Construction Of Mathematical Model Research Articles

Construction of a deterministic mathematical model for the spatial-mass distribution of random fragments produced by cased charge explosion

To evaluate the destructive effects of fragment impacts on structures or personnel, it is crucial to assess the velocity, mass, size, and impact location of the fragments, as well as establish the correlation between these factors. This paper presents the experimental measurement of fragment velocities produced by the explosion of a cased charge, the fragments resulting from the explosion are collected and steel plates are used to record the impact locations and sizes of the fragments. Based on the experimental results, the calculation models of fragment velocity, fragment mass distribution and fragment scattering angle are corrected, the spatial distribution models of fragment size and number are established, and the functional relationship between fragment mass and size is constructed. Given the aforementioned research findings, the fragment spatial-mass distribution models based on the size distribution function and based on the mass distribution function are constructed, and the fragment space-mass distributions corresponding to the number of impact regions of 1, 5 and 10 are analyzed, and the effect of the number of impact location divisions on the fragment space-mass distribution is explored. The research results show that, for the current test charge, the fragment spatial-mass distribution model based on the size distribution function aligns most accurately with experimental results when the impact regions is divided into 10. The number of impact locations designated within each region is directly proportional to the number of fragments in that specific region. Notably, the impact location of the largest fragment occurs at 0.8 times the length of the impact region, whereas the peak fragment impact density occurs at 0.743 times the length of the impact region. The spatial-mass distribution model proposed in this paper successfully correlates the velocity, mass, size and impact location of the fragments, providing a realistic theoretical representation of the spatial geometric distribution of the fragments.

Changes in IOL power after laser peripheral iridotomy based on multivariate analysis

BackgroundThis study aimed to investigate the effect of laser peripheral iridotomy (LPI) on intraocular lens (IOL) power in patients with primary angle closure disease (PACD), and to construct mathematical models to assess changes in IOL power.MethodsThis study included 58 eyes of PACD patients. IOL Master700 was used to analyze and compare the changes of IOL power and ocular related parameters in each formula before and after LPI. The number of cases with IOL power changes greater than 0.5 diopters (D) in each group were counted and significant differences were analyzed using Fisher’s exact test. Pearson’s linear correlation analysis was used to ascertain the relationship between IOL power changes and ocular parameter changes to establish mathematical models.ResultsNo significant difference was found in calculated IOL power changes before and after LPI in each group. There was significant difference in the number of cases with IOL change values greater than 0.5D between the primary angle closure glaucoma (PACG) and the other two groups for each formula. IOL power changes were mainly associated with △K and △AL. Mathematical models of IOL power changes after LPI were constructed based on linear regression analysis.(PAC group: △IOLHaigis=0.026–2.950×△AL-1.414×△K, △IOLHoffer Q=-3.578×△AL-1.412×△K, △IOLSRK/T=-3.152×△AL-1.114×△K, △IOLHolladay 1=-3.405×△AL-1.291×△K, △IOLHolladay 2=-3.467×△AL-1.483×△K, △IOLBUII=-3.185×△AL-1.301×△K; PACG group:△IOLHaigis=-1.632×△K, △IOLHoffer Q=-3.770×△AL-1.434×△K, △IOLSRK/T=-3.427×△AL-1.102×△K, △IOLHolladay 1=-3.625×△AL-1.278×△K, △IOLHolladay 2=-4.764×△AL-1.272×△K, △IOLBUII=-4.935×△AL-1.304×△K).ConclusionsLPI will cause changes in some ocular parameters in patients with PACD, with great effects on IOL power calculations was observed in patients with PACG. Mathematical models based on multivariate analysis hold promise for predicting IOL power changes subsequent to LPI.

Research on the characteristics of a pneumatic proportional valve

Abstract The execution of autonomous driving in heavy-duty trucks necessitates stringent regulation of their braking torque output. Hydraulic retarder serves as a widely auxiliary braking system in heavy-duty vehicles, with the pneumatic proportional valve functioning as the core component of its control system, regulating the output response and control precision of the braking torque of the hydraulic retarder. To improve the accuracy of brake torque control for hydraulic retarders, it is critical to conduct thorough research on the control system, especially the pneumatic proportional valve. Therefore, A detailed analysis of the working mechanism of pneumatic proportional valves was conducted, encompassing the construction of mathematical and simulation models. The efficacy of the simulation model was confirmed via experimental validation. When the control pressure increases, the simulation results are close to the experimental results, with a maximum discrepancy of 18%; when the control pressure decreases, the simulation results show a similar trend to the experimental results. The research can aid in formulating control methodologies for pneumatic proportional valves and offer theoretical guidelines for future exploration into boosting the precision of hydraulic retarder braking torque control.

