We present the full VRI light curves and the times of minima of TY UMa to provide a complete photometric solution and a long‐term trend of period variation. The light curves show a high degree of asymmetry (the O'Connell effect). The maxima at 0.25 phase (Max I) are 0.021, 0.015, and 0.020 mag fainter than those at 0.75 phase (Max II) in V, R, and I, respectively. The period of TY UMa has varied in a sinusoidal way, superimposed on the long‐term upward parabolic variation. The secularly increasing rate of the period is deduced as 1.83 s per century (P˙/P=5.788×10‐10 d d‐1). The period of sinusoidal variation is about 57.4 yr. The spot model has been applied to fit the asymmetric light curves of TY UMa, to explain light variations. By changing only the spot parameters, the model light curves can fit the observed light curves for three epochs. This indicates that the variation of the spot location and size is the main reason for changing the shape of light curves, including two different maxima and the interchanging depths of occultation and transit minima.

We present new multicolor charge-coupled device (CCD) photometry for the short-period close binary V432 Per, made on six nights between 2006 February and December. A period study of the system, based on all published and newly observed times of minimum light, reveals that the orbital period has varied as a beat effect due to the combination of a secular period increase and a sinusoidal variation, with a period of 35.3 yr and semi-amplitude of 0.0104 d. The continuous period increase can be interpreted as mass transfer from the less massive secondary star to the more massive primary component in the system with a rate of about 1.16 × 10 −7 M yr −1 . The sinusoidal component of the period variability could, in principle, be produced by either a light-time effect due to a third body or a magnetic modulation seated in at least one component star, but light variations do not conform to a prediction of the second mechanism. New light curves, showing a total eclipse at secondary minimum and a variable O'Connell effect, are best modeled by including a third light source and a cool spot on the primary star. The model also represents Agerer's light curves. Our results indicate V432 Per, at present, to be in a broken or a marginal contact stage, investing a hotter, more massive primary star with a spectral type of G4 and a cooler, less massive secondary star with a spectral type of G8−G9. We suggest that the most likely explanation of the sinusoidal variation is the existence of a gravitationally bound M-type tertiary companion. When all of this is verified and understood more comprehensively, the formation and evolution of this binary system should be greatly advanced.

New CCD photometric observations of the near-contact binary RU UMi were obtained from1999 December to 2000 April and later during 2003 March. All available times of minimum light, including our own measurements, have been examined and indicate that the orbital period of the system has experienced a continuous period decrease with a rate of ðdP =dtÞ obs ¼ À1:6 × 10 À8 d yr À1 . This period decrease cannot be explained trivially by mass transfer from the more massive primary to the less massive secondary, because our light-curve synthesis indicates that RU UMi is in a semidetached configuration with the primary star filling 95% of its inner Roche lobe and the secondary filling its limiting lobe completely. We present the case that the observed period change may be produced by a combination of AML due to magnetic braking with a rate of ðdP =dtÞ mb ¼ À1:0 × 10 À7 d yr À1 and of mass transfer from the secondary to the primary at a rate of _ M 2 ¼ À6:0 × 10 À8 M ⊙ yr À1 . Historical light curves of RU UMi over a 32-yr interval display variably asymmetrical secondary minima. From analyses of velocity and light curves and of the light curves alone, the light variations are best represented by a variable cool spot that has consistently existed on the inner hemisphere of the secondary component. There is a weak indication that the hot star is no longer a main sequence one.

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