Searches for the lepton number violating K+→π−μ+e+ decay and flavor K+→π+μ−e+ π0→μ−e+ decays are reported using data collected by NA62 experiment at CERN in 2017–2018. No evidence these is found upper limits of branching ratios obtained 90% confidence level: B(K+→π−μ+e+)<4.2×10−11, B(K+→π+μ−e+)<6.6×10−11 B(π0→μ−e+)<3.2×10−10. These results improve 1 order magnitude over previous modes.Received ...

Let G be a locally compact group and μ measure on G. In this paper we find conditions for the convolution operators λp(μ):Lp(G)→Lp(G) to mean ergodic uniformly ergodic. The properties of λp(μ) are related as well.

We generalize the notion of a fat subset of a regular cardinal κ to a fat subset of Pκ(X), where κ ⊆ X. Suppose μ < κ, μ<μ = μ, and κ is supercompact. Then there is a generic extension in which κ = μ++, and for all regular λ ≥ μ++, there are stationarily many N in [H(λ)]μ which are internally club but not internally approachable. Suppose μ is an infinite cardinal. A set N is internally approach...