A Big Horizontal Solar Telescope of the Main Astronomical Observatory of the Ukrainian National Academy of Sciences in the caucasus

This paper presents the Big Horizonal Solar Telescope of the Main Astronomical Observatory of the Ukrainian National Academy of Sciences installed at the Peak Terskol high-altitude station near Elbrus (the main mirror diameter is 650 mm and the focal length is 17.5 m). The telescope is equipped with a five-camera spectrograph intended for photographic spectral observations of active regions in the solar atmosphere and photoelectric measurements of the solar spectra with high spectral and spatial resolution. The observation procedure is described, and the results of the quality analysis of the recorded spectra and of the early measurements are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 10, pp. 1326–1333, October, 1996.The authors wish to express their gratitude to C.I.Gandzha, V.V.Kul'beda, and Yu. M. Gavrilyuk from the Solar Physics Department of the PAO of the Ukrainian NAS and to the Board of Directors of the Observatory and of the High-Altitude Station for help in the development of the instrument.This paper is dedicated to the memory of E. A. Gurtovenko, D.Sc. in Phys. and Math., who initiated the installation of the telescope at Peak Terskol and who was the leader, an executor, and an observer in this project.     

On a multiplicative function on the set of shifted primes

It is proved that if ?(n) is a multiplicative function taking a valueζ on the set of primes such thatζ ³ = 1,ζ ≠ 1 and? ³(p ^r)=1 forr≥2, then there exists aθ ∈ (0, 1), for which $$|\sum\limits_{p \leqslant x} f (p + 1)| \leqslant \theta \pi (x)$$ , where $$\pi (x) = \sum\limits_{p \leqslant x} 1$$ .     

Reducibility behavior of polynomials with varying coefficients

LetK be a number field, and leth∈K[Y] be a polynomial of degreen. Fix an integer 0≤i≤n and compare the set ν of those integersa ofK such thath(Y)−aY ⁱhas a root inK with the set of those integersa, such thath(Y)−aY ⁱis reducible overK. Ifi is coprime ton, then we classify the rare cases where ν is not cofinite in . The main tools are a theorem of Siegel about integral points on algebraic curves and the theory of finite groups.     

On the location parameter confidence intervals based on a random size sample from a partially known population

The problem of constructing confidence intervals of a fixed length for the location parameter based on a random size sample is considered. It is proposed to use the confidence interval $$\theta _p^* - u\sqrt p /\sigma< \theta< \theta _p^* + u\sqrt p /\sigma $$ , whereθ _p ^* is an adaptive estimator,σ ² is the Fisher information, and p^?1 is the mean of the sample size. Nonparametric bounds are given for the limit as p → 0 confidence probability. Bibliography: 5 titles.