COMPARATIVE ANALYSIS OF METHODS AND MODELS FOR ESTIMATING SIZE AND EFFORT IN DESIGNING MOBILE APPLICATIONS

Mobile applications have long become an integral part of everyday life and have gained popularity among ordinary users, small companies, and large enterprises. However, this is a completely separate area of software. We can say that this is a whole separate ecosystem. Creating functional software for this ecosystem comes with new requirements, constraints, and characteristics that were not used in previous software metrics evaluation methods such as desktop programs or web applications. Mobile applications have new features, limitations and capabilities that are different from other software. Estimating the size and effort helps the software development team approximate the costs needed to more successfully develop a software product such as a mobile application. An early estimate of size and effort is necessary to identify resources that can help in the early stages of implementation a software project within budget and on time. The reliability of the assessment is also of great importance. Low reliability can lead to overestimation or underestimation, which can have bad consequences for any software development company, especially mobile applications. However, the suitability of methods and models for measuring size and efforts that are used for traditional software (PC applications and web applications) do not always provide sufficient reliability for mobile applications.The main goal of this article is to analyze the usage of various methods and models for estimating size and effort the development of mobile applications, including for the Android OS at the initial stages of their design. There is a brief description of the main and widespread methods and models that are used to estimate the size and effort, such as: Lines of Code (LOC), Function Points (FP), COCOMO and COCOMO 2, COSMIC, FiSMA, application of regression analysis for construction of mathematical models. The methods and models proposed by various authors are directly analyzed.

Solid-State Fermentation Engineering of Traditional Chinese Fermented Food.

Solid-state fermentation (SSF) system involves solid, liquid, and gas phases, characterized by complex mass and heat transfer mechanisms and microbial complex interactions. The SSF processes for traditional Chinese fermented foods, such as vinegar, soy sauce, and baijiu primarily rely on experience, and most of the operations are replaced by auto machine now. However, there is still a lack of engineering in-depth study of the microbial process of SSF for complete process control. To meet the demands of smart manufacturing and green production, this paper emphasizes the engineering analysis of the mechanisms behind SSF. It reviews the progress in the engineering aspects of Chinese traditional SSF, including raw material pretreatment, process parameter detection, mathematical model construction, and equipment innovation. Additionally, it summarizes the challenges faced during intelligent upgrades and the opportunities brought by scientific and technological advancements, proposing future development directions. This review provides an overview of the SSF engineering aspects, offering a reference for the intelligent transformation and sustainable development of the Chinese traditional SSF food industry.

Molecule Empowerment and Crystal Desensitization: A Multilevel Structure-Property Analysis toward Designing High-Energy Low-Sensitivity Layered Energetic Materials.

Layered energetic materials (LEMs) can effectively balance energy and mechanical sensitivity, making them a current research focus in the field of energetic materials. However, the influence of the layered stacking pattern on impact sensitivity is still unclear, leading to the lack of advanced design strategies for high-energy low-sensitivity LEMs. Herein, we first utilize novel indicators such as maximum plane separation and hydrogen bond dimension to perform high-throughput screening on over 106 candidate structures, resulting in 17 target crystals. A systematic analysis was then conducted on the relationships between the bond dissociation energy (BDE) of the weakest energy-storing bond at the molecular level, the intralayer hydrogen bond energy (HBE), and the sliding energy barrier (SEB) at the crystal level with impact sensitivity. The findings suggest that a material can have low sensitivity only if at least two of the three properties perform well, and the interlayer sliding resistance can be reduced by enhancing the intermolecular hydrogen bond interactions, which reasonably explains the experimental phenomena. More importantly, we developed a prediction model for the impact sensitivity of LEMs with a coefficient of determination of 0.88. Additionally, factors affecting HBE and SEB were identified, and a linear model was established based on molecular-level feature variables. Finally, a new strategy for designing high-energy low-sensitivity LEMs was proposed, namely, empowerment at the molecular scale and desensitization at the crystal scale. This study integrates high-throughput screening, multilevel structure-property relationship analysis, and mathematical model construction, offering new perspectives for the development of novel high-energy and low-sensitivity energetic materials.

