The sum number of the cocktail party graph

A graph G is called a sum graph if there exists a labelling of the vertices of G by distinct positive integers such that the vertices labelled u and v are adjacent if and only if there exists a vertex labelled u + v. If G is not a sum graph, adding a finite number of isolated vertices to it will always yield a sum graph, and the sum number oe(G) of G is the smallest number of isolated vertices that will achieve this result. A labelling that realizes G + K oe(G) as a sum graph is said to be optimal. In this paper we consider G = H m;n , the complete n-partite graph on n 2 sets of m 2 nonadjacent vertices. We give an optimal labelling to show that oe(H 2;n ) = 4n \Gamma 5, and in the general case we give constructive proofs that oe(H m;n ) 2 \Omega\Gamma mn) and oe(H m;n ) 2 O(mn 2 ). We conjecture that oe(H m;n ) is asymptotically greater than mn, the cardinality of the vertex set; if so, then H m;n is the first known graph with this property. We also provide for the first time an optimal labelling of the complete bipatite graph Kmn whose smallest label is 1

The Effects of Quantum Entropy on the Bag Constant

The effects of quantum entropy on the bag constant are studied at low temperatures and small chemical potentials. The inclusion of the quantum entropy of the quarks in the equation of state provides the hadronic bag with an additional heat which causes a decrease in the effective latent heat inside the bag. We have considered two types of baryonic bags, $\Delta$ and $\Omega^-$. In both cases we have found that the bag constant without the quantum entropy almost does not change with the temperature and the quark chemical potential. The contribution from the quantum entropy to the equation of state clearly decreases the value of the bag constant.Comment: 7 pages, 2 figures (two parts each

Cationic sterically stabilized diblock copolymer nanoparticles exhibit exceptional tolerance toward added salt

For certain commercial applications such as enhanced oil recovery, sterically stabilized colloidal dispersions that exhibit high tolerance toward added salt are desirable. Herein, we report a series of new cationic diblock copolymer nanoparticles that display excellent colloidal stability in concentrated aqueous salt solutions. More specifically, poly(2-(acryloyloxy)ethyltrimethylammonium chloride) (PATAC) has been chain-extended by reversible addition–fragmentation chain transfer aqueous dispersion polymerization of diacetone acrylamide (DAAM) at 70 °C to produce PATAC100–PDAAMx diblock copolymer spheres at 20% w/w solids via polymerization-induced self-assembly. Transmission electron microscopy and dynamic light scattering (DLS) analysis confirm that the mean sphere diameter can be adjusted by systematic variation of the mean degree of polymerization of the PDAAM block. Remarkably, DLS studies confirm that highly cationic PATAC100–PDAAM1500 spheres retain their colloidal stability in the presence of either 4.0 M KCl or 3.0 M ammonium sulfate for at least 115 days at 20 °C. The mole fraction of PATAC chains within the stabilizer shell was systematically varied by the chain extension of various binary mixtures of non-ionic poly(N,N-dimethylacrylamide) (PDMAC) and cationic PATAC with DAAM to produce ([n] PATAC100 + [1 – n] PDMAC67)–PDAAMz diblock copolymer spheres at 20% w/w. DLS studies confirmed that a relatively high mole fraction of cationic PATAC stabilizer chains (n ≥ 0.75) is required for the dispersions to remain colloidally stable in 4.0 M KCl. Cationic worms and vesicles could also be synthesized using a binary mixture of PATAC and PDMAC precursors, where n = 0.10. However, the vesicles only remained colloidally stable up to 1.0 M KCl, whereas the worms proved to be stable up to 2.0 M KCl. Such block copolymer nanoparticles are expected to be useful model systems for understanding the behavior of aqueous colloidal dispersions in extremely salty media. Finally, zeta potentials determined using electrophoretic light scattering are presented for such nanoparticles dispersed in highly salty media

