed in the Mediterranean Sea by the ANTARES and NEMO Collaborations

Lyapunov functions for a non-linear model of the X-ray bursting of the microquasar GRS 1915+105

This paper introduces a biparametric family of Lyapunov functions for a non-linear mathematical model based on the FitzHugh-Nagumo equations able to reproduce some main features of the X-ray bursting behaviour exhibited by the microquasar GRS 1915+105. These functions are useful to investigate the properties of equilibrium points and allow us to demonstrate a theorem on the global stability. The transition between bursting and stable behaviour is also analyzed.Comment: Published on International Journal of Non-Linear Mechanics, vol. 88, pp. 142-14

An Instrument for Describing Mathematical Curves

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The complex time behaviour of the microquasar GRS 1915+105 in the \rho-class observed with BeppoSAX. III: The hard X-ray delay and limit cycle mapping

The microquasar GRS1915+105 was observed by BeppoSAX in October 2000 for about ten days while the source was in \rho-mode, which is characterized by a quasi-regular type I bursting activity. This paper presents a systematic analysis of the delay of the hard and soft X-ray emission at the burst peaks. The lag, also apparent from the comparison of the [1.7-3.4] keV light curves with those in the [6.8-10.2] keV range, is evaluated and studied as a function of time, spectral parameters, and flux. We apply the limit cycle mapping technique, using as independent variables the count rate and the mean photon rate. The results using this technique were also cross-checked using a more standard approach with the cross-correlation methods. Data are organized in runs, each relative to a continuous observation interval. The detected hard-soft delay changes in the course of the pointing from about 3 s to about 10 s and presents a clear correlation with the baseline count rate.Comment: accepted for publication in A&

Semi-Teleparallel Theories of Gravitation

A class of theories of gravitation that naturally incorporates preferred frames of reference is presented. The underlying space-time geometry consists of a partial parallelization of space-time and has properties of Riemann-Cartan as well as teleparallel geometry. Within this geometry, the kinematic quantities of preferred frames are associated with torsion fields. Using a variational method, it is shown in which way action functionals for this geometry can be constructed. For a special action the field equations are derived and the coupling to spinor fields is discussed.Comment: 14 pages, LaTe

La formació històrica per a l’ensenyament de les matemàtiques

L’ensenyament i aprenentatge de la història de les matemàtiques pot millorar la formació integral de l’alumnat. Els contextos històrics en les matemàtiques transmeten als alumnes una percepció de la matemàtica com a ciència útil, dinàmica, humana, interdisciplinària i heurística. En aquesta comunicació mostrarem a través de la programació d’un curs d’història de la ciència els objectius que cal assolir. La formació del professorat ha de contemplar que aquest conegui les fonts en què es basa el coneixement del passat, reconegui els canvis més significatius de la disciplina de Matemàtiques i reflexionin sobre el desenvolupament del pensament matemàtic i les transformacions de la filosofia natural. Finalment, cal assenyalar en aquesta formació la importància de les relacions socioculturals de les matemàtiques

Determination of Wave Function Functionals: The Constrained-Search--Variational Method

In a recent paper [Phys. Rev. Lett. \textbf{93}, 130401 (2004)], we proposed the idea of expanding the space of variations in variational calculations of the energy by considering the approximate wave function $\psi$ to be a functional of functions $\chi: \psi = \psi[\chi]$ rather than a function. The space of variations is expanded because a search over the functions $\chi$ can in principle lead to the true wave function. As the space of such variations is large, we proposed the constrained-search-- variational method whereby a constrained search is first performed over all functions $\chi$ such that the wave function functional $\psi[\chi]$ satisfies a physical constraint such as normalization or the Fermi-Coulomb hole sum rule, or leads to the known value of an observable such as the diamagnetic susceptibility, nuclear magnetic constant or Fermi contact term. A rigorous upper bound to the energy is then obtained by application of the variational principle. A key attribute of the method is that the wave function functional is accurate throughout space, in contrast to the standard variational method for which the wave function is accurate only in those regions of space contributing principally to the energy. In this paper we generalize the equations of the method to the determination of arbitrary Hermitian single-particle operators as applied to two-electron atomic and ionic systems. The description is general and applicable to both ground and excited states. A discussion on excited states in conjunction with the theorem of Theophilou is provided.Comment: 26 pages, 4 figures, 5 table