International Journal of Mathematics and Physics
International Journal of Mathematics and Physics (IJMPH) is a trusted journal for significant developments in mathematics and physics. Advancing Mathematical and Physical Sciences Established in 2012, IJMPH is a peer-reviewed, open-access journal published by Al-Farabi Kazakh National University. It serves as a global platform for researchers, scholars, and professionals working in mathematics, theoretical physics, and applied physics. IJMPH publishes original research articles and review papers that advance fundamental theory, mathematical methods, and computational modeling in mathematics, as well as theoretical and experimental research in physics. The journal maintains a rigorous and collegial editorial process, upholding high standards of peer review, scholarly quality, and academic integrity. Published twice a year, IJMPH is committed to the open and accessible dissemination of scientific knowledge in mathematical sciences and physics. International Journal of Mathematics and Physics metrics (2025) Published Papers Total Citations 87 86 Journal Impact Factor CiteScore 0.4 1.0 SJR Downloads 0.283 24,786 1st decision (desk review) 1st decision after peer review 14 days 40 days Submission to acceptance Submission to publication 90 days 150 days IJMPH Scope IJMPH publishes rigorous theoretical, computational, and experimental research that advances fundamental understanding in mathematical sciences and physics. The journal particularly encourages work that strengthens the conceptual and analytical links between mathematics and physical theory. Mathematics • Algebra, Number Theory, and Mathematical Analysis • Calculus and Differential Equations • Computational Mathematics and Applied Analysis • Mathematical Modeling and Simulation Theoretical and Experimental Physics • Astronomy and Space Research • Quantum Mechanics and Quantum Field Theory • Relativity and Gravitation • Statistical Mechanics and Thermodynamics • Plasma Physics and Magnetohydrodynamics • Particle and Nuclear Physics • Condensed Matter and Materials Physics IJMPH Acceptance Criteria Submitted manuscripts should meet the following criteria: • Add significant new knowledge to the fields of mathematics, theoretical physics, or applied physics. • Make a substantial contribution within a clearly defined research area and be of interest to the international readership of IJMPH. • Represent an authoritative, rigorous, and substantive addition to the existing body of literature in mathematical sciences and physics. Open Access Model The IJMPH operates under a Gold Open Access model with a partial Article Processing Charge (APC) waiver. All published articles are made freely and permanently accessible online immediately upon publication. Article Processing Charges (APC) Authors affiliated with institutions in Kazakhstan are required to pay a publication fee of 100,000 KZT upon acceptance of the manuscript. Authors without institutional affiliation in Kazakhstan are granted a full APC waiver and are not required to pay any publication fee. All articles are published under the Creative Commons Attribution–NonCommercial 4.0 International License (CC BY-NC 4.0). Editorial Board The IJMPH Editorial Board is composed of experienced scholars in mathematics and physics, appointed to support the journal’s editorial standards and peer-review process. The journal is led by Editor-in-Chief Kuantay A. Boshkayev, Professor at Al-Farabi Kazakh National University (Kazakhstan), together with Associate and Executive Editors. Board members may advise at any stage of the review process and support the resolution of editorial appeals. Editorial Team IJMPH is managed by an experienced editorial team of Ph.D. scholars and researchers affiliated with leading academic institutions. The editorial team oversees the peer-review process and ensures that all editorial decisions are made in accordance with the journal’s acceptance criteria and established ethical standards. Indexing & Abstracting: Scopus Clarivate Web of Science EBSCO Crossref Science Index Academic Resource Index (ResearchBib) Scilit ROAD WorldCat CiteFactor Science and Higher Education Quality Assurance Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan Editorial and Publishing Policies The International Journal of Mathematics and Physics (IJMPH) follows established Editorial and Publishing Policies covering Editorial Oversight and Decision Making, Authorship, Submissions, Resubmissions, and Publication Terms, Peer Review, Ethics and Research Integrity, Post-Publication Policies, and Open Access and Publication Rights. IJMPH is published electronically twice per year. Articles are assigned a volume and issue number, for example, Vol. X, No. X (year). In exceptional cases, the editors may prioritize the review of manuscripts that report particularly significant theoretical advances or high-impact research findings.
