Recent results of the searches for Supersymmetry in final states with one or two leptons at CMS are presented. Many Supersymmetry scenarios, including the Constrained Minimal Supersymmetric extension of the Standard Model (CMSSM), predict a substantial amount of events containing leptons, while the largest fraction of Standard Model background events -which are QCD interactions -gets strongly reduced by requiring isolated leptons. The analyzed data was taken in 2011 and corresponds to an integrated luminosity of approximately L = 1 fb −1 . The center-of-mass energy of the pp collisions was √ s = 7 TeV.

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We prove an estimate of Carleman type for the one dimensional heat equationwhere a(·) is degenerate at 0. Such an estimate is derived for a special pseudo-convex weight function related to the degeneracy rate of a(·). Then, we study the null controllability on [0, 1] of the semilinear degenerate parabolic equationwhere (t, x) ∈ (0, T ) × (0, 1), ω = (α, β) ⊂⊂ [0, 1], and f is locally Lipschitz with respect to u.

A measurement of the cosmic ray positron fraction e+/(e++e−)e+/(e++e−) in the energy range of 1–30 GeV is presented. The measurement is based on data taken by the AMS-01 experiment during its 10 day Space Shuttle flight in June 1998. A proton background suppression on the order of 106 is reached by identifying converted bremsstrahlung photons emitted from positrons

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Given α ∈ [0, 2) and f ∈ L 2 ((0, T) × (0, 1)), we derive new Carleman estimates for the degenerate parabolic problem wt + (x α wx)x = f , where (t, x) ∈ (0, T) × (0, 1), associated to the boundary conditions w(t, 1) = 0 and w(t, 0) = 0 if 0 ≤ α < 1 or (x α wx)(t, 0) = 0 if 1 ≤ α < 2. The proof is based on the choice of suitable weighted functions and Hardy-type inequalities. As a consequence, for all 0 ≤ α < 2 and ω ⊂⊂ (0, 1), we deduce null controllability results for the degenerate one-dimensional heat equation ut − (x α ux)x = hχω with the same boundary conditions as above.

This paper develops a unified method to derive decay estimates for general second order integro-differential evolution equations with semilinear source terms. Depending on the properties of convolution kernels at infinity, we show that the energy of a mild solution decays exponentially or polynomially as t -> +infinity. Our approach is based on integral inequalities and multiplier techniques. These decay results can be applied to various partial differential equations. We discuss three examples: a semilinear viscoelastic wave equation, a linear anisotropic elasticity model, and a Petrovsky type system. (C) 2007 Elsevier Inc. All rights reserved

The primary proton spectrum in the kinetic energy range 0.2 to 200 GeV was measured by the Alpha Magnetic Spectrometer (AMS) during space shuttle flight STS–91 at an altitude of 380 km. The complete data set combining three shuttle attitudes and including all known systematic effects is presented