A note on the convexity number for complementary prisms

In the geodetic convexity, a set of vertices $S$ of a graph $G$ is $\textit{convex}$ if all vertices belonging to any shortest path between two vertices of $S$ lie in $S$. The cardinality $con(G)$ of a maximum proper convex set $S$ of $G$ is the $\textit{convexity number}$ of $G$. The $\textit{complementary prism}$ $G\overline{G}$ of a graph $G$ arises from the disjoint union of the graph $G$ and $\overline{G}$ by adding the edges of a perfect matching between the corresponding vertices of $G$ and $\overline{G}$. In this work, we we prove that the decision problem related to the convexity number is NP-complete even restricted to complementary prisms, we determine $con(G\overline{G})$ when $G$ is disconnected or $G$ is a cograph, and we present a lower bound when $diam(G) \neq 3$.Comment: 10 pages, 2 figure

X-ray powder diffraction of high-absorption materials at the XRD1 beamline off the best conditions: Application to (Gd,Nd)5Si4 compounds

Representative compounds of the new family of magnetic materials Gd5-xNdxSi4 were analyzed by X-ray diffraction at the XRD1 beamline at LNLS. To reduce X-ray absorption, thin layers of the powder samples were mounted outside the capillaries and measured in Debye-Scherrer geometry as usual. The X-ray diffraction analyses and the magnetometry results indicate that the behavior of the magnetic transition temperature as a function of Nd content may be directly related to the average of the four smallest interatomic distances between different rare earth sites of the majority phase of each compound. The quality and consistency of the results show that the XRD1 beamline is able to perform satisfactory X-ray diffraction experiments on high-absorption materials even off the best conditions.Comment: 12 pages, 3 figures, 3 table

Born-Infeld magnetars: larger than classical toroidal magnetic fields and implications for gravitational-wave astronomy

Magnetars are neutron stars presenting bursts and outbursts of X- and soft-gamma rays that can be understood with the presence of very large magnetic fields. Thus, nonlinear electrodynamics should be taken into account for a more accurate description of such compact systems. We study that in the context of ideal magnetohydrodynamics and make a realization of our analysis to the case of the well-known Born-Infeld (BI) electromagnetism in order to come up with some of its astrophysical consequences. We focus here on toroidal magnetic fields as motivated by already known magnetars with low dipolar magnetic fields and their expected relevance in highly magnetized stars. We show that BI electrodynamics leads to larger toroidal magnetic fields when compared to Maxwell's electrodynamics. Hence, one should expect higher production of gravitational waves (GWs) and even more energetic giant flares from nonlinear stars. Given current constraints on BI's scale field, giant flare energetics and magnetic fields in magnetars, we also find that the maximum magnitude of magnetar ellipticities should be $10^{-6}-10^{-5}$. Besides, BI electrodynamics may lead to a maximum increase of order $10\%-20\%$ of the GW energy radiated from a magnetar when compared to Maxwell's, while much larger percentages may arise for other physically motivated scenarios. Thus, nonlinear theories of the electromagnetism might also be probed in the near future with the improvement of GW detectors.Comment: 8 pages, no figures, accepted for publication in The European Physical Journal C (EPJC

A grid of Synthetic Spectra for Hot DA White Dwarfs and Its Application in Stellar Population Synthesis

In this work we present a grid of LTE and non-LTE synthetic spectra of hot DA white dwarfs (WDs). In addition to its usefulness for the determination of fundamental stellar parameters of isolated WDs and in binaries, this grid will be of interest for the construction of theoretical libraries for stellar studies from integrated light. The spectral grid covers both a wide temperature and gravity range, with 17,000 K <= T_eff <= 100,000 K and 7.0 <= log(g) <= 9.5. The stellar models are built for pure hydrogen and the spectra cover a wavelength range from 900 A to 2.5 microns. Additionally, we derive synthetic HST/ACS, HST/WFC3, Bessel UBVRI and SDSS magnitudes. The grid was also used to model integrated spectral energy distributions of simple stellar populations and our modeling suggests that DAs might be detectable in ultraviolet bands for populations older than ~8 Gyr.Comment: to be published in The Astrophysical Journal Supplement Serie

On the nature of some SGRs and AXPs as rotation-powered neutron stars

We investigate the possibility that some SGRs/AXPs could be canonical rotation-powered pulsars using realistic NS structure parameters instead of fiducial values. We show that realistic NS parameters lowers the estimated value of the magnetic field and radiation efficiency, $L_X/\dot{E}_{\rm rot}$, with respect to estimates based on fiducial NS parameters. We show that nine SGRs/AXPs can be described as canonical pulsars driven by the NS rotational energy, for $L_X$ computed in the soft (2--10~keV) X-ray band. We compute the range of NS masses for which $L_X/\dot{E}_{\rm rot}<1$. We discuss the observed hard X-ray emission in three sources of the group of nine potentially rotation-powered NSs. This additional hard X-ray component dominates over the soft one leading to $L_X/\dot{E}_{\rm rot}>1$ in two of them. We show that 9 SGRs/AXPs can be rotation-powered NSs if we analyze their X-ray luminosity in the soft 2--10~keV band. Interestingly, four of them show radio emission and six have been associated with supernova remnants (including Swift J1834.9-0846 the first SGR observed with a surrounding wind nebula). These observations give additional support to our results of a natural explanation of these sources in terms of ordinary pulsars. Including the hard X-ray emission observed in three sources of the group of potential rotation-powered NSs, this number of sources with $L_X/\dot{E}_{\rm rot}<1$ becomes seven. It remains open to verification 1) the accuracy of the estimated distances and 2) the possible contribution of the associated supernova remnants to the hard X-ray emission.Comment: 11 pages, 14 figures, to appear in A&