Bases of the quantum cluster algebra of the Kronecker quiver

We construct bar-invariant Z[q ±1/2 ]-bases of the quantum cluster algebra of Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the corresponding cluster algebra. As a byproduct, we prove positivity of the elements in these bases.     

A study of hadronic shower development in the ECAL of the alpha magnetic spectrometer Ⅱ

In this paper, we studied the development of hadronic shower in an electromagnetic calorimeter of Alpha Magnetic Spectrometer Ⅱ. Two parametrized empirical formulae were proposed to describe the hadronic shower shape in calorimeter. Using 100 GeV proton beam incident on the center of the ECAL, detailed plots of lateral and longitudinal hadronic shower behavior were given and we found the formulae can describe the development of the hadronic shower with the test beam data. The possible application of the parametrized formulae including e^±-π^± discrimination and tau jet reconstruction was discussed.