Mathematical Analysis Research Articles

ECONOMIC EFFICIENCY OF APPLICATION OF OPTIMIZED MILL BED

This paper presents the selection of optimization parameters for the bed geometry of a long metal cutting machine (MCM), the design problem and boundary conditions were given. Five different geometries were designed for further mathematical analysis to meet the requirements of the problem. Static analysis of the mathematical model of the bed shells was performed by finite element method (FEM) using BETA CAE System tool, ABAQUS, which showed that by using stiffeners in the form of two variable pitch spirals and three hollow tubes, as well as changing the design at the connection point of the beam support to the bollards of the long bed of the metal cutting machine, the stresses that occurred in these places at an angle of 90° were reduced. The geometries were chosen in such a way that it was possible to reduce the stresses occurring at the point of cutting, to reduce the deflection, to increase the rigidity of the structure. The economic calculation aimed at determining the cost of a long metal-cutting machine tool with the proposed geometry has been carried out. The analysis of the unit cost of the product (long bed of the metal-cutting machine tool made of polymer concrete with optimized geometry) has been carried out, the calculation of the annual economic effect from the use of the proposed method of manufacturing has been carried out. Keywords: MCM, FEM, statistical analysis, product cost, economic calculation.

Metabolomic signature identifies HDL and apolipoproteins as potential biomarker for systemic sclerosis with interstitial lung disease

BackgroundHigh-density lipoproteins (HDL) affect endothelial functions such as the expression of endothelial cell adhesion molecules and exert anti-apoptotic/-thrombotic functionalities. Therefore, profound analysis of lipoproteins may unveil biomarkers for (micro-)vasculopathy in systemic sclerosis (SSc) and mortality determining disease manifestations like interstitial lung disease (SSc-ILD). Because nuclear magnetic resonance (NMR) spectroscopy provides a wide range of lipoprotein parameters beyond the capabilities of classical analyses it has been used herein to examine lipoprotein profiles in SSc. MethodsTo detect the metabolic and lipidomic profile serum samples from clinically well-characterized SSc patients (n = 100) and age-and sex-matched healthy controls (n = 40) were analyzed by 1H NMR spectroscopy using Bruker's in-vitro diagnostic research (IVDr) protocol. Statistical analyses were performed to validate significant findings and to search for associations between lipoproteins and clinical phenotypes. ResultsPatients with SSc-ILD and lung fibrosis displayed reduced HDL levels. Furthermore, a reduction in apolipoprotein A1 + A2 and its HDL fractions reflected a distinct lipoprotein profile for SSc-ILD patients. This association was independent of potential clinical confounders for dyslipidemia. Notably, in SSc-ILD HDL levels correlate with FVC (forced vital capacity), DLCO (diffusion capacity of the lungs for carbon monoxide), and the modified Rodnan-Skin-Score. ConclusionThese results suggest HDL and its lipoproteins may be considered as potential new biomarkers for SSc-ILD. Immune-mediated HDL effects on the endothelium facilitate microvasculopathy - one of the pathophysiological hallmarks in SSc. Therefore, a closer prospective evaluation of the capability of HDL-determination and its lipoproteins regarding a more individualized evaluation of SSc-ILD is warranted.

Mathematical analysis and optimal control of age‐structured social interaction model with law enforcement

Optimal use of available resources is one of the major issues in many situations. Apart from this, age is also an important factor in modeling social interaction in a society. In this article, we consider an age‐dependent social interaction model and study the stability and optimal control. Law enforcement is an important factor in controlling crime, and the deployment of police to enforce it is important. Now cost is a major issue, so optimal deployment is very important to study. Stability results are derived in terms of threshold parameters. Basic reproduction number is calculated for stability analysis. Using the adjoint system, the form of the law enforcement factor is obtained in terms of state space variables. We see that the cost functional increases with the increase in the population density of criminal population. Numerical results are also added to visually illustrate our theoretical results.

Mathematical modelling and performance analysis of an AEM electrolyzer

In this study, an analytical model including electrochemical reactions and mass transfer in an anion-exchange membrane electrolyzer (AEMEL) has been developed by considering water sorption/desorption in electrodes. The model developed was used to investigate the performance of the AEMEL in terms of efficiency, transport phenomena and operating parameters. The numerical results revealed that the voltage losses in the AEMEL are mainly due to activation losses. The effects of important parameters such as membrane thickness, operating pressure on cell performance, and species transport were also investigated. The results also revealed that the AEMEL performance improves with decreasing membrane thickness, but the membrane thickness should be considered together with hydrogen permeability and differential operating pressure to operate the electrolyzer safely.

