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Transport of respiratory gases by respiratory and circulatory systems is one of the most important processes associated with living conditions of the human body. Significant and/or long-term deviations of oxygen and carbon dioxide concentrations from the normal values in blood can be a reason of significant pathological changes with irreversible consequences: lack of oxygen (hypoxia and ischemic events), the change in the acidbase balance of blood (acidosis or alkalosis), and others. In the context of a changing external environment and internal conditions of the body the action of its regulatory systems aimed at maintaining homeostasis. One of the major mechanisms for maintaining concentrations (partial pressures) of oxygen and carbon dioxide in the blood at a normal level is the regulation of minute ventilation, respiratory rate and depth of respiration, which is caused by the activity of the central and peripheral regulators.

In this paper we propose a mathematical model of the regulation of pulmonary ventilation parameter. The model is used to calculate the minute ventilation adaptation during hypoxia and hypercapnia. The model is developed using a single-component model of the lungs, and biochemical equilibrium conditions of oxygen and carbon dioxide in the blood and the alveolar lung volume. A comparison with laboratory data is performed during hypoxia and hypercapnia. Analysis of the results shows that the model reproduces the dynamics of minute ventilation during hypercapnia with sufficient accuracy. Another result is that more accurate model of regulation of minute ventilation during hypoxia should be developed. The factors preventing from satisfactory accuracy are analysed in the final section.

Respiratory function is one of the main limiting factors of the organism during intense physical activities. Thus, it is important characteristic of high performance sport and extreme physical activity conditions. Therefore, the results of this study have significant application value in the field of mathematical modeling in sport. The considered conditions of hypoxia and hypercapnia are partly reproduce training at high altitude and at hypoxia conditions. The purpose of these conditions is to increase the level of hemoglobin in the blood of highly qualified athletes. These conditions are the only admitted by sport committees.

A critical analysis of existing approaches, methods and models to solve the problem of financial resources operational management has been carried out in the article. A number of significant shortcomings of the presented models were identified, limiting the scope of their effective usage. There are a static nature of the models, probabilistic nature of financial flows are not taken into account, daily amounts of receivables and payables that significantly affect the solvency and liquidity of the company are not identified. This necessitates the development of a new model that reflects the essential properties of the planning financial flows system — stochasticity, dynamism, non-stationarity.

The model for the financial flows distribution has been developed. It bases on the principles of optimal dynamic control and provides financial resources planning ensuring an adequate level of liquidity and solvency of a company and concern initial data uncertainty. The algorithm for designing the objective cash balance, based on principles of a companies’ financial stability ensuring under changing financial constraints, is proposed.

Characteristic of the proposed model is the presentation of the cash distribution process in the form of a discrete dynamic process, for which a plan for financial resources allocation is determined, ensuring the extremum of an optimality criterion. Designing of such plan is based on the coordination of payments (cash expenses) with the cash receipts. This approach allows to synthesize different plans that differ in combinations of financial outflows, and then to select the best one according to a given criterion. The minimum total costs associated with the payment of fines for non-timely financing of expenses were taken as the optimality criterion. Restrictions in the model are the requirement to ensure the minimum allowable cash balances for the subperiods of the planning period, as well as the obligation to make payments during the planning period, taking into account the maturity of these payments. The suggested model with a high degree of efficiency allows to solve the problem of financial resources distribution under uncertainty over time and receipts, coordination of funds inflows and outflows. The practical significance of the research is in developed model application, allowing to improve the financial planning quality, to increase the management efficiency and operational efficiency of a company.

The article is devoted to the construction and investigation of an averaged mathematical model of an aluminum-cobalt-molybdenum hydrocracking catalyst oxidative regeneration. The oxidative regeneration is an effective means of restoring the activity of the catalyst when its granules are coating with coke scurf.

The mathematical model of this process is a nonlinear system of ordinary differential equations, which includes kinetic equations for reagents’ concentrations and equations for changes in the temperature of the catalyst granule and the reaction mixture as a result of isothermal reactions and heat transfer between the gas and the catalyst layer. Due to the heterogeneity of the oxidative regeneration process, some of the equations differ from the standard kinetic ones and are based on empirical data. The article discusses the scheme of chemical interaction in the regeneration process, which the material balance equations are compiled on the basis of. It reflects the direct interaction of coke and oxygen, taking into account the degree of coverage of the coke granule with carbon-hydrogen and carbon-oxygen complexes, the release of carbon monoxide and carbon dioxide during combustion, as well as the release of oxygen and hydrogen inside the catalyst granule. The change of the radius and, consequently, the surface area of coke pellets is taken into account. The adequacy of the developed averaged model is confirmed by an analysis of the dynamics of the concentrations of substances and temperature.