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THREE FRACTIONAL INEQUALITIES BASED ON A SINGLE PARAMETER IN THECONTEXT OF AG-MULTIPLICATIVE h-CONVEX FUNCTIONS
Abstract. This article introduces novel three parameterized fractional inequalities based on a one parameter ν derived from functions that are AG-multiplicative differentiable, as characterized by AG-multiplicatively Riemann-Liouville operators (classical, middle starting point, and middle ending point). By employing the multiplicative absolute value and supposing the function is AG-multiplicative h-convex, we can develop three identities and utilize them to derive a series of inequalities for AG-multiplicatively h-convex mappings. We additionally present these findings for AG-multiplicative P-functions convex mapping and AG-multiplicative s-convex functions. The last section delineates specific instances, including trapezoid, midpoint, Bullen, Milne, Simpson and corrected Simpson AG-multiplicative fractional inequalities. We further illustrate that certain results reported here improve established results, while others represent generalizations. Keywords: Parameterized inequality, AG-multiplicative fractional integrals, Multiplicative absolute value, AG-multiplicative h-convex functions
ENTROPY SOLUTIONS FOR P-LAPLACIAN TYPE PROBLEMS WITH LOWER-ORDER PERTURBATION AND SINGULAR TERMS IN WEIGHTED FRAMEWORK
Abstract. This paper is devoted to the study of a class of nonlinear elliptic problems involving weighted degenerate operators of p-Laplacian type, lower-order perturbations, and singular source terms. Such problems arise in the mathematical modeling of heterogeneous media and diffusion processes characterized by nonuniform physical properties, where degeneracy and singular behavior significantly complicate the analysis. The main objective of the work is to establish the existence of entropy solutions for a broad family of weighted elliptic equations with merely integrable data. The analysis is carried out within the framework of weighted Sobolev spaces associated with Muckenhoupt weights, which provide a suitable setting for handling both degeneracy and lack of regularity. The methodology relies on the construction of appropriate approximating problems, truncation techniques, uniform a priori estimates, compactness arguments, and convergence methods adapted to entropy solutions. Under suitable assumptions on the weight function, the nonlinear perturbation term, and the singular nonlinearity, the existence of at least one entropy solution is proved. The obtained results extend several earlier existence theorems by simultaneously incorporating weighted degeneracy, lower order perturbations, and singular reaction terms into a unified framework. This study contributes to the theory of nonlinear elliptic partial differential equations by enlarging the class of problems for which solvability can be guaranteed with low regularity data. Moreover, the developed approach provides useful analytical tools for future investigations of weighted singular problems arising in mathematical physics, engineering, and related applied sciences. Keywords: Entropy solutions, Existence results, Singular non-linearity, Weighted Sobolev spaces.
Performance Evaluation of Three Types of Air-to-Water Cascade Heat Pumps for Cold Climate Applications Using Different Refrigerant Pairs
Abstract. The performance of conventional air-to-water heat pumps significantly deteriorates at low ambient temperatures due to high temperature lift and compressor limitations. This study investigates the thermodynamic performance of three cascade air-to-water heat pump configurations for cold climate applications using sixteen refrigerant pairs. A numerical model was developed in Python using CoolProp for thermophysical properties, considering ambient temperatures down to −50 °C and a heating supply temperature of +60 °C. The results indicate that R32/R134a and R410A/R134a achieve the highest COP, reaching up to 2.56 at +10 °C and approximately 1.98 at −30 °C; however, their operation is limited by environmental constraints and operating range. R744-based systems enable operation at extreme low temperatures down to −41 °C, with COP values of 1.62 (R744/R134a) and 1.60 (R744/R290). Among the configurations, the first and third show the highest efficiency (COP ≈ 2.0), while the second exhibits a ~4.6% lower COP but offers operational flexibility, including single-stage operation above −10 °C. Considering both performance and environmental impact, R744/R290 is identified as the most promising refrigerant pair for future applications. Keywords: Cascade heat pump; cold climate; COP; pressure ratio; environmentally friendly refrigerant
NUMERICAL STUDY OF GIMBAL JOINT GAP INFLUENCE ON NOZZLE FLOW
Gimbaled thrust vector control (TVC) systems are widely employed in modern launch vehicles to provide attitude control during powered flight. However, the aerodynamic influence of the circumferential geometric discontinuity introduced by the gimbal joint gap on nozzle internal and external flow remains insufficiently studied in open literature. The purpose of this study is to evaluate aerodynamic losses and flow field modifications of bell-shaped rocket nozzles with the presence of a gimbal joint gap using computational fluid dynamics (CFD) simulation. These calculations were done using the Reynolds-Averaged Navier–Stokes (RANS) model in 2D axisymmetric flow in ANSYS Fluent software. For modelling the flow properties in compressible separated flows, the k-ω SST turbulence model was selected. Two nozzle configurations, with and without the gap of the gimbal joint, were compared. The Sutherland viscosity law and the NASA polynomial thermodynamic data were used for the working fluid and it was modeled as an ideal compressible gas representative of the combustion products of LOX/Kerosene. The exit to throat area expansion ratio for nozzle geometry is 8.97, which means that the nozzle is designed to have a supersonic exit condition. The CFD results showed a good agreement with the theoretical results, showing the validity of the numerical approach. The nozzle studied here operates under overexpanded conditions at sea level, where the nozzle exit static pressure falls below ambient pressure, giving rise to oblique shock waves in the exhaust plume and making the accurate characterisation of flow disturbances particularly important. The presence of the gimbal joint gap was found to introduce aerodynamic losses in Mach number of 6.74%, providing quantitative design-relevant data for gimbaled nozzle systems in launch vehicles. Keywords: gimbal joint gap, bell nozzle, TVC, CFD.
INVERSE PARAMETER IDENTIFICATION IN A NONLINEAR HEMODYNAMIC MODEL OF THROMBUS FORMATION
Abstract. In this paper a nonlinear inverse problem in hemodynamics associated with thrombus formation in blood flow is studied. The inverse problem is formulated as the identification of an unknown constant diffusion coefficient in a twodimensional diffusion equation from final-time observations. The diffusion coefficient is reconstructed by minimizing a normalized least-squares objective functional using a gradient descent algorithm. The direct model describes blood flow in a planar vessel and incorporates a fibrin formation mechanism on the vessel wall. The governing diffusion equation is solved numerically by an alternating direction implicit (ADI) scheme, which provides unconditional stability for the twodimensional problem. To reduce the computational complexity, the gradient of the objective functional with respect to the unknown coefficient is evaluated numerically via a central finite-difference approximation, thereby avoiding the construction of an adjoint problem. Numerical experiments with synthetically generated data demonstrate stable convergence of the iterative process and accurate recovery of the diffusion coefficient for a wide range of initial guesses and step-size parameters. The results confirm the robustness, simplicity, and computational efficiency of the proposed gradient-based reconstruction approach for hemodynamic inverse problems. Keywords: nonlinear inverse problem; diffusion coefficient identification; thrombosis; gradient descent.
