Making use of our extended version of ¨ O p i k ′ s convection theory, we have calculated magnetic cycle periods of the sun and late type stars by using Parker's dynamo theory, where we have included the non-linear effect. We presented a relationship between the computed cycle period and spectral type to analyze observed magnetic activities of the late type stars and long-term luminosity variations. It is found that (1) the stellar magentic-cycle period increases towards the later spectral type, (2) the rapid rotation facilitates the activity-related luminosity variation of stars later than about K5, (3) differential rotation plays a critical role in determining the magnetic activity-cycle period, and (4) the non-local effect should be taken into account in order to understand the observed long-term luminosity variations.

A generalization of the original ¨ O p i k ′ s cellular convection theory has been made to accomodate a rotating convective medium. With the use of the formulation, a set of rotating model envelopes of the sun and late type main sequence stars have been constructed under three different rotation periods. Their thermal structures are presented and characteristics of their convection are discussed in the context of stellar dynamo. In the present study it is noted that the rotational angular velocity increases in wards with depth, and its increase turns out to be about 6% at the bottom of the solar convection zone.