The article presents a numerical experiment for a mathematical model of oxidative regeneration of an aluminum-cobalt-molybdenum hydrocracking catalyst. The experiment was carried out using the Kutta–Merson method. This method belongs to the methods of the Runge–Kutta family, but is designed to solve stiff systems of ordinary differential equations. The results of a computational experiment are visualized.

The paper presents the dynamics of the concentrations of substances involved in the oxidative regeneration process. A conclusion on the adequacy of the constructed mathematical model is drawn on the basis of the correspondence of the obtained results to physicochemical laws. The heating of the catalyst granule and the release of carbon monoxide with a change in the radius of the granule for various degrees of initial coking are analyzed. There are a description of the results.

In conclusion, the main results and examples of problems which can be solved using the developed mathematical model are noted.

Nowadays the situation of supply-demand imbalances in the professionals’ labor markets causes human capital losses as far as hampers scientific and innovation development. In Russia, supply-demand imbalances in the engineering labor market are associated with deindustrialization processes and manufacturing decline, resulted in a negative public perception of the engineering profession and high rates of graduates not working within the specialty or changing their occupation.

For analysis of the supply-demand imbalances in the engineering labor market, we elaborated a macroeconomic model. The model consists of 14 blocks, including blocks for demand and supply for engineers and technicians, along with the blocks for macroeconomic indicators as industry and service sector output, capital investment. Using this model, we forecasted the perspective supply-demand imbalances in the engineering labor market in a short-term period and examined the parameters of getting supply-demand balance in the medium-term perspective.

The results obtained show that situation of more balanced supply and demand for engineering labor is possible if there is simultaneous increase in the share of investments in fixed assets of manufacturing and relative wages in industry, besides getting to balance is facilitated by a decrease of the share of graduates not working by specialty. It is worth noting that a decrease in the share of graduates not working by specialty may be affected whether by the growth of relative wages in industry and number of vacancies or by the implementation of measures aimed at improving the working conditions of the engineering workforce and increasing the attractiveness of the profession. To summarize, in the case of the simplest scenario, not considering additional measures of working conditions improvement and increasing the attractiveness of the profession, the conditions of supply-demand balance achievement implies slightly lower growth rates of investment in industry than required in scenarios that involve increasing the share of engineers and technicians working in their specialty after graduation. The latter case, where a gradual decrease in the proportion of those who do not work in engineering specialty is expected, requires, probably, higher investment costs for attracting specialists and creating new jobs, as well as additional measures to strengthen the attractiveness of the engineering profession.

Certifying a transport airplane for the flights under icing conditions in Russia was carried out within the framework of the requirements of Annex С to the AP-25 Aviation Rules. In force since 2023 to replace AP-25 the new Russian certification document “Airworthiness Standards” (NLG-25) proposes the introduction of Appendix O. A feature of Appendix O is the need to carry out calculations in conditions of high liquid water content and with large water drops (500 microns or more). With such parameters of the dispersed flow, such physical processes as the disruption and splashing of a water film when large drops enter it become decisive. The flow of a dispersed medium under such conditions is essentially polydisperse. This paper describes the modifications of the IceVision technique implemented on the basis of the FlowVision software package for the ice accretion calculations within the framework of Appendix O.

The main difference between the IceVision method and the known approaches is the use of the Volume of fluid (VOF) technology to the shape of ice changes tracking. The external flow around the aircraft is calculated simultaneously with the growth of ice and its heating. Ice is explicitly incorporated in the computational domain; the heat transfer equation is solved in it. Unlike the Lagrangian approaches, the Euler computational grid is not completely rebuilt in the IceVision technique: only the cells containing the contact surface are changed.

The IceVision 2.0 version accounts for stripping the film, as well as bouncing and splashing of falling drops at the surfaces of the aircraft and ice. The diameter of secondary droplets is calculated using known empirical correlations. The speed of the water film flow over the surface is determined taking into account the action of aerodynamic forces, gravity, hydrostatic pressure gradient and surface tension force. The result of taking into account surface tension is the effect of contraction of the film, which leads to the formation of water flows in the form of rivulets and ice deposits in the form of comb-like growths. An energy balance relation is fulfilled on the ice surface that takes into account the energy of falling drops, heat exchange between ice and air, the heat of crystallization, evaporation, sublimation and condensation. The paper presents the results of solving benchmark and model problems, demonstrating the effectiveness of the IceVision technique and the reliability of the obtained results.

