Construction Of Mathematical Model Research Articles

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.

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.

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

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.

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

Construction of mathematical and computer models for calculating contact characteristics of interaction between a rigid punch and an elastic half-space

The subject of this study is a punch-elastic half-space system under compressive force. The paper solves the problem of determining contact stresses and displacements. The content of results is the constructed models and the assessment of their adequacy. This work considers the problem of pressing a rigid plane double-connected punch on a homogeneous and isotropic elastic half-space. To obtain an analytical solution, a variant of the perturbation method based on the expansion of the potential of a simple layer distributed over a double-connected region by a small parameter was applied. The problem of pressing a flat punch in the form of a non-circular ring is reduced to a sequence of problems for a punch in the form of a circular ring. This allows us to use a known solution for a circular ring. Finite element models were built using ANSYS. A group of models was constructed to take into account possible damage in the event that the punch-elastic half-space system is exposed to difficult natural conditions or an aggressive environment during a certain time of modeling. A database was formed for the purpose of further transferring it to CLIPS. Sets of rules and knowledge were compiled. A generalizing algorithm was developed for the problems of constructing and analyzing mathematical and computer models of contact interaction between a rigid cylindrical punch with a flat double-connected base with an elastic half-space under the action of a compressive force. The problem of determining the geometric shape of the cross-section of an annular punch in the plan for the punch-elastic half-space system was solved for the case when the contact zone is not known in advance. The devised approach could be employed in engineering calculations for strength and durability

TEMPERATURE ERROR OF THE MEANS OF MEASURING THE GEOMETRIC CHARACTERISTICS OF BORES OF FIREARMS: MATHEMATICAL MODEL AND QUANTITATIVE EVALUATION

The work is devoted to the construction of mathematical models and quantitative assessment of the components of the temperature error of a laser triangulation sensor for measuring the geometric characteristics of bores of firearms.
 The existence of problematic issues in the field of evaluating the metrological characteristics of laser triangulation means for technical diagnostics of firearms barrel channels is highlighted. An analysis of publications
 on the evaluation of the error of a laser triangulation sensor caused by the influence of ambient temperature is carried out, and known approaches to their mathematical modeling are considered. The need to develop mathematical models of the components of the temperature error of a laser triangulation sensor and to quantify this error is substantiated.
 The parameters of the optical scheme of the laser triangulation sensor, whose deviation from their nominal (calculated) values will affect the conversion function, are determined. It is shown that the presence of a temperature error during the processing of measurement information will be perceived as an apparent change in the measured value with a constant input signal.
 On the basis of algebraic transformations of expressions reflecting the relationship between the output value of a laser triangulation sensor and deviations of the optical circuit parameters from their nominal values, mathematical models of the temperature error components are obtained and presented in the form of error component limits at the input of the measuring instrument. The expressions for determining the confidence limits of the total temperature error, taking into account the correlation between its components, are substantiated.
 A quantitative assessment of the temperature error for the characteristic combinations of weapon parameters (for four ranges of barrel calibers) in the range of ambient temperature variations inherent in the region where measurements are made is carried out. The results of the quantitative evaluation are presented in the form of graphs of the dependence of the limits of relative and absolute temperature errors on temperature and on the increase in the bore radius in the measurement range. The data obtained were analyzed, the peculiarities of the dependencies were determined, and conclusions were drawn about the compliance of the temperature error characteristics of the measuring instrument with the requirements for its accuracy.

Symmetric physically unclonable functions of the arbiter type

Objectives. The problem of constructing a new class of physically unclonable functions of the arbiter type (APUF) that combines the advantages of both classical and balanced APUF is solved. The relevance of such a study is associated with the active development of physical cryptography. The following goals are pursued in the work: research and analysis of classical APUF, construction of a new mathematical model of APUF and development of a new basic element of APUF.Methods. The methods of synthesis and analysis of digital devices are used, including those based on programmable logic integrated circuits, the basics of Boolean algebra and circuitry.Results. It has been established that classical APUF uses a standard basic element that performs three functions, namely, the function of generating two random variables Generate, the function of choosing a pair of paths Select and the function of switching paths Switch, which are specified by one bit of the challenge. It is shown that the joint use of these functions, on the one hand, makes it possible to achieve high characteristics of the APUF, and on the other hand, leads to the formation of an asymmetric behavior of the APUF. In order to analyze the main characteristics of APUF and their ideal behavior, a new mathematical model of APUF was considered, similar to the model of random coin toss. To implement APUF functioning according to the proposed model, a new basic element was developed. It is shown that the use of the proposed basic element allows to build symmetrical physically unclonable functions (C_APUF), which differ from the classical APUF in that the Generate, Select and Switch functions of the basic element are performed by their independent components and are specified by different bits of challenge.Conclusion. The proposed approach to the construction of symmetrical physically unclonable functions, based on the implementation of the Generate, Select and Switch functions by various components of the base element, has shown its efficiency and promise. The effect of improving the characteristics of similar C_APUF has been experimentally confirmed, and, first of all, a noticeable improvement in their probabilistic properties expressed in equal probability of responses. It seems promising to further develop the ideas of building C_APUF, experimental study of their characteristics, as well as analysis of resistance to various types of attacks, including using machine learning.

