This study is concerned with the mass transfer, mass accretion and binary evolution of long-period Algol-type eclipsing binaries (LPAs), which are semi-detached binaries with the secondary star filled with its Roche lobe. The Algol-type eclipsing binaries have undergone a mass ratio inversion and are currently in a slow phase of matter transfer from the secondary to the primary. They are important samples for the study of mass transfer and binary evolution, as well as the formation and evolution of accretion disks. However, due to the limitations of ground-based observations, the observation and identification of long-period samples has been severely limited. The Kepler and TESS space surveys now provide a good opportunity to study these long-period variables, and we are able to obtain long-term continuous photometric data from which a number of candidate sources of LPAs can be selected. And We have performed detailed studies of the candidate source RZ Hor for LPAs and the extremely low mass ratio LPA system V583 Lyr, including photometric analysis, pulsation analysis, spectral observation, and analytical processing.We obtain RZ Hor as an Algol-type eclipsing binary (oEA) with a δ Sct type primary. With a low mass ratio of q=0.161, the secondary star fills its Roche critical volume and is in a state of slow mass transfer, the rate of mass loss due to stellar wind is 10-8Msun yr-1 < dot{M} < 10-6Msun yr-1. The pulsation analysis of RZ Hor detected 25 frequency signals with a signal-to-noise ratio higher than 5.2, including 4 groups of tidal split frequencies and 17 independent frequencies, and identified 2 radial modes and 10 non-radial p mode pulsations.V583 Lyr is a long-period Algol system with a very low mass ratio (q=0.1) and a massive primary (M1=6.133Msun). The O-C analysis of the orbital period indicates that the mass transfer of V585Lyr is conservative, that mass transfer from the secondary star to the primary star is dominant, and we get the rate of increase of the period to be dP/dt =2.92×10-7 d yr-1. At the same time, the pulsation analysis of V583 Lyr found the multi-period optical variations, with two main pulsation frequency F1=4.369131(1)d-1, F2=2.246231(2)d-1 periodic oscillation. According to the current analysis results, whose mass is as high as M1 = 6.133 Msun, the pulsation frequencies are in the range of less than 10d-1 , we suggest that the primary star may be a slow pulsating B-type star.The outlook and work preparation for the near future which consists mainly of four parts: 1. The disk model fitting and asteroseismological study of Hα characteristic spectral lines of V583 Lyr as an example; 2. The statistics and screening of LPAs candidate sources from TESS, Kepler and OGLE surveys, and then the study and statistical analysis of the special sample of Algol-type eclipsing binaries for a large sample; 3. The O-C data of the long-term variation of the orbital period of Algol-type eclipsing binaries are collected and counted, and the corresponding physical mechanisms are investigated according to the long-term variation of their orbital period.
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