  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.).

Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Theory