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New observational data on the last two outbursts of the EXor star V1118 Ori are presented. The combined light curve of the last outburst is derived and fitted. The dates of the start of the outburst, its maximum, and end, as well as the maximum magnitude, and the rates of increase and decrease of the brightness were determined.

Data from the Kepler Orbital Observatory are used in a statistical study of the periodic/cyclical variability of the flare frequency of 76 flare stars. Corresponding periodic functions of the flare frequency are obtained and a possible periodicity of the flare frequency with a period equal to the star’s rotation period is tested. The periodicities of the function of the flare frequency turned out to be close to the axial rotation periods of the stars. Theoretical distributions of the flares with respect to phase are constructed and compared with the analogous observed distribution of the flares for a given period. For all the stars, without exception, this comparison (using the χ2 criterion) supports a periodicity of the flare frequency. These results indicate that (a) the flare frequency is modulated by the axial rotation of the stars and (b) structural and physical variations in the active regions of these stars proceeded relatively slowly. Some of these stars have planetary systems. It is suspected that the orbital rotation of a planet affects the flare frequency of the star KIC 5791720.

This is a statistical study of a sample of 1547 superflares in 270 stars found during an analysis of data on more than 80000 stars of the sun’s type (obtained by the Kepler orbital observatory during the first 500 days of observations). Estimates are given of the total number of stars capable of superflares and the superflare distribution frequency function is determined.

This is a statistical study of the variability in the frequency of superflares in 46 stars of the solar type observed with the Kepler orbital observatory. Two possible scenarios for changes in the superflare frequency are examined. In the first, the time sequence of superflares is treated as a piecewise stationary Poisson process. 5 stars are found to have statistically significant changes by several times in their superflare frequency. The times at which the frequency changes are accompanied by changes in the behavior of a star’s brightness outside the flares. For a short time the star’s brightness becomes irregular, with a substantial reduction in its luminosity amplitude. In the second scenario, the time sequence of the superflares is treated as a Poisson process with a periodic parameter (the superflare frequency). This scenario confirms the existence of a possible periodicity of the superflare frequency with a period equal to the period of the star’s orbital or axial rotation. The star KIC 7264976 is found to have a frequency periodicity with a period that is the same as the possible period of its orbital rotation. A frequency periodicity with a period equal to the probable axial rotation period is found for the star KIC 10422252.

A statistical study of solar-type stars for which superflares have been observed with the Kepler orbital observatory is presented. Methods developed for solving similar problems for flare stars are invoked to do this. The total number of stars capable of superflares is estimated and the flare frequency distribution is determined for the complete set of stars and for separate subsamples constructed by breaking the complete sample into two parts in terms of the rotation periods and variability amplitudes of the stars. The star KIC 7264976 is found to have a statistically significant variation in its frequency of superflares.

The frequency distribution of x-ray flares is determined for the young, lowest-mass stellar objects in the Orion nebula. The methods used to do this have been developed previously for determining the analogous function for optical flares of flare stars. For this sample it is found that the x-ray flaring frequency distribution can be described by an exponential function.

Methods for determining the frequency distribution function of optical flares have been developed and successfully applied in statistical studies of flare stars. X-ray observations of flare stars provide a basis for extending the use of these methods to statistical studies of X-ray flares of young stellar objects. This article gives a brief description of methods which can be used for determining the frequency distribution of the X-ray flares of young stellar objects. The corresponding function is determined for a sample of 195 low-mass young stellar objects in the cloud L1688, which forms part of the complex of dark clouds ρ Oph. It is found to have an exponential form.

Methods of detecting probable cycles in the flaring activity of flare stars and determining the cycle durations are examined. A new method of detecting a cycle of flaring activity and determining its duration is proposed assuming periodic flaring activity. This method is applied to two stars from the list of flare stars in the Pleiades cluster, Ton91 and Ton377. Variable flaring activity is found in both stars and the periods are estimated to be P=15.2 and 17.7 years for Ton91 and Ton377, respectively.

The frequency of flares is one of the basic characteristics of the activity of flare stars. Long-term variations in the flaring frequency are determined by comparing the distribution functions of the flaring frequency for systems of flare stars with different ages.

A new method is proposed for determining the frequency distribution of bursts from randomly flashing objects based on fitting Pearson distributions by the method of moments. This method is applied to flare stars in the Pleiades cluster and the Orion association. The desired frequency distribution of the bursts from flare stars can be approximated by a gamma distribution. The burst frequency distribution describes the observed statistical picture fairly well. The result is compared with other methods.

The possible variation of the flare frequency of flare stars in the Orion association is considered. It is shown that of the 23 chosen stars, each having exhibited four or more flares, a change in flare frequency at the 0.1 significance level can be suspected for 13.

The distribution of proper motions of stars in the Pup-CMa association is presented. The stars' velocities are approximately parallel to each other, which indicates that the stars are close together in space. The mutual distribution of stars and molecular clouds in the association is interpreted as proof that the stars emerged from a single gigantic primordial molecular cloud (or several large clouds), destroyed by radiation and/or stellar wind coming from those stars. It is assumed that part of that cloud is being dissipated, while part is being broken into several small clouds, which we are observing at present.

The possible variation of the flare frequencies of flare stars in the Pleiades cluster is considered. It is shown that of the 75 chosen stars that each exhibit five or more flares, 33 can be suspected of variation of flare frequency at the 0.1 significance level.

The question of the possible variation of the flare frequency of flare stars is considered.

The analysis of the proper motions of bright members of the Per OB2 association on the basis of Hipparcos high-accuracy astromethc observations is presented. The existence of two different subgroups of OB-stars in the Per OB2 association that are in the state of expansion is considered. The expansion ages are calculated as 1.3 and 1.9×106 years. The membership of the observed OB-stars to these subgroups is considered.

The emission from a charged particle moving in a medium containing randomly distributed dust particles is considered. It is shown that in certain cases, the diffusional mechanism of emission is the principal one in the x-ray range. Possible astrophysical applications of this mechanism are considered. Spectral indices in the x-ray range are calculated, in particular. The calculated spectral indices agree well with those of active galactic nuclei.

New estimates are proposed for the number of flare stars. They are compared with Ambartsumian’s well-known estimate. Using the new estimates, it is found that flare stars of the same luminosity in the Orion association have the same average flare frequency.

The results of spectroscopic observations of 30 galaxies from the Second Byurakan Spectral Sky Survey in a field of 16 square degrees centered at coordinates a = 15h30m, δ = + 53°are presented. The spectra were obtained on the 6-m telescope of the Special Astrophysical Observatory, Russian Academy of Sciences, in the wavelength range of 4000–7400 A with 15 A resolution. Emission lines are present in the spectra of most of the galaxies. Redshifts and absolute stellar magnitudes were determined for all the galaxies.

A method is suggested for the determination of the distribution function for the mean frequency of supernova explosions, which is similar to the Ambartsumian method for the determination of the distribution function for the mean flare frequency of flare stars. This method has not been applied because of the lack of the required data.