Study on the 2D equivalent nonlinear dynamics simulation model related to high speed precision bearing and spindle

The stiffness and contact stress of the bearing spindle system are the key factors affecting its machining accuracy and service life under the condition of high-speed service, which will be affected by different structural parameters and service conditions. It is essential to establish an efficient and accurate computational simulation model to understand the influence of complex factors on the nonlinear dynamic characteristics of the bearing spindle system. Firstly, in the paper, a 2D axisymmetric finite element model of the bearing, aims at the relationship between stiffness and contact stress of the bearing under high-speed service, has been built based on a classical dynamic analysis model and the reversed method of material parameters of equivalent rolling balls. Additionally, for the BT30 spindle, the 2D axisymmetric finite element model of the bearing spindle system also has been built and applied in mechanical analysis of spindle under different conditions of assembly and service, based on the bearing model. The results show that the axial force of bearings decreases as the rotational speed increases, and an augmentation in speed will result in a reduction in the axial stiffness of the BT30 spindle. In addition, the maximum contact stress exhibits a slight decline as the rotational speed increases. Furthermore, with an escalating preload, the stiffness and contact stress of the spindle undergo substantial increments, however, these parameters will cease to alter once a certain threshold is reached.

Study on the spatial distribution characteristics of traditional villages and their response to the water network system in the lower yangtze river basin

Traditional villages hold significant historical and cultural value as the precious heritage of China’s agricultural civilization. Currently, against the backdrop of increasing urbanization and rapid expansion of urban construction land, the spatial patterns of traditional villages across various regions in China are being encroached upon and damaged, with protection pressures growing daily. As one of the important cradles of Chinese civilization, the Lower Yangtze River Basin (LYRB) has traditional villages closely linked with its water systems, forming a unique human-land relationship and spatial distribution pattern. However, influenced by the rapid urbanization process, the spatial patterns of traditional villages in this region also face a crisis, and the contradiction between protection and development is becoming increasingly prominent. How to balance this contradiction and ensure the reasonable protection and sustainable development of traditional villages has become an urgent issue to address. Therefore, this study focuses on the LYRB. Using ArcGIS tools and combined with mathematical analysis methods, the spatial distribution characteristics and essential influencing factors of traditional villages in this area were screened and analyzed. The objective was to examine the spatial structural relationship between traditional villages, four water system types, and nine sub-basin units, intending to reveal the unique interdependence between the water system and traditional villages in this area. This would provide scientific support for the formulation of scientific conservation strategies. The research results show that: (1) Traditional villages in The LYRB form two core clusters spatially and exhibit substantial spatial accumulation; (2) Water system characteristics are the main factors affecting the distribution of traditional villages; (3) In the LYRB, the spatial distribution of the nine sub-basins is closely related to the spatial distribution of traditional villages, resulting in typical regional spatial differentiation of traditional villages in this area. This study is based on a watershed perspective, and the results highlight the importance of the water system network in the development of traditional villages, revealing a unique spatial dependency relationship between traditional villages and the water network in the LYRB. In order to ensure the comprehensive protection of the traditional village system in this region, it is essential to adhere to the fundamental principles that govern its spatial configuration. A tripartite collaborative protection system based on the watershed should be formulated from the perspective of the overall distribution relationship between the water network and the traditional villages. This system would serve to protect the overall landscape, the water network pattern, and the traditional villages. Establishing an overall pattern view of integrating the water system network and the traditional villages is essential.

Enhancement of Teaching Methods of Main Mathematical Disciplines in Higher School

Innovations are proposed in the courses of mathematical analysis, linear algebra and discrete mathematics taught in the first year of study. Innovations are aimed at improving methods of teaching basic mathematical disciplines in higher education.

Detrended fluctuation analysis to determine physiologic thresholds, investigation and evidence from incremental cycling test.

