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12 stable single sunspots were investigated in two aspects. The outer boundaries of the sunspots umbra were determined by an independent mathematical method and the vertical component of the magnetic field at these boundaries was found. We analyzed data from the SDO station using the segments of the continuum and magnetic field. It is shown that in a wide range of sunspot fields, the field average along the contour changes weakly, while the vertical component of the magnetic field itself, in a particular spot, changes significantly along the defined contour which reflects the fibrous structure of the penumbral field.

The main small-scale elements observed in the solar photosphere at high resolution are discussed: granules, faculaes, micropores. As a separate element of the fine structure, a continuous network of dark intergranular gaps is considered. The results of image processing of micropores and faculaes knots obtained using modern adaptive telescopes are presented. For intergranular gaps and micropores, a stationary regime of magnetic diffusion is determined, in which horizontal-vertical plasma flows converging to the gap (and micropores) compensate for the dissipative spreading of the magnetic flux on a given scale. A theoretical assessment of the characteristic scales of these structures in the photosphere is obtained: 20-30 km for the thickness of dark intergranular spaces and 200-400 km for the diameter of micropores.

The global oscillations of the Sun are investigated on the base of three independent sets of data: 1. Records of Total Solar Irradiance (TSI). 2. The average brightness of the photosphere in MDI (SOHO) and HMI (SDO) images. 3. Records of the time variations of sunlight reflected from the planets during their passage in the field of view of the LASCO C3 coronagraph. It is found that in the low-frequency spectrum of solar oscillations as a star there are modes of 8-10, 36-38 hours and the main stable 9-day mode. The last mode can be regarded as a reflection of oscillatory processes near the fast rotating core of the Sun according to Fossat et al. (2017)., Comment: 21 pages

A specific type of artifacts, that originate due to displacement of the image of a moving object along the digital (pixel) matrix of receiver are analyzed in detail. The criteria of appearance and the influence of these artifacts on the study of long-term oscillations of sunspots are deduced. The obtained criteria suggest us methods for reduction or even elimination of these artifacts. It is shown that the use of integral parameters can be very effective against the artifact distortions. The simultaneous observations of sunspot magnetic field and ultraviolet intensity of the umbra have given the same periods for the long-term oscillations. In this way the real physical nature of the oscillatory process, which is independent of the artifacts have been confirmed again. A number of examples considered here confirm the dependence between the periods of main mode of the sunspot magnetic field long-term oscillations and its strength. The dependence was derived earlier from both the observations and the theoretical model of the shallow sunspot. The anti-phase behavior of time variations of sunspot umbra area and magnetic field of the sunspot demonstrates that the umbra of sunspot moves in long-term oscillations as a whole: all its points oscillate with the same phase., Comment: 25 pages, 12 figures

We investigate the long-period fluctuations in the brightness of the Sun as a star using the measurements of sunlight reflected from the planets (Jupiter, Mars) when the light hits the field of view of the LASCO C3 coronagraph (Large Angle and Spectrometric Coronagraph Experiment)., Comment: 7 pages,3 figures

The data of ground-based telescopes of Global Oscillation Network Group (GONG) obtained in the H-alpha line provide an opportunity to study the long-period oscillations of chromospheric filaments (quiescent prominence). For the first time, on the base of time-series of 5 days duration, combined from the observations of three observatories of the GONG, a new ultra-low mode, with period between 20 and 30 hours, was reliably detected in oscillations of a long-lived dark filament on the solar disc.

We processed magnetograms that were obtained with the Michaelson Doppler Imager onboard the Solar and Heliospheric Observatory (SOHO/MDI). The results confirm the basic properties of long-period oscillations of sunspots that have previously been established and also reveal new properties. We show that the limiting (lowest) eigenmode of low-frequency oscillations of a sunspot as a whole is the mode with a period of 10 - 12 up to 32 - 35 hours (depending on the sunspot's magnetic- field strength). This mode is observed consistently throughout the observation period 5 - 7 days, but its amplitude is subject to quasi-cyclic changes, which are separated by about 1.5 - 2 days. As a result, the lower mode with periods of about 35 - 48 hours appears in the power spectrum of sunspot oscillations. But this lowest mode is apparently not an eigenmode of a sunspot because its period does not depend on the magnetic field of the sunspot. Perhaps, the mode reflects the quasi-periodic sunspot perturbations caused by supergranulation cells that surround it. We also analyze SOHO/MDI artifacts, which may affect the low-frequency power spectra of sunspots.