THE ILL-POSEDNESS OF A MIXED PROBLEM IN A CYLINDRICAL DOMAIN FOR MULTIDIMENSIONAL HYPERBOLIC-ELLIPTIC EQUATIONS IN CANCER MODELING
Abstract. This paper investigates a mixed boundary value problem in a cylindrical domain for a class of multidimensional hyperbolic-elliptic equations arising in mathematical models of malignant tumor growth. In particular, axisymmetric approximations and local models of tumor spread in brain tissues lead to problem formulations in cylindrical geometry. Under assumptions, the problem leads to a class of multidimensional hyperbolic-elliptic equations, i.e., mixed-type equations whose properties may change between hyperbolic and elliptic in different subdomains or according to the parameters and coefficients. Idealized cylindrical geometry is used as a convenient framework for rigorous mathematical analysis. The main results establish the ambiguity of the solutions to the mixed problem and provide an explicit representation of its classical solutions. These results contribute to the analysis of multidimensional mixed-type equations in bounded domains and may support further computational investigations of tumor growth models. Keywords: ill-posedness, mixed problem, hyperbolic-elliptic equations, cylindrical domain, glioma growth modeling.
INVESTIGATION OF THE EFFECT OF REACTIVE DILUENTS ON THE MECHANICAL PROPERTIES OF EPOXY BINDERS
The effect of various types of curing agents and reactive diluents on the rheological and mechanical properties of epoxy binders was investigated. “Etal Inject-T” and “Larit L-285” epoxy resins were used as matrices. “Etal Inject-T”, iso-MTHPA, dicyandiamide (DICY), and diaminodiphenylsulfone (DDS) were used as curing agents. The effect of reactive diluents – glycerol triglycidyl ether, pentaerythritol tetraglycidyl ether, and butyl glycidyl ether – was also studied. Maximum strength characteristics were achieved using DDS curing agent at 25%. For the “Etal Inject-T” system, compressive strength values of 140 MPa were obtained. It was shown that the addition of pentaerythritol tetraglycidyl ether at 10% simultaneously reduces the viscosity of the epoxy composition from 400 mPa·s to 280 mPa·s and increases compressive strength from 140 MPa to 155 MPa. The results demonstrate the high effectiveness of multifunctional glycidyl ethers for controlling the structure and mechanical properties of epoxy binders. Keywords: epoxy resins, reactive diluents, curing agents, mechanical properties, viscosity, epoxy compositions.
This review article explains the properties of virtual states and discusses their impact on realistic nuclear structure and nuclear reaction problems. The first half of the paper defines virtual states as poles of the scattering matrix, i.e., zeros of the Jost function, and discusses their similarities and differences with bound and (zero energy) resonant states. The second half of the paper provides concrete examples of the effects of virtual states in real nuclear systems. Regarding nuclear structure problems, we demonstrate the valence neutron occupying virtual state plays important roles in the formation of the anomalous structures in the binary and three-body systems: 9Li + neutron and α + α + neutron. On the other hand, in reaction problems, we address thermal neutron scattering by various targets and discuss the close relationship between the peak structure in the so-called S-wave strength function and the virtual states. By synthesizing the calculation about the neutron scattering, we propose a new reaction picture for thermal neutron absorption reactions. Keywords: Virtual states, nuclear structure, neutron scattering, neutron capture, nuclear reactions.
This paper investigates the optical characteristics of a static spherically symmetric dilatonic black hole. The primary objective of the study is to examine the effect of the dilatonic charge Q and the dilaton coupling parameter a on the shadow geometry and the structure of Einstein rings. The research methodology is based on numerical simulations using the backward ray-tracing method, employing the Lagrangian formalism for the photon equations of motion. The main results show that an increase in the dilatonic parameters leads to a significant "compactification" effect of the shadow, the diameter of which can decrease by 31% relative to the Schwarzschild limit at extreme parameter values. Furthermore, a characteristic visual thickening of higher-order photon rings is observed, while maintaining complete topological stability of the image. The scientific value of this work lies in identifying specific optical signatures that allow distinguishing dilatonic black holes from the classical objects of General Relativity. The practical significance of the results is related to their potential application in interpreting observational data from the Event Horizon Telescope (EHT) and searching for manifestations of physics beyond standard models. Keywords: Dilatonic Black holes, Ray tracing, Lensing images, Shadow geometry.
