Core-collapse supernovae are among the most magnificent events in the observable universe. They produce many of the chemical elements necessary for life to exist and their remnants-neutron stars and black holes-are interesting astrophysical objects in their own right. However, despite millennia of observations and almost a century of astrophysical study, the explosion mechanism of core-collapse supernovae is not yet well understood.

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The first results are reported from a search for activity cycles in stars similar to the sun based on modelling their spotting with an algorithm developed at the Crimean Astrophysical Observatory. Of the more than thirty program stars, 10 manifested a cyclical variation in their central latitudes and total starspot area. The observed cycles have durations of 4-15 years, i.e., analogous to the 11 year Schwabe sunspot cycle. Most of the stars have a rough analog of the solar butterfly pattern, with a reduction in the average latitude of the spots as their area increases. A flip-flop effect during the epoch of the maximum average latitude is noted in a number of these objects (e.g. , the analog LQ Hya of the young sun or the RS CVn-type variable V711 Tau), as well as a reduction in the photometric rotation period of a star as the spots drift toward the equator, an analog of the differential rotation effect in the sun. Unlike in the sun, the observed spot formation cycles do not correlate uniquely with other indicators of activity-chromospheric emission in the CaII HK lines (Be Cet, EK Dra, Dx Leo), Hα line emission (LQ Hya, VY Ari, EV Lac), or cyclical flare activity (EV Lac). In V833Tau, BY Dra, EK Dra, and VY Ari short Schwabe cycles coexist with long cycles that are analogous to the Gleissberg solar cycle, in which the spotted area can approach half the entire area of the star.

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