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References
Singular limit problem for the two-dimensional Keller-Segel system in scaling critical space
We consider the singular limit problem of the Cauchy problem to the Keller-Segel equation in the two dimensional critical space. It is shown that the solution to the Keller-Segel system in the scaling critical function space converges to the solution to the drift-diffusion system of parabolic-elliptic equations (the simplified Keller-Segel equation) in the critical space strongly as the relaxation time parameter tau -> infinity. For the proof, we show generalized maximal regularity for the heat equations and use it systematically with the sequence of embeddings between the interpolation spaces (B) over dot(q,sigma)(s) (R-2) and (F) over dot(q,sigma)(s) (R-2) for the proof of singular limit problem. (c) 2020 Elsevier Inc. All rights reserved.
Recent results on B -> mu(+)mu(-) decays with the CMS experiment
Results on B -> mu(+)mu(-) decays with the CMS experiment are reported, using 61 fb(-1) of data recorded during LHC Run 1 and 2016. With an improved muon identification algorithm and refined unbinned maximum likelihood fitting methods, the decay B-s(0) -> mu(+)mu(-) is observed with a significance of 5.6 standard deviations. Its branching fraction is measured to be (B) over bar (B-s(0) -> mu(+)mu(-) ) = [2.9 +/- 0.7 (exp)+/- 0.2 (frag)]x 10(-9), where the first error is the combined statistical and systematic uncertainty and the second error quantifies the uncertainty of the B-s(0) and B+ fragmentation probability ratio. The B-s(0) -> mu(+)mu(-) effective lifetime is tau(mu+mu)- = 1.70+(+0.61)(-0.44) ps. No evidence for the decay B-0 -> mu(+)mu(-) is found and an upper limit of B(B-0 -> mu(+)mu(-)) < 3.6 x 10(-10) (at 95% confidence level) is determined. All results are consistent with the standard model of particle physics.