Herald of Kazakh-British technical university

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1998-6688

2959-8109

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COMPARATIVE ANALYSIS OF X-RAY LUMINOSITY OF PERSISTENT AND TRANSIENT HIGH-MASS X-RAY BINARIES
(2026-03-29)
Zhantay Muratkhan
;
Manas Khassanov
;
Aray Muratkhan
;
Aliya Taukenova
;
A. Sadu
High-mass X-ray binaries (HMXBs) are commonly divided into persistent sources, which emit X-rays steadily over long periods, and transient sources, which remain mostly in a quiescent state and exhibit episodic X-ray outbursts. The aim of this work is to statistically compare the X-ray luminosity properties of these two classes, focusing on the maximum luminosity and the luminosity variability range . For this purpose, catalog data for Galactic HMXB pulsars were used, including 18 persistent and 64 transient systems. The distributions of and were analyzed using histograms, box plots, cumulative distribution functions (CDFs), and the non-parametric Mann–Whitney test. It is shown that both classes reach similar values of on the order of – erg/s), with no statistically significant difference between their distributions. However, transient systems exhibit a much wider luminosity variability range, reaching increases of 4–5 orders of magnitude (up to ), whereas persistent sources typically show lower variability. This difference is statistically confirmed, with transients demonstrating significantly higher variability p ≈ 0.05). Thus, the main distinction between persistent and transient HMXBs lies not in their peak X-ray luminosity, but in their accretion regime. In persistent systems, the compact object continuously accretes matter from a relatively stable stellar wind of an OB supergiant, resulting in steady X-ray emission. In contrast, transient systems are characterized by intermittent accretion (for example, episodic mass capture from a Be-star circumstellar disc), which leads to their extreme luminosity variability.
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NUMERICAL STUDY OF ORBITAL STABILITY IN THE RELATIVISTIC RESTRICTED THREE-BODY PROBLEM
(2026-03-29)
Ayazhan Orazymbet
;
Aliya Taukenova
;
Daniya Utepova
;
Nurzada Beissen
;
N. Sandibayeva
This paper presents a numerical study of the relativistic restricted three-body problem within the framework of General Relativity. Using the Lagrangian and Hamiltonian formalisms, the equations of motion with relativistic corrections up to the order of 1/c2 were derived and solved numerically in Wolfram Mathematica. The developed model allows one to analyze orbital stability under small relativistic perturbations. Numerical simulations were performed using the Runge–Kutta integration method for three systems: “Earth–Sun–Moon,” “Earth–Sun– Mercury,” and an equal-mass configuration. The results confirm the stability of circular orbits and reproduce the observed relativistic precession of Mercury’s perihelion. For the equal-mass system, the calculations reveal a transition from quasi-periodic to chaotic motion, depending on the initial conditions. The study demonstrates the reliability and efficiency of the Mathematica environment for modeling nonlinear relativistic dynamics and shows that the proposed approach can be useful for further research in celestial mechanics and gravitational physics.
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ON A BOUNDARY VALUE PROBLEM FOR A LOADED FRACTIONAL DIFFERENTIAL EQUATION
(2026-09-25)
Narkesh B. Iskakova
;
E. А. Bakirova
;
K. I. Usmanov
;
N.T. Orumbayeva
The paper investigates a two-point boundary value problem for a loaded differential e quation with a Caputo fractional derivative. The Dzhumabaev parametrization method is applied to study the problem. Within this approach, the initial interval is divided into a finite n umber of s ubintervals, a nd additional parameters and new functions are introduced, which makes it possible to reduce the original boundary value problem to an equivalent multipoint boundary value problem with unknown parameters. The equivalence of the original and transformed problems is established. Based on the obtained integral representations, a system of algebraic equations with respect to the introduced parameters is constructed. Sufficient conditions for the existence and uniqueness of a solution are established and related to the invertibility of the corresponding matrix. An algorithm based on the method of successive approximations is developed to determine the unknown parameters and functions. A numerical example demonstrating the application of the proposed algorithm and confirming its e ffectiveness is presented. The ob tained results de monstrate the efficiency of the pa rametrization me thod for in vestigating bo undary va lue pr oblems for lo aded fractionalorder differential e quations and c onstructing t heir a pproximate solutions.
