82,638 research outputs found
A metric property of umbilic points
In the space of cubic forms of surfaces, regarded as a
-space and endowed with a natural invariant metric, the ratio of the volumes
of those representing umbilic points with negative to those with positive
indexes is evaluated in terms of the asymmetry of the metric, defined here. A
connection of this ratio with that reported by Berry and Hannay (1977) in the
domain of Statistical Physics, is discussed.Comment: 8 pages, 1 figur
Sigma pole position and errors of a once and twice subtracted dispersive analysis of pi-pi scattering data
We show how the new precise data on kaon decays together with forward
dispersion relations, sum rules and once- and twice-subtracted
Roy's equations allow for a precise determination of the sigma meson pole
position. We present a comparison and a study of the different sources of
uncertainties when using either once- or twice-subtracted Roy's equations to
analyze the data. Finally we present a preliminary determination of the sigma
pole from the constrained dispersive data analysis.Comment: 4 pages, 6 figures. Contribution to the proceedings of the QCD08 14th
International QCD Conference. 7-12th July 2008 Montpellier (France); one
reference removed, changed errors in Eqs (4), (5) and (7
Invariance principles for switched systems with restrictions
In this paper we consider switched nonlinear systems under average dwell time
switching signals, with an otherwise arbitrary compact index set and with
additional constraints in the switchings. We present invariance principles for
these systems and derive by using observability-like notions some convergence
and asymptotic stability criteria. These results enable us to analyze the
stability of solutions of switched systems with both state-dependent
constrained switching and switching whose logic has memory, i.e., the active
subsystem only can switch to a prescribed subset of subsystems.Comment: 29 pages, 2 Appendixe
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