3,695 research outputs found
Abstract Ces\`aro spaces: Integral representations
The Ces\`aro function spaces , , have
received renewed attention in recent years. Many properties of are
known. Less is known about when the Ces\`aro operator takes its values
in a rearrangement invariant (r.i.) space other than . In this paper
we study the spaces via the methods of vector measures and vector
integration. These techniques allow us to identify the absolutely continuous
part of and the Fatou completion of ; to show that is
never reflexive and never r.i.; to identify when is weakly sequentially
complete, when it is isomorphic to an AL-space, and when it has the
Dunford-Pettis property. The same techniques are used to analyze the operator
; it is never compact but, it can be completely continuous.Comment: 21 page
Elastic theory of icosahedral quasicrystals - application to straight dislocations
In quasicrystals, there are not only conventional, but also phason
displacement fields and associated Burgers vectors. We have calculated
approximate solutions for the elastic fields induced by two-, three- and
fivefold straight screw- and edge-dislocations in infinite icosahedral
quasicrystals by means of a generalized perturbation method. Starting from the
solution for elastic isotropy in phonon and phason spaces, corrections of
higher order reflect the two-, three- and fivefold symmetry of the elastic
fields surrounding screw dislocations. The fields of special edge dislocations
display characteristic symmetries also, which can be seen from the
contributions of all orders.Comment: 13 pages, 11 figure
Incremental verification of co-observability in discrete-event systems
Existing strategies for verifying co-observability, one of the properties that must be satisfied for synthesizing solutions to decentralized supervisory control problems, require the construction of the complete system model. When the system is composed of many subsystems, these monolithic approaches may be impractical due to the state-space explosion problem. To address this issue, we introduce an incremental verification of co-observability approach. Selected subgroups of the system are evaluated individually, until verification of co-observability is complete. The new method is potentially much more efficient than the monolithic approaches, in particular for systems composed of many subsystems, allowing for some intractable state-space explosion problems to be manageable. Properties of this new strategy are presented, along with a corresponding algorithm and an example
Non-spectrality of generators of some classical analytic semigroups
AbstractA simple proof is given of the facts that the infinitesimal generator of the heat semigroup and the Poisson semigroup are scalar operators in Lp (Rn), 1<p<∞, n≥1, if and only if, p=2. We exploit the fact that these semigroups consist of Fourier p-multiplier operators in the right-half plane which cannot be extended to a group of p-multiplier operators at the boundary Re(z)=0 if p≠2
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