34,172 research outputs found
Langlands duality for finite-dimensional representations of quantum affine algebras
We describe a correspondence (or duality) between the q-characters of
finite-dimensional representations of a quantum affine algebra and its
Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this
duality for the Kirillov-Reshetikhin modules and their irreducible tensor
products. In the course of the proof we introduce and construct "interpolating
(q,t)-characters" depending on two parameters which interpolate between the
q-characters of a quantum affine algebra and its Langlands dual.Comment: 40 pages; several results and comments added. Accepted for
publication in Letters in Mathematical Physic
Neutrino production coherence and oscillation experiments
Neutrino oscillations are only observable when the neutrino production,
propagation and detection coherence conditions are satisfied. In this paper we
consider in detail neutrino production coherence, taking \pi\to \mu \nu \ decay
as an example. We compare the oscillation probabilities obtained in two
different ways: (1) coherent summation of the amplitudes of neutrino production
at different points along the trajectory of the parent pion; (2) averaging of
the standard oscillation probability over the neutrino production coordinate in
the source. We demonstrate that the results of these two different approaches
exactly coincide, provided that the parent pion is considered as pointlike and
the detection process is perfectly localized. In this case the standard
averaging of the oscillation probability over the finite spatial extensions of
the neutrino source (and detector) properly takes possible decoherence effects
into account. We analyze the reason for this equivalence of the two approaches
and demonstrate that for pion wave packets of finite width \sigma_{x\pi} the
equivalence is broken. The leading order correction to the oscillation
probability due to \sigma_{x\pi}\ne 0 is shown to be \sim
[v_g/(v_g-v_\pi)]\sigma_{x\pi}/l_{osc}, where v_g and v_\pi \ are the group
velocities of the neutrino and pion wave packets, and l_{osc} is the neutrino
oscillation length.Comment: LaTeX, 40 pages, 4 figures. v2: minor typos correcte
Superisolated Surface Singularities
In this survey, we review part of the theory of superisolated surface
singularities (SIS) and its applications including some new and recent
developments. The class of SIS singularities is, in some sense, the simplest
class of germs of normal surface singularities. Namely, their tangent cones are
reduced curves and the geometry and topology of the SIS singularities can be
deduced from them. Thus this class \emph{contains}, in a canonical way, all the
complex projective plane curve theory, which gives a series of nice examples
and counterexamples. They were introduced by I. Luengo to show the
non-smoothness of the -constant stratum and have been used to answer
negatively some other interesting open questions. We review them and the new
results on normal surface singularities whose link are rational homology
spheres. We also discuss some positive results which have been proved for SIS
singularities.Comment: Survey article for the Proceedings of the Conference "Singularities
and Computer Algebra" on Occasion of Gert-Martin Greuel's 60th Birthday, LMS
Lecture Notes (to appear
How effective are conditional cash transfers? Evidence from Colombia
Conditional cash transfer (CCT) programmes are becoming an extremely popular tool for improving the education and health outcomes of poor children in developing countries. An incomplete list of countries in which they are being implemented under the support of the World Bank and other international financial institutions includes Mexico, Honduras, Nicaragua, Brazil, Turkey and Mozambique. While the implementation details vary from country to country, many are modelled on the Mexican PROGRESA. In a typical CCT, mothers from poor backgrounds receive cash conditional on their promoting certain activities on behalf of their children. For their youngest children - usually those below the age of 6 - the conditionality involves visits to preventive healthcare centres in which their growth is monitored. School attendance is the most common stipulation for receipt of cash transfers for older children - usually those between 7 and 17 years old. This targeting of health and education of children is at the essence of the long-term poverty alleviation objective of CCT programmes. Such transfer programmes are also aimed at the short-term reduction of poverty, through the provision of immediate funds to indigent households.
In this Briefing Note, we will focus on the programme Familias en Acción (FA), the CCT implemented by the Colombian government from 2001/02. In particular, we will provide estimates of how the programme has influenced key welfare indicators such as school attendance, child nutrition and health status, as well as household consumption. In this respect, we will update the preliminary results that were reported in Attanasio et al. (2003 and 2004)
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