Modeling banking systems using a network approach has received growing attention in recent years. One of the notable models is that developed by Iori et al, who proposed a banking system model for analyzing systemic risks in interbank networks. The model is built based on the simple dynamics of several bank balance sheet variables such as deposit, equity, loan, liquid asset, and interbank lending (or borrowing) in the form of difference equations. Each bank faces random shocks in deposits and loans. The balance sheet is updated at the beginning or end of each period. In the model, banks are grouped into either potential lenders or borrowers. The potential borrowers are those that have lack of liquidity and the potential lenders are those which have excess liquids after dividend payment and channeling new investment. The borrowers and the lenders are connected through the interbank market. Those borrowers have some percentage of linkage to random potential lenders for borrowing funds to maintain their safety net of the liquidity. If the demand for borrowing funds can meet the supply of excess liquids, then the borrower bank survives. If not, they are deemed to be in default and will be removed from the banking system. However, in their paper, most part of the interbank borrowing-lending mechanism is described qualitatively rather than by detailed mathematical or computational analysis. Therefore, in this paper, we enhance the mathematical parts of borrowing-lending in the interbank market and present an algorithm for simulating the model. We also perform some simulations to analyze the effects of the model’s parameters on banking stability using the number of surviving banks as the measure. We apply this technique to analyze the effects of a macroprudential policy called loan-to-deposit ratio based reserve requirement for banking stability.

The article dwells upon investigating the issue of the most adequate tools developing and justifying to forecast the interregional migration flows value and structure. Migration processes have a significant impact on the size and demographic structure of the population of territories, the state and balance of regional and local labor markets.

To analyze the migration processes and to assess their impact an economic-mathematical tool is required which would be instrumental in modelling the migration processes and flows for different areas with the desired precision. The current methods and approaches to the migration processes modelling, including the analysis of their advantages and disadvantages, were considered. It is noted that to implement many of these methods mass aggregated statistical data is required which is not always available and doesn’t characterize the migrants behavior at the local level where the decision to move to a new dwelling place is made. This has a significant impact on the ability to apply appropriate migration processes modelling techniques and on the projection accuracy of the migration flows magnitude and structure.

The cellular automata model for interregional migration flows modelling, implementing the integration of the households migration behavior model under the conditions of the Bounded Rationality into the general model of the area migration flow was developed and tested based on the Primorye Territory data. To implement the households migration behavior model under the conditions of the Bounded Rationality the integral attractiveness index of the regions with economic, social and ecological components was proposed in the work.

To evaluate the prognostic capacity of the developed model, it was compared with the available cellular automata models used to predict interregional migration flows. The out of sample prediction method which showed statistically significant superiority of the proposed model was applied for this purpose. The model allows obtaining the forecasts and quantitative characteristics of the areas migration flows based on the households real migration behaviour at the local level taking into consideration their living conditions and behavioural motives.

The nonlinear restrictive (with restrictions of the inequalities type) dynamic mathematical model of the committed competition vacant market of many goods in conditions of the goods deliveries time-lag and of the linear dependency of the demand vector from the prices vector is offered. The problem of finding of prices and deliveries of goods into the market which are optimal (from seller’s profit standpoint) is formulated. It is shown the seller’s total profit maximum is expressing by the continuous piecewise smooth function of vector of volumes of deliveries with breakup of the derivative on borders of zones of the goods deficit, of the overstocking and of the dynamic balance of demand and offer of each of goods. With use of the predicate functions technique the computing algorithm of optimization of the goods deliveries into the market is built.

The article considers the problem of forecasting the number of employed and unemployed persons in a multisectoral labor market using a balance mathematical model of labor force intersectoral dynamics.

The balance mathematical model makes it possible to calculate the values of intersectoral dynamics indicators using only statistical data on sectoral employment and unemployment provided by the Federal State Statistics Service. Intersectoral dynamics indicators of labor force calculated for several years in a row are used to build trends for each of these indicators. The found trends are used to calculation of forecasted intersectoral dynamics indicators of labor force. The sectoral employment and unemployment of researched multisectoral labor market is forecasted based on values these forecasted indicators.