Warehouse layout optimization for fishbone robotic mobile fulfillment systems

The rapid development of electronic commerce has increased demands for order fulfillment efficiency, making this a crucial challenge for warehouse systems. The study proposes a novel fishbone robotic mobile fulfillment system (FRMFS) to optimize warehouse layout and enhance the picking efficiency of automated warehouse systems, such as robotic mobile fulfillment systems (RMFS). Through the construction and analysis of mathematical models, the research demonstrates that FRMFS can significantly reduce the travel distance of robots when compared to traditional RMFS. This leads to an improvement in the overall picking efficiency of the warehouse system. The study also examines the impact of warehouse parameters, cross-aisle angles, and the number of picking stations on system operational efficiency. Simulation experiments confirm that FRMFS can reduce picking distances by 18%–28% compared to traditional RMFS. This makes it particularly suitable for complex warehouse systems with high requirements for operational response time and system throughput. Furthermore, the study introduces a point-based layout design method for picking stations in FRMFS, demonstrating its efficiency as a heuristic approach. This research presents a scientific analysis framework and model support for the operational design and optimization of FRMFS, offering valuable insights for management practices.

Construction of mathematical models of thermal conductivity for modern electronic devices with elements of a layered structure

This paper considers a heat conduction process for isotropic layered media with internal thermal heating. As a result of the heterogeneity of environments, significant temperature gradients arise as a result of the thermal load. In order to establish the temperature regimes for the effective operation of electronic devices, linear and non-linear mathematical models for determining the temperature field have been constructed, which would make it possible to further analyze the temperature regimes in these heat-active environments. The coefficient of thermal conductivity for the above structures was represented as a whole using asymmetric unit functions. As a result, the conditions of ideal thermal contact were automatically fulfilled on the surfaces of the conjugation of the layers. This leads to solving one heat conduction equation with discontinuous and singular coefficients and boundary conditions at the boundary surfaces of the medium. For linearization of nonlinear boundary value problems, linearizing functions were introduced. Analytical solutions to both linear and nonlinear boundary value problems were derived in a closed form. For heat-sensitive environments, as an example, the linear dependence of the coefficient of thermal conductivity of structural materials on temperature, which is often observed when solving many practical problems, was chosen. As a result, analytical relations for determining the temperature distribution in these environments were obtained. Based on this, a numerical experiment was performed, and it was geometrically represented depending on the spatial coordinates. This proves that the constructed linear and nonlinear mathematical models testify to their adequacy to the real physical process. They make it possible to analyze heat-active media regarding their thermal resistance. As a result, it becomes possible to increase it and protect it from overheating, which can cause the destruction of not only individual nodes and their elements but also the entire structure

