32,657 research outputs found
The number of ramified coverings of the sphere by the double torus, and a general form for higher genera
An explicit expression is obtained for the generating series for the number
of ramified coverings of the sphere by the double torus, with elementary branch
points and prescribed ramification type over infinity. Thus we are able to
prove a conjecture of Graber and Pandharipande, giving a linear recurrence
equation for the number of these coverings with no ramification over infinity.
The general form of the series is conjectured for the number of these coverings
by a surface of arbitrary genus that is at least two.Comment: 14pp.; revised version has two additional results in Section
A proof of a conjecture for the number of ramified coverings of the sphere by the torus
An explicit expression is obtained for the generating series for the number
of ramified coverings of the sphere by the torus, with elementary branch points
and prescribed ramification type over infinity. This proves a conjecture of
Goulden, Jackson and Vainshtein for the explicit number of such coverings.Comment: 10 page
Transitive factorizations of permutations and geometry
We give an account of our work on transitive factorizations of permutations.
The work has had impact upon other areas of mathematics such as the enumeration
of graph embeddings, random matrices, branched covers, and the moduli spaces of
curves. Aspects of these seemingly unrelated areas are seen to be related in a
unifying view from the perspective of algebraic combinatorics. At several
points this work has intertwined with Richard Stanley's in significant ways.Comment: 12 pages, dedicated to Richard Stanley on the occasion of his 70th
birthda
Lax matrices for Yang-Baxter maps
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical
solutions to the quantum Yang-Baxter equation) the Lax representation can be
derived straight from the map itself. A similar phenomenon for 3D consistent
equations on quad-graphs has been recently discovered by A. Bobenko and one of
the authors, and by F. Nijhoff
Universal factorized formula for the cross-section of two-particle scattering
We analyze the process of two-particle scattering with unstable particle in
an intermediate state. It was shown that the cross-section can be represented
in the universal factorized form for an arbitrary set of particles.
Phenomenological analysis of factorization effect is fulfilled.Comment: 8 pages, corrected typos. change conten
The Parkes quarter-Jansky flat-spectrum sample 3. Space density and evolution of QSOs
We analyze the Parkes quarter-Jansky flat-spectrum sample of QSOs in terms of
space density, including the redshift distribution, the radio luminosity
function, and the evidence for a redshift cutoff. With regard to the luminosity
function, we note the strong evolution in space density from the present day to
epochs corresponding to redshifts ~ 1. We draw attention to a selection effect
due to spread in spectral shape that may have misled other investigators to
consider the apparent similarities in shape of luminosity functions in
different redshift shells as evidence for luminosity evolution. To examine the
evolution at redshifts beyond 3, we develop a model-independent method based on
the V_max test using each object to predict expectation densities beyond z=3.
With this we show that a diminution in space density at z > 3 is present at a
significance level >4 sigma. We identify a severe bias in such determinations
from using flux-density measurements at epochs significantly later than that of
the finding survey. The form of the diminution is estimated, and is shown to be
very similar to that found for QSOs selected in X-ray and optical wavebands.
The diminution is also compared with the current estimates of star-formation
evolution, with less conclusive results. In summary we suggest that the
reionization epoch is little influenced by powerful flat-spectrum QSOs, and
that dust obscuration does not play a major role in our view of the QSO
population selected at radio, optical or X-ray wavelengths.Comment: 18 pages, 11 figures, accepted 18 Dec 2004, Astron. & Astrophys. The
accepted version is expanded to include an analysis of the form of the
decline in radio-QSO space density at high redshifts. This is compared with
the forms of epoch dependence derived for optically-selected QSOs, for
X-ray-selected QSOs, and for star formation rat
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Facing up to the challenge of behavioural observation in infant hearing assessment
The ability to assess detection and discrimination of speech by infants has proved elusive. Dr Iain Jackson and colleagues discuss how new technologies and fresh approaches might offer valuable insight into young infants’ behavioural responses to sound
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