The problems of optimal inventory control under uncertainty are considered. The approaches to the construction of nearly optimal strategies in models with external support of resources are proposed. The examples of stockpiling processes in logistics systems, which are characterized by the existence of moments of regeneration, illustrate the methodology of analytical computer modeling and algorithms for finding optimal solutions. Keywords: logistics processes, inventory control, decisions under uncertainty, external supply, optimal strategy, computer modeling.

The author proposes an adjustment and analyzes the variability of the mathematical models of the dynamics of the world financial and economic system (FES) caused by financial flows of capital movements of decentralized currencies. These models are generated based on the matrix of cross-border movement of capital and are used to calculate the governing influences of regulators, aimed at optimizing the management of the world FES for anti-crisis protection. Computational problems related to the mathematical features and correction of models are analyzed. Calculations of changes in the eigenvalues of the model matrices during capital flows of decentralized currencies are given. Keywords: mathematical modeling, world (global) financial and economic system, management optimization, cross-border capital movement matrix, numerical methods, decentralized currencies.

An algorithm for the rehabilitation process is created, considering the constraints of the patient’s rehabilitation program. The identifications of rehabilitation participants, the stages, and the means of the rehabilitation efficiency evaluation are presented. Two families of optimization models are generated to find patient rehabilitation programs optimal in terms of cost and weight. The first family allows for the selection of interventions for specialists in the multidisciplinary team, and the second family forms a multidisciplinary team for implementing the rehabilitation program. Calculations are provided for a model example, where the patient’s rehabilitation program is determined by four specialists of the multidisciplinary team and three codes of the International Classification of Functioning, Disability, and Health (ICF). Keywords: patient-centric approach, patient rehabilitation program, rehabilitation algorithm, integer linear (quadratic) programming problem, Gurobi.

The author considers the optimization problem for the triharmonic equation in the presence of specific boundary conditions. As a result, the triharmonic Poisson integral was constructed in Cartesian coordinates for the upper half-plane. The asymptotic properties of this operator on Lipschitz classes in a uniform metric were studied. An exact equality was found for the upper bound of the deviation of the Lipschitz class functions from the triharmonic Poisson integral defined in Cartesian coordinates for the upper half-plane in the metric space. The results obtained in the article demonstrate the connection between the methods of approximation theory and the principles of optimal decision theory. Keywords: optimization problem, class of Lipschitz functions, uniform metric, triharmonic Poisson integral.

Closed-form solutions are obtained to some one-dimensional boundary-value problems for modeling anomalous filtration dynamics in a layered geoporous medium, posed within the framework of the fractional-differential generalization of the biparabolic evolutionary partial differential equation of the fourth order. In particular, the formulation and solution of the direct and inverse model boundary-value problems of geofiltration dynamics based on the mathematical model with conjugation conditions are presented, and the conditions of the existence of regular solutions to these problems are defined. Keywords: mathematical modeling, fractional-differential dynamics of geofiltration processes, nonclassical models, biparabolic evolutionary equation, the fractional-differential analog of the biparabolic evolutionary equation, nonstationary boundary-value problems on a finite interval, direct and inverse problems, conjugation conditions, closed-form solutions.

Chebyshev polynomials of the first kind are used to construct the generalized Chebyshev–Poisson integral. The optimization problem for the generalized Chebyshev–Poisson operator as a functional of a function defined on a segment is solved, and its approximate properties on Hölder classes H 1 are analyzed. An exact equality is obtained for the deviation of Hölder class functions from the generalized Chebyshev–Poisson integral. Keywords: Chebyshev polynomials, generalized Chebyshev–Poisson integral, class of Hölder functions, optimization problem.

A multichannel queueing system with a Poisson input flow is considered. The input flow rate depends on the current state of a semi-Markov process. This state also determines the type of the customer. Each channel contains several service lines. To be serviced, the customer requires several lines with the distribution dependent on the customer’s type. Not each channel is accessible for customers of a given type. The accessibility is determined by some distribution depending both on the customer’s type and on the required number of lines. If the channel does not have sufficient service lines, it is possible to reorient this customer to another channel. The service time has a general distribution function depending on the customer’s type and the number of lines required for servicing. A fast simulation method is proposed to evaluate the blocking probability of customers of a certain type demanding a given number of service lines. A comparison with the Monte Carlo method is made using a numerical example, and the change in the relative error of the estimate for decreasing blocking probability is analyzed. Keywords: queueing system, semi-Markov process, channel, line, blocking probability, Monte Carlo method, fast simulation, estimate, relative error.

Spatial static boundary-value problems of mathematical physics for a layer with a non-circular cylindrical through hole have hardly been solved using the method of singular integral equations (SIE) despite the fact that numerous fundamental theoretical issues have been developed. Methods for the calculation of spectral characteristics are also absent. The paper provides an overview of the methods for solving these problems. A new mathematical model has been constructed, and a new method based on a system of three SIEs has been developed and tested numerically. As a result of a high-precision numerical study, it was found that with an increase in the thickness of the layer, an increase in the relative circumferential stress occurs. In the case of a circular hole, a shift of the maximum relative circumferential stress from the ends to the depth of the layer is observed. In the case of an elliptical hole, with a decrease in one of the radii, an increase in the relative circumferential stress is also observed. Keywords: three-dimensional boundary-value problems, singular integral equations, numerical experiment, static bending, a through hole.

We analyze the problem of identifying the constant parameters involved in the right-hand sides of a linear non-autonomous system of differential equations with first-order ordinary derivatives. The specificity of the problem is that additional conditions for identifying parameters, first, are non-local, and second, include derivatives of an unknown function. We examine the conditions for the existence and uniqueness of a solution to the problem and propose two different approaches to the numerical solution of the problem. The results of computer experiments are presented. Keywords: dynamic system, parametric identification, loaded differential equation, conditions for the existence of a solution, computer experiments.

To study the relationship between the dynamics of the COVID-19 pandemic and the state of the economy, a stochastic model is developed that covers the epidemic and economic blocks and the system of relationships between them. An approach is proposed to analyze the interrelations of economic sectors related to food production, transport chains of their delivery, and the medical sector, using the three-sector Lorenz model. This model combines the described sectors of the economy into a single structure, each of which is considered from the point of view of the level of productivity, the number of jobs, and structural disturbances. Model studies are carried out to analyze the dependence of the dynamics of the pandemic on the initial conditions and parameters for managing the epidemic process and the impact of the pandemic on changes in the balance of supply and demand in sectors of the economy related to food production, transport, and the medical sector. Keywords: mathematical modeling, spread of COVID-19, deterministic chaos, economic consequences of the pandemic.