MORPHOMETRIC CHARACTERISTICS OF NECK PARAMETERS IN THE PERINATAL PERIOD OF ONTOGENESIS

This study aims – to establish the normative morphometric parameters of the neckcircumference, anterior- posterior diameter, height, and width during the perinatal periodof ontogenesis, after which the parameters will be used to construct anatomical models. Material and Methods. The study was conducted on 63 human fetuses aged 4 to10 months and 7 newborns (including 5 isolated organ systems). To create anatomicalmodels, the well-known dimensions of the neck in all age groups were determined usinga centimeter tape and a caliper. The neck circumference was measured at the level of thehyoid bone. The anteroposterior neck diameter was defined as the distance between thebody of the hyoid bone and the VII spinous process of the cervical vertebra. Neck heightwas measured from the upper to the lower neck borders. Neck width was determined inthe frontal plane at the level of the hyoid bone between the lateral edges of the neck.Statistical analysis of the data was performed using the licensed program RStudio.Results. A morphometric analysis of the average values of the well-known neck parameters,namely its circumference, anterior- posterior diameter, height, and width, was conductedin the perinatal period of ontogenesis. The analysis revealed that these parameters exhibitnon-synchronous growth throughout the studied period of the development, with periodsof intensive and relative growth. A correlation analysis was conducted between allmorphometric parameters of the neck of fetuses and newborns. The results demonstratedthat the correlation coefficients between the values of all paired correlation coefficientswere positive and close to 1 (≥0.90), indicating a strong positive correlation between allstudied parameters. A statistical analysis of the data from the Conover- Iman test indicatesthat the median values of the morphometric parameters of the neck cannot be consideredreliable for the pairs «9 months – 10 months» and «10 months – Newborns». This isjustified by the fact that individual anatomical variability is inherent in each individual,and these periods of the development are critical for the neck area. The constructedstandard anatomical models of the morphometric parameters of the neck will serve asa norm for the subsequent determination of certain morphological deviations, which willthen be used to establish variants of the structure and developmental defects of the neck.Conclusions. 1. During the perinatal period of the development, the well-known parametersof the neck, namely its circumference, anterior- posterior diameter, height and width,increase asynchronously. 2. The average values of the morphometric parameters of the neckcircumference and anterior- posterior diameter during the perinatal period of ontogenesisindicate that one period of accelerated development is evident, occurring between the 7thand 9th month of intrauterine development for the neck circumference and between the 6thand 9th month of development for the anterior- posterior diameter of the neck. Two periods ofaccelerated development are observed for the parameters of neck height and width. For neckheight, these periods are from the 5th to the 7th month of development and from the 8th to the9th month of development. For neck width, the periods are from the 4th to the 5th month ofthe development and from the 7th to the 9th month of intrauterine development. In all otherperiods of development, the morphometric parameters of the neck exhibit a slight increase. 3.Based on the arithmetic mean data of the circumference, anterior- posterior diameter, height,and width of the neck, models for predicting the normative morphometric parameters of fetusesand newborns were constructed. The systematized data on the peculiarities of spatial andtemporal transformations of the morphometric parameters of the neck circumference, anteriorposterior diameter, neck height and width, followed by their construction of mathematicalmodels, will contribute to the individualization of the norm, improvement of early diagnosticmethods and development of new methods of surgical correction of congenital neck defects.

Machine Learning-Driven Biomarker Discovery for Skeletal Complications in Type 1 Gaucher Disease Patients.

Type 1 Gaucher disease (GD1) is a rare, autosomal recessive disorder caused by glucocerebrosidase deficiency. Skeletal manifestations represent one of the most debilitating and potentially irreversible complications of GD1. Although imaging studies are the gold standard, early diagnostic/prognostic tools, such as molecular biomarkers, are needed for the rapid management of skeletal complications. This study aimed to identify potential protein biomarkers capable of predicting the early diagnosis of bone skeletal complications in GD1 patients using artificial intelligence. An in silico study was performed using the novel Therapeutic Performance Mapping System methodology to construct mathematical models of GD1-associated complications at the protein level. Pathophysiological characterization was performed before modeling, and a data science strategy was applied to the predicted protein activity for each protein in the models to identify classifiers. Statistical criteria were used to prioritize the most promising candidates, and 18 candidates were identified. Among them, PDGFB, IL1R2, PTH and CCL3 (MIP-1α) were highlighted due to their ease of measurement in blood. This study proposes a validated novel tool to discover new protein biomarkers to support clinician decision-making in an area where medical needs have not yet been met. However, confirming the results using in vitro and/or in vivo studies is necessary.

Effects of different natural soundscapes on human psychophysiology in national forest park

Most of the current soundscape research content is limited to the discussion of the restoration effect of single-element soundscapes, but it is the combination of sounds that is common in outdoor activities, and there is no evidence that the restoration of natural soundscapes is better with multi-element combinations. In this study, the Zhangjiajie National Forest Park in China was used as the research object, and the physiological indices of the subjects were collected through electroencephalogram signals, and the POMS short-form psychological scale was used to understand the subjective psychological responses of the subjects to the soundscape. The results showed that (1) The psychophysiological restorative ability of the natural soundscape of the National Forest Park was confirmed, and the subjects’ psychological and physiological indices changed significantly and positively after listening to each section of the natural soundscape (p = 0.001). (2) The restorative effect of the multi-natural sound combination was ranked first in the overall ranking of the five natural soundscapes, and the multi-natural sound combination did indeed provide better restorative effects than the single-element sounds. (3) Gender does not usually have a significant effect on the restoration effect, and only Windy Sound among the four single-element nature sound landscapes and one multi-element combination of nature sound landscapes showed a significant gender difference, so in general, the effect of gender on the restoration effect of nature sound landscapes is not significant. In terms of research methodology, this study used cluster analysis to cluster the five types of natural soundscapes according to psychological and physiological recovery ability, and used ridge regression to construct mathematical models of the psychological and physiological recovery of each of the four natural soundscapes. The study of human physiological and psychological recovery from different types of natural soundscapes in China’s national forest parks will provide a basis for soundscape planning, design, and policy formulation in national forest parks.

