This paper presents the first analysis of the contact binary TYC 3801-1529-1. We observed four sets of multiple bands complete light curves and one set of radial velocity curve of the primary component. Based on a simultaneous investigation of our observed and TESS light curves and the radial velocity curve, we found that TYC 3801-1529-1 is an extremely low-mass-ratio, medium contact binary with q = 0.0356, with the contribution of the third light at a level of about 10%. Its mass ratio is lower than V1187 Her, making TYC 3801-1529-1 the lowest mass-ratio contact binary ever found in the universe. The light curves observed in 2022 are asymmetric, which is aptly explained by a hot spot on the primary component. A 16-year eclipse timings analysis indicates a secular increase orbital period with a rate of dp/dt = 7.96(±0.35)×10⁻⁷ d yr⁻¹. We studied the stability of this target and identified that not only the value of J_spin/J_orb, but also the mass ratio surpass the unstable boundary. Hence, TYC 3801-1529-1 presents a challenge to theoretical research and ought to be considered a progenitor of a contact binary merger.

Photometric observations for the totally eclipsing binary system TYC 4002-2628-1, were obtained between November 2020 and November 2021. To determine the stellar atmospheric parameters, a spectral image was taken with the 2.16 m telescope at National Astronomical Observatory of China (NAOC). TYC 4002-2628-1 is a low-amplitude (about 0.15 mag for Vband) short-period (0.3670495 d) contact eclipsing binary with a total secondary eclipse. Intrinsic light curve variations and the reversal of the O’Connell effect are detected in the light curves, which may be due to spot activity. Based on the photometric solutions derived from the multiband time series light curves, TYC 4002-2628-1 is an extremely low-mass ratio contact binary with a mass ratio of q ∼ 0.0482 and a fill-out factor of |$f\sim 5{{\ \rm per\ cent}}$|⁠. By analysing the O− C variations, we find that its orbital period remains unchanged when BJD < 2458321. Then the orbital period changed suddenly around BJD 2458743 and has an increasing rate of |$\mathrm{ d}P/\mathrm{ d}t=1.62\times {10^{-5}}\,\mathrm{ d}\cdot \mathrm{ yr}^{-1}=140\, \mathrm{ s}\cdot \mathrm{ century}^{-1}$|⁠. If confirmed, TYC 4002-2628-1 would be the contact binary with the highest orbital period increasing rate so far. By investigating the ratio of orbital angular momentum to the spin angular momentum (J_orb/|$J_{\mathrm{ spin}}\, \lt\, 3$|⁠), the instability mass ratio (q_inst/q = 1.84) and the instability separation (A_inst/A = 1.35), TYC 4002-2628-1 can be regarded as a merger candidate.

In this paper, the total eclipsing binary WISE J185503.7+592234 (hereinafter J185503), whose mass ratio is around the mass ratio limit, was observed and investigated for the first time. The stellar atmospheric parameters of the primary (more massive) component were calculated by the spectral fitting, and the following results are obtained: T_eff = 5747 ±25 K, [Fe/H] = -0.16±0.04 dex, logg= 4.78 ±0.05 cms⁻². Although J185503 has a very small amplitude ( ∼ 0.17 mag in V band) and a short period (0.2800782 d), its light curves exhibit total eclipses (eclipse duration: ∼ 40 minutes, which is about 0.1 phase). The light curves derived from TESS exhibit some unusual behavior, such as inversion of the O’Connell effect, exchange of occultation, and transit depths. Photometric solutions obtained from the multi-band observations suggest that J185503 has a particularly low mass ratio (q=0.0514) and a moderate contact degree of |$26\%$|⁠. Based on 103 newly determined times of minimum spanning 14 years, a secular period decrease was found, which is calculated to be dP/dt = −2.24 × 10⁻⁷ days yr⁻¹. Through analyzing the instability criterion, such as the instability separation, the instability mass ratio, and the ratio of spin angular momentum (J_spin) to the orbital angular momentum (J_orb), J185503 can be regarded as a progenitor of luminous red novae.

LX Ser is a deeply eclipsing cataclysmic variable with an orbital period of 0.1584325 d. 62 new eclipse times were determined by our observations and the AAVSO International Data base. Combining all available eclipse times, we analyzed the O − C behavior of LX Ser. We found that the O − C diagram of LX Ser shows a sinusoidal oscillation with a period of 22.8 yr and an amplitude of 0.00035 d. Two mechanisms (i.e., the Applegate mechanism and the light-travel time effect) are applied to explain the cyclic modulation. We found that it is difficult to apply the Applegate mechanism to explain the cyclic oscillation in the orbital period. Therefore, the cyclic period change is most likely to be caused by the light-travel time effect due to the presence of a third body. The mass of the tertiary component was determined to be M₃ ∼ 7.5 M_Jup. We supposed that the tertiary companion is plausibly a giant planet. The stability of the giant planet was checked, and we found that the multiple system is stable.