We calculate the complete next-to-next-to-leading order QCD correction of the charm quark contribution to the branching ratio for the rare decay K + → π + ν ¯ ν in the standard model. The inclusion of these O(αs) contributions leads to a significant reduction of the theoretical uncertainty from ±10.1% down to ±2.4% in the relevant parameter Pc, implying the left over scale uncertainties in B(K ...

The matrix shifts of the H-Xe stretching frequency of noble-gas hydrides, HXeCCH, HXeBr, and HXeI in various noble-gas matrices (in Ne, Ar, Kr, and Xe matrices) are investigated via the hybrid quantum-classical simulations. The order of the H-Xe stretching frequencies is found to be ν(gas) < ν(Ne) < ν(Xe) < ν(Kr) < ν(Ar) for HXeCCH and HXeBr, while it is ν(gas) < ν(Ne) < ν(Xe) < ν(Ar) < ν(Kr) f...

Atanassov (Fuzzy Sets and Systems 20 (1986) 87-96) defined basic operations over the intuitionistic fuzzy sets. Here we shall introduce two operations, subtraction and division, derived from the deconvolution for equations using addition and multiplication operations, respectively. In addition, we shall give some conditions to examine the correctness regarding the defined operations. The remark...

The proof I gave in class was perfectly correct ( except for one minor omission), but the last part was a little bit unclear, and I made it sound more complicated than it really should have been. So let me make the proof completely transparent. Recall that the situation under consideration was this: we had a signed measure ν on a measurable space (X,M). Knowing that such a measure cannot take b...