Long (up to 100 hours) time series of SOHO/MDI Doppler data are analyzed. The power spectrum of radial velocity time series in the quiet photosphere is observed to have, along with the known 5-min mode, a stable strong mode with a period of about 32 h, which is close to the supergranulation cell lifetime. The spatial distribution of the amplitudes of these oscillations also coincides with the characteristic size scale of supergranulation (~35 Mm)., Comment: 6 pages, 4 figures

Three independent sets of data: i). series of filtergrams obtained in line CaII K (393.416 nm) with the ground-based telescope Precision Solar Photometric Telescope (PSPT) of Mauna Loa Solar Observatory; ii). series of filtergrams of Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) in {\lambda}160 nm and iii). series of magnetograms of Helioseismic and Magnetic Imager (HMI) of SDO have been processed to reveal reliably the existence of spatial cellular structures on the solar photosphere at scale about of 300 arcsec. This scale is intermediate between supergranules and giant cells (~30,000 and ~300,000 kilometers across, respectively). To identify the different spatial structures the tens of two-dimensional power spectra (2DFFT) have been averaged. For one-dimensional photometric cross sections of frames, the Fourier power spectra (FFT) and wavelet transforms (Morlet 5-th order) have been calculated., Comment: 10 pages, 6 figures. Accepted in Astrophys Space Sci

A model of topological field theory is presented in which the vacuum coupling constants are topological invariants of the four-dimensional spacetime. Thus the coupling constants are theoretically computable, and they indicate the topological structure of our universe., Comment: 3 pages, a talk delivered at the 11th Marcel Grossmann Meeting (2006)

We present the results of the observations of the giant bursts from the X-ray pu lsar A0535+26 made by HEXE onboard Mir-Kvant in April 1989, November 1993 and February 1994. The pulse periods were measured, pulse profiles in different energy bands were produced, and their variability was investigated. The power density spectra (PDS) in 2x10^(-3)-1 Hz range is presented, which shape is typical for flicker-noise processes, usually observed in black hole candidates. The noise rms grows with energy from ~20% at 20 keV to ~30% at 80 keV. The source photon spectrum in the 15-200 keV energy range and its variability over the pulse phase are reported. Approximately the shape of the spectrum can be described by the "canonical" model for X-ray pulsars with power-law index g~1.1, cut-off energy E_c~23 keV and folding energy E_f~19 keV. All these parameters are weakly dependent on the luminosity. The most significant deviation from this continuum is observed at ~100 keV in the spectrum of the main pulse maximum. This feature is interpreted as a cyclotron line. Comparison of the HEXE data with the data from BATSE/CGRO (Bildsten et al., 1997) shows that in the high luminosity state (L~10^38 erg/s) the pulsar's pulse profile differs substantially from the pulse profile in the low-luminosity (L~5x10^36 erg/s) state. This difference is explained by the qualitative change of the polar cap structure with formation of the accretion columns., Comment: 15 pages

In 1993-1994 a series of observations of the X-ray pulsar GX 301-2 by HEXE onboard Mir-Kvant was made. A period of pulsations was measured (it varied between 675 and 678 s) and pulse profiles in different energy bands were produced. The measured luminosity in the 20-100 keV energy range changed substantially between 8x10^34 and 7x10^35 d^2 erg/s (d is the distance to the source in kpc). The obtained spectrum is quite satisfactory described by the canonical model for X-ray pulsars with gamma=1.3, E_c~23 keV, E_f~9 keV. It changed weakly between the observations, but was softest at brightness maximum. Significant variations of the spectral hardness over the pulse phase were detected, but the accumulated data are insufficient to quantify variations in spectral parameters. No significant traces of cyclotron lines were found. An interpretation of the pulse profiles as superposition of emissions from two flat polar caps (with inclusion of gravitational lensing) leads to an estimate of the angle between the magnetic axis and axis of rotation of 40-70 deg and an angle between the direction to the observer and the rotation axis of 75-85 deg., Comment: 12 pages, 7 figures