Training zones are generally assessed by gas-exchange thresholds (GET). Several mathematical analyses of heart rate variability (HRV) are proposed for indirect GET determination. Our study aimed to investigate the accordance of the detrend fluctuation analysis (DFA α1) for determining GET with first (VT1) and second ventilatory (VT2) thresholds in well-trained subjects. Eighteen female and 38 male sub-elite cyclists performed a maximal incremental cycling test of 2-min stage duration with continuous gas exchange and HR measurements. Power output (PO), Oxygen uptake ( O2) and HR at VT1 and VT2 were compared with DFA α1 0.75 (HRVT1) and 0.50 (HRVT2). Agreements between PO, O2 and HR values were analyzed using Bland-Altman analysis. Large limits of agreement between VT1 and HRVT1 were observed for measures of O2 expressed in mL.min-1.kg-1 [-21.3; + 14.1], HR [39.2; + 26.9] bpm and PO [-118; + 83] watts. Indeed, agreements were also low between VT2 and HRVT2 for measures of O2 [-26.7; + 4.3] mL.min-1.kg-1, HR [-45.5; + 10.6] bpm and PO [-157; + 35] watts. Our results also showed a sex effect: women obtained worst predictions based on DFA α1 than men for HR (p = 0.014), PO (p = 0.044) at VT1 and (p = 0.045), HR (p = 0.003) and PO (p = 0.004) at VT2. There was unsatisfactory agreement between the GET and DFA α1 methods for VT1 and VT2 determination in both sex well-trained cyclists. Trial registrationnumber 2233534 on 2024/03/05 retrospectively registered.

A multi-step calibration strategy for reliable parameter determination of salt rock mechanics constitutive models

The storage of renewable hydrogen in salt caverns requires fast injection and production rates to cope with the imbalance between energy production and consumption. This raises concerns about the mechanical stability of salt caverns under such operational conditions. The use of appropriate constitutive models for salt mechanics is an important step in investigating this issue, therefore many constitutive models with several parameters have been presented in the literature. However, a robust calibration strategy to reliably determine which model and parameter set represents the given rock, based on stress–strain data sets, remains an unsolved challenge. In this paper, for the first time in the community, we present a multi-step strategy to determine a single parameter set based on many deformation data sets for salt rocks. Towards this end, we first develop a comprehensive constitutive model able to capture all relevant nonlinear deformation physics of transient, reverse, and steady-state creep. The determination of the single set of representative material parameters is then achieved by framing the calibration process as an optimization problem, for which the global Particle Swarm Optimization algorithm is employed. To allow for dynamic data integration, a multi-step calibration strategy is developed for a situation where experiments are included one at a time, as they become available. Additionally, due to the existing mild heterogeneity in the experimental rock samples, our optimization strategy is made flexible to allow for this slight heterogeneity. The devised optimization strategy, based on the multi-physics comprehensive constitutive modeling framework, results in a single set of representative material properties of all the deformation data sets. As a rigorous mathematical analysis for the presented method and the lack of relevant experimental data sets, we consider a wide range of synthetic experimental data sets, inspired by the existing sparse relevant data in the literature. The results of our performance analyses show that the proposed calibration strategy is robust. Moreover, the results become increasingly more accurate as more data sets become available.

STRUCTURE OF THE AUTOMATED CONTROL SYSTEM OF TECHNOLOGICAL PARAMETERS OF TREATMENT FACILITIES OF THE CITY SEMEY

Increasing the efficiency of control of treatment facilities can be achieved by automation of control at the stages of observation, collection, processing and analysis of information by means of mathematical data analysis packages, implementation of automated control systems of technological processes.This article is devoted to the issues of technical modernization of automatic control system of water disposal in Semey city. The need to modernize the concept of building the ACS has arisen in connection with the technical re-equipment of production and introduction of new energy-saving technologies in it.The hypothesis of the research suggests the possibility of improving the efficiency of wastewater treatment facilities of Semey city through the use of modern methods of collection and transmission of technological parameters to the control panel of the dispatcher in order to make operational decisions on the management of technological and technological process of wastewater treatment based on monitoring of equipment operation. Due to the complexity of the whole complex of treatment facilities, the main sewage pumping station (GKNS-2) and air blower pumping station (ABPS) were selected as objects for the development of automated control system of technological parameters (ACS TP).The article considers the proposed structural scheme of the automated system of control of technological parameters of treatment facilities of Semey city, gives a description of each level of the system and the principle of their interaction.

Strong Solutions of Brusselator System

The study involves a mathematical analysis of the Brusselator system on a convex bounded three-dimensional open domain, considering Neumann boundary conditions. We establish the global existence and uniqueness of the strong solution for this system. Achieving high regularity for the strong solution requires stringent conditions on the initial data. The study demonstrates the continuous dependence of the solution on the initial conditions.

Analysis and design of voltage-source parallel resonant class [formula omitted] inverter

In this paper, a detailed mathematical analysis process of the voltage-source parallel resonant (VSPR) class E/F3 inverter at 50% duty ratio is proposed. Combining the advantages of VSPR class E and F inverters, the performance of the proposed inverter can be improved greatly compared to the traditional. The transistor in the VSPR class E/F3 inverter is satisfied with zero-voltage switching(ZVS) and zero-voltage derivative switching(ZVDS) conditions. Moreover, two design freedoms can be obtained and the proposed analysis process is based on them, which can provide more flexible selections. Finally, a VSPR class E/F3 inverter is fabricated and the experiment is carried out. The measured normalized peak transistor voltage decreases by 25.6%. The output power reaches 5.06 W, and the efficiency reaches 93.75%. The measured results are well agreed with the theoretical and simulated.

