985 research outputs found

    Orbital compactness and asymptotic behaviour of nonlinear parabolic systems with functionals

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    SynopsisWeakly coupled semilinear parabolic systems of the form with homogeneous boundary conditions are studied. The nonlinear function g: C([−r, 0] × Ω ℝn) → ℝn is assumed to be locally Lipschitz continuous with r≧0 a given real number and Ω ⊂ ℝm a bounded domain, , ut for t ≧ 0 is denned by ut (σ, ξ) = u(t + σ, ξ), − r ≦σ ≦ 0 ξ ∊Ω and A is a uniformly elliptic second order diagonal operator. Let u be a bounded classical solution. We first establish precompactness results for the orbit of u in several function spaces. Using these results and assuming that a Liapunov function V is known for the corresponding ordinary functional differential equation ż =g(zt), we then show under some general conditions that the limit set ω+ (as t→∞) of u consists of spatially homogeneous functions only. Moreover, ω+ is invariant with respect to z = g(z,) and V = 0 on ω+. The proof uses a Liapunov function for the full system whichis obtained from V via a simple construction (cf. (3.3)). The theory is illustrated with an example.</jats:p

    Über die C<sup>2</sup>-Kompaktheit der Bahn von Lösungen semflinearer parabolischer Systeme

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    SynopsisThe semilinear parabolic systemut+A(x, D)u=g(u) in (0, ∞) × Ω, Ω⊂ℝnbounded,u∈ ℝN, with homogeneous boundary conditionsB(x, D)u=0 on (0, ∞)×∂Ω is considered. The non-linearitygis assumed to be locally Lipschitz-continuous. It is shown that the orbit of a bounded regular solutionuis relatively compact in.</jats:p

    Searches for Supersymmetry with the ATLAS Detector

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    This is a review of searches for supersymmetry (SUSY) with the ATLAS detector in proton-proton collisions at a center-of-mass energy of 7 TeV at the Large Hadron Collider at CERN. The review covers results that have been published, or submitted for publication, up to September 2012, many of which cover the full 7 TeV data-taking period. No evidence for SUSY has been seen; some possibilities for future directions are discussed.This is a review of searches for supersymmetry (SUSY) with the ATLAS detector in proton-proton collisions at a center-of-mass energy of 7 TeV at the Large Hadron Collider at CERN. The review covers results that have been published, or submitted for publication, up to September 2012, many of which cover the full 7 TeV data-taking period. No evidence for SUSY has been seen/ some possibilities for future directions are discussed

    Inclusive Searches in ATLAS: How can we discover SUSY in 2009

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    Version of slides actually delivered for the U.Michigan LHC-Dark Matter Workshop, 6-10 Jan 200

    Recent results on SUSY and BSM searches from ATLAS and CMS

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    This is a draft of my slides for Pheno2011. The time allocated was originally 45 minutes, but now has been cut back to 30 minutes. There might be too much material here; some of it might have to go to the backup pages

    Performance of the ALEPH silicon vertex detector

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