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
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.
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 25nm and a height of 500nm, 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 Schr & ouml;dinger 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 height V-0(P) = chi(ZnO) - chi(eff)(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.
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.
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 alpha + alpha + 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.
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.
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-w 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.
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-w 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.
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.
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.
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 InjectT", 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 & centerdot;s to 280 mPa & centerdot;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.
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.
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.
In the paper the steady flow of a viscous incompressible fluid past a circular cylinder with attached splitter plates is considered. The mathematical representation of the problem takes the form of an external boundary value problem for the stream function. To solve the problem, a numerical method combining the R-functions and the nonlinear Galerkin method is used. The R-functions method is employed to construct a problem solution structure that exactly satisfies all the boundary conditions of the problem and has the required behavior at infinity. The Galerkin method is then applied to approximate the undetermined components of this structure, ensuring accuracy and efficiency in the solution process. A series of computational experiments was conducted to investigate the flow past a single circular cylinder and past a circular cylinder with triangular and rectangular splitter plates at various Reynolds numbers. For the case of a single cylinder, a quantitative error analysis confirms the convergence of the numerical method, with relative errors dropping below 1% when using a moderate number of basis functions. The computational cost remains practical, with each solution obtained in approximately 11 minutes on a standard workstation. Drag and lift coefficients are computed for the single-cylinder case, allowing for quantitative assessment of aerodynamic performance and validation of the numerical model against known reference data. The influence of splitter plate geometry on the flow structure is explored through visualizations, highlighting changes in vortex patterns and symmetry. The proposed approach demonstrates strong numerical accuracy and computational robustness for the single-cylinder case and offers a flexible framework for studying external viscous flows with complex boundary configurations. Keywords: Viscous incompressible fluid, External boundary value problem, Stream function, R-functions method, Nonlinear Galerkin method.
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.
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 ofvelocity, 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.
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 writtenby S. Gramenitsky (1897) andM. Dulatuly (1914). Inthefirstfifteenyears 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.
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.
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.
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.
