175 research outputs found
Pairs of dual periodic frames
10.1016/j.acha.2011.12.003Applied and Computational Harmonic Analysis333315-329ACOH
Unitary Extension Principle for Nonuniform Wavelet Frames in
We study the construction of nonuniform tight wavelet frames for the Lebesgue
space , where the related translation set is not necessary a
group. The main purpose of this paper is to prove the unitary extension
principle (UEP) and the oblique extension principle (OEP) for construction of
multi-generated nonuniform tight wavelet frames for . Some
examples are also given to illustrate the results
The Solution of a Problem of Coifman, Meyer, and Wickerhauser on Wavelet Packets.
Wavelet packets provide an algorithm with many applications in signal processing together with a large class of orthonormal bases of L^2(R), each one corresponding to a different splitting of L^2(R) into a direct sum of its closed subspaces.
The definition of wavelet packets is due to the work of Coifman, Meyer, and Wickerhauser, as a generalization of the Walsh system. A question has been posed since then: one asks if a (general) wavelet packet system can be an orthonormal basis for
L2(R) whenever a certain set linked to the system, called the “exceptional set” has zero Lebesgue measure. This question is reflected in the quality of wavelet packet approximation. In this paper we show that the answer to this question is negative by
providing an explicit example. In the proof we make use of the “local trace function” by Dutkay and the generalized shift-invariant system machinery developed by Ron and Shen
The braneology of 3D dualities
In this paper we study the reduction of four-dimensional Seiberg duality to
three dimensions from a brane perspective. We reproduce the non-perturbative
dynamics of the three-dimensional field theory via a T-duality at finite radius
and the action of Euclidean D-strings. In this way we also overcome certain
issues regarding the brane description of Aharony duality. Moreover we apply
our strategy to more general dualities, such as toric duality for M2-branes and
dualities with adjoint matter fields.Comment: 20 pages, 8 figures, published versio
The monodromy of T-folds and T-fects
We construct a class of codimension-2 solutions in supergravity that realize
T-folds with arbitrary monodromy and we develop a geometric
point of view in which the monodromy is identified with a product of Dehn
twists of an auxiliary surface fibered on a base . These
defects, that we call T-fects, are identified by the monodromy of the mapping
torus obtained by fibering over the boundary of a small disk
encircling a degeneration. We determine all possible local geometries by
solving the corresponding Cauchy-Riemann equations, that imply the equations of
motion for a semi-flat metric ansatz. We discuss the relation with the
F-theoretic approach and we consider a generalization to the T-duality group of
the heterotic theory with a Wilson line.Comment: 60 pages, 12 figure
Liftings and stresses for planar periodic frameworks
We formulate and prove a periodic analog of Maxwell's theorem relating
stressed planar frameworks and their liftings to polyhedral surfaces with
spherical topology. We use our lifting theorem to prove deformation and
rigidity-theoretic properties for planar periodic pseudo-triangulations,
generalizing features known for their finite counterparts. These properties are
then applied to questions originating in mathematical crystallography and
materials science, concerning planar periodic auxetic structures and ultrarigid
periodic frameworks.Comment: An extended abstract of this paper has appeared in Proc. 30th annual
Symposium on Computational Geometry (SOCG'14), Kyoto, Japan, June 201
Morita Duality and Large-N Limits
We study some dynamical aspects of gauge theories on noncommutative tori. We
show that Morita duality, combined with the hypothesis of analyticity as a
function of the noncommutativity parameter Theta, gives information about
singular large-N limits of ordinary U(N) gauge theories, where the large-rank
limit is correlated with the shrinking of a two-torus to zero size. We study
some non-perturbative tests of the smoothness hypothesis with respect to Theta
in theories with and without supersymmetry. In the supersymmetric case this is
done by adapting Witten's index to the present situation, and in the
nonsupersymmetric case by studying the dependence of energy levels on the
instanton angle. We find that regularizations which restore supersymmetry at
high energies seem to preserve Theta-smoothness whereas nonsupersymmetric
asymptotically free theories seem to violate it. As a final application we use
Morita duality to study a recent proposal of Susskind to use a noncommutative
Chern-Simons gauge theory as an effective description of the Fractional Hall
Effect. In particular we obtain an elegant derivation of Wen's topological
order.Comment: 41 pages, Harvmac. Some corrections to section 6.3. Comments added on
Hall Effec
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