The proposed approach was applied to forecast the employed persons in the economic sectors of the Russian Federation in 2011–2016. The following types of trends were used to describe changes of intersectoral dynamics indicators values: linear, non-linear, constant. The procedure for selecting trends is clearly demonstrated by the example of indicators that determine the labor force movements from the “Transport and communications” sector to the “Healthcare and social services” sector, as well as from the “Public administration and military security, social security” sector to the “Education” sector.

Several approaches to forecasting was compared: a) naive forecast, within which the labor market indicators was forecasted only using a constant trend; b) forecasting based on a balance model using only a constant trend for all intersectoral dynamics indicators of labor force; c) forecasting directly by the number employed persons in economic sectors using the types of trends considered in the article; d) forecasting based on a balance model with the trends choice for each intersectoral dynamics indicators of labor force.

The article shows that the use of a balance model provides a better forecast quality compared to forecasting directly by the number of employed persons. The use of trends in intersectoral dynamics indicators improves the quality of the forecast. The article also provides analysis examples of the multisectoral labor market in the Russian Federation. Using the balance model, the following information was obtained: the labor force flows distribution outgoing from concrete sectors by sectors of the economy; the sectoral structure of the labor force flows ingoing in concrete sectors. This information is not directly contained in the data provided by the Federal State Statistics Service.

The data of episodic field measurements of carbon dioxide balance components (soil respiration — R_soil, ecosystem respiration — R_eco, net ecosystem exchange — NEE) of hayfields under use and abandoned one are interpreted by modelling. The field measurements were carried within five field campaigns in 2018 and 2019 on the drained part of the Dubna Peatland in Taldom District, Moscow Oblast, Russia. The territory is within humid continental climate zone. Peatland drainage was done out for milled peat extraction. After extraction was stopped, the residual peat deposit (1–1.5 m) was ploughed and grassed (Poa pratensis L.) for hay production. The current ground water level (GWL) varies from 0.3–0.5 m below the surface during wet and up to 1.0 m during dry periods. Daily dynamics of CO2 fluxes was measured using dynamic chamber method in 2018 (August) and 2019 (May, June, August) for abandoned ditch spacing only with sanitary mowing once in 5 years and the ditch spacing with annual mowing. NEE and Reco were measured on the sites with original vegetation, and Rsoil — after vegetation removal. To model a seasonal dynamics of NEE, the dependence of its components (Reco, Rsoil, and Gross ecosystematmosphere exchange of carbon dioxide — GEE) from soil and air temperature, GWL, photosynthetically active radiation, underground and aboveground plant biomass were used. The parametrization of the models has been carried out considering the stability of coefficients estimated by the bootstrap method. R2 (α = 0.05) between simulated and measured Reco was 0.44 (p < 0.0003) on abandoned and 0.59 (p < 0.04) on under use hayfield, and GEE was 0.57 (p < 0.0002) and 0.77 (p < 0.00001), respectively. Numerical experiments were carried out to assess the influence of different haymaking regime on NEE. It was found that NEE for the season (May 15 – September 30) did not differ much between the hayfield without mowing (4.5±1.0 tC·ha–1·season–1) and the abandoned one (6.2±1.4). Single mowing during the season leads to increase of NEE up to 6.5±0.9, and double mowing — up to 7.5±1.4 tC·ha–1·season–1. This means increase of carbon losses and CO2 emission into the atmosphere. Carbon loss on hayfield for both single and double mowing scenario was comparable with abandoned hayfield. The value of removed phytomass for single and double mowing was 0.8±0.1 tC·ha^–1·season^–1 and 1.4±0.1 (45% carbon content in dry phytomass) or 3.0 and 4.4 t·ha^–1·season^–1 of hay (17% moisture content). In comparison with the fallow, the removal of biomass of 0.8±0.1 at single and 1.4±0.1 tC·ha^–1·season^–1 double mowing is accompanied by an increase in carbon loss due to CO2 emissions, i.e., the growth of NEE by 0.3±0.1 and 1.3±0.6 tC·ha–1·season–1, respectively. This corresponds to the growth of NEE for each ton of withdrawn phytomass per hectare of 0.4±0.2 tС·ha–1·season–1 at single mowing, and 0.9±0.7 tС·ha^–1·season^–1 at double mowing. Therefore, single mowing is more justified in terms of carbon loss than double mowing. Extensive mowing does not increase CO2 emissions into the atmosphere and allows, in addition, to “replace” part of the carbon loss by agricultural production.