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The temporal variability of exergy of short-wave and long-wave radiation and its relationships with sensible heat, water vapor (H₂O) and carbon dioxide (CO₂) fluxes on a recently clear-cut area in a mixed coniferous and small-leaved forest in the Tver region is discussed. On the basis of the analysis of radiation and exergy efficiency coefficients suggested by Yu.M. Svirezhev it was shown that during the first eight months after clearcutting the forest ecosystem functions as a "heat engine" i.e. the processes of energy dissipation dominated over processes of biomass production. To validate the findings the statistical analysis of temporary variability of meteorological parameters, as well as, daily fluxes of sensible heat, H₂O and CO₂ was provided using the trigonometrical polynomials. The statistical models that are linearly depended on an exergy of short-wave and long-wave radiation were obtained for mean daily values of CO₂ fluxes, gross primary production of regenerated vegetation and sensible heat fluxes. The analysis of these dependences is also confirmed the results obtained from processing the radiation and exergy efficiency coefficients. The splitting the time series into separate time intervals, e.g. “spring–summer” and “summer–autumn”, allowed revealing that the statistically significant relationships between atmospheric fluxes and exergy were amplified in summer months as the clear-cut area was overgrown by grassy and young woody vegetation. The analysis of linear relationships between time-series of latent heat fluxes and exergy showed their statistical insignificance. The linear relationships between latent heat fluxes and temperature were in turn statistically significant. The air temperature was a key factor improving the accuracy of the models, whereas effect of exergy was insignificant. The results indicated that at the time of active vegetation regeneration within the clear-cut area the seasonal variability of surface evaporation is mainly governed by temperature variation.

The paper proposes a mathematical model for the therapy of glioma, taking into account the blood-brain barrier, radiotherapy and antibody therapy. The parameters were estimated from experimental data and the evaluation of the effect of parameter values on the effectiveness of treatment and the prognosis of the disease were obtained. The possible variants of sequential use of radiotherapy and the effect of antibodies have been explored. The combined use of radiotherapy with intravenous administration of $mab$ $Cx43$ leads to a potentiation of the therapeutic effect in glioma.

Radiotherapy must precede chemotherapy, as radio exposure reduces the barrier function of endothelial cells. Endothelial cells of the brain vessels fit tightly to each other. Between their walls are formed so-called tight contacts, whose role in the provision of BBB is that they prevent the penetration into the brain tissue of various undesirable substances from the bloodstream. Dense contacts between endothelial cells block the intercellular passive transport.

The mathematical model consists of a continuous part and a discrete one. Experimental data on the volume of glioma show the following interesting dynamics: after cessation of radio exposure, tumor growth does not resume immediately, but there is some time interval during which glioma does not grow. Glioma cells are divided into two groups. The first group is living cells that divide as fast as possible. The second group is cells affected by radiation. As a measure of the health of the blood-brain barrier system, the ratios of the number of BBB cells at the current moment to the number of cells at rest, that is, on average healthy state, are chosen.

The continuous part of the model includes a description of the division of both types of glioma cells, the recovery of BBB cells, and the dynamics of the drug. Reducing the number of well-functioning BBB cells facilitates the penetration of the drug to brain cells, that is, enhances the action of the drug. At the same time, the rate of division of glioma cells does not increase, since it is limited not by the deficiency of nutrients available to cells, but by the internal mechanisms of the cell. The discrete part of the mathematical model includes the operator of radio interaction, which is applied to the indicator of BBB and to glial cells.

Within the framework of the mathematical model of treatment of a cancer tumor (glioma), the problem of optimal control with phase constraints is solved. The patient’s condition is described by two variables: the volume of the tumor and the condition of the BBB. The phase constraints delineate a certain area in the space of these indicators, which we call the survival area. Our task is to find such treatment strategies that minimize the time of treatment, maximize the patient’s rest time, and at the same time allow state indicators not to exceed the permitted limits. Since the task of survival is to maximize the patient’s lifespan, it is precisely such treatment strategies that return the indicators to their original position (and we see periodic trajectories on the graphs). Periodic trajectories indicate that the deadly disease is translated into a chronic one.

Atherosclerotic diseases such as carotid artery diseases (CAD) and chronic kidney diseases (CKD) are the major causes of death worldwide. The onset of these atherosclerotic diseases in the arteries are governed by complex blood flow dynamics and hemodynamic parameters. Atherosclerosis in renal arteries leads to reduction in arterial efficiency, which ultimately leads to Reno-vascular hypertension. This work attempts to identify the localization of atherosclerotic plaque in human abdominal aorta — renal artery junction using Computational fluid dynamics (CFD).

The atherosclerosis prone regions in an idealized human abdominal aorta-renal artery junction are identified by calculating relevant hemodynamic indicators from computational simulations using the rheologically accurate shear-thinning Yeleswarapu model for human blood. Blood flow is numerically simulated in a 3-D model of the artery junction using ANSYS FLUENT v18.2.