ОБОСНОВАНИЕ ИСПОЛЬЗОВАНИЯ БИОМОДИФИЦИРОВАННОЙ СОИ В ПРОИЗВОДСТВЕ ПРОДУКЦИИ НИЗКОГЛИКЕМИЧЕСКОГО ДЕЙСТВИЯ

The objective of the study is to substantiate and develop the technology of soybean-mineral concentrate (SMC) and soybean-mineral paste (SMP) based on biomodified soybeans for the use of SMC and SMP in the formulations of low-glycemic products. Objectives: to study the dynamics of accumulation of chelated ions of mineral substances in the process of biomodification of soybeans in a vanadium minera¬lized aqueous medium, to determine the chemical composition of the obtained SMC. The objects of the study are soybean seeds of zoned varieties Oktyabr-70, Lydia, SMC. To determine the chemical composition of the developed SMC, standard methods for studying food products were used, corresponding to the normative and technical documentation valid in the Russian Federation. Determination of mineral substances was carried out by mass spectrometry in inductively coupled argon plasma on an ICP-MS ELAN DRC II device by Perkin Elmer (USA). Construction of mathematical models in the form of second-order regression equations and their analysis were carried out using the Appol program and the Pareto-optimal solution method (KPS program). The paper indicates the features of diabetes mellitus development based on modern research, substantiates the possibility of using chelated vanadium as an ingredient in the production of hypoglycemic food products. A number of literary sources indicating the oxidative and hypoglycemic ability of vanadium compounds are analyzed. The paper presents the results of a study of soybean seed biomodification in a vanadium mineralized aqueous medium and the accumulation of minerals by endoproteinases of germinating soybean seeds. As a result, a two-fold increase in chelated mineral elements is noted: Na1+, Ca2+, K1+, Mg2+, V4+. A technology has been developed for the production of soybean-mineral concentrate (SMC) and soybean-mineral paste (SMP) for the subsequent use of these ingredients in the formulation of low-glycemic products. The chemical composition of the SMC is represent¬ted by proteins 40 %, fats – 20, carbohydrates – 10, water – 6 %.

Assessment of Dynamic States of Railway Vehicles: Structural Mathematical Modeling

Introduction. The speed rise of railway transport and an increase in the loads on the axles of wheelsets necessitate the modernization of the existing fleet. Scientific studies in the field of rolling stock dynamics are aimed at taking into account the oscillatory processes that occur during the movement of railway vehicles in a traditional design. The attachment of supplementary elements was considered at the coupling level of two cars and the attachment of a third trolley in the center of gravity of the railway platform. The scientific literature has not paid enough attention to the construction of mathematical models that make it possible to assess the dynamic states of such constructive solutions. The objective of this study is to create a method for evaluating the dynamic conditions of a car. The situation is considered when an additional set of mass-inertial and elastic elements is introduced into its structure, and the general dynamic condition of the vehicle depends on the adjustment of their parameters.Materials and Methods. The basic research tool is the structural mathematical modeling, which is based on an approach where the source design scheme is a mechanical oscillatory system in the form of a solid body on elastic supports with supplementary typical elements introduced into its structure. The dynamic analogue of the calculation scheme used is the block diagram of the automatic control system, the use of which provides detailing the connections between typical elastic and mass-inertia elements.Results. A method for estimating the dynamic states of railway vehicles is proposed. It is based on the construction of mathematical models, taking into account the introduction of an additional structure of mass-inertia and elastic elements. The impact of additional parameters on the dynamic condition of the vehicle is investigated. Analytical relations have been obtained that provide reducing the dynamic loads on the major structural elastic elements when changing the corresponding parameters of a technical object. The transfer function of interpartial relations is given, which provides controlling the interaction between the coordinates of the vehicle movement under the action of two kinematic disturbances of the in-phase type.Discussion and Conclusion. The generated mathematical model provides for assessment, monitoring and control of the dynamic state of the vehicle under conditions of kinematic disturbances. The research results can be used to modernize existing vehicles and create new ones with improved dynamics.

