Herald of Kazakh-British technical university

ISSN

1998-6688

2959-8109

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Differential Equation...

Advanced Topology and...

Enhanced Oil Recovery...

Nonlinear Differentia...

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Публикации в журнале

Показано: 1 - 10 из 12

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MATHEMATICAL THEORY OF THE INCLINED PLANE
(2024-03-26)
Т. Б. Қоштыбаев
;
Kutkeldiyeva Elzira
;
К. К. Жантлеуов
;
E. Zhamenkeev
The laws of mutual transformation of statistical and dynamic effects on an inclined plane are shown, a mathematical justification is given for obtaining a gain from the action or the possibility of saving the main useful action and facilitating the actions of Gravity. All the above statements are carried out using the basic elements of the theories of dynamics, statics and trigonometric calculations. The influence of the geometric dimensions of the inclined plane on the transformation of actions is estimated. The mechanism of statistical and dynamic equilibrium of actions on an inclined plane is substantiated through mathematical expressions of the conservation law and the relationship between the components of the vector.
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ON A BOUNDARY VALUE PROBLEM FOR HIGH-ORDER HYPERBOLIC EQUATION WITH IMPULSE DISCRETE MEMORY
(2024-10-02)
A. T. Assanova
;
R. A. Bimenova
;
B. B. Мinglibayeva
;
A. P. Sabalakhova
The investigation focuses on a boundary value problem for a high-order hyperbolic equation with impulse discrete memory in a rectangular domain. By introducing new functions, the problem is transformed into a set of boundary value problems for a first-order differential equation with impulse discrete memory, which depends on unknown functions and integral relations. D.S. Dzhumabaev's parametrization method is applied to this equivalent problem. The domain is divided according to the time variable, and functional parameters representing discrete memory values are introduced within the interior domains. As a result, the family of boundary value problems for the first-order differential equation with impulse discrete memory and unknown functions is converted into an equivalent family of integral-multipoint boundary value problems involving functional parameters and unknown functions. These equivalent problems include initial value problems for first-order differential equations related to the new functions. The solutions to the initial value problems are expressed using Volterra integral equations. By substituting these solutions into the boundary and impulse conditions, a system of linear functional equations concerning the functional parameters is derived. An algorithm is developed to solve the equivalent problem, and sufficient conditions for the unique solvability of the family of integral-multipoint boundary value problems with functional parameters and unknown functions are provided. Additionally, sufficient conditions for the unique solvability of the original boundary value problem for the high-order hyperbolic equation with impulse discrete memory are established based on the initial data.
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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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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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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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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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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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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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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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