8,638 research outputs found
Frequently hypercyclic semigroups
We study frequent hypercyclicity in the context of strongly continuous
semigroups of operators. More precisely, we give a criterion (sufficient
condition) for a semigroup to be frequently hypercyclic, whose formulation
depends on the Pettis integral. This criterion can be verified in certain cases
in terms of the infinitesimal generator of semigroup. Applications are given
for semigroups generated by Ornstein-Uhlenbeck operators, and especially for
translation semigroups on weighted spaces of -integrable functions, or
continuous functions that, multiplied by the weight, vanish at infinity
Mean Li-Yorke chaos in Banach spaces
We investigate the notion of mean Li-Yorke chaos for operators on Banach
spaces. We show that it differs from the notion of distributional chaos of type
2, contrary to what happens in the context of topological dynamics on compact
metric spaces. We prove that an operator is mean Li-Yorke chaotic if and only
if it has an absolutely mean irregular vector. As a consequence, absolutely
Ces\`aro bounded operators are never mean Li-Yorke chaotic. Dense mean Li-Yorke
chaos is shown to be equivalent to the existence of a dense (or residual) set
of absolutely mean irregular vectors. As a consequence, every mean Li-Yorke
chaotic operator is densely mean Li-Yorke chaotic on some infinite-dimensional
closed invariant subspace. A (Dense) Mean Li-Yorke Chaos Criterion and a
sufficient condition for the existence of a dense absolutely mean irregular
manifold are also obtained. Moreover, we construct an example of an invertible
hypercyclic operator such that every nonzero vector is absolutely mean
irregular for both and . Several other examples are also presented.
Finally, mean Li-Yorke chaos is also investigated for -semigroups of
operators on Banach spaces.Comment: 26 page
The Specification Property for -Semigroups
We study one of the strongest versions of chaos for continuous dynamical
systems, namely the specification property. We extend the definition of
specification property for operators on a Banach space to strongly continuous
one-parameter semigroups of operators, that is, -semigroups. In addition,
we study the relationships of the specification property for -semigroups
(SgSP) with other dynamical properties: mixing, Devaney's chaos, distributional
chaos and frequent hypercyclicity. Concerning the applications, we provide
several examples of semigroups which exhibit the SgSP with particular interest
on solution semigroups to certain linear PDEs, which range from the hyperbolic
heat equation to the Black-Scholes equation.Comment: 13 page
Matrix Elements of Electroweak Penguin Operators in the 1/Nc Expansion
It is shown that the K -> pi pi matrix elements of the four-quark operator
Q_7, generated by the electroweak penguin-like diagrams of the Standard Model,
can be calculated to first non-trivial order in the chiral expansion and in the
1/Nc expansion. Although the resulting B factors B_7^(1/2) and B_7^(3/2) are
found to depend only logarithmically on the matching scale, mu, their actual
numerical values turn out to be rather sensitive to the precise choice of mu in
the GeV region. We compare our results to recent numerical evaluations from
lattice-QCD and to other model estimates.Comment: 10 pages, LateX, two figures (inserted). Improved comparison with the
lattice results. Results unchange
On the relation between low-energy constants and resonance saturation
Although there are phenomenological indications that the low-energy constants
in the chiral lagrangian may be understood in terms of a finite number of
hadronic resonances, it remains unclear how this follows from QCD. One of the
arguments usually given is that low-energy constants are associated with chiral
symmetry breaking, while QCD perturbation theory suggests that at high energy
chiral symmetry is unbroken, so that only low-lying resonances contribute to
the low-energy constants. We revisit this argument in the limit of large Nc,
discussing its validity in particular for the low-energy constant L8, and
conclude that QCD may be more subtle that what this argument suggests. We
illustrate our considerations in a simple Regge-like model which also applies
at finite Nc.Comment: 15 pages, one figur
A Projective Description of the Nachbin-Ported Topology
AbstractIn this article we give a projective description of the Nachbin-ported topology τωin H(U,X), the space of holomorphic mappings on a balanced open subsetUof a Fréchet spaceE(which satisfies certain general conditions) with values in a Banach spaceXwhich is complemented in its bidual. To do this we use the topology τbintroduced by Dineen [Math. Scand.,74(1994) 215–236]. As a consequence we characterize when the compact open topology τ0and τωcoincide on H(U,X′) for every Banach spaceX, in terms of a condition onE. Among the techniques we use to obtain these results are the BB-property, the density condition, a version of quasinormability, and Taylor series expansions
Resummation of Threshold, Low- and High-Energy Expansions for Heavy-Quark Correlators
With the help of the Mellin-Barnes transform, we show how to simultaneously
resum the expansion of a heavy-quark correlator around q^2=0 (low-energy), q^2=
4 m^2 (threshold, where m is the quark mass) and q^2=-\infty (high-energy) in a
systematic way. We exemplify the method for the perturbative vector correlator
at O(alpha_s^2) and O(alpha_s^3). We show that the coefficients, Omega(n), of
the Taylor expansion of the vacuum polarization function in terms of the
conformal variable \omega admit, for large n, an expansion in powers of 1/n (up
to logarithms of n) that we can calculate exactly. This large-n expansion has a
sign-alternating component given by the logarithms of the OPE, and a fixed-sign
component given by the logarithms of the threshold expansion in the external
momentum q^2.Comment: 27 pages, 8 figures. We fix typos in Eqs. (18), (27), (55) and (56).
Results unchange
Relative localization for aerial manipulation with PL-SLAM
The final publication is available at link.springer.comThis chapter explains a precise SLAM technique, PL-SLAM, that allows to simultaneously process points and lines and tackle situations where point-only based methods are prone to fail, like poorly textured scenes or motion blurred images where feature points are vanished out. The method is remarkably robust against image noise, and that it outperforms state-of-the-art methods for point based contour alignment. The method can run in real-time and in a low cost hardware.Peer ReviewedPostprint (author's final draft
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