Mathematical Modelling of Astrophysical Objects and Processes

In this review, we present some advanced algorithms and programs used in our scientific school with short description of types of astrophysical systems, which we study. However, we discuss mainly mathematical methods, which may be applied to analysis of signal of any nature - in computer science, engineering, economics, social studies, decision making etc. The variety of types of signals need a diversity of adequate complementary specific methods, in an addition to common algorithms. As an example, one may refer to vibrations, stability of mechanisms. Many mathematical equations are common in Science, Technics and Humanities.Comment: 20 pages. A review devoted to the 90-th anniversry of the Odessa National Maritime University. Chapter of a monograp

THE MATHEMATICAL MODEL OF THE PHOTOMETRIC VARIABILITY AND CLASSIFICATION OF SEMIREGULAR PULSATING ASYMPTOTIC GIANTS BRANCH STARS

The modern review of the stars which are located at the position of asymptotic giant branch at the HRdiagram is presented. The most interesting problems connected to these objects are noted, as well as attention is paid to classification and to the evolutionary status. We provided mathematical modeling of the mean light curve of the semiregular supergiant S Per. It is shown, that by means of the periodogram analysis, it is possible to determine the period of the main variability and to provide further detailed classification of semiregular pulsating stars, approximating their mean light curves with a trigonometric polynomial. It is offered to use the photometric period for estimates of physical parameters of pulsing stars

THE MEAN LIGHT CURVES OF THE MIRA-TYPE STARS IN THE H- AND K-BANDS

For nine Mira-type stars (o Cet, R Leo, S Car, U Her, X Oph, R Aql, RR Aql, S Ori, S Scl,) and one semi-regular star (L2 Pup), the mean light curves have been obtained. The initial values of the brightness (observations) were fitted by a trigonometric polynomial of the statistically optimal order.The Fourier coefficients and the additional parameters (degree of the trigonometric polynomial, amplitude of the brightness, the maximal slope of ascending and descending branch, semi-amplitudes and initial epochs for the brightness maximum (minimum magnitude) of each harmonic contribution, etc., were given in the tables reported earlier by Kudashkina (2016). In this study, we have received several interesting correlations between these parameters in the bands H and K. It was particularly noted the anomalous position on the figures of the star X Oph.The mean light curves of the investigated stars are commonly symmetric in the near infrared region (H and K).. For nine Mira-type stars (o Cet, R Leo, S Car, U Her, X Oph, R Aql, RR Aql, S Ori, S Scl,) and one semi-regular star (L2 Pup), the mean light curves have been obtained. The initial values of the brightness (observations) were fitted by a trigonometric polynomial of the statistically optimal order.The Fourier coefficients and the additional parameters (degree of the trigonometric polynomial, amplitude of the brightness, the maximal slope of ascending and descending branch, semi-amplitudes and initial epochs for the brightness maximum (minimum magnitude) of each harmonic contribution, etc., were given in the tables reported earlier by Kudashkina (2016). In this study, we have received several interesting correlations between these parameters in the bands H and K. It was particularly noted the anomalous position on the figures of the star X Oph.The mean light curves of the investigated stars are commonly symmetric in the near infrared region (H and K).Stars: Pulsating: Mira-type: S

THE MEAN LIGHT CURVES OF THE MIRA-TYPE STARS IN THE H- AND K-BANDS

For nine Mira-type stars (o Cet, R Leo, S Car, U Her, X Oph, R Aql, RR Aql, S Ori, S Scl,) and one semi-regular star (L2 Pup), the mean light curves have been obtained. The initial values of the brightness (observations) were fitted by a trigonometric polynomial of the statistically optimal order.The Fourier coefficients and the additional parameters (degree of the trigonometric polynomial, amplitude of the brightness, the maximal slope of ascending and descending branch, semi-amplitudes and initial epochs for the brightness maximum (minimum magnitude) of each harmonic contribution, etc., were given in the tables reported earlier by Kudashkina (2016). In this study, we have received several interesting correlations between these parameters in the bands H and K. It was particularly noted the anomalous position on the figures of the star X Oph.The mean light curves of the investigated stars are commonly symmetric in the near infrared region (H and K).. For nine Mira-type stars (o Cet, R Leo, S Car, U Her, X Oph, R Aql, RR Aql, S Ori, S Scl,) and one semi-regular star (L2 Pup), the mean light curves have been obtained. The initial values of the brightness (observations) were fitted by a trigonometric polynomial of the statistically optimal order.The Fourier coefficients and the additional parameters (degree of the trigonometric polynomial, amplitude of the brightness, the maximal slope of ascending and descending branch, semi-amplitudes and initial epochs for the brightness maximum (minimum magnitude) of each harmonic contribution, etc., were given in the tables reported earlier by Kudashkina (2016). In this study, we have received several interesting correlations between these parameters in the bands H and K. It was particularly noted the anomalous position on the figures of the star X Oph.The mean light curves of the investigated stars are commonly symmetric in the near infrared region (H and K).Stars: Pulsating: Mira-type: S