Анализ компромисса между точностью и сложностью идентифицированных моделей динамических систем

One of the rapidly developing areas of the modern control theory is the identification of systems associated with the construction of mathematical models of systems in the form of a set of mathematical relationships that adequately reflect the basic properties of the system. Symbolic regression methods are becoming more and more popular in the problems of structural-parametric identification of systems based on available observations and experimental data, which allow building regression models in the form of codes of mathematical expressions in a symbolic form. Among the known numerical evolutionary methods of symbolic regression, the universally acknowledged “favorite” is the method of genetic programming”, the application of which allows us to describe the search for solving a problem as the construction of a regression model by enumerating various arbitrary superpositions of functions from some predetermined set. In this case, the important indicators determining the quality of identification of the mathematical model of the system are the accuracy and complexity of the identified model. Often, the system model obtained as a result of solving identification problem is not accurate enough or excessively complex. As a result, the solution to the identification problem is inextricably linked to ensuring sufficient accuracy and simplicity of the identified model. In this connection, it is natural to adhere to the principle of balanced identification, which indicates the search for a compromise between the accuracy of reproduction and the measure of complexity of the identified model. The purpose of this paper, which develops the concept of balanced identification, is to analyze the trade-off between the accuracy and complexity of models of dynamic systems identified by genetic programming. In this paper we introduce a functional "accuracy-complexity", which allows us to balance the trade-off between these key indicators of the identified models when solving the identification problem. The effectiveness of the proposed functional is demonstrated on the example of computer identification by genetic programming of a Lorentz dynamical system.

Revealing the evolution of spatiotemporal patterns of urban expansion using mathematical modelling and emerging hotspot analysis

The rapid expansion of cities in developing countries has led to many environmental problems, and the mechanism of urban expansion (UE), as a more complex human-land coupled system, has always been a difficult issue to research. This paper introduces a new approach by establishing an analytical framework for spatiotemporal pattern mining, exemplified by studying the urban growth of Changsha City from 1990 to 2019. Initially, an emerging hotspot analysis model (EHA) is employed to examine the spatiotemporal changes of urban growth on a macro scale. Mathematical models are subsequently utilized to quantify the correlations between urban expansion and selected infrastructural and topographical factors. Building on these findings, the paper constructs mathematical models to further quantify the spatiotemporal evolution of various urban sprawl patterns across different regions, aiming to elucidate and quantify the significant variations in UE over time and space. The study reveals that, as an emerging city, Changsha's hotspots of urban expansion prior to 2003 were primarily concentrated in the city centre, subsequently spreading to the periphery. The radial influence of metro stations on UE is notably less than that of railway stations—approximately 3 km versus 8 km—and the impact diminishes rapidly before gradually tapering off. Moreover, UE in Changsha predominantly occurs on slopes with gradients ranging from 1.1° to 7.5°, and significant development capacity is observed at elevations between 36.1 m and 78.3 m above sea level, with a tendency for urban sprawl to migrate to lower elevations. The paper also identifies three distinct patterns of urban expansion across different regions: an initial slow-growth phase, followed by a rapid escalation to a peak, and subsequently a swift decline to near stagnation. Additionally, it highlights a significant correlation between the proportion of built-up areas at the micro-regional scale and the stages of UE. This correlation was quantitatively analysed by constructing a logistic function, which demonstrated a robust fit that effectively captures spatiotemporal heterogeneity in the dynamics of UE. These insights enhance the selection of drivers in urban simulation models and deepen the understanding of the complex dynamics that influence urban development.

Mathematical Models of the Arabidopsis Circadian Oscillator

We review the construction and evolution of mathematical models of the Arabidopsis circadian clock, structuring the discussion into two distinct historical phases of modeling strategies: extension and reduction. The extension phase explores the bottom-up assembly of regulatory networks, introducing as many components and interactions as possible to capture the oscillatory nature of the clock. The reduction phase deals with functional decomposition, distilling complex models to their essential dynamical repertoire. Current challenges in this field, including the integration of spatial considerations and environmental influences like light and temperature, are also discussed. The review emphasizes the ongoing need for models that balance molecular detail with practical simplicity.

