Herald of Kazakh-British technical university

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1998-6688

2959-8109

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Differential Equation...

Advanced Topology and...

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Показано: 1 - 10 из 13

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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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ANALYZING RUSSIAN BORROWINGS IN KAZAKH SOCIAL MEDIA USING MACHINE LEARNING
(2024-12-24)
Saya Sapakova
;
Б. Ғ. Қамбарова
This study explores the influence of Russian words on the development of the Kazakh language in social networks. The rapid advancement of information technology significantly impacts the language used in online communications. While the chaotic nature of online interactions can complicate language use and create confusion, it also accelerates the spread of information in Kazakh. This research examines how foreign words affect modern Kazakh internet discourse, including direct borrowings that enter the language without modification, mixedphrases that retain the lexical and semantic properties of foreign words, the emergence of new abbreviations, and the influence of barbarisms. The study utilizes machine learning methods to analyse social media content from Instagram and Facebook. This approach enabled the processing of over 100,000 posts, revealing key linguistic shifts associated with the integration of Russian borrowings into Kazakh. The use of machine learning algorithms, such as the Naive Bayes classifier, automated the data analysis process and uncovered hidden patterns, providing a deeper understanding of how these borrowings affect the Kazakh language in the digital environment.
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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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MICRO- AND NANOMICROMATERIALS IN PYROTECHNICS
(2024-07-02)
Zh.K. Aimasheva
;
Д. В. Исмаилов
;
Valentina Grichshenko
;
Stefano Bellucci
;
Г. Партизан
Due to their unique physical and chemical properties, which play an unrivaled role in enhancing the performance and safety of pyrotechnic substances, carbon nanomaterials have garnered significant interest from researchers in recent years. In this paper, carbon nanostructures prepared by electric arc synthesis are identified as C60 and C70 fullerene carbon blacks. The carbon black particles derived from the synthesized fullerenes exhibit a porous and rough morphology, with sizes ranging from 32 to 190 nm. The experimental results indicate the potential use of synthesized fullerene soot as a constituent component of pyrotechnic composites. The dependence of pyrotechnic composite compositions on combustion time has been determined by selecting potassium nitrate, nanoscale fullerenes, composite carbon blacks, wood coals, and aluminum fillers as matrix materials. According to the findings, the combustion time of the composite composition increases as the content of fullerene soot in the pyrotechnic composite composition increases.
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ON THE UNIQUE SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR DIFFERENTIAL EQUATIONS WITH PARAMETER
(2024-03-25)
E. А. Bakirova
;
Narkesh B. Iskakova
;
Svetlana Temesheva
;
Zh. М. Каdirbayeva
A linear boundary value problem for a differential equation with a parameter is investigated on a finite interval by the parameterization method. The studied boundary value problem with parameter is reduced to an equivalent multipoint boundary value problem with parameters by splitting the interval, introducing additional parameters at the points of splitting and new functions. The obtained equivalent boundary value problem contains Cauchy problems for ordinary differential equations with respect to new functions. By substituting the solution representation of the Cauchy problem into the boundary conditions and continuity conditions of the solution, a system of linear algebraic equations with respect to the introduced parameters is compiled. An algorithm for finding a solution to the boundary value problem with parameters is constructed. The formulation of the theorem on sufficient conditions of unique solvability of the boundary value problem with parameters is given. Sufficient conditions of its unique solvability are obtained in terms of the data of the original boundary value problem. An example showing the fulfillment of the conditions of the theorem is given.
Цитирования (OpenAlex) 1Цитирования (OpenCitations) 1
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Study of the influence of gamma irradiation on ferrite-spinel monocrystals
(2023-12-12)
N. N. Shinikulova
;
N. B. Shambulov
;
А. М. Татенов
;
S. Ertürk
;
G. N. Shinikulova
The mechanisms of redistribution of metal ions and the formation of defects in ferrite spinel upon irradiation are complex and depend on a number of factors. Therefore, computer simulations and experimental studies are important for understanding the behavior of the physical properties of these materials under the influence of radiation. The development of new materials that can withstand radiation damage is of great importance for a range of applications, including solid state physics, nuclear physics, space research and medical applications. In this work, the effect of gamma irradiation on Co0,75Cu0,25Fe2O4 ferrite single crystals has been investigated. An earlier study using Mössbauer spectroscopy was carried out to determine the changes in the metal ion content in the sublattices of ferrite spinels. These changes affect the magnetic crystallographic anisotropy of the material [1]. Data can be found in the scientific literature that indicate that gamma irradiation leads to changes in the magnetic susceptibility of materials and to changes in the magnetization curve [2,3]. These changes in physical properties can be explained by redistribution of metal ions in octahedral and tetrahedral sublattices, since metal ions in sublattices have splitting of atomic levels.
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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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