AMMONIA SENSING PROPERTIES OF FLUORINATED SI@C CORESHELL HYBRIDS
Silicon nanoparticles encapsulated in carbon shells (Si@C) were synthesized via polymer-derived carbonization and subsequently fluorinated by gas-phase treatment to tailor their interfacial electronic properties. The resulting Si@C–F core–shell nanostructures were investigated as chemiresistive sensors for ammonia detection at room temperature. The fluorinated hybrids exhibit a 2–2.5-fold enhancement in response toward NH3 in the 1–20 ppm range, while maintaining linear behavior (R2>0.99) at low concentrations. The enhanced performance is attributed to fluorination induced modulation of interfacial electronic states and the barrier height at the Si/SiOx/C:F heterojunction. The introduction of electron-withdrawing C–F groups increases the work function of the carbon shell and strengthens interfacial dipole fields, leading to amplified resistance modulation under NH3 adsorption. Owing to the nanoscale dimensions of the silicon cores (20–40 nm), comparable to the Debye length, surface charge variations significantly influence charge transport. The sensors demonstrate high selectivity toward ammonia over alcohol vapors (ppm-normalized selectivity >104) and stable operation under moderate humidity. These findings establish fluorination as an effective strategy for engineering interfacial charge transfer in Si–C hybrids for room-temperature gas sensing. Keywords: Si@C hybrids; fluorinated carbon; ammonia sensing; coreshell nanostructures; chemiresistive gas sensor.
ELECTRONIC STATES IN ZnO/porousZnSe/ZnSe HETEROSTRUCTURES
ZnO nanowires have attracted considerable attention due to their wide band gap, high chemical stability, and pronounced quantumscale effects, making them promising components for optoelectronic and sensor devices. The electronic states of such nanostructures strongly depend on the properties of the substrate, especially in heterostructures containing porous materials. In this work, the formation of quantum levels and the electronic properties of ZnO nanowires in two systems ZnO/ZnSe(bulk) and ZnO/porousZnSe/ZnSe with porosity ranging from 20% to 80% were theoretically investigated. The base nanowire model, with a radius of 25 nm and a height of 500 nm, describes the structure as a cylindrical infinite potential well, while the influence of porous ZnSe is incorporated through porositydependent barrier parameters: dielectric constant, and electron affinity. Analytical solutions of the Schrödinger equation obtained using Bessel functions, together with numerical simulations in Matlab, revealed strong radial quantum confinement: the radial quantization energy significantly exceeds the longitudinal one for the first levels, and the groundstate energy is about 0.0015eV. To quantitatively analyze the effect of substrate porosity, a finite cylindrical potential well model is employed, in which the barrier heightV0(P)=χZnO−χeff(P) explicitly depends on porosity through the dielectric constant and electron affinity of porous ZnSe, calculated using the Bruggeman effective medium equation and the Penn relation, respectively. Numerical simulations performed for nanowire radii in the range 5−20 nm showed that increasing ZnSe porosity leads to systematic upward shifts of the ground-state energy, with absolute changes reaching up to 3−4 meV for nanowires with radius R < 10 nm. The obtained results confirm that porous ZnSe is an effective tool for tuning the electronic states of ZnO nanowires and open up opportunities for optimizing UV photodetectors and photovoltaic converters by controlling substrate porosity. Keywords: ZnO nanowires, porous ZnSe, quantum confinement, electronic states, optoelectronic applications.
PREPARATION OF TRANSPARENT SUPERHYDROPHOBIC COATINGS WITH ANTI-ICING, ANTI-FOGGING AND SELF-CLEANING PROPERTIES BY PLASMA POLYMERISATION AT ATMOSPHERIC PRESSURE
This study analyses the stability of superhydrophobic coatings produced by plasma polymerisation at atmospheric pressure using argon (Ar) as the base gas and hexamethyldisiloxane (HMDSO) as the precursor. The evaluation was aimed at determining the strength and durability of these coatings when exposed to various environmental factors such as fogging, anti-icing and temperature fluctuations. The superhydrophobic properties of the coatings were investigated by measuring contact angles and surface roughness values. The results show that the coatings obtained by the above mentioned method have significant water repellent property and retain their superhydrophobic characteristics for a long time. The results indicate that the combination of Ar and HMDSO in plasma polymerisation at atmospheric pressure is a promising approach to create stable and durable superhydrophobic surfaces suitable for various applications. The main focus is on the stability of coatings, their ability to resist icing and fogging. The study showed that the hydrophobic properties of the coatings can be improved by optimising the process parameters, resulting in coatings with a water contact angle of more than 154±2 degrees and high transparency of up to 98.5% in the visible range. The obtained results testify to the high efficiency of the proposed method of obtaining coatings, which opens up prospects for their application in various fields where high resistance and transparency to external influences are required. Keywords: plasma polymerization, atmospheric pressure, superhydrophobic coatings.
HISTORICAL EVOLUTION OF MATHEMATICS EDUCATION IN KAZAKHSTAN: FROM THE MIDDLE AGES TO INDEPENDENCE
Abstract. Over the past three centuries, Kazakhstan has been part of various states. It was initially a part of the Russian Empire; from 1920 to 1991, it was among the republics that formed the Soviet Union; and since 1992, it has existed as an independent country. In this context, it is important for the public of Kazakhstan to understand how mathematics was taught to the population at different stages of historical development. The subject of this study is the historical evolution of mathematics education in Kazakhstan from the Middle Ages to the present day. The main focus is on the teaching of mathematics in national schools. This study represents the first research conducted in this direction; its scientific and methodological significance is undeniable, and it also has practical value for specialists in the field of mathematics education. The primary attention is devoted to the study of literary sources and materials from state archives. Since many authors were subjected to repression in the 1940s, their works were removed from libraries and remained inaccessible for a long period. An in-depth methodological and mathematical analysis of these materials was conducted. During the period of the Russian Empire, the first mathematics textbooks in the Kazakh language were written by S. Gramenitsky (1897) and M. Dulatuly (1914). In the first fifteen years of Soviet rule, mathematics textbooks were authored by mathematicians associated with the national movement “Alash.” However, in 1935, the country transitioned to instruction in the Russian language across schools nationwide, and national schools began using translated Russian textbooks. This policy remained in effect until the collapse of the Soviet Union. Following the independence of Kazakhstan, all mathematics textbooks in the country began to be published in the Kazakh language. The results of the study, based on authentic archival materials, reveal the actual state of mathematics teaching in the Kazakh language. These materials can be incorporated into modern mathematics textbooks and teaching methodologies, taking into account the importance of the historical evolution of mathematics education among the Kazakh population. Keywords: mathematics education, historical evolution, textbooks, school, pedagogical university, Bologna process.
