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We present the results of polarimetric and photometric observations of four near-Earth asteroids (NEAs) 162082 (1998 HL1), 163373 (2002 PZ39), 52768 (1982 OR2), and 159402 (1999 AP10). The observations were carried out at the 2.6-m and 1.25-m telescopes of the Crimean Astrophysical Observatory, the 2.0-m telescope of the Peak Terskol Observatory, and the 6-m telescope of the Special Astrophysical Observatory during the period of 2019–2020. The phase angles covered in the observations were 3°–27°, 69°–109°, 70°–76°, and 32°–72° for NEAs 162082, 163373, 52768, and 159402, respectively. We estimated the main polarimetric parameters of the phase curves for each asteroid. The geometrical albedo for NEAs 162082, 163373, and 159402 were found to be 0.348 ± 0.050, 0.192 ± 0.050, and 0.124 ± 0.020, respectively. The diameters for asteroids 162082, 163373, 52768, and 159402 were determined as 0.37 ± 0.05, 0.50 ± 0.05, 2.61 ± 0.20, and 2.27 ± 0.20 km, respectively. The polarization data for NEA 52768 and 159402 are similar. Their orbital elements a, e, q , and periods for these asteroids also showed close similarities, indicating a potential common parent body in the past. We found deviation of the polarization of NEAs 163373, 52768, and 159402 from the synthetic phase dependences of the polarization of the main taxonomic С, S, and E classes. To explain this, the modified Sh-matrix method was used. The computer simulation has shown that different values of the maximum of positive polarization of asteroids can be explained by different content of highly absorbing carbon matter. [ABSTRACT FROM AUTHOR]

We present results of polarimetric, photometric, and spectral observations of the near-Earth asteroid (3200) Phaethon carried out at the 6-m BTA telescope of the Special Astrophysical Observatory and the 2.6-m and 1.25-m telescopes of the Crimean Astrophysical Observatory over a wide range of phase angles during its close approach to the Earth at the end of 2017 (α = 19°–135°) and in 2020 at α = 52.2°. Using our and other available in literature data, we found that the maximum degree of linear polarization of Phaethon in the V band is P max = (45 ± 1) per cent at the phase angle α max = 124.0° ± 0.4°, whereas the inversion angle α inv = 21.4° ± 1.2° and polarimetric slope is h  = (0.326 ± 0.027) per cent per degree. Using the dependence 'polarimetric slope – albedo,' we have found the geometric albedo of asteroid Phaethon to be p v = 0.060 ± 0.005. This value falls into the lower range of albedo values for asteroids determined by different methods. The mean colour indices U–B  = 0.207 m ± 0.053 m and B–V  = 0.639 m ± 0.054 m of the asteroid are derived at heliocentric and geocentric distances 1.077 au and 0.102 au, respectively, and phase angle α  = 23.78°. The absolute magnitude of Phaethon is V (1,1,0) = 14.505 m ± 0.059 m. The effective diameter of Phaethon is estimated from obtained absolute magnitude and geometrical albedo, it is equal to 6.8 ± 0.3 km. The best fit to the observed polarimetric data was obtained with the Sh-matrix model of conjugated random Gaussian particles composed of Mg-rich silicate (90 per cent) and amorphous carbon (10 per cent). [ABSTRACT FROM AUTHOR]

ABSTRACT We report the detection of a faint optical flash by the 2-m Faulkes Telescope North simultaneously with the second of two prompt γ-ray pulses in INTEGRAL gamma-ray burst (GRB) 080603A, beginning at trest= 37 s after the onset of the GRB. This optical flash appears to be distinct from the subsequent emerging afterglow emission, for which we present comprehensive broad-band radio to X-ray light curves to 13 d post-burst and rigorously test the standard fireball model. The intrinsic extinction towards GRB 080603A is high ( A V, z= 0.8 mag), and the well-sampled X-ray-to-near-infrared spectral energy distribution is interesting in requiring an LMC2 extinction profile, in contrast to the majority of GRBs. Comparison of the γ-ray and extinction-corrected optical flux densities of the flash rules out an inverse-Compton origin for the prompt γ-rays; instead, we suggest that the optical flash could originate from the inhomogeneity of the relativistic flow. In this scenario, a large velocity irregularity in the flow produces the prompt γ-rays, followed by a milder internal shock at a larger radius that would cause the optical flash. Flat γ-ray spectra, roughly F∝ν−0.1, are observed in many GRBs. If the flat spectrum extends down to the optical band in GRB 080603A, the optical flare could be explained as the low-energy tail of the γ-ray emission. If this is indeed the case, it provides an important clue to understanding the nature of the emission process in the prompt phase of GRBs and highlights the importance of deep ( R > 20 mag), rapid follow-up observations capable of detecting faint, prompt optical emission. [ABSTRACT FROM AUTHOR]

formal analysis of so-called diffusion algorithms is performed. They are frequently used in structural recognition but are rather poorly theoretically studied. These algorithms are analyzed from the viewpoint of their ability to optimize a function of many discrete variables, which is represented as the sum of many terms each of which depends on only two variables. It is proved that, under some stop condition, a diffusion algorithm approximately solves certain subclasses of optimization problems with any predefined nonzero error. The totality of problems solved by diffusion algorithms includes all so-called acyclic and supermodular optimization problems and also some other problems for which solution algorithms are unknown. [ABSTRACT FROM AUTHOR]