ASSESSING THE DYNAMICS OF CHANGES IN ROAD SAFETY INDICATORS IN UKRAINE

Purpose. A study of road traffic in Ukraine shows that despite several legislative and regulatory documents aimed at improving road safety, the total number of road traffic accidents (RTAs) is increasing from 2015 to 2021. According to statistical data, each road traffic accident involves more than one injured person on average. A significant reduction in the accident rate can be achieved by developing a national action programme to improve road safety, which should be based on a systematic analysis of the nature and causes of road accidents. Therefore, the purpose of this paper is to conduct a comprehensive study of the level of road safety in Ukraine based on a systematic approach to assessing road accident data. Methodology. In the course of the research, the methods of regression analysis were used to study the absolute, specific and relative accident rates and the causes of accidents. All calculations were performed using Excel software. Results. This paper studies the international regulatory framework and national legislative documents aimed at improving traffic safety. An analysis of changes in absolute, specific and relative accident rates in 22 regions of the country is carried out. The general trends in accident rates in Ukraine from 2015 to 2021 are identified. The total number of road accidents in Ukraine, with some fluctuations in some years, has been increasing from 2015 to 2021. However, the percentage of road accidents with victims in the total number of accidents is decreasing. The social risk indicator in 2021 decreased by 15.86% compared to 2015. However, this figure remains almost twice as high as in top countries, where even those who died within 30 days of being injured in a road accident are taken into account. The scientific novelty. Based on the methods of mathematical statistics and regression analysis, the methods of estimating absolute, specific and relative accident rates, which take into account the number of victims, injured and killed in road accidents in the study of different regions of Ukraine, have been further developed. The practical significance. The obtained regression dependencies of accident rates can be used to formulate the provisions of an effective national road safety system aimed at significantly reducing the number of people killed and injured in road accidents, as well as reducing the economic losses caused by them.

Mathematical modeling and analysis for radiative MHD peristaltic flow of Bingham nanofluid

Mathematical modeling and analysis for radiative MHD peristaltic flow of Bingham nanofluid

Assessment of the functional capabilities of the heart and the severity of the stress response in women 30-49 years old who are starting to engage in fitness

In this article, based on the results of scientific publications, the current state of the fitness industry development in Kazakhstan in terms of the volume of fitness services and the number of people involved is studied. The results of our own research are presented using modern technologies: in particular, using the method of cardioscanning of cardiovascular system indicators, assessing the fitness level and cardiostress index, as well as based on bioimpedance analysis, the body mass index of untrained women (30-49 years old) of the Royal Club Bukhar Zhyrau fitness club in Almaty in a state of relative rest was determined. The bicycle ergometry method was used to assess the response of hemodynamic indicators of the surveyed contingent to standard physical activity of subthreshold intensity. The obtained data were processed using the methods of mathematical statistics and correlation analysis, analyzed, summarized and formulated in the research results.

Numerical modeling and the ultimate bending experiment of the directional drill pipes bending at the dog-leg of the multi-branch well

Directional drill pipes are prone to failure in the fish-bone branch wells. The primary cause of the directional drill pipes failure is excessive bending. This paper established a mathematical analysis model for the bending stress of the directional drill pipes at any point along its trajectory. Tested the mechanical properties of the directional drill pipe. An ultimate bending experiment was conducted on the directional drill pipes based on the pure bending moment theory. Additionally, a non-linear finite element model(FEM) of the directional drill pipes was established to analyze the influence of different bending loads on the stress distribution of the directional drill pipes connection. The FEM results were consistent with the results of the ultimate bending experiment. The FEM results indicate that the Box bending under transverse force is the primary cause of the failure for the Tooth top. The research results enable engineers and operators to easily obtain the stress distribution of the directional drill pipes under borehole curvature.

Improved reduced order model for study of coupled phenomena

Abstract Many interesting phenomena in applications are based on interactions between their constituent sub-systems. The first principle exact models of these phenomena can be quite complicated. Therefore, many practitioners prefer to use so-called phenomenological models, which are generally known as models based on coupled mode theory (CMT). This type of reduced-order model captures the dominant behavior of the system under appropriate conditions. Quite often, these validity conditions are qualitatively described, but no detailed mathematical analysis is provided. This work addresses this issue and presents improvements in the traditional phenomenological models. Although an LC circuit model is used for illustration due to its simplicity, the results in this work are equally applicable to a wide variety of coupled models. A detailed mathematical analysis is carried out to quantify the order of approximation involved in the model-based CMT. Using it, the validity of the model in the regime from weak coupling to strong coupling is analytically investigated. An improved reduced-order model is proposed, which gives better results than the traditional phenomenological model. The analytical studies are verified with numerical simulations, which clearly show better validity of the proposed improved model of coupled systems.

