\begin{document}$ \Lambda = 3 \nu H^2 + \Lambda_0 $\end{document} , where \begin{document}$ H $\end{document} is the Hubble parameter. In this model, dark energy decreases in time and decays to both matter and radiation. By using the Markov chain Monte Carlo method, we constrain the model parameter \begin{document}$ \nu $\end{document} as well as the cosmological observables. Explicitly, we obtain \begin{document}$ \nu \leqslant 1.54 \times 10^{-4} $\end{document} (68% confidence level) in the RVM with the best-fit \begin{document}$\chi^2_{\mathrm{RVM}} = 13968.8$\end{document} , which is slightly smaller than \begin{document}$\chi^2_{\Lambda \mathrm{CDM}} = 13969.8$\end{document} in the \begin{document}$\Lambda{\rm{CDM}}$\end{document} model of \begin{document}$ \nu=0 $\end{document} ."> Observational constraints on running vacuum model -
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