The purpose of this work is to choose the most optimal method of data transmission for conducting research on improving the reliability and ensuring safe operation of products obtained by 3D printing, operated at low temperatures. This is very important, since any error that occurs when transmitting the results of the study is fraught with further inaccuracies, and, subsequently, possibly human lives or environmental and economic disasters. The article describes the main methods of data transmission suitable for this case. Their advantages and disadvantages, possible problems when deploying networks in production or when scaling the experiment are analyzed in detail. Further, a comparison of each method is made by assigning estimates for the required groups of indicators. Based on the results of the comparison, conclusions were drawn about the best way to transfer data for this study, which may be useful in carrying out further work, as well as in similar studies in the future.

Machine learning methods use data trees to organize and store information. Each of these structures has certain advantages and allows improving the quality of a particular algorithm. If all tree nodes have no more than two descendants, then it is called binary; its main advantage is the high efficiency of implementing search and sorting algorithms. In this regard, it is important to note that dendrograms of hierarchical agglomerative clustering methods are also binary trees reflecting the taxonomy of elements of a data set. Any cluster that is not a singleton can be divided into subclusters, and this allows us to form a hierarchical structure in a metric space (metric tree) with additional properties. For example, automatically set the height of the tree, considering by definition that the number of levels on which its nodes are located coincides with the number of options for dividing the sample set into clusters, subclusters, subclusters of subclusters, etc. This problem can be solved using approximation-estimation tests, the change in sensitivity of which, using the trend coefficient, allows us to obtain various clustering options. When conducting computational experiments, a synthetic set of points on the Euclidean plane was used and were studied the results of centroid based clustering. Markov moments of stopping the clustering process were determined using approximation-estimation test. Verification of the results obtained in numerical modeling was carried out by changing the step size of the trend coefficient.

The expression for the potential energy of interaction of two neutral atoms in the absence of a chemical bond consists of the sum of multiple and improper integrals. Due to the cumbersome nature of the functions, finding these integrals in explicit form is not possible. Software systems widely used in practice based on standard methods of computational mathematics are also not capable of providing satisfactory accuracy in their numerical calculations in a short time. In quantum chemistry and computational physics, the above greatly limits approaches to modeling the properties and structures of atomic/molecular systems. You have to rely on Monte-Carlo integration methods or formulas of the Gauss — Laguerre type, which are not so effective in terms of accuracy. In this article, in relation to this problem, we propose a method for transferring Newton — Cotes quadrature formulas to the architecture of graphic processors. The features of such a transfer are discussed in detail, designed to eliminate bottlenecks and maximize the performance of the corresponding calculation programs. The platform for massively parallel computing is CUDA technology from NVIDIA. Testing has shown that in typical tasks, the efficiency of programs for GPUs based on parallel analogues is on average an order of magnitude higher than classical ones. Within the framework of the proposed approach, it was possible to calculate interatomic interaction potentials in a wide range of changes in distances between atoms with high accuracy and in an acceptable computer time, as well as determine the equilibrium interaction parameters. the results obtained are in good agreement with the data known from the literature.

Field emission and structural characteristics of carbon nanotube fibers, polyacrylonitrile fibers, pyrolytic graphite and micrograined dense graphite were experimentally studied before and after their operation as a field cathode using registration of the current-voltage characteristics, optical microscopy, scanning electron microscopy and Raman spectroscopy in the spectral range from 1000 to 2000 cm-1. The experiments carried out showed large and small structural rearrangements of carbon-containing cathodes and their surfaces in the process of field emission. In addition to the G, D and D' lines characteristic of carbon materials, a line was detected in the range of 1450–1480 cm-1, which is observed in the starting materials of pyrolytic graphite, carbon nanotube fibers and persists after operation, and also appears in the micrograined dense graphite sample after operation in as a cathode. The relative integral intensity of line D in pyrolytic graphite, micrograined dense graphite, and carbon nanotube fibers undergoes the greatest change. In pyrolytic graphite and carbon nanotube fiber, its increase is observed, and in micrograined dense graphite its decrease is observed after operation as a cathode. This made it possible to use the relative integral intensity of the D-line to quantify the change in the surface properties of carbon materials as a result of field emission when using these materials as cathodes, in particular. to assess changes in crystallite sizes. Thus, the possibility of using Raman spectra to control the surface structure of carbon-containing materials has been demonstrated, which significantly facilitates the possibility of further analysis of the relationship between the surface structure and its emission characteristics. The prospects for improving the field emission characteristics of carbon-containing cathodes were discussed.

