18,671 research outputs found
Valadier-like formulas for the supremum function I
We generalize and improve the original characterization given by Valadier
[18, Theorem 1] of the subdifferential of the pointwise supremum of convex
functions, involving the subdifferentials of the data functions at nearby
points. We remove the continuity assumption made in that work and obtain a
general formula for such a subdiferential. In particular, when the supremum is
continuous at some point of its domain, but not necessarily at the reference
point, we get a simpler version which gives rise to the Valadier formula. Our
starting result is the characterization given in [11, Theorem 4], which uses
the epsilon-subdifferential at the reference point.Comment: 27 page
Valadier-like formulas for the supremum function II: The compactly indexed case
We generalize and improve the original characterization given by Valadier
[20, Theorem 1] of the subdifferential of the pointwise supremum of convex
functions, involving the subdifferentials of the data functions at nearby
points. We remove the continuity assumption made in that work and obtain a
general formula for such a subdifferential. In particular, when the supremum is
continuous at some point of its domain, but not necessarily at the reference
point, we get a simpler version which gives rise to Valadier formula. Our
starting result is the characterization given in [10, Theorem 4], which uses
the epsilon-subdiferential at the reference point.Comment: 23 page
Dilatation operator and the Super Yang-Mills duals of open strings on AdS Giant Gravitons
We study the one-loop anomalous dimensions of the Super Yang-Mills dual
operators to open strings ending on AdS giant gravitons. AdS giant gravitons
have no upper bound for their angular momentum and we represent them by the
contraction of scalar fields, carrying the appropriate R-charge, with a totally
symmetric tensor. We represent the open string motion along AdS directions by
appending to the giant graviton operator a product of fields including
covariant derivatives. We derive a bosonic lattice Hamiltonian that describes
the mixing of these excited AdS giants operators under the action of the
one-loop dilatation operator of N=4 SYM. This Hamiltonian captures several
intuitive differences with respect to the case of sphere giant gravitons. A
semiclassical analysis of the Hamiltonian allows us to give a geometrical
interpretation for the labeling used to describe the fields products appended
to the AdS giant operators. It also allows us to show evidence for the
existence of continuous bands in the Hamiltonian spectrum.Comment: 28 page
Surface Waves and Forced Oscillations in QHE Planar Samples
Dispersion relations and polarizations for surface waves in infinite planar
samples in the QHE regime are explicitly determined in the small wavevector
limit in which the dielectric tensor can be considered as local. The wavelength
and frequency regions of applicability of the results extends to the infrared
region for typical experimental conditions. Then, standard samples with
millimetric sizes seem to be able to support such excitations. Forced
oscillations are also determined which should be generated in the 2DEG by
external electromagnetic sources. They show an almost frequency independent
wavevelength which decreases with the magnetic field. A qualitative model based
in these solutions is also presented to describe a recently found new class of
resonances appearing near the edge of a 2DEG in the QHE regime.Comment: latex file, 18 pages, 3 figures, spelling correcte
Coupled scalar fields Oscillons and Breathers in some Lorentz Violating Scenarios
In this work we discuss the impact of the breaking of the Lorentz symmetry on
the usual oscillons, the so-called flat-top oscillons, and the breathers. Our
analysis is performed by using a Lorentz violation scenario rigorously derived
in the literature. We show that the Lorentz violation is responsible for the
origin of a kind of deformation of the configuration, where the field
configuration becomes oscillatory in a localized region near its maximum value.
Furthermore, we show that the Lorentz breaking symmetry produces a displacement
of the oscillon along the spatial direction, the same feature is present in the
case of breathers. We also show that the effect of a Lorentz violation in the
flat-top oscillon solution is responsible by the shrinking of the flat-top.
Furthermore, we find analytically the outgoing radiation, this result indicates
that the amplitude of the outgoing radiation is controlled by the Lorentz
breaking parameter, in such away that this oscillon becomes more unstable than
its symmetric counterpart, however, it still has a long living nature
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