PARAMETRIC IDENTIFICATION OF A MATHEMATICAL MODEL FOR THE COPPER MATTE CONVERSION PROCESS

The paper provides data on the construction of mathematical models using parametric identification of objects, as well as the development of algorithms that allow calculating optimal charge plans in production, and also addresses issues related to modeling and control of electric melting. As a result of the work, the issues of partial automation through channels have been solved: regulation of electric power, charge loading control, melt level measurement, research on mechanization and automation of smelting products, as well as theoretical, experimental and pilot industrial studies on automation of electric furnaces of non-ferrous metallurgy. This control system of the electrothermal furnace operates in open mode, solves individual functional tasks of process control and management and provides solutions to the problems of optimal control of the technological process of electric melting. The paper also discusses issues related to the automatic control of the electric power of electrothermal furnaces. The furnace is considered as an object of channel control: electrode deepening-electrode currents.

Application and Quality of Model-Based Meta-Analysis in Pharmaceutical Research: A Systematic Cross-Sectional Analysis and Practical Considerations.

Model-based meta-analysis (MBMA) can be used in assisting drug development and optimizing treatment in clinical practice, potentially reducing costs and accelerating drug approval. We aimed to assess the application and quality of MBMA studies. We searched multiple databases to identify MBMA in pharmaceutical research. Eligible MBMA should incorporate pharmacological concepts to construct mathematical models and quantitatively examine and/or predict drug effects. Relevant information was summarized to provide an overview of the application of MBMA. We used AMSTAR-2 and PRISMA 2020 checklists to evaluate the methodological and reporting quality of included MBMA, respectively. A total of 143 MBMA studies were identified. MBMA was increasingly used over time for one or more areas: drug discovery and translational research (n = 8, 5.6%), drug development decision making (n = 42, 29.4%), optimization of clinical trial design (n = 46, 32.2%), medication in special populations (n = 15, 10.5%), and rationality and safety of drug use (n = 71, 49.7%). The included MBMA covered 17 disease areas, with the top three being nervous system diseases (n = 19, 13.2%), endocrine/nutritional/metabolic diseases (n = 17, 11.8%), and neoplasms (n = 16, 11.1%). Of these MBMA studies, 138 (96.5%) were rated as very low quality. The average rate of compliance with PRISMA was only 51.4%. Our findings suggested that MBMA was mainly used to evaluate the efficacy and safety of drugs, with a focus on chronic diseases. The methodological and reporting quality of MBMA should be further improved. Given AMSTAR-2 and PRISMA checklists were not specifically designed for MBMA, adapted assessment checklists for MBMA should be warranted.

Construction and investigation of differential hierarchical models for the Newtonian fluids

AbstractWe construct mathematical hierarchical models in Eulerian coordinates for an ideal and a Newtonian viscous fluid flow in the prismatic shell‐like domains. The peculiarities of well‐posedness of boundary conditions for angular domains are discussed.

Construction of the mathematical model of magnetic transmission for an autonomous wind power plant

The object of research is electromagnetic and mechanical processes in magnetic transmission for an autonomous wind power plant of small power. The use of magnetic transmission as part of an autonomous wind power plant makes it possible to improve the reliability and efficiency of such a system. In the current work, a study of magnetic transmission as part of an autonomous wind power plant was carried out to investigate the parameters and characteristics of magnetic transmission. This paper reports the construction of a numerical simulation mathematical model of a magnetic reducer operating as part of an autonomous wind power plant with a permanent magnet generator. The model takes into account discrete structure of internal and external rotors and modulator; changes in model parameters when input parameters change. It also takes into account losses, change of load angle and electromagnetic moment; the effect of changing the generator load. The built model of the magnetic reducer system differs in that the change in the generator load leads to a shift of the operating point on the mechanical characteristics of the rotor of the wind power plant (WPP). The model also works in the opposite direction: changes in wind parameters affect power, voltage, current, and electromagnetic moment. With the help of the model built, the parameters and characteristics of not only the magnetic reducer but also other components of the system were investigated. The efficiency at the output of the electric generator was determined, which is ≈75 % at a load of 2.0 kW. The magnetic transmission moment at a wind speed of 7.8 m/s for the high-speed rotor is 0.91 N∙m, and the low-speed rotor is 7.8 N∙m, which corresponds to a transmission ratio of 8.6. This expands opportunities for exploratory research