93,643 research outputs found
From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality
By means of Dirac procedure, we re-examine Yang's quantized space-time model,
its relation to Snyder's model, the de Sitter special relativity and their
UV-IR duality. Starting from a dimensionless dS_5-space in a 5+1-d Mink-space a
complete Yang model at both classical and quantum level can be presented and
there really exist Snyder's model, the dS special relativity and the duality.Comment: 7 papge
Boltzmann Equation with a Large Potential in a Periodic Box
The stability of the Maxwellian of the Boltzmann equation with a large
amplitude external potential has been an important open problem. In this
paper, we resolve this problem with a large potential in a periodic box
, . We use [1] in framework to
establish the well-posedness and the stability of the Maxwellian
Atomic data from the Iron Project.XLIV. Transition probabilities and line ratios for Fe VI with fluorescent excitation in planetary nebulae
Relativistic atomic structure calculations for electric dipole E1, electric
quadrupole E2 and magnetic dipole M1 transition probabilities among the first
80 fine-structure levels of Fe VI, dominated by configurations 3d^3, 3d^24s,
and 3d^24p, are carried out using the Breit-Pauli version of the code
Superstructure. Experimental energies are used to improve the accuracy of these
transition probabilities. Employing the 80-level collision-radiative (CR) model
with these dipole and forbidden transition probabilities, and Iron Project
R-matrix collisional data, we present a number of [Fe VI] line ratios
applicable to spectral diagnostics of photoionized H II regions. It is shown
that continuum fluorescent excitation needs to be considered in CR models in
order to interpret the observed line ratios of optical [Fe VI] lines in
planetary nebulae NGC 6741, IC 351, and NGC 7662. The analysis leads to
parametrization of line ratios as function of, and as constraints on, the
electron density and temperature, as well as the effective radiation
temperature of the central source and a geometrical dilution factor. The
spectral diagnostics may also help ascertain observational uncertainties. The
method may be generally applicable to other objects with intensive background
radiation fields, such as novae and active galactic nuclei. The extensive new
Iron Project radiative and collisional calculations enable a consistent
analysis of many line ratios for the complex iron ions.Comment: 25 pages, 8 figures, submitted to Astron.Astrophys. Suppl.Se
Free Rota-Baxter algebras and rooted trees
A Rota-Baxter algebra, also known as a Baxter algebra, is an algebra with a
linear operator satisfying a relation, called the Rota-Baxter relation, that
generalizes the integration by parts formula. Most of the studies on
Rota-Baxter algebras have been for commutative algebras. Two constructions of
free commutative Rota-Baxter algebras were obtained by Rota and Cartier in the
1970s and a third one by Keigher and one of the authors in the 1990s in terms
of mixable shuffles. Recently, noncommutative Rota-Baxter algebras have
appeared both in physics in connection with the work of Connes and Kreimer on
renormalization in perturbative quantum field theory, and in mathematics
related to the work of Loday and Ronco on dendriform dialgebras and
trialgebras.
This paper uses rooted trees and forests to give explicit constructions of
free noncommutative Rota--Baxter algebras on modules and sets. This highlights
the combinatorial nature of Rota--Baxter algebras and facilitates their further
study. As an application, we obtain the unitarization of Rota-Baxter algebras.Comment: 23 page
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