Articles

Initial problems for the equations of motion of a viscous incompressible fluid and gas in Lagrangian variables are considered. It is shown that the motion of an incompressible fluid is not related to pressure. The pressure in the absence of external forces is constant, what allows the fluid to move freely. This motion is purely vortex in nature and is described by quasi-linear equations of the parabolic type. The existence and uniqueness of the classical periodic solution of the initial problem in Rn at n > 2 is proved. The equations of motion of liquid and gas in steady-state mode are obtained. The problem of turbulent flow of partially compressible liquid and gas is solved. It is established that there is no turbulent flow in an incompressible fluid. It is shown that as a result of frequency synchronization, spatially stable periodic structures arise.

Type I diabetes, also known as insulin-dependent diabetes, is a serious disease. There are two main approaches to the management of patients with this disease: the use of insulin pens and various types of insulin (such as ultrashort, short-acting and long-acting insulins) or the use of an insulin pump with ultrashort insulin. An important task remains the development of a reliable system for the accurate calculation of insulin doses using insulin pens in the treatment of type I diabetes. In this study, we investigate the accuracy of calculating insulin doses based on historical data. To solve this problem, we propose using various artificial intelligence (AI) methods, including decision trees, gradient acceleration, support vector machine (SVM) methods and various neural network architectures. We are conducting a comparative analysis of these approaches to determine their effectiveness.

The traffic load balancing problem is relevant in modern networks that have many alternative routes between any pair of nodes. Balancing provides a uniform load of network resources. The paper proposes a method for adaptive queueing policy configuration on a switch to get a uniform queue load on the switch output ports. Because modern applications require the data transmission delay to be around milliseconds, reinforcement learning method DQN was applied to solve the problem. An experimental study demonstrated the convergence of the proposed method during the training to uniform queue load at output ports.

One of the main tools for describing and predicting the occurrence of events is survival analysis, which allows you to predict not only the probability and time of events but also the changing of probability over time. This article presents Survivors, an open-source Python library that helps solve problems of survival analysis, build individual forecasts of survival and risk functions, investigate data dependencies, evaluate the quality of forecasts, and conduct experimental studies. The library uses new methods of constructing tree-based models of survival analysis with high sensitivity to real datasets. In particular, the paper presents a new histogram approach for searching the best split of censored data. The models can handle categorical and missing values, cases of informative censorship, and multimodal time distribution. The paper describes the architecture and components of the library, the features of the software implementation, and an experimental comparison with existing libraries of survival analysis.

A one-line queueing system with three incoming Poissonian flows is studied. Service time distributions are general and absolutely continuous for each flow. The first class requirements have nonpreemptive priority over the second class requirements and preemptive-repeat-different priority over the third class requirements. The second class requirements have nonpreemptive priority over the third class requirements. The heavy traffic limiting distribution of the queue length for the third class is obtained while the system load tends to 1 and time tends to infinity.

The paper considers the asymptotic behavior of the reserve of an organization subjected to risk in the case when the number of factors leading to loss is random. Burr distribution is considered as loss distribution. An asymptotic comparison of the activities of such organizations is carried out in terms of the necessary additional number of such factors (asymptotic deficiency). Two examples illustrating tne obtained results are presented. The first example concerns extreme order statistics, and the second one deals with the truncated Poisson and binomial distributions.

The concept of steady-state solutions of the Navier–Stokes equation is defined. Such solutions expand the concept of stationary, exponentially decrease in time, have a constant spatial velocity field and constant pressure in the absence of external fields. The method of their construction is considered, and the problem of Taylor vortices is solved. A mathematical model of a tornado is proposed. Within the framework of this model, a steady-state solution is obtained as an eigenfunction of the problem in the form of a vortex. Based on the Navier–Stokes equation, a model of the formation of the structure of a gas cloud is proposed. It is shown that due to the Coriolis force, spiral arms arise from flows of gas moving outward. It is proved that the number of arms m is even, and their structure does not depend on the angular velocity of rotation. A formula is obtained for the spiral twist angle depending on the cloud parameters for the case of m=2.

The paper considers inverse problems for hyperbolic equation with singular perturbation in which the function entering the source is unknown. The existence of inverse problems solutions is proved, numerical methods for inverse problems solving are developed and the results of computational experiments illustrating effectiveness of numerical methods are presented.

Technique of data preparation for hemodynamic calculations in a quasi-one-dimensional approximation on complex spatial graphs of elastic vessels is considered. A method is described for the automatic construction of volumetric (3D) models of graphs of the vascular system according to their frame models. The main approaches to carrying out calculations in parallel with the visualization of their results on volumetric models are discussed.

We consider representations of regular languages over symmetric groups such as finite automata and regular expressions. We show that the problem of computing cardinality of such representations is NP-hard.

Polynomiality characterizations are proposed for k-valued logic functions of one variable for a composite modulo k which is a power of a prime number. Based on these characterizations, for each prime number p, polynomiality checking algorithms are obtained for pm-valued logic functions of one variable, m > 1. In these algorithms, the calculations are performed in the residue ring modulo pm. In the case of the positive answer, the algorithms find the canonical polynomial of a input function. The complexity of the obtained algorithms are evaluated (with respect to number of operations from the field of p elements with possible constants).

The paper investigates a two-server system with a Poisson input, in which the service times on the servers have a Pareto distribution with the parameter a > 1. Using known asymptotics for the distribution of stationary waiting time, the distribution of the maximum stationary delay is obtained for two cases: p < 1 and 1 < p < 2. Estimates of the extremal index of stationary waiting time were obtained in numerical experiments using regenerative modeling.

A method of intelligent forecasting of random processes is described. This method is based on a more comprehensive use of statistical regularities inherent in the evolution of the process under consideration. Within the framework of the proposed approach, on the stage of training, the feature space is complemented by the parameters of mixed probability models that make it possible to reconstruct the coefficients of the stochastic differential equation describing the process under consideration. The additional statistical information imposes supplementary restrictions on the research area and thus, narrows the set of possible solutions and directs learning by preliminary rejection of improbable or highly unlikely decisions, and hence, makes the training more efficient and the forecasts more accurate.

The matrix equation XAX = AXA is called the equation of the Young–Baxter type. We examine this equation for matrices of order 2 under the assumption that A is a nonsingular matrix, and we are only interested in the nonsingular solutions. Using a unified rule, one can associate with every such solution a matrix commuting with A. In other words, this matrix is an element of the centralizer MA of A. No obvious reasons exist for two distinct solutions X1 and X2 to generate the same element of MA. Nevertheless, all the solutions (and there are infinitely many of them) generate one and the same matrix in the centralizer. We give an explanation of this surprising fact.

The paper considers an approach to solving the problem of removing noise in a large data set from the sparsity class mp under condition of weak dependence. The approach is based on the method of controlling the false discovery rate (FDR). An upper asymptotic bound for the mean-square risk is obtained.