Does the proton-to-electron mass ratio vary in the course of cosmological evolution?

The possible cosmological variation of the proton-to-electron mass ratio was estimated by measuring the H_2 wavelengths in the high-resolution spectrum of the quasar Q~0347-382. Our analysis yielded an estimate for the possible deviation of \mu value in the past, 10 Gyr ago: for the unweighted value $\Delta \mu / \mu = (3.0\pm2.4)\times10^{-5}$; for the weighted value $$\Delta \mu / \mu = (5.02\pm1.82)\times10^{-5}$$ Since the significance of the both results does not exceed 3$\sigma$, further observations are needed to increase the statistical significance. In any case, this result may be considered as the most stringent estimate on an upper limit of a possible variation of \mu (95% C.L.): $$|\Delta \mu / \mu| < 8\times 10^{-5}$$ This value serves as an effective tool for selection of models determining a relation between possible cosmological deviations of the fine-structure constant \alpha and the elementary particle masses (m$_p$, m$_e$, etc.).