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A simple model was developed to describe the dependence of net CO₂ exchange in a sphagnum peat bog as a function of incoming solar radiation, air temperature, and soil moisture. It was parameterized using the field measurement data from two neighboring sites in an undisturbed peat bog (the pine mire with shrub and sphagnum and the shrub-sphagnum mire with rare pine) in Moscow Region. Measurements were conducted during the second part of the growing season, when the groundwater level was below 30 cm. It was shown that is a key parameter influencing the photosynthesis and respiration rates of a sphagnum moss and peat soil. The developed model allows to explain from 71 % to 74 % of the variation of CO₂ exchange in the peat bog.

Numerical simulation of moving sportsman external flow is presented. The unique method is developed for obtaining integral aerodynamic characteristics, which were the function of the flow regime (i.e. angle of attack, flow speed) and body position. Individual anthropometric characteristics and moving boundaries of sportsman (or sports equipment) during the race are taken into consideration.

Numerical simulation is realized using FlowVision CFD. The software is based on the finite volume method, high-performance numerical methods and reliable mathematical models of physical processes. A Cartesian computational grid is used by FlowVision, the grid generation is a completely automated process. Local grid adaptation is used for solving high-pressure gradient and object complex shape. Flow simulation process performed by solutions systems of equations describing movement of fluid and/or gas in the computational domain, including: mass, moment and energy conservation equations; state equations; turbulence model equations. FlowVision permits flow simulation near moving bodies by means of computational domain transformation according to the athlete shape changes in the motion. Ski jumper aerodynamic characteristics are studied during all phases: take-off performance in motion, in-run and flight. Projected investigation defined simulation method, which includes: inverted statement of sportsman external flow development (velocity of the motion is equal to air flow velocity, object is immobile); changes boundary of the body technology defining; multiple calculations with the national team member data projecting. The research results are identification of the main factors affected to jumping performance: aerodynamic forces, rotating moments etc. Developed method was tested with active sportsmen. Ski jumpers used this method during preparations for Sochi Olympic Games 2014. A comparison of the predicted characteristics and experimental data shows a good agreement. Method versatility is underlined by performing swimmer and skater flow simulation. Designed technology is applicable for sorts of natural and technical objects.

We comsider a model of the dynamics a political system of several parties, accompanied and controlled by the growth of social tension. A system of nonlinear ordinary differential equations is proposed with respect to fractions and an additional scalar variable characterizing the magnitude of tension in society the change of each party is proportional to the current value multiplied by a coefficient that consists of an influx of novice, a flow from competing parties, and a loss due to the growth of social tension. The change in tension is made up of party contributions and own relaxation. The number of parties is fixed, there are no mechanisms in the model for combining existing or the birth of new parties.

To study of possible scenarios of the dynamic processes of the model we derive an approach based on the selection of conditions under which this problem belongs to the class of cosymmetric systems. For the case of two parties, it is shown that in the system under consideration may have two families of equilibria, as well as a family of limit cycles. The existence of cosymmetry for a system of differential equations is ensured by the presence of additional constraints on the parameters, and in this case, the emergence of continuous families of stationary and nonstationary solutions is possible. To analyze the scenarios of cosymmetry breaking, an approach based on the selective function is applied. In the case of one political party, there is no multistability, one stable solution corresponds to each set of parameters. For the case of two parties, it is shown that in the system under consideration may have two families of equilibria, as well as a family of limit cycles. The results of numerical experiments demonstrating the destruction of the families and the implementation of various scenarios leading to the stabilization of the political system with the coexistence of both parties or to the disappearance of one of the parties, when part of the population ceases to support one of the parties and becomes indifferent are presented.

This model can be used to predict the inter-party struggle during the election campaign. In this case necessary to take into account the dependence of the coefficients of the system on time.