Hemodynamic indicators calculated are average wall shear stress (AWSS), oscillatory shear index (OSI), and relative residence time (RRT). Simulations of pulsatile flow (f=1.25 Hz, Re = 1000) show that low AWSS, and high OSI manifest in the regions of renal artery downstream of the junction and on the infrarenal section of the abdominal aorta lateral to the junction. High RRT, which is a relative index and dependent on AWSS and OSI, is found to overlap with the low AWSS and high OSI at the cranial surface of renal artery proximal to the junction and on the surface of the abdominal aorta lateral to the bifurcation: this indicates that these regions of the junction are prone to atherosclerosis. The results match qualitatively with the findings reported in literature and serve as initial step to illustrate utility of CFD for the location of atherosclerotic plaque.

The paper analyzes the methods of studying the process of interaction of soil environments with the tillage tools of soil processing machines. The mathematical methods of numerical modeling are considered in detail, which make it possible to overcome the disadvantages of analytical and empirical approaches. A classification and overview of the possibilities the continuous (FEM — finite element method, CFD — computational fluid dynamics) and discrete (DEM — discrete element method, SPH — hydrodynamics of smoothed particles) numerical methods is presented. Based on the discrete element method, a mathematical model has been developed that represents the soil in the form of a set of interacting small spherical elements. The working surfaces of the tillage tool are presented in the framework of the finite element approximation in the form of a combination of many elementary triangles. The model calculates the movement of soil elements under the action of contact forces of soil elements with each other and with the working surfaces of the tillage tool (elastic forces, dry and viscous friction forces). This makes it possible to assess the influence of the geometric parameters of the tillage tools, technological parameters of the process and soil parameters on the geometric indicators of soil displacement, indicators of the self-installation of tools, power loads, quality indicators of loosening and spatial distribution of indicators. A total of 22 indicators were investigated (or the distribution of the indicator in space). This makes it possible to reproduce changes in the state of the system of elements of the soil (soil cultivation process) and determine the total mechanical effect of the elements on the moving tillage tools of the implement. A demonstration of the capabilities of the mathematical model is given by the example of a study of soil cultivation with a disk cultivator battery. In the computer experiment, a virtual soil channel of 5×1.4 m in size and a 3D model of a disk cultivator battery were used. The radius of the soil particles was taken to be 18 mm, the speed of the tillage tool was 1 m/s, the total simulation time was 5 s. The processing depth was 10 cm at angles of attack of 10, 15, 20, 25 and 30°. The verification of the reliability of the simulation results was carried out on a laboratory stand for volumetric dynamometry by examining a full-scale sample, made in full accordance with the investigated 3D-model. The control was carried out according to three components of the traction resistance vector: $F_x$, $F_y$ and $F_z$. Comparison of the data obtained experimentally with the simulation data showed that the discrepancy is not more than 22.2%, while in all cases the maximum discrepancy was observed at angles of attack of the disk battery of 30°. Good consistency of data on three key power parameters confirms the reliability of the whole complex of studied indicators.

A method is proposed for analyzing the tremor of the earth’s surface, measured by means of space geodesy, in order to highlight the prognostic effects of seismicity activation. The method is illustrated by the example of a joint analysis of a set of synchronous time series of daily vertical displacements of the earth’s surface on the Japanese Islands for the time interval 2009–2023. The analysis is based on dividing the source data (1047 time series) into blocks (clusters of stations) and sequentially applying the principal component method. The station network is divided into clusters using the K-means method from the maximum pseudo-F-statistics criterion, and for Japan the optimal number of clusters was chosen to be 15. The Huang decomposition method into a sequence of independent empirical oscillation modes (EMD — Empirical Mode Decomposition) is applied to the time series of principal components from station blocks. To provide the stability of estimates of the waveforms of the EMD decomposition, averaging of 1000 independent additive realizations of white noise of limited amplitude was performed. Using the Cholesky decomposition of the covariance matrix of the waveforms of the first three EMD components in a sliding time window, indicators of abnormal tremor behavior were determined. By calculating the correlation function between the average indicators of anomalous behavior and the released seismic energy in the vicinity of the Japanese Islands, it was established that bursts in the measure of anomalous tremor behavior precede emissions of seismic energy. The purpose of the article is to clarify common hypotheses that movements of the earth’s crust recorded by space geodesy may contain predictive information. That displacements recorded by geodetic methods respond to the effects of earthquakes is widely known and has been demonstrated many times. But isolating geodetic effects that predict seismic events is much more challenging. In our paper, we propose one method for detecting predictive effects in space geodesy data.

