Sabidussi versus Hedetniemi for three variations of the chromatic number

We investigate vector chromatic number (χ _vec ), Lovász V-function of the complement \((\bar \vartheta )\), and quantum chromatic number (χ _q ) from the perspective of graph homomorphisms. We prove an analog of Sabidussi's theorem for each of these parameters, i.e., that for each of the parameters, the value on the Cartesian product of graphs is equal to the maximum of the values on the factors. Interestingly, as a consequence of this result for \(\bar \vartheta\), we obtain analog of Hedetniemi's conjecture, i.e., that the value of \(\bar \vartheta\) on the categorical product of graphs is equal to the minimum of its values on the factors. We conjecture that the analogous results hold for vector and quantum chromatic number, and we prove that this is the case for some special classes of graphs.     

Morphology of isotactic polypropylene-polyamide 66 blends and their mechanical properties

Compounds were prepared with isotactic polypropylene (iPP) matrix and recycled polyamide 66 fibres (PA66), which were obtained as soft waste in industrial production process. Blends with pristine PA66 pellets were prepared as comparison. The blends showed the presence of PA66 particles dispersed in the PP continuous phase. Considering the incompatibility of the two polymers the addition of isotactic polypropylene grafted with maleic anhydride (iPPgMA) as compatibilizer was investigated: the blends were characterized by thermal, mechanical, dynamic-mechanical and morphological analyses. The presence of the compatibilizer significantly influences the morphology of the blends, inducing a finer dispersion and promoting interfacial adhesion. The characterization of pristine and recycled PA66 did not show a meaningful difference in the value of molecular weight, on the other hand marked differences were presented in the flexural moduli of the two materials; analogous differences were exhibited by the blends: compounds prepared with recycled PA66 showed flexural moduli higher than compatibilized blends with pristine PA66.     

Differential scanning calorimetry study of the thermal decomposition of peroxides in the absence of a solvent

The thermal decompositions of benzoyl peroxide (Bz₂O₂), dicumyl peroxide (DICUP) and α, α′-bis (t-butylperoxy)m/p-diisopropylbenzene (Peroximon F) in the absence of solvents have been studied by means ofDSC alone. The DSC curves allowed calculation of the half-lifetime (t _1/2) and the time (t ₁) required to decompose the whole of the peroxides. Thet ₁, andt _1/2 values found for the pure peroxides are lower than those in the literature for decomposition in solution. The heat of decomposition and the activation energy for each peroxide are reported.     

Observation of Upsilon(3S)-->tau+tau- and tests of lepton universality in Upsilon decays

Using data collected with the CLEO III detector at the CESR e+e- collider, we report on a first observation of the decay Upsilon(3S)-->tau+tau-, and precisely measure the ratio of branching fractions of Upsilon(nS), n=1, 2, 3, to tau+tau- and mu+mu- final states, finding agreement with expectations from lepton universality. We derive absolute branching fractions for these decays, and also set a limit on the influence of a low mass CP-odd Higgs boson in the decay of the Upsilon(1S).     

Precision determination of the D0 mass

A precision measurement of the D0 meson mass has been made using approximately 281 pb(-1) of e+e- annihilation data taken with the CLEO-c detector at the psi(3770) resonance. The exclusive decay D0-->K_{S}phi has been used to obtain M(D0)=1864.847+/-0.150(stat)+/-0.095(syst) MeV. This corresponds to M(D0D*0)=3871.81+/-0.36 MeV, and leads to a well-constrained determination of the binding energy of the proposed D0D*0 molecule X(3872), as Eb=0.6+/-0.6 MeV.     

Integrated likelihood computation methods

Suppose a model has parameter \(\theta =(\psi , \lambda )\), where \(\psi \) is the parameter of interest and \(\lambda \) is a nuisance parameter. The integrated likelihood method eliminates \(\lambda \) from the likelihood function \(L(\psi , \lambda )\) by integrating with respect to a weight function \(\pi (\lambda | \psi )\). The resulting integrated likelihood function \(\bar{L}(\psi )\) can be used for inference for \(\psi \). However, the analytical form for the integrated likelihood is not always available. This paper discusses 12 different approaches to computing the integrated likelihood. Some methods were originally developed for other computation purposes and they are modified to fit in the integrated likelihood framework. Methods considered include direct numerical integration methods such as Monte Carlo integration method, importance sampling, Laplace method; marginal likelihood computation methods; and methods for computing the marginal posterior density. Simulation studies and real data example are presented to evaluate and compare these methods empirically.