Special Section: History & Didactics of Mathematics
CFD Study of the Effect of Coarctation on the Distribution of Velocities, Pressures, and Shear Stresses in the Thoracic Aorta
This study focuses on numerical modeling of thoracic aortic hemodynamics in patients with coarctation, a congenital narrowing of the vessel lumen that impairs blood flow and increases hemodynamic load. The aim of the study was to identify the influence of geometric changes in the aorta on the distribution of velocity, pressure, and shear stress using computational fluid dynamics (CFD) methods. The mathematical model is based on the Navier-Stokes equations for an incompressible non-Newtonian fluid, which describes the rheological properties of blood. Calculations were performed using the finite volume method with an explicit time-dependent scheme for two geometric configurations—normal and pathological. Analysis of the resulting velocity and pressure fields revealed that with coarctation, the maximum velocity increases by approximately 1.6 times, and the pressure difference between the ascending and descending aorta reaches 0.6 kPa. The shear stress distribution revealed localized areas of extreme values that potentially contribute to endothelial dysfunction. This study contributes to the development of personalized blood flow modeling and demonstrates the potential of CFD methods for assessing hemodynamic disturbances in vascular pathologies, which has practical implications for preliminary diagnosis and treatment planning. Keywords: hemodynamics, coarctation of the aorta, computational fluid dynamics, CFD, numerical modeling.
Numerical solution of the inverse problem of magnetotelluric sounding
This study focuses on the coefficient inverse problem arising in magnetotelluric (MT) sounding, which plays a crucial role in geophysical exploration and subsurface characterization. The main objective is twofold: first, to construct a reliable forward numerical model based on the Helmholtz equation with a complex-valued conductivity coefficient, and second, to develop a stable inversion procedure for reconstructing the conductivity distribution from boundary measurements. The forward problem is discretized using a finite-difference approximation, ensuring numerical stability and accuracy for both the direct and adjoint formulations. To address the ill-posed nature of the inverse problem, a misfit functional is introduced, measuring the discrepancy between simulated and observed boundary data. This functional is minimized using the iterative Landweber method, which provides a simple yet robust tool for stabilizing reconstructions. Numerical experiments are carried out for a synthetic conductivity model consisting of a smooth background medium with an embedded localized anomaly. The obtained results demonstrate the ability of the proposed method to recover key structural features of the anomaly. The presented framework offers a promising foundation for the development of practical inversion algorithms applicable to real geophysical MT data. Key words: Helmholtz equation, magnetotelluric sounding, inverse problem, Landweber method, numerical solution.
A STUDY OF THE INFLUENCE OF THE HEIGHT OF NOISE PROTECTION BARRIERS ON THE DISPERSION OF POLLUTANTS IN A STREET CANYON BY THE METHOD OF COMPUTATIONAL FLUID DYNAMICS
Abstract. Urban air pollution poses a serious threat to public health, particularly in areas with heavy traffic, such as street canyons. This paper numerically investigates the effect of noise barriers of varying heights (0.1H, 0.2H, 0.3H, where H is the building height) on the dispersion of a passive pollutant (ethylene) in a street canyon model. The simulation is based on the Reynolds-averaged Navier-Stokes (RANS) equations and the SST k-ω turbulent model. The numerical model is verified by comparison with published experimental data and large eddy simulation (LES) results. Spatiotemporal distributions of pollutant concentrations are analyzed. The results show that a barrier of medium height (0.2H) forms a stable recirculation zone, acting as a "trap" for pollutants with maximum concentrations. A low barrier (0.1H) has a negligible effect, while a high barrier (0.3H) effectively screens the leeward zone but promotes pollutant accumulation on the windward side. A conclusion is drawn about the dual effect of barriers and the need to consider aerodynamic effects in their design. Keywords: computational fluid dynamics (CFD), air pollution, street canyon, noise barrier, pollutant dispersion, RANS, SST k-ω.
