40,475 research outputs found
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 matrix
whose ()-entry is where denotes the degree of the vertex . 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 or its eigenvalues, we obtain tight bounds on the
studied parameters.Comment: arXiv admin note: text overlap with arXiv:math/060243
Formation of corner waves in the wake of a partially submerged bluff body
We study theoretically and numerically the downstream flow near the corner of a bluff body partially submerged at a deadrise depth Δh into a uniform stream of velocity U, in the presence of gravity, g. When the Froude number, Fr=U/√gΔh, is large, a three-dimensional steady plunging wave, which is referred to as a corner wave, forms near the corner, developing downstream in a similar way to a two-dimensional plunging wave evolving in time. We have performed an asymptotic analysis of the flow near this corner to describe the wave's initial evolution and to clarify the physical mechanism that leads to its formation. Using the two-dimensions-plus-time approximation, the problem reduces to one similar to dam-break flow with a wet bed in front of the dam. The analysis shows that, at leading order, the problem admits a self-similar formulation when the size of the wave is small compared with the height difference Δh. The essential feature of the self-similar solution is the formation of a mushroom-shaped jet from which two smaller lateral jets stem. However, numerical simulations show that this self-similar solution is questionable from the physical point of view, as the two lateral jets plunge onto the free surface, leading to a self-intersecting flow. The physical mechanism leading to the formation of the mushroom-shaped structure is discussed
Dynamical quarks effects on the gluon propagation and chiral symmetry restoration
We exploit the recent lattice results for the infrared gluon propagator with
light dynamical quarks and solve the gap equation for the quark propagator.
Chiral symmetry breaking and confinement (intimately tied with the analytic
properties of QCD Schwinger functions) order parameters are then studied.Comment: Contribution to QCD-TNT-III: "From quarks and gluons to hadronic
matter: A bridge too far?
A brief comment on the similarities of the IR solutions for the ghost propagator DSE in Landau and Coulomb gauges
This brief note is devoted to reconcile the conclusions from a recent
analysis of the IR solutions for the ghost propagator Dyson-Schwinger equations
in Coulomb gauge with previous studies in Landau gauge.Comment: 4 pages, 1 figur
UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces
We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square
functions associated with Poisson semigroups for Bessel operators are defined
by using fractional derivatives. If B is a UMD Banach space we obtain for
B-valued Hardy and BMO spaces equivalent norms involving -radonifying
operators and square functions. We also establish characterizations of UMD
Banach spaces by using Hardy and BMO-boundedness properties of g-functions
associated to Bessel-Poisson semigroup
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
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