678 research outputs found

    Lower Bounds on the Chromatic Number of Random Graphs

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    We prove that a formula predicted on the basis of non-rigorous physics arguments [Zdeborová and Krzakala: Phys. Rev. E (2007)] provides a lower bound on the chromatic number of sparse random graphs. The proof is based on the interpolation method from mathematical physics. In the case of random regular graphs the lower bound can be expressed algebraically, while in the case of the binomial random we obtain a variational formula. As an application we calculate improved explicit lower bounds on the chromatic number of random graphs for small (average) degrees. Additionally, we show how asymptotic formulas for large degrees that were previously obtained by lengthy and complicated combinatorial arguments can be re-derived easily from these new results

    Enzymes of carbohydrate metabolism in normal and pathological human tissues

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    Gamma-Ray Spectra & Variability of the Crab Nebula Emission Observed by BATSE

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    We report ~ 600 days of BATSE earth-occultation observations of the total gamma-ray (30 keV to 1.7 MeV) emission from the Crab nebula, between 1991 May 24 (TJD 8400) and 1994 October 2 (TJD 9627). Lightcurves from 35-100, 100-200, 200-300, 300-400, 400-700, and 700-1000 keV, show that positive fluxes were detected by BATSE in each of these six energy bands at significances of approximately 31, 20, 9.2, 4.5, 2.6, and 1.3 sigma respectively per day. We also observed significant flux and spectral variations in the 35-300 keV energy region, with time scales of days to weeks. The spectra below 300 keV, averaged over typical CGRO viewing periods of 6-13 days, can be well described by a broken power law with average indices of ~ 2.1 and ~ 2.4 varying around a spectral break at ~ 100 keV. Above 300 keV, the long-term averaged spectra, averaged over three 400 d periods (TJD 8400-8800, 8800-9200, and 9200-9628, respectively) are well represented by the same power law with index of ~ 2.34 up to ~ 670 keV, plus a hard spectral component extending from ~ 670 keV to ~ 1.7 MeV, with a spectral index of ~ 1.75. The latter component could be related to a complex structure observed by COMPTEL in the 0.7-3 MeV range. Above 3 MeV, the extrapolation of the power-law continuum determined by the low-energy BATSE spectrum is consistent with fluxes measured by COMPTEL in the 3-25 MeV range, and by EGRET from 30-50 MeV. We interpret these results as synchrotron emission produced by the interaction of particles ejected from the pulsar with the field in different dynamical regions of the nebula system, as observed recently by HST, XMM-Newton, and Chandra.Comment: To be published in the November 20, 2003, Vol 598 issue of the Astrophysical Journa

    Children of prisoners: exploring the impact of families' reappraisal of the role and status of the imprisoned parent on children's coping strategies

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    Qualitative data from a larger study on the impact of parental imprisonment in four countries found that children of prisoners face fundamentally similar psychological and social challenges. The ways that children cope, however, are influenced by the interpretative frame adopted by the adults around them, and by how issues of parental imprisonment are talked about in their families. This article argues that families have to reappraise their view of the imprisoned parent and then decide on their policy for how to deal with this publicly. Their approach may be based on openness and honesty or may emphasise privacy and secrecy, or a combination of these. Children are likely to be influenced by their parents'/carers' views, although these may cause conflict for them. Where parents/carers retain a positive view of the imprisoned parent, children are likely to benefit; where parents/carers feel issues of shame and stigma acutely, this is likely to be transmitted to their children. This is important for social workers and practitioners involved in supporting prisoners' families and for parenting programmes

    Weld-bonded stainless steel to carbon fibre-reinforced plastic joints

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    This paper investigates a resistance spot welded reinforced adhesive (weld-bonded) joint between 304 stainless steel to carbon fibre reinforced plastic (CFRP), where welds are made both with and without the reinforcing carbon fibres present. Successful welds with the fibres present could only be produced with high electrode pinch forces, which helped reduce contamination of the weld nugget. Similar joint strengths were achieved in both cases, however the joints without fibres exhibited an increased strain to failure. Both joints were significantly stronger than either an adhesive joint or a comparable bolt reinforced adhesive joint. These techniques provide an alternative for joining thin metallic components to CFRP structures where increased strength and integrity is required
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