Does the proton-to-electron mass ratio μ=mp/me vary in the course of cosmological evolution?

The possible cosmological variation of the proton-to-electron mass ratio mu=m(p)/m(e) 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 Deltamu/mu=(3.0+/-2.4)x10(-5); for the weighted value Deltamu/mu=(5.02+/-1.82)x10(-5). Since the significance of the both results does not exceed 3sigma, 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.): \Deltamu/mu\ < 8x10(-5). This value serves as an effective tool for selection of models determining a relation between possible cosmological deviations of the fine-structure constant and the elementary particle masses (m,m, etc.).