The connection between the accumulation of structural defects caused by proton irradiation and the destruction of the near-surface layer of Li4SiO4 – Li2TiO3 ceramics

The key problem of using lithium-containing ceramics as materials of breeders for the propagation of tritium in thermonuclear reactors is phase stability, as well as the preservation of strength and thermophysical parameters of ceramics during their operation, which is accompanied by the accumulation of fission products in the near-surface layers, alongside mechanical influences from the outside. Moreover, in contrast to other types of ceramics, the presence of lithium in the composition of the samples under study leads to limitations in the use of classical analysis methods (scanning electron microscopy, energy dispersive analysis or optical spectroscopy) of structural changes caused by the accumulation of radiation damage, which requires the use of more complex methods for the assessment of the defect concentration in the structure, as well as establishing their relationship with the deterioration of strength and thermophysical parameters, playing a key role in determining the stability mechanisms and further exploitation of ceramics for tritium production. In this regard, the aim of the study is to determine the kinetics of changes in the near-surface layer of two-phase Li4SiO4 – Li2TiO3 ceramics associated with the accumulation of structural distortions caused by irradiation, as well as their relationship with strain embrittlement and disorder. During the studies, it was found that the accumulation of implanted hydrogen in the near-surface layer under high-dose irradiation initiates deformation distortion processes, the intensity of which depends on the ratio of components in the ceramics, according to which the optimal compositions of two-phase ceramics are ratios of components from 0.3 to 0.6. Determination of the type of defects in the composition of the damaged layer, as well as their concentration, was carried out using the electron spin resonance (ESP) method. During the studies, it was found that at low irradiation fluences, the dominant role in the accumulation of structural defects is played by vacancy defects associated with E′-centers, the formation of which is associated with structural distortions, while as the fluence grows, the structure is dominated by deformation disordering caused by the accumulation of Ti3+ defects and HC2 centers (SiO43-), the concentrations of which have a clear dependence on the phase composition of the ceramics.

Topological Data Analysis for Particulate Gels.

Soft gels, formed via the self-assembly of particulate materials, exhibit intricate multiscale structures that provide them with flexibility and resilience when subjected to external stresses. This work combines particle simulations and topological data analysis (TDA) to characterize the complex multiscale structure of soft gels. Our TDA analysis focuses on the use of the Euler characteristic, which is an interpretable and computationally scalable topological descriptor that is combined with filtration operations to obtain information on the geometric (local) and topological (global) structure of soft gels. We reduce the topological information obtained with TDA using principal component analysis (PCA) and show that this provides an informative low-dimensional representation of the gel structure. We use the proposed computational framework to investigate the influence of gel preparation (e.g., quench rate, volume fraction) on soft gel structure and to explore dynamic deformations that emerge under oscillatory shear in various response regimes (linear, nonlinear, and flow). Our analysis provides evidence of the existence of hierarchical structures in soft gels, which are not easily identifiable otherwise. Moreover, our analysis reveals direct correlations between topological changes of the gel structure under deformation and mechanical phenomena distinctive of gel materials, such as stiffening and yielding. In summary, we show that TDA facilitates the mathematical representation, quantification, and analysis of soft gel structures, extending traditional network analysis methods to capture both local and global organization.

Computer Analysis of Scientific Texts to Identify Ideological Narratives

This article is devoted to the problem of identifying hidden ideological attitudes in scientific articles on economics, as well as defining methods for analyzing the ideological landscape of Russian economic science. The problem of this review article lies in the absence of a developed generally accepted approach to the textual analysis of scientific publications. Thus, there is an extremely wide list of methods that can be used in this case. Nevertheless, the development of the most effective methodology requires a comprehensive analysis of existing approaches individually and a comparison of each of them with the others. The authors associate the solution of the problem of choice in the presence of several approaches and a variety of methods with the definition of such a basis that would allow the formation of a methodology that includes ideological classification within the framework of economic scientific literature, the use of computational linguistics tools, in particular natural language processing, in addition to classical narrative analysis tools to identify "ideological narratives". In this regard, the methods of identifying implicit meanings in economic texts are considered in detail. The proposed tools can be used in further research on this or related topics.