On the Randi\'{c} index and conditional parameters of a graph

The aim of this paper is to study some parameters of simple graphs related with the degree of the vertices. So, our main tool is the $n\times n$ matrix ${\cal A}$ whose ($i,j$)-entry is $$a_{ij}= \left\lbrace \begin{array}{ll} \frac{1}{\sqrt{\delta_i\delta_j}} & {\rm if }\quad v_i\sim v_j ; \\ 0 & {\rm otherwise,} \end{array} \right.$$ where $\delta_i$ denotes the degree of the vertex $v_i$. We study the Randi\'{c} index and some interesting particular cases of conditional excess, conditional Wiener index, and conditional diameter. In particular, using the matrix ${\cal A}$ or its eigenvalues, we obtain tight bounds on the studied parameters.Comment: arXiv admin note: text overlap with arXiv:math/060243

Reactions induced by 9^9Be in a four-body continuum-discretized coupled-channels framework

We investigate the elastic scattering of $^9$Be on $^{208}$Pb at beam energies above (50 MeV) and below (40 MeV) the Coulomb barrier. The reaction is described within a four-body framework using the Continuum-Discretized Coupled-Channels (CDCC) method. The $^9$Be projectile states are generated using the analytical Transformed Harmonic Oscillator (THO) basis in hyperspherical coordinates. Our calculations confirm the importance of continuum effects at low energies.Comment: 2 pages, 1 figure. Proceedings of the International Scientific Meeting on Nuclear Physics, RABIDA15, La R\'abida (Spain), June 1-5, 201

Analytical transformed harmonic oscillator basis for three-body nuclei of astrophysical interest: Application to 6He

Recently, a square-integrable discrete basis, obtained performing a simple analytical local scale transformation to the harmonic oscillator basis, has been proposed and successfully applied to study the properties of two-body systems. Here, the method is generalized to study three-body systems. To test the goodness of the formalism and establish its applicability and limitations, the capture reaction rate for the nucleosynthesis of the Borromean nucleus 6He (4He + n + n) is addressed. Results are compared with previous publications and with calculations based on actual three-body continuum wave functions, which can be generated for this simple case. The obtained results encourage the application to other Borromean nuclei of astrophysical interest such as 9Be and 12C, for which actual three-body continuum calculations are very involved.Comment: Accepted in Phys. Rev.

Polydispersity Effects in the Dynamics and Stability of Bubbling Flows

The occurrence of swarms of small bubbles in a variety of industrial systems enhances their performance. However, the effects that size polydispersity may produce on the stability of kinematic waves, the gain factor, mean bubble velocity, kinematic and dynamic wave velocities is, to our knowledge, not yet well established. We found that size polydispersity enhances the stability of a bubble column by a factor of about 23% as a function of frequency and for a particular type of bubble column. In this way our model predicts effects that might be verified experimentally but this, however, remain to be assessed. Our results reinforce the point of view advocated in this work in the sense that a description of a bubble column based on the concept of randomness of a bubble cloud and average properties of the fluid motion, may be a useful approach that has not been exploited in engineering systems.Comment: 11 pages, 2 figures, presented at the 3rd NEXT-SigmaPhi International Conference, 13-18 August, 2005, Kolymbari, Cret