The Wiener and Terminal Wiener indices of trees

Heydari \cite{heydari2013} presented very nice formulae for the Wiener and terminal Wiener indices of generalized Bethe trees. It is pity that there are some errors for the formulae. In this paper, we correct these errors and characterize all trees with the minimum terminal Wiener index among all the trees of order $n$ and with maximum degree $\Delta$.Comment: 13 page

Light-front wavefunction dependence of the quark recombination

We present an extension of the recombination formalism to analyze the effects from the variation of the hadron wavefunctions. The hadron spectra are sensitive to the shape of the wavefunctions. However, when we fit the wavefunction parameters to the physical observables, such as the average charge radius, the final spectra are very similar each other. We discuss our numerical results in comparison with the published PHENIX and STAR data at RHIC. In the hadron spectra, the recombination of thermal partons dominates at intermediate transverse momentum ($P_{T}$ = 2 $\sim$ 5 GeV), and the fragmentation dominates at high $P_{T}$ ($>$ 5 GeV). The yield ratios and the nuclear modification factors for various hadron species are also estimated and compared to the experimental data. We present a new prediction on $\bar{p}/p$ and $K^{-}/K^{+}$ ratios, including the jet quenching effects to the fragmentation mechanism.Comment: 26 pages, 7 figure