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

Investigation of the existence of hybrid stars using Nambu-Jona-Lasinio models

We investigate the hadron-quark phase transition inside neutron stars and obtain mass-radius relations for hybrid stars. The equation of state for the quark phase using the standard NJL model is too soft leading to an unstable star and suggesting a modification of the NJL model by introducing a momentum cutoff dependent on the chemical potential. However, even in this approach, the instability remains. In order to remedy the instability we suggest the introduction of a vector coupling in the NJL model, which makes the EoS stiffer, reducing the instability. We conclude that the possible existence of quark matter inside the stars require high densities, leading to very compact stars.Comment: 4 pages, 2 figures; prepared for IV International Workshop on Astronomy and Relativistic Astrophysics (IWARA 2009), Maresias, 4-8 Oct 200

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&

Gene identification for the cblD defect of vitamin B12 metabolism

Background Vitamin B12 (cobalamin) is an essential cofactor in several metabolic pathways. Intracellular conversion of cobalamin to its two coenzymes, adenosylcobalamin in mitochondria and methylcobalamin in the cytoplasm, is necessary for the homeostasis of methylmalonic acid and homocysteine. Nine defects of intracellular cobalamin metabolism have been defined by means of somatic complementation analysis. One of these defects, the cblD defect, can cause isolated methylmalonic aciduria, isolated homocystinuria, or both. Affected persons present with multisystem clinical abnormalities, including developmental, hematologic, neurologic, and metabolic findings. The gene responsible for the cblD defect has not been identified. Methods We studied seven patients with the cblD defect, and skin fibroblasts from each were investigated in cell culture. Microcell-mediated chromosome transfer and refined genetic mapping were used to localize the responsible gene. This gene was transfected into cblD fibroblasts to test for the rescue of adenosylcobalamin and methylcobalamin synthesis. Results The cblD gene was localized to human chromosome 2q23.2, and a candidate gene, designated MMADHC (methylmalonic aciduria, cblD type, and homocystinuria), was identified in this region. Transfection of wild-type MMADHC rescued the cellular phenotype, and the functional importance of mutant alleles was shown by means of transfection with mutant constructs. The predicted MMADHC protein has sequence homology with a bacterial ATP-binding cassette transporter and contains a putative cobalamin binding motif and a putative mitochondrial targeting sequence. Conclusions Mutations in a gene we designated MMADHC are responsible for the cblD defect in vitamin B12 metabolism. Various mutations are associated with each of the three biochemical phenotypes of the disorder