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SOLVABILITY OF A MULTIPOINT BOUNDARY VALUE PROBLEM FOR LOADED DIFFERENTIAL EQUATIONS WITH A PARAMETER
(2025-09-27)
Svetlana Temesheva
;
Zh. М. Каdirbayeva
;
S. Ashirov
This article is devoted to the solvability questions of a multipoint boundary value problem for a system of loaded differential equations with a parameter. The investigation is carried out using the Dzhumabaev parameterization method. This allows us to reduce the solving of the original boundary value problem to the solving of a system of algebraic equations and Cauchy problems for ordinary differential equations. Modifications have been introduced into the parametrization method algorithms to reduce the influence of boundary conditions on the convergence of the algorithm. Following the specifics of the parametrization method, sufficient conditions for the existence and uniqueness of a solution to the multipoint boundary value problem for systems of loaded differential equations with a parameter have been established. These conditions also ensure the convergence of the modified algorithms. The research results provide a constructive tool for analyzing the behavior of various models described by boundary value problems for loaded differential equations with parameters. The presented example clearly demonstrates the feasibility and effectiveness of the proposed method.
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ON THE SOLUTION OF A BOUNDARY VALUE PROBLEM FOR AN IMPULSIVE HYPERBOLIC EQUATION WITH A PIECEWISE-CONSTANT ARGUMENT
(2026-06-27)
Altynai Molybaikyzy
;
Symbat Seisenbekovna Kabdrakhova
;
Narkesh B. Iskakova
;
B. B. Мinglibayeva
This article investigates a boundary value problem for an impulsive hyperbolic equation with a piecewise constant argument. Impulsive hyperbolic equations with a piecewise constant argument arise as mathematical models of physical processes in neural networks, continuous dynamical systems, hybrid systems, and other fields. Issues related to the existence of boundary value problems and the construction of their solutions for such equations remain among the most relevant and challenging problems at present. To obtain solvability conditions for the considered problem, the Dzhumabaev parametrization method is employed, and an iterative algorithm for constructing an approximate solution is developed. For each step of the iterative process, integral formulas are derived and expressed in terms of the matrix Q(x), which describes the relationship between the functional parameters. If this matrix is invertible, the existence and uniqueness of the solution are proved both for the parametric and the original problems. The proposed method is not limited to proving theoretical solvability; it also provides a concrete constructive procedure for obtaining the solution. This is of significant importance for subsequent numerical implementations and for the analysis of solution stability. Moreover, the proposed approach can be applied to other types of problems with a piecewise constant argument, including systems with impulsive conditions, neural networks with memory effects, and nonlinear hybrid models.
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SPECTRAL ANALYSIS OF THE STAR MWC 645
(2025-12-23)
A. S. Nodyarov
;
A. E. Rassylova
;
Aruzhan Omar
This study presents results of high-resolution spectroscopic observations of the star MWC 645, a representative of the poorly studied FS CMa-type objects. These stars are characterized by strong emission lines and significant infrared excess caused by circumstellar dust. For the first time, a cool secondary component has been detected in this system. Fundamental parameters were determined for both components: for the hot (B-type) star, an effective temperature of 18,000 ± 2000 K and luminosity log(L/L☉ ) = 3.9 ± 0.4; and for the cool (K-type) star, Teff = 4250 ± 250 K and log(L/L☉ ) = 3.1 ± 0.4. The system is located at a distance of 6.5 ± 0.9 kpc and shows clear signs of active interaction, including ongoing mass transfer indicated by the complex profiles of many emission lines. The results confirm the binary nature of MWC 645 and its classification as an FS CMa-type object. This work highlights the need for further observations to refine the system’s parameters and improve our understanding of the structure and origin of its circumstellar environment.