Simulation of combat and military operations is the most important scientific and practical task aimed at providing the command of quantitative bases for decision-making. The first models of combat were developed during the First World War (M. Osipov, F. Lanchester), and now they are widely used in connection with the massive introduction of automation tools. At the same time, the models of combat and war do not fully take into account the moral potentials of the parties to the conflict, which motivates and motivates the further development of models of battle and war. A probabilistic model of combat is considered, in which the parameter of combat superiority is determined through the parameter of moral (the ratio of the percentages of the losses sustained by the parties) and the parameter of technological superiority. To assess the latter, the following is taken into account: command experience (ability to organize coordinated actions), reconnaissance, fire and maneuverability capabilities of the parties and operational (combat) support capabilities. A game-based offensive-defense model has been developed, taking into account the actions of the first and second echelons (reserves) of the parties. The target function of the attackers in the model is the product of the probability of a breakthrough by the first echelon of one of the defense points by the probability of the second echelon of the counterattack repelling the reserve of the defenders. Solved the private task of managing the breakthrough of defense points and found the optimal distribution of combat units between the trains. The share of troops allocated by the parties to the second echelon (reserve) increases with an increase in the value of the aggregate combat superiority parameter of those advancing and decreases with an increase in the value of the combat superiority parameter when repelling a counterattack. When planning a battle (battles, operations) and the distribution of its troops between echelons, it is important to know not the exact number of enemy troops, but their capabilities and capabilities, as well as the degree of preparedness of the defense, which does not contradict the experience of warfare. Depending on the conditions of the situation, the goal of an offensive may be to defeat the enemy, quickly capture an important area in the depth of the enemy’s defense, minimize their losses, etc. For scaling the offensive-defense model for targets, the dependencies of the losses and the onset rate on the initial ratio of the combat potentials of the parties were found. The influence of social costs on the course and outcome of wars is taken into account. A theoretical explanation is given of a loss in a military company with a technologically weak adversary and with a goal of war that is unclear to society. To account for the influence of psychological operations and information wars on the moral potential of individuals, a model of social and information influence was used.

Radiopharmaceuticals with iodine radioisotopes are now widely used in imaging and non-imaging methods of nuclear medicine. When evaluating the results of radionuclide studies of the structural and functional state of organs and tissues, parallel modeling of the kinetics of radiopharmaceuticals in the body plays an important role. The complexity of such modeling lies in two opposite aspects. On the one hand, excessive simplification of the anatomical and physiological characteristics of the organism when splitting it to the compartments that may result in the loss or distortion of important clinical diagnosis information, on the other – excessive, taking into account all possible interdependencies of the functioning of the organs and systems that, on the contrary, will lead to excess amount of absolutely useless for clinical interpretation of the data or the mathematical model becomes even more intractable. Our work develops a unified approach to the construction of mathematical models of the kinetics of radiopharmaceuticals with iodine isotopes in the human body during diagnostic and therapeutic procedures of nuclear medicine. Based on this approach, three- and four-compartment pharmacokinetic models were developed and corresponding calculation programs were created in the C⁺⁺ programming language for processing and evaluating the results of radionuclide diagnostics and therapy. Various methods for identifying model parameters based on quantitative data from radionuclide studies of the functional state of vital organs are proposed. The results of pharmacokinetic modeling for radionuclide diagnostics of the liver, kidney, and thyroid using iodine-containing radiopharmaceuticals are presented and analyzed. Using clinical and diagnostic data, individual pharmacokinetic parameters of transport of different radiopharmaceuticals in the body (transport constants, half-life periods, maximum activity in the organ and the time of its achievement) were determined. It is shown that the pharmacokinetic characteristics for each patient are strictly individual and cannot be described by averaged kinetic parameters. Within the framework of three pharmacokinetic models, “Activity–time” relationships were obtained and analyzed for different organs and tissues, including for tissues in which the activity of a radiopharmaceutical is impossible or difficult to measure by clinical methods. Also discussed are the features and the results of simulation and dosimetric planning of radioiodine therapy of the thyroid gland. It is shown that the values of absorbed radiation doses are very sensitive to the kinetic parameters of the compartment model. Therefore, special attention should be paid to obtaining accurate quantitative data from ultrasound and thyroid radiometry and identifying simulation parameters based on them. The work is based on the principles and methods of pharmacokinetics. For the numerical solution of systems of differential equations of the pharmacokinetic models we used Runge–Kutta methods and Rosenbrock method. The Hooke–Jeeves method was used to find the minimum of a function of several variables when identifying modeling parameters.

Numerical modeling of shear-induced platelet activation in haemodialysis arteriovenous fistulas was carried out in this work. The goal was to investigate the mechanisms of threshold shear-induced platelet activation in fistulas. For shear-induced platelet activation to take place, shear stress accumulated by platelets along corresponding trajectories in blood flow had to exceed a definite threshold value. The threshold value of cumulative shear stress was supposed to depend on the multimer size of von Willebrand factor macromolecules acting as hydrodynamic sensors for platelets. The effect of arteriovenous fistulas parameters, such as the anastomotic angle, blood flow rate, and the multimer size of von Willebrand factor macromolecules, on platelet activation risk was studied. Parametric diagrams have been constructed that make it possible to distinguish the areas of parameters corresponding to the presence or absence of shear-induced platelet activation. Scaling relations that approximate critical curves on parametric diagrams were obtained. Analysis showed that threshold fistula flow rate is higher for obtuse anastomotic angle than for sharp ones. This means that a fistula with obtuse angle can be used in wider flow rate range without risk of platelet activation. In addition, a study of different anastomosis configurations of arteriovenous fistulas showed that the configuration “end of vein to end of artery” is among the safest. For all the investigated anastomosis configurations, the critical curves on the parametric diagrams were monotonically decreasing functions of von Willebrand factor multimer size. It was shown that fistula flow rate should have a significant impact on the probability of thrombus formation initiation, while the direction of flow through the distal artery did not affect platelet activation. The obtained results allowed to determine the safest fistula configurations with respect to thrombus formation triggering. The authors believe that the results of the work may be of interest to doctors performing surgical operations for creation of arteriovenous fistulas for haemodialysis. In the final section of the work, possible clinical applications of the obtained results by means of mathematical modeling are discussed.