Solar-Assisted Auto-Cascade Heat Pump for Water Heating in the Continental Climates
Heat pumps are widely recognized as energy-efficient technologies for domestic hot water production. However, conventional single-stage vapor compression heat pumps utilizing ambient air as the heat source are limited in delivering outlet water temperatures above 323 K under low ambient conditions. This limitation restricts their applicability in continental climates characterized by large diurnal and seasonal temperature variations. Two-stage cascade systems can achieve higher outlet temperatures exceeding 343 K, but they require two compressors, resulting in increased energy consumption and higher capital costs. To overcome these drawbacks, the present study proposes an auto-cascade compression heat pump system employing an environmentally friendly binary zeotropic refrigerant mixture to achieve water outlet temperatures above 343 K with improved efficiency and reduced system complexity. In addition, solar collectors are integrated to enhance low-grade heat extraction from the environment. A numerical simulation of the proposed auto-cascade system was conducted for binary zeotropic refrigerant mixtures including R32/R134a, R32/R1234yf, R32/R1234ze, and R32/R245fa within an ambient temperature range of 223–273 K. The results show that the coefficients of performance (COP) for R32/R134a, R32/R1234yf, and R32/R1234ze mixtures vary between 2.72 and 2.75, while that of R32/R600a reaches 2.55. Based on the comparative analysis, the R32/R134a mixture demonstrated the best performance and is recommended as a promising working fluid for auto-cascade heat pump systems designed for water heating applications in continental climate regions. Keywords: Auto-cascade Heat Pump, Zeotropic Mixture, Continental Climate, Water Heating, COP
Response of Liver and Gastric Cancer Cells to Electron and X-ray Radiation
Radiotherapy remains a critical pillar of cancer treatment worldwide. This study evaluates the in vitro efficacy of high-energy ionizing radiation, specifically 6 MV electrons and 12 MV X-rays, generated by a Varian Clinac iX linear accelerator (linac), on human HepG2 (liver) and AGS (gastric) cell lines. Cell samples (1 ml) were irradiated with doses ranging from 0.5 Gy to 4 Gy. Cell viability was assessed using the WST assay 4-5 hours post-irradiation. The measured survival rates were critically compared with those predicted using the established linear-quadratic (LQ) model. The results revealed significant and consistent discrepancies between the experimental measurements and the theoretical predictions for both cell lines. For HepG2 cells, the measured survival rate at 4 Gy was higher than the predicted rate. Interestingly, AGS cells irradiated with 12 MV X-rays exhibited minimal cytotoxicity, with a viability rate of 99.0% at 3 Gy versus a predicted rate of 73.6%. These findings suggest a discrepancy between theoretical predictions and the short-term biological responses observed under the shallow in vitro irradiation conditions employed in this study. While the present study was not designed to isolate the underlying mechanisms, the results imply that factors inherent to high-energy beam delivery in thin in vitro geometries, together with the early (four to five hour) post-irradiation assessment window, may have contributed to the limited cytotoxicity observed in both cell lines. Further studies employing extended observation periods or complementary assays would be valuable in clarifying the temporal progression of MV-beam-induced cellular effects. Keywords: Varian Clinac iX, high-energy radiation, HepG2, AGS, cell viability, WST assay, Monitor Unit (MU).
Comprehensive Structural and Stress Analysis Of Zno/Sic/Porous-Si/Si Multilayer Heterostructures Synthesized via Sequential Deposition Techniques
This research explores the fabrication and structural characteristics of ZnO/SiC/porous-Si/Si multilayer heterostructures synthesized through a controlled multi-step deposition process. The study combines electrochemical porosification of monocrystalline Si substrates, solid-phase epitaxial growth of silicon carbide films, and magnetron sputtering of ZnO layers under varied oxygen partial pressures. Two samples of ZnO films were synthesized under distinct oxygen atmospheres: 0.06 Pa and 0.1 Pa. Comparative XRD analysis reveals that films deposited at lower pressure (0.06 Pa) exhibit enhanced crystallinity, indicated by reduced peak broadening and distinct polycrystalline features. Residual stress analysis confirms compressive biaxial stress in both samples (−0.511 GPa and −0.287 GPa), indicating high crystalline quality and structural integrity of the ZnO films. These findings highlight the effectiveness of buffer layering and deposition control for optimizing ZnO film properties on complex silicon-based architectures. Keywords: ZnO thin film, porous silicon, silicon carbide, heterostructure, residual stress, structural characterization, X-ray diffraction.
Elemental analysis and X-ray irradiation effect on the Mongolian dairy product – “Khorkhoi Aaruul”
Aaruul is a traditional dairy product from Mongolia, recognized for its nutritional qualities and potential health benefits. Traditionally produced through manual milk processing at home, aaruul is increasingly mass-produced for commercial markets. This study aimed to investigate the effects of X-ray irradiation on Khorkhoi aaruul, a widely consumed small-curd variety. Samples were exposed to irradiation doses of 1 kGy, 3 kGy, and 5 kGy to evaluate reductions in bacterial contamination, extension of shelf life, and compliance with international food safety standards. The changes in vitamin C content and organoleptic properties (taste, texture, and appearance) were systematically assessed. Trace element composition was quantified using Energy-Dispersive X-ray Fluorescence (ED-XRF) spectrometry, focusing on phosphorus (P), calcium (Ca), zinc (Zn), iron (Fe), manganese (Mn), copper (Cu), and bromine (Br). Results indicated a substantial reduction in bacterial counts, achieving a 95.5% decrease at the 5 kGy dose (from 4.2×106 to 2×105 CFU). Critically, irradiation did not induce significant alterations in chemical composition, sensory quality, or vitamin C levels. These findings demonstrate the effectiveness of X-ray irradiation as a viable approach to enhancing microbial safety and prolonging the shelf life of traditional Mongolian dairy products without compromising their nutritional or sensory characteristics. Keywords: Aaruul, irradiation, trace elements, ED-XRF, colony formation unit
Quasi-2D Vortex Structures in Turbulent Flows: a Lagranjian Model with Fractal Effects
This paper presents a physically motivated model of quasi-two-dimensional vortex structures in turbulent flows. The theory of quasi-two-dimensional turbulence explains many phenomena in geophysical hydrodynamics, since due to the rapid rotation of the Earth, large-scale movements of the atmosphere and ocean almost two-dimensional. Quasi-2D turbulence is approximately two-dimensional and is described by equations containing additional terms. Such additions allow us to take into account weak three-dimensional effects that arise in real conditions, for example, in the atmosphere or ocean. We consider the basic equations for the velocity and pressure fields using the Lagrangian frame and incorporating centrifugal and Coriolis forces, as well as fractal disturbances on the vortex surface. Numerical simulations implemented in MatLab reproduce classical vortex behavior and reveal the influence of fractal corrections on field asymmetry. The model aligns well with existing experimental data and offers a foundation for analyzing energy transport and vortex interactions in stratified or thin-layered turbulent systems. Keywords: quasi- two-dimensional turbulence, fractal boundary, Lagrangian frame, streamfunction, vortex elements, numerical simulations.