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STUDY OF THE W40 STAR-FORMING REGION BASED ON OBSERVATIONS BY THE WISE INFRARED SPACE TELESCOPE
(2026-03-29)
N.Sh. Alimgazinova
;
A.B. Manapbayeva
;
Aruzhan Omar
;
Aizat Demessinova
;
Kunduz M. Turekhanova
The study of the mechanisms of star formation and evolution is based on comprehensive research into interstellar regions, including the analysis and identification of young stellar objects (YSOs). The identification of young stellar objects by their radiation at various wavelengths in the infrared range is a relatively recent development - the first studies in this field appeared only at the end of the 20th century. The development of this field has been made possible by improvements in observation techniques and data processing methods, the acquisition of more reliable characteristics of stellar sources, and the creation of catalogs containing extensive arrays of information about cosmic objects. In this study, the star-forming region W40 of the Aquilla molecular cloud was investigated in the infrared wavelength range to detect previously unidentified young stellar objects at various stages of evolution. Identification was carried out using two approaches: photometric criteria and spectral indices. This made it possible to more reliably identify the evolutionary stages of 37 newly discovered and previously unexplored YSO candidates (5 objects of class I, 2 objects of class II, 4 objects – class “transitional disks” and 26 objects — class III), which indicates an active and ongoing process of star formation in W40.
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KINEMATICS AND STRUCTURE OF THE MASSIVE STAR-FORMING REGION G350.29+0.12
(2026-03-29)
Aidana Abdirakhman
;
Aruzhan Omar
;
Zhomartkali Islyam
;
N.Sh. Alimgazinova
;
Aizat Demessinova
We present high–angular resolution 1.3 mm continuum and molecular line observations toward the highmass star-forming region G350.29+0.12, using CH₃CN and CH₃¹³CN rotational transitions. The continuum emission resolves two main cores: a bright, compact northern core G350.29+0.12 A and a weaker southern core G350.29+0.12 B. Core A exhibits six compact substructures embedded within more extended emission. M K-components of the CH3CN J = 14→13 and CH3 13CN J = 14→13 transitions are detected, with the emission arising primarily from core A. The CH3CN moment 0 maps show that the integrated intensities peak at the main continuum position, indicating that the molecular emission traces warm and dense gas. The moment 1 maps reveal a pronounced velocity gradient of ∼2 km s-1 across core A, oriented from northwest to southeast, while the moment 2 maps show K-dependent variations in velocity dispersion. Position–velocity diagrams further indicate organized rotational motions, exhibiting a compact velocity structure with a central peak and systematic gradients. Rotational temperature analysis yields = 360.6 ± 34.8 K for CH3CN, tracing the hottest and densest gas and Trot = 138 ± 45 K for CH3 13CN, consistent with cooler and more extended material. Together, these results demonstrate that G350.29+0.12 A is a rotating hot molecular core undergoing active high-mass star formation.
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ON THE APPROXIMATION OF A BOUNDARY VALUE PROBLEM FOR DELAY INTEGRO-DIFFERENTIAL EQUATIONS
(2025-07-06)
E. А. Bakirova
;
Narkesh B. Iskakova
;
Askarbek E. Imanchiyev
;
Sayakhat G. Karakenova
A linear two-point boundary value problem for a system of integro-differential equations with a constant delay argument is investigated on a finite interval. By dividing the interval by parts, the integral term of the integrodifferential equation with constant delay argument is replaced by the quadrature formula. With this replacement, the linear two-point boundary value problem for a system of integro-differential equations with a constant delay argument is approximated by the linear boundary value problem for a system of loaded differential equations with a constant delay argument. Definitions of correct solvability of boundary value problem for system of integro-differential equations with delay argument and constructed boundary value problem for system of loaded differential equations with constant delay argument are introduced. Conditions of correct solvability of linear boundary value problem for system of integro-differential equations with delay argument and linear boundary value problem for system of loaded differential equations with delay argument are established. Relationship between correct solvabilities of linear two-point boundary value problem for system of integro-differential equations with constant delay argument and approximating linear two-point boundary value problem for system of loaded differential equations with constant delay argument is shown.

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