Construction of mathematical model for integration of engineering cost prediction and multiple algorithms

As a key link in engineering construction, reasonable evaluation of engineering cost can effectively control the budget and save costs. Therefore, the reliability of the engineering cost estimation will directly affect the economic status of the whole project. However, traditional prediction models are based on a single machine learning method, which is not generalized enough and has low accuracy. In view of this, a mathematical model for engineering cost prediction is constructed by combining a random forest algorithm, ridge regression algorithm, and extreme gradient boosting (XG Boost) algorithm to obtain a prediction model with higher generalization and accuracy, and to evaluate the cost of engineering projects reasonably and scientifically. The average relative error between predicted and actual values was only 0.872%. The root mean square error and average percentage error of the fusion model were relatively small. The superiority of the proposed mathematical model of prediction cost is verified, and the model possesses a certain application value in construction engineering, providing practical reference and guidance for engineering cost prediction.

Fuzzy algorithm-based active control method for vibration of a mechanical gear transmission system

The detached raft automatic frequency isolation system is a complicated system with high exceptionally nonlinear, high electromagnetic, and multi-source vibration modes. However, it generates a statistical method and it is hard to operate the organization. The fuzzy control algorithm, as an astute control method, can give a keen path to the active management of a complicated system of floating rafts. This study uses a system identification approach to construct mathematical models for a floating raft active vibration isolation system with discrete transfer work. The fuzzy model is used in tests and simulations controller is built using two contributions of acceleration and its variation, as well as a single result of control voltage. The control isolation system is a complicated system with many moving parts. A lot of moving parts profoundly nonlinear, high electromagnetic and multi-source vibration modes, generating a statistical method and it is hard to operate the organization. The fuzzy control algorithm, as a smart control method, can give a keen path to the active management of a sophisticated floating raft system. This research uses an identification strategy to construct a floating raft active vibration isolation technology discrete transfer work mathematical models. The fuzzy controller is then put together using two contributions: acceleration and variation, as well as a single outcome of control voltage for simulations and experiments research.

Defining compromise area in the processes of multimodal delivery organization within the agile approach

The level of competition in the transport market requires delivery organizers to implement better approaches based on modern management methodologies, in particular, agile, which makes it possible to provide a modern level of service to cargo owners. The object of this research is the processes of organizing multimodal delivery. The subject of the study is the area of compromise in the processes of organizing multimodal delivery based on the agile approach. The term «compromise area» is introduced, which reflects the numerical limits of product parameters in the general case. For the transportation domain under consideration, the «trade-off area» reflects the limits of the characteristics of multimodal delivery, which is the «product» for the multimodal operator. A set of alternative options for multimodal delivery forms the basis for establishing the dependence of the cost of delivery on time and its reliability (possible time deviation). The area in the «time-reliability-cost» space, which is formed on the basis of this dependence, on the one hand, and the requirements of the cargo owner, taking into account their possible adjustment, on the other hand, is the area of compromise. This area is proposed for use in agile approaches to the organization of multimodal delivery. Balancing the interests of the cargo owner and the multimodal operator allows changing the limits of the compromise area within the framework of the proposed scheme of agile cycles in the process of planning and organizing delivery. On the example of delivering a container with cargo from China to Kyiv, regression linear models were built. These models formalize the dependence of delivery cost on reliability and/or time. Using the example of varying the requirements of the cargo owner regarding the limitations of some delivery characteristics, the formation of the compromise area and its adjustment was carried out, which demonstrated the practical aspects of the formation of the compromise area for multimodal delivery. The results are the basis for the implementation of the agile approach in the field of multimodal transportation. The further development of these results consists in the construction of mathematical models that could form the basis for finding solutions in the area of compromise

A multiparameter mathematical model for the problem of nonlinear filtration of fluids in two-layer media

In the realm of fluid dynamics and porous media, the nonlinear filtration of fluids in two-layer media presents a complex and intriguing challenge that demands a comprehensive mathematical framework for accurate representation and analysis. This paper introduces a multiparameter mathematical model designed to elucidate the intricacies of fluid filtration in heterogeneous environments, specifically focusing on two-layer media. The authors research the construction of a multiparameter mathematical model and numerical solution of nonlinear problems of the theory of filtration of unstructured and structured fluids in hydrodynamically connected multilayer formations with different characteristics. The developed models and solution algorithms were tested on hypothetical data.