On the inverse problem of identifying the source term in a pseudoparabolic equation with a final time overdetermination condition
In this paper, we consider the inverse problem for a linear pseudoparabolic equation describing the temperature distribution taking into account external forces that depend only on the spatial variable. The classical solution to the inverse problem under consideration satisfies the usual pseudoparabolic equation, initial and nonlocal boundary conditions, and a final additional condition. The issues of existence and uniqueness of the solution to the inverse problem are the subject of study in the work presented by the author. As the main result, theorems on the existence and uniqueness of the classical solution to the problem under study are formulated and rigorously proven. These theorems are completely proven in a mathematically rigorous language using the method of separation of variables. In the course of the proof, a system of orthogonal and biorthogonal basis functions of a special type was chosen in accordance with the nonlocal boundary conditions. First of all, to prove the theorem on the existence of a solution, an analytical formula for the solution was derived in the form of a series in the system of these functions, their uniform convergence was analyzed according to the Weierstrass theorem, and the convergence to the classical solution of the inverse problem under consideration was investigated. The proof of the theorem on uniqueness was carried out by the method of the opposite assumption. Keywords: inverse problem, pseudoparabolic equation, existence of solution, uniqueness of solution, nonlocal boundary condition.
Exploring the Impact of Anisotropy Parameters on Stellar Structure
In this study, we examine how variations in local pressure anisotropy affect the internal structure and equilibrium of white dwarfs. A generalized anisotropy model is developed, defined by three parameters: the amplitude coefficient α₀ and the shape exponents l and k. This formulation ensures that the anisotropic pressure continuously vanishes at both the center and surface of the star while reaching a single peak in the intermediate region. By applying appropriate boundary and regularity conditions, the model allows us to determine physically stable parameter domains consistent with realistic stellar configurations. Our analysis shows that even a small degree of anisotropy can have a measurable effect on the mass–radius relation and overall compactness of white dwarfs, which may help explain the origin of super-Chandrasekhar systems observed in astrophysical data. This modeling approach provides a clear and flexible way to describe compact stars with anisotropic pressures and can also be applied to neutron and quark stars. Keywords: compact stars, white dwarfs, anisotropic pressure, stability analysis, generalized anisotropic factor
Selection of a Propellant Feed System for the LPRE of a Small Upper Stage
The design of small upper stages must meet many propulsion requirements: repeated restarts, stable operation at low mass flow rate, strict limits on mass and volume, and compatibility with limited ground infrastructure. The central engineering task is a justified selection of the liquid propellant rocket engine feed architecture for a given mission profile and propellant pair, since this choice affects specific impulse, service life, risk, and ground processing effort. This work systematizes propellant feed schemes for a small upper stage and proposes a unified analytical framework that links engine cycle and feed method with propellant selection and tank pressurization modes. Pressure fed and turbopump schemes are treated as mature solutions; pump cycles are used mainly with cryogenic propellants and in high energy demand cases that require high efficiency and compact hardware. In parallel, electro pump schemes are actively studied as a promising direction due to lower mechanical complexity, precise control, and straightforward integration with modern control systems. The analysis shows how chamber pressure, allowable throttling range, restart capability, and the mass and volume metrics of tanks and hardware bound the rational domain of each scheme. The outcome is a set of criteria for early design that maps mission requirements to feed system architecture and supports a technologically feasible choice for small upper stages. Keywords: pressure-fed system, turbopump-fed supply system, small upper stages, rocket engines, liquid rocket engine.
THE CONTROL PROBLEM ASSOCIATED WITH HEATING PROCESS OF A ROD
In this paper, the control problem for a heat conduction equation with periodic boundary condition is considered. The solution with the control function on the border of the rod is given. The constraints on the control are determined to ensure that the average value of the solution within the considered domain attains a given value. The considered control problem is reduced to the Volterra integral equation, which is the first type, using the Fourier method. The proof of the existence of admissible control is related to the existence of a solution of the integral equation. The existence of the solution of the integral equation is shown using the Laplace transform method and the admissibility of the solution is proved. In the last section, the control function needed to achieve the average temperature given certain values of the parameters is found. Keywords: heat conduction equation, average temperature, periodic boundary condition, control problem, Volterra integral equation, Laplace transform.
