On the Clebsch-Gordan coefficients for the two-parameter quantum algebra SU(2)p,qSU(2)_{p,q}

We show that the Clebsch - Gordan coefficients for the $SU(2)_{p,q}$ - algebra depend on a single parameter Q = $\sqrt{pq}$ ,contrary to the explicit calculation of Smirnov and Wehrhahn [J.Phys.A 25 (1992),5563].Comment: 5 page

Modelling chemical reactions using semiconductor quantum dots

We propose using semiconductor quantum dots for a simulation of chemical reactions as electrons are redistributed among such artificial atoms. We show that it is possible to achieve various reaction regimes and obtain different reaction products by varying the speed of voltage changes applied to the gates forming quantum dots. Considering the simplest possible reaction, $H_2+H\to H+H_2$, we show how the necessary initial state can be obtained and what voltage pulses should be applied to achieve a desirable final product. Our calculations have been performed using the Pechukas gas approach, which can be extended for more complicated reactions

On a possible manifestation of the four color symmetry Z′Z' boson in μ+μ−\mu^+\mu^- events at the LHC

The cross section of the $\mu^+\mu^-$ pair production in $pp$-collisions at the LHC is calculated with acount of the $Z'$ boson induced by the minimal four color quark-lepton symmetry($MQLS$). The $\mu^+\mu^-$ invariant mass spectrum with account of the $MQLS$ $Z'$ boson is analysed in dependence on the $Z'$ mass. The mass region for the $MQLS$ $Z'$ boson observable at the LHC is found in dependence on the significance and on the integrated luminosity.Comment: 11 pages, 2 figures, accepted for publication in Modern Physics Letters