The performance of Mini Wright peak flow meters after prolonged use

AbstractThe accuracy of 84 new and 35 old Mini Wright peak flow meters were tested using a servo-controlled pump system. The 95% confidence limits for flow measurement across the range of the new meters was between ± 151 min−1 at the lower end of the range and ± 281 min−1 at the top of the range. The readings for 22 (63%) of the old meters (age range 1–13 yr) were within these 95% confidence limits. For the remaining 13 old meters (age range 1–13 yr) whose readings were not within these limits, there were 11 meters with readings falling below and two meters with readings above these limits. Twelve of these old meters were washed and retested and there was no significant change in their readings. Twenty of the new meters were retested after 1 yr of continuous use and their readings were significantly higher with a median value of 51 min−1 across the range, although only two of these 20 meters had readings outside the 95% confidence limits set from the 84 new meters. It is concluded that whilst Mini Wright meters aged up to 14 yr can give readings which are as good as new meters, some meters demonstrate significant changes in readings after only 1 yr and washing did not correct this change. It is recommended that clinicians prescribing peak expiratory flow (PEF) meters should be responsible for checking the patient's meter as well as their PEF readings at clinic visits

SUSY-QCD decoupling properties in H+ -> t \bar b decay

The SUSY-QCD radiative corrections to the \Gamma (H+ -> t \bar b) partial decay width are analyzed within the Minimal Supersymmetric Standard Model at the one-loop level, {\mathcal O}(\alpha_s), and in the decoupling limit. We present the analytical expressions of these corrections in the large SUSY masses limit and study the decoupling behaviour of these corrections in various limiting cases. We find that if the SUSY mass parameters are large and of the same order, the one loop SUSY-QCD corrections {\it do not decouple}. The non-decoupling contribution is enhanced by \tan \beta and therefore large corrections are expected in the large \tan \beta limit. In contrast, we also find that the SUSY-QCD corrections decouple if the masses of either the squarks or the gluinos are separately taken large.Comment: LaTeX, 33 pages, 7 figure included. Uses cite.st

Comment on ``Phase ordering in chaotic map lattices with conserved dynamics''

Angelini, Pellicoro, and Stramaglia [Phys. Rev. E {\bf 60}, R5021 (1999), cond-mat/9907149] (APS) claim that the phase ordering of two-dimensional systems of sequentially-updated chaotic maps with conserved ``order parameter'' does not belong, for large regions of parameter space, to the expected universality class. We show here that these results are due to a slow crossover and that a careful treatment of the data yields normal dynamical scaling. Moreover, we construct better models, i.e. synchronously-updated coupled map lattices, which are exempt from these crossover effects, and allow for the first precise estimates of persistence exponents in this case.Comment: 3 pages, to be published in Phys. Rev.

Measuring Black Hole Spin using X-ray Reflection Spectroscopy

I review the current status of X-ray reflection (a.k.a. broad iron line) based black hole spin measurements. This is a powerful technique that allows us to measure robust black hole spins across the mass range, from the stellar-mass black holes in X-ray binaries to the supermassive black holes in active galactic nuclei. After describing the basic assumptions of this approach, I lay out the detailed methodology focusing on "best practices" that have been found necessary to obtain robust results. Reflecting my own biases, this review is slanted towards a discussion of supermassive black hole (SMBH) spin in active galactic nuclei (AGN). Pulling together all of the available XMM-Newton and Suzaku results from the literature that satisfy objective quality control criteria, it is clear that a large fraction of SMBHs are rapidly-spinning, although there are tentative hints of a more slowly spinning population at high (M>5*10^7Msun) and low (M<2*10^6Msun) mass. I also engage in a brief review of the spins of stellar-mass black holes in X-ray binaries. In general, reflection-based and continuum-fitting based spin measures are in agreement, although there remain two objects (GROJ1655-40 and 4U1543-475) for which that is not true. I end this review by discussing the exciting frontier of relativistic reverberation, particularly the discovery of broad iron line reverberation in XMM-Newton data for the Seyfert galaxies NGC4151, NGC7314 and MCG-5-23-16. As well as confirming the basic paradigm of relativistic disk reflection, this detection of reverberation demonstrates that future large-area X-ray observatories such as LOFT will make tremendous progress in studies of strong gravity using relativistic reverberation in AGN.Comment: 19 pages. To appear in proceedings of the ISSI-Bern workshop on "The Physics of Accretion onto Black Holes" (8-12 Oct 2012). Revised version adds a missing source to Table 1 and Fig.6 (IRAS13224-3809) and corrects the referencing of the discovery of soft lags in 1H0707-495 (which were in fact first reported in Fabian et al. 2009