SYNTHESIS OF TWO-DIMENSIONAL NANOSTRUCTURES AT LOW TEMPERATURES
The paper presents the results of experiments on synthesizing two-dimensional carbon nanostructures by thermal chemical vapor deposition using iron slugs as catalysts and substrates. The synthesis was conducted at a temperature of 250 ° C, a working pressure of 500 mbar, and a duration of 1 hour. The SEM results show that a two-dimensional structure is synthesized on the surface layer of the Fe slug with a vertical alignment. According to the detailed morphological characteristics of the results obtained by the scanning electron microscope, the nanostructures are two-dimensional carbon nanostructures, i.e. graphene-like. For a detailed determination of the structure of the obtained samples, a study was carried out by the method of Raman scattering and scanning electron microscopy. According to the Raman spectroscopy results, all spectra show the main carbon peaks D and G. In the high-frequency region of the spectra, second-order peaks D′, 2D and D + G are also observed, indicating the presence of graphene. Keywords: two-dimensional carbon nanostructures, iron catalyst, thermal chemical vapor deposition method, scanning electron microscope, Raman spectroscopy.
ENERGETIC EFFICIENCY OF TURBULENT BIOFUEL COMBUSTION FOR ADVANCED BIOENERGY TECHNOLOGIES
The combustion processes of biodiesel droplets in a combustion chamber using numerical modeling of two-phase reacting flows and complex turbulent currents are investigated in this study. The focus is on analyzing temperature fields, aerodynamic characteristics, and soot particle distribution at varying Reynolds numbers. The results show that optimal combustion conditions for biodiesel are achieved at Reynolds numbers between 20,000 and 25,000, where maximum combustion temperatures reach up to 2700 K, indicating high thermal efficiency and intense combustion processes. Additionally, this range of Reynolds numbers leads to a significant reduction in soot particle concentration (50–75 g/g), suggesting more complete fuel combustion and improved oxidation conditions. The findings confirm that increasing Reynolds numbers not only enhances combustion temperature but also improves the environmental performance of biodiesel by reducing emissions of solid combustion products. This research demonstrates the potential of biodiesel as an environmentally friendly alternative to traditional hydrocarbon fuels, offering optimal combustion characteristics under high turbulence conditions. Keywords: biodiesel, combustion, numerical modeling, soot emissions, turbulent flow.
DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH BOUNDARY TERMS
In the referenced study, a differential equation (DE) exhibiting a hybrid structure is examined. The principal objective of this manuscript is to determine the feasibility of substituting the given supplementary boundary conditions with alternative equivalent conditions. This is achieved through the establishment and proof of four theorems, providing a rigorous foundation for the proposed substitutions. Incipiently, the existing (3) conditions are considered in a nonhomogeneous context. Subsequently, new conditions, denoted as (7), are introduced. These newly formulated conditions are demonstrated to be equivalent to the original ones, ensuring the unique solvability of the hybrid-structured system labeled as (1). The system under consideration is characterized as hybrid due to the presence of both unknown and algebraic components. This dual nature necessitates a nuanced approach to boundary condition formulation and analysis. The methodology employed in this study underscores the importance of flexibility in boundary condition specification, particularly in complex or hybrid configurations. By establishing the equivalence of different boundary conditions, article provides valuable insights into the solvability and analysis of such frameworks. Furthermore, the study meticulously details prior research in this domain, delineating the specific conditions and configurations previously explored. This comprehensive review situates the current manuscript within the broader context of hybrid DE analysis. Key words: boundary, hybrid, dissipative, DAE, BVP.
STATISTICAL ANALYSIS OF THE SITUATION IN GEOSTATIONARY ORBITS
Statistical analyses of near-miss events involving geostationary zone objects from 2011 to 2024, derived from orbital propagation based on geostationary zone object orbital element catalogs and observational data of events, are presented. The data reveal a general increase in the number of near-miss events, attributable to the newly launched satellites and enhanced detection capabilities for space debris fragments. Notably, the average daily distribution of near-miss events exhibits longitudinal asymmetry, with a higher number of such events at 75°E longitude compared to 255°E. Conversely, potentially hazardous mutual approaches with distances as low as 10 km are more prevalent at 255°E. An investigation into the relationship between the average daily number of such events and the minimum object separation as a function of the catalog epoch indicates an increase in daily dangerous approaches within 1 km from 0.24 events/day in 2011 to 0.39 events/day in 2024. When considering a 20-meter collision threshold, the 2024 data suggest a potential collision event probability in geostationary orbit of one event per eight years. Projections based on the current trajectory of orbit occupancy suggest that, if prevailing trends persist, collision events in GEO could occur every six years by 2030 and every four years by 2040. Keywords: Space debris, Near-Earth Space, Geostationary orbit, Near-Miss Events, Space situational awareness.
SIMULATION OF RESONANT REACTIONS IN TTIK APPROACH BY C++ CODE
We studied the interaction of ¹⁵N with hydrogen at low energies using the Thick Target Inverse Kinematics (TTIK) method combined with the Time of Flight (ToF) technique. This combination enables a clear identification of different light recoil particles without compromising energy resolution in the extended gas target. The use of a gas target ensures minimal background and allows precise measurement of energy loss and reaction kinematics across a broad excitation function. At the same time, the ToF technique provides particle separation without degrading energy resolution. In this paper, we presented the results of theoretical calculations of energy losses in the gas target, implemented using a custom C++ code. The obtained results show reasonable agreement with experimental data. The simulations agree well with the experimental results for α-particles and ¹²C nuclei, confirming the accuracy of the theoretical predictions for these reaction products. However, further improvements or theoretical refinements are required due to the insufficient fit observed in the proton-related calculations. Keywords: TTIK, inverse kinematics, time of flight, resonant reaction, C++ simulation.