In the presented work, a hybrid optimal simulation model of an assembly shop in the AnyLogic environment has been developed, which allows you to select the parameters of production systems. To build a hybrid model of the investigative approach, discrete-event modeling and aggressive modeling are combined into a single model with an integrating interaction. Within the framework of this work, a mechanism for the development of a production system consisting of several participants-agents is described. An obvious agent corresponds to a class in which a set of agent parameters is specified. In the simulation model, three main groups of operations performed sequentially were taken into account, and the logic for working with rejected sets was determined. The product assembly process is a process that occurs in a multi-phase open-loop system of redundant service with waiting. There are also signs of a closed system — scrap flows for reprocessing. When creating a distribution system in the segment, it is mandatory to use control over the execution of requests in a FIFO queue. For the functional assessment of the production system, the simulation model includes several functional functions that describe the number of finished products, the average time of preparation of products, the number and percentage of rejects, the simulation result for the study, as well as functional variables in which the calculated utilization factors will be used. A series of modeling experiments were carried out in order to study the behavior of the agents of the system in terms of the overall performance indicators of the production system. During the experiment, it was found that the indicator of the average preparation time of the product is greatly influenced by such parameters as: the average speed of the set of products, the average time to complete operations. At a given limitation interval, we managed to select a set of parameters that managed to achieve the largest possible operation of the assembly line. This experiment implements the basic principle of agent-based modeling — decentralized agents make a personal contribution and affect the operation of the entire simulated system as a whole. As a result of the experiments, thanks to the selection of a large set of parameters, it was possible to achieve high performance indicators of the assembly shop, namely: to increase the productivity indicator by 60%; reduce the average assembly time of products by 38%.

Large Language Models (LLMs) are transforming software engineering by bridging the gap between natural language and programming languages. These models have revolutionized communication within development teams and the Software Development Life Cycle (SDLC) by enabling developers to interact with code using natural language, thereby improving workflow efficiency. This survey examines the impact of LLMs across various stages of the SDLC, including requirement gathering, system design, coding, debugging, testing, and documentation. LLMs have proven to be particularly useful in automating repetitive tasks such as code generation, refactoring, and bug detection, thus reducing manual effort and accelerating the development process. The integration of LLMs into the development process offers several advantages, including the automation of error correction, enhanced collaboration, and the ability to generate high-quality, functional code based on natural language input. Additionally, LLMs assist developers in understanding and implementing complex software requirements and design patterns. This paper also discusses the evolution of LLMs from simple code completion tools to sophisticated models capable of performing high-level software engineering tasks. However, despite their benefits, there are challenges associated with LLM adoption, such as issues related to model accuracy, interpretability, and potential biases. These limitations must be addressed to ensure the reliable deployment of LLMs in production environments. The paper concludes by identifying key areas for future research, including improving the adaptability of LLMs to specific software domains, enhancing their contextual understanding, and refining their capabilities to generate semantically accurate and efficient code. This survey provides valuable insights into the evolving role of LLMs in software engineering, offering a foundation for further exploration and practical implementation.

Hemostatic system serves the organism for urgent repairs of damaged blood vessel walls. Its main components – platelets, the smallest blood cells, – are constantly contained in blood and quickly adhere to the site of injury. Platelet migration across blood flow and their hit with the wall are governed by blood flow conditions and, in particular, by the physical presence of other blood cells – erythrocytes. In this review we consider the main regularities of this influence, available mathematical models of platelet migration across blood flow and adhesion based on "convection-diffusion" PDEs, and discuss recent advances in this field. Understanding of the mechanisms of these processes is necessary for building of adequate mathematical models of hemostatic system functioning in blood flow in normal and pathological conditions.

A comparative analysis of the applicability of several variants of the production function models for the analysis of modern Russian economy is presented in a paper. Through regression analysis, the effect of such factors as the oil prices on the world market, the innovation, the hypothesis of constant returns to factors of production is estimated. Calculations were made both for the economy as a whole and for separate industries. It is shown that the models of the economy of Russia as a whole and some of its industries in relation to real data have significant increasing returns to labor. Limits of applicability for the models are discussed.