Approbation of calculation of borders of water quality classes for the purpose of ecological diagnosis and standardization by data of the Rybinsk reservoir is carried out. For bioindication indicators of phytoplankton fluorescence and the contents of pigments of phytoplankton are used. Chesnokov's importance coefficient proved to be the most preferred measure of connection for analyzing the effects of environmental factors on indicators. The factors important for environmental condition are identified. Comparison of borders between quality classes “valid” and “invalid” of factors values and boundaries of the classifications of water quality.

The work discusses the methodological basis and problems of modeling of world dynamics. Outlines approaches to the construction of a new simulation model of global development and the results of the simulation. The basis of the model building is laid empirical approach which based on the statistical analysis of the main socio-economic indicators. On the basis of this analysis identified the main variables. Dynamic equations (in continuous differential form) were written for these variables. Dependencies between variables were selected based on the dynamics of indicators in the past and on the basis of expert assessments, while econometric techniques were used, based on regression analysis. Calculations have been performed for the resulting dynamic equations system, the results are presented in the form of a trajectories beam for those indicators that are directly observable, and for which statistics are available. Thus, it is possible to assess the scatter of the trajectories and understand the predictive capability of this model.

The paper has a goal to identify a set of parameters of the environment and infrastructure with the most significant impact on institutional-matrices that dominate in different countries. Parameters of environmental conditions includes raw statistical indices, which were directly derived from the databases of open access, as well as complex integral indicators that were by method of principal components. Efficiency of discussed parameters in task of dominant institutional matrices type recognition (X or Y type) was evaluated by a number of methods based on machine learning. It was revealed that greatest informational content is associated with parameters characterizing risk of natural disasters, level of urbanization and the development of transport infrastructure, the monthly averages and seasonal variations of temperature and precipitation.

The aim of the work was to study and develop methods of forecasting the dynamics of the human respiratory reactions, based on mathematical modeling. To achieve this goal have been set and solved the following tasks: developed and justified the overall structure and formalized description of the model Respiro-reflex system; built and implemented the algorithm in software models of gas exchange of the body; computational experiments and checking the adequacy of the model-based Lite-ture data and our own experimental studies.

In this embodiment, a new comprehensive model entered partial model modified version of physicochemical properties and blood acid-base balance. In developing the model as the basis of a formalized description was based on the concept of separation of physiologically-fi system of regulation on active and passive subsystems regulation. Development of the model was carried out in stages. Integrated model of gas exchange consisted of the following special models: basic biophysical models of gas exchange system; model physicochemical properties and blood acid-base balance; passive mechanisms of gas exchange model developed on the basis of mass balance equations Grodinza F.; chemical regulation model developed on the basis of a multifactor model D. Gray.

For a software implementation of the model, calculations were made in MatLab programming environment. To solve the equations of the method of Runge–Kutta–Fehlberga. It is assumed that the model will be presented in the form of a computer research program, which allows implements vat various hypotheses about the mechanism of the observed processes. Calculate the expected value of the basic indicators of gas exchange under giperkap Britain and hypoxia. The results of calculations as the nature of, and quantity is good enough co-agree with the data obtained in the studies on the testers. The audit on Adek-vatnost confirmed that the error calculation is within error of copper-to-biological experiments. The model can be used in the theoretical prediction of the dynamics of the respiratory reactions of the human body in a changed atmosphere.

In the conditions of the development of modern economy, human capital is one of the main factors of economic growth. The formation of human capital begins with the birth of a person and continues throughout life, so the value of human capital is inseparable from its carriers, which in turn makes it difficult to account for this factor. This has led to the fact that currently there are no generally accepted methods of calculating the value of human capital. There are only a few approaches to the measurement of human capital: the cost approach (by income or investment) and the index approach, of which the most well-known approach developed under the auspices of the UN.

This paper presents the assigned task in conjunction with the task of demographic dynamics solved in the time-age plane, which allows to more fully take into account the temporary changes in the demographic structure on the dynamics of human capital.

The task of demographic dynamics is posed within the framework of the Mac-Kendrick – von Foerster model on the basis of the equation of age structure dynamics. The form of distribution functions for births, deaths and migration of the population is determined on the basis of the available statistical information. The numerical solution of the problem is given. The analysis and forecast of demographic indicators are presented. The economic and mathematical model of human capital dynamics is formulated on the basis of the demographic dynamics problem. The problem of modeling the human capital dynamics considers three components of capital: educational, health and cultural (spiritual). Description of the evolution of human capital components uses an equation of the transfer equation type. Investments in human capital components are determined on the basis of budget expenditures and private expenditures, taking into account the characteristic time life cycle of demographic elements. A one-dimensional kinetic equation is used to predict the dynamics of the total human capital. The method of calculating the dynamics of this factor is given as a time function. The calculated data on the human capital dynamics are presented for the Russian Federation. As studies have shown, the value of human capital increased rapidly until 2008, in the future there was a period of stabilization, but after 2014 there is a negative dynamics of this value.