The continued economic development of various countries or regions has resulted in increased competition in global markets, leading to a concentration of investors and skilled labour in locations with high investment attractiveness. The investment attractiveness of a given country or region is determined by its investment potential and risk, which are characterized by a combination of various significant factors.This paper seeks to develop an econometric model to estimate the amount of investment in fixed capital in a specific region, taking into consideration the linear relationship between the observed results, in order to determine the main conditions that are necessary for achieving stable and high economic growth. These conditions include the acceleration of investment activity and the implementation of major national reforms to ensure the effectiveness of the investment process. To assess the overall influence of the financial and economic indicators studied on the volume of investment, multiple regression analysis was utilized as the primary mathematical tool of the study. Furthermore, assumptions were made regarding the rank of the observations. To validate this hypothesis, a cluster analysis was conducted, grouping the observations into four clusters based on their results, depending on the volume of investment or the geographical characteristics of the region.

An efficient method for calculating the location of stationary gas leakage in wells and gas pipelines with medium and ultra-high pressures is presented. An algorithm for constructing the dependence of the compressibility factor of the gas mixture with a predominance of methane in the region of ultra-high pressures based on experimental data of pressure and temperature is proposed. The algorithm for calculating the leakage location is based on the Bellman method of quasi-linearization of nonlinear problems, with an additional hypothesis of the linear dependence of pressure and temperature on the leakage location coordinates used at each iteration. The issue of selecting the initial approximation is considered, and the advantage of calculating the initial approximation using a simplified non-isothermal flow model is justified. Examples of solving practical problems of high interest are given, and the high accuracy of calculating the gas leakage location using the proposed algorithm in gas pipelines with medium pressures (around 9 MPa) and ultra-high pressures (around 20 MPa) for small and medium gas leaks is demonstrated.

The article presents the sufficient conditions for stability and asymptotic stability with respect to a part of the variables of the zero solution of a nonlinear system in the linear approximation. the case is considered when the matrix of the linear approximation may contain eigenvalues with zero real parts and the algebraic and geometric multiplicities of these eigenvalues may not coincide. The approach is based on establishing some correspondence between the solutions of the investigated system and its linear approximation. The solutions of such systems starting in a sufficiently small zero neighborhood and the systems themselves possess the same componentwise asymptotic properties in this case. Such solutions’ properties are stability and asymptotic stability with respect to some variables, and for systems componentwise local asymptotic equivalence and componentwise local asymptotic equilibrium. Considering the correspondence between the solutions of systems as an operator defined in a Banach space, there is proved that it has at least one fixed point according to the Schauder’s principle. The operator allows to construct a mapping that establishes the relationship between the initial points of the investigated system and its linear approximation. Further, a conclusion about the componentwise asymptotic properties of solutions of the nonlinear system is made on the basis of estimates of the fundamental matrix of the linear approximation rows’ entries. There is given an example of the investigation of stability and asymptotic stability with respect to a part of the variables of the zero solution of a nonlinear system is given, when the linear approximation matrix contains one negative and one zero eigenvalues, and the algebraic and geometric multiplicities of the zero eigenvalue do not coincide.

The paper describes an approach to the formation of ontology based on descriptions of objects in terms of the predicate calculus language. With this approach, an object is represented as a set of its elements, on which a set of predicates is defined that defines the properties of these elements and the relationship between them. A description of an object is a conjunction of literals that are true on elements of an object. In the present work, ontology is understood as an oriented graph with descriptions of subsets as nodes and such that the elements of a set at the end of an oriented edge have the properties of the elements of the set at the beginning of this edge. Three settings of an ontology construction problem are considered: 1) all predicates are binary and subsets of the original set of objects are given; 2) all predicates are binary and it is required to find subsets of the original set; 3) among the predicates there are many-valued ones and subsets of the original set of objects are given. The main tool for construction such a description is to extract an elementary conjunction of literals of predicate formulas that is isomorphic to subformulas of some formulas. The definition of an isomorphism of elementary conjunctions of atomic predicate formulas is given. The method of ontology construction is formulated. An illustrative example is provided.

We propose a mathematical model of the malaria epidemic in the human population (host), where the transmission of the disease is produced by a vector population (mosquito) known as the malaria mosquito. The malaria epidemic model is defined by a system of ordinary differential equations. The host population at any time is divided into four sub-populations: susceptible, exposed, infectious, recovered. Sufficient conditions for stability of equilibrium without disease and endemic equilibrium are obtained using the Lyapunov’s function theory. We define the reproductive number characterizing the level of disease spreading in the human population. Numerical modeling is made to study the influence of parameters on the spread of vector-borne disease and to illustrate theoretical results, as well as to analyze possible behavioral scenarios.

The problem of storing and transporting hydrogen in containers based on fullerenes and carbon nanotubes is relevant to hydrogen energy. This problem theoretically can be solved using quantum chemistry methods and powerful computer technology to calculate molecules with a large number of atoms, polymers, nanostructures and nanotubes. It is necessary to create a theoretical model of the electromagnetic field in the cavity of fullerene molecules and nanotubes in order to understand how atoms and molecules of hydrogen or any other substances behave in it. Computer simulation of the filling process by hydrogen molecules fullerenes and nanotubes was performed by quantum mechanics methods DFT with GAUSSIAN 09 program.