Since September 2018, LAMOST starts a new 5-year medium-resolution spectroscopic survey (MRS) using bright/gray nights. We present the scientific goals of LAMOST-MRS and propose a near optimistic strategy of the survey. A complete footprint is also pro-

The stability of mass transfer is important in the formation of contact binaries from detached binaries when the primaries of the initially detached binaries fill their Roche lobes. Using Eggleton's stellar evolution code, we investigate the formation and the short-period limit of contact binaries by considering the effect of the instability of mass transfer. It is found that with decreasing initial primary mass from 0.89M$_{\rm \odot}$ to 0.63M$_{\rm \odot}$, the range of the initial mass ratio decreases for detached binaries that experience stable mass transfer and evolve into contact. If the initial primary mass is less than 0.63M$_{\rm \odot}$, detached binaries would experience dynamically unstable mass transfer when the primaries of detached binaries fill their Roche lobes. These systems would evolve into a common envelope situation and probably then to a complete merger of two components on a quite short timescale. This results in a low mass limit at about 0.63M$_{\rm \odot}$ for the primary mass of contact binaries, which might be a main reason why the period distribution of contact binaries has a short limit of about 0.22 days. By comparing the theoretical period distribution of contact binaries with the observational data, it is found that the observed contact binaries are above the low mass limit for the primary mass of contact binaries and no observed contact binaries are below this limit. This suggests that the short-period limit of contact binaries can be explained by the instability of the mass transfer that occurs when the primaries of the initially detached binaries fill their Roche lobes.Comment: 11 pages, 4 figures, Accepted for publication in Monthly Notice

Well-determined physical parameters of 130 W UMa systems have been collected from the literature. Based on these data, the evolutionary status and dynamical evolution of W UMa systems are investigated. It is found that there is no evolutionary difference between W- and A-type systems in $M-J$ diagram which is consistent with the results derived from the analysis of observed spectral type, $M-R$ and $M-L$ diagrams of W UMa systems. $M-R$ and $M-L$ diagrams of W- and A-type systems indicate that a large amount of energy should be transferred from the more massive to the less massive component so that they are not in thermal equilibrium and undergo thermal relaxation oscillation (TRO). Meanwhile, the distribution of angular momentum, together with the distribution of mass ratio, suggests that the mass ratio of the observed W UMa systems is decreased with the decrease of their total mass. This could be the result of the dynamical evolution of W UMa systems which suffer angular momentum loss (AML) and mass loss due to magnetic stellar wind (MSW). Consequently, the tidal instability forces these systems towards the lower q values and finally to fast rotating single stars.Comment: 8 pages, 5 figures, accepted for publication in MNRA