Objectives. The problem of developing hardware effective method for estimating the total electron content in the ionosphere based on retransmission of the L1, L2 signals of the global navigation satellite system GPS using a repeater nanosatellite is solved.
Methods. It is shown that with the retransmission of L1, L2 signals at frequencies of 150/400 MHz allocated for geophysical research, a coherent multi-position radar system is formed, including navigation satellites (NS) – signal sources, repeater nanosatellite (SR) and ground receiving points (RP). The delay time and phase of the four received signals contain the information about the total TEC on the propagation paths NS – SR and SR – RP. It is shown that due to retransmission and subsequent processing, it is possible to isolate TECs on each of the propagation paths as well as determination of the coordinates of the SR.
Results. The content of the method, the procedure for evaluating TEC based on the results of processing the relayed signals, and the technical requirements for the relay equipment are determined. The accuracy characteristics of the proposed method are obtained. Simulation results are given.
Conclusion. The information presented in the article may be useful for specialists and researchers who interested in the issues of radio tomographic research of the ionosphere and forecasting hazardous natural phenomena.

Objectives. Morphological analysis of papillary thyroid cancer is a cornerstone for further treatment planning. Traditional and neural network methods of extracting parts of images are used to automate the analysis. It is necessary to prepare a set of data for teaching neural networks to develop a system of similar anatomical region in the histopathological image. Authors discuss the second selection of signs for the marking of histological images, methodological approaches to dissect whole-slide images, how to prepare raw data for a future analysis. The influence of the representative size of the fragment of the full-to-suction image of papillary thyroid cancer on the accuracy of the classification of trained neural network EfficientNetB0 is conducted. The analysis of the resulting results is carried out, the weaknesses of the use of fragments of images of different representative size and the cause of the unsatisfactory accuracy of the classification on large increase are evaluated.
Materials and methods. Histopathological whole-slide imaged of 129 patients were used. Histological micropreparations containing elements of a tumor and surrounding tissue were scanned in the Aperio AT2 (Leica Biosystems, Germany) apparatus with maximum resolution. The marking was carried out in the ASAP software package. To choose the optimal representative size of the fragment the problem of classification was solved using the pre-study neural network EfficientNetB0.
Results. A methodology for preparing a database of histopathological images of papillary thyroid cancer was proposed. Experiments were conducted to determine the optimal representative size of the image fragment. The best result of the accuracy of determining the class of test sample showed the size of a representative fragment as 394.32×394.32 microns.
Conclusion. The analysis of the influence of the representative sizes of fragments of histopathological images showed the problems in solving the classification tasks because of cutting and staining images specifics, morphological complex and textured differences in the images of the same class. At the same time, it was determined that the task of preparing a set of data for training neural network to solve the problem of finding invasion of vessels in a histopathological image is not trivial and it requires additional stages of data preparation.

Objectives. The problem of circuit implementation of incompletely specified (partial) k-valued logic functions given by tabular representations is considered. The stage of technologically independent optimization is studied to obtain minimized representations of systems of completely specified Boolean functions from tabular representations of partial functions of k-valued logic. According to these representations of Boolean functions, technological mapping is performed at the second stage of the synthesis of logic circuits.
Methods. Using additional definitions of Multi-valued Decision Diagrams (MDD) representing partial functions of k-valued logic, and Binary Decision Diagrams (BDD) representing partial systems of Boolean functions at the stage of technologically independent optimization is proposed. The task of additional definition of MDD is oriented to reducing the number of vertices of the MDD graph that correspond to the cofactors of the Shannon expansion of a multi-valued function.
Results. The MDD minimization problem is reduced to solving the problems of coloring undirected graphs of incompatibility of cofactors by minimum number of colors. Encoding of multi-valued values of arguments and values of functions of k-valued logic by binary codes leads to systems of partial Boolean functions, which are also further defined in order to minimize their multi-level BDD representations.
Conclusion. The proposed approach makes it possible to define partial multi-valued functions to fully defined Boolean functions in two stages. At the second stage, well-known and effective methods are used to redefine BDD representing systems of partial Boolean functions. As a result of this two-step approach, minimized BDD representations of systems of completely defined functions are obtained. According to completely defined Boolean functions, a technological mapping into a given library of logical elements is performed, i.e. the optimized descriptions of Boolean function systems are covered with descriptions of logical elements

Objectives. The problem of parallelizing computations on multicore systems is considered. On the Floyd – Warshall blocked algorithm of shortest paths search in dense graphs of large size, two types of parallelism are compared: fork-join and network dataflow. Using the CAL programming language, a method of developing actors and an algorithm of generating parallel dataflow networks are proposed. The objective is to improve performance of parallel implementations of algorithms which have the property of partial order of computations on multicore processors.
Methods. Methods of graph theory, algorithm theory, parallelization theory and formal language theory are used.
Results. Claims about the possibility of reordering calculations in the blocked Floyd – Warshall algorithm are proved, which make it possible to achieve a greater load of cores during algorithm execution. Based on the claims, a method of constructing actors in the CAL language is developed and an algorithm for automatic generation of dataflow CAL networks for various configurations of block matrices describing the lengths of the shortest paths is proposed. It is proved that the networks have the properties of rate consistency, boundedness, and liveness. In actors running in parallel, the order of execution of actions with asynchronous behavior can change dynamically, resulting in efficient use of caches and increased core load. To implement the new features of actors, networks and the method of their generation, a tunable multi-threaded CAL engine has been developed that implements a static dataflow model of computation with bounded sizes of buffers. From the experimental results obtained on four types of multi-core processors it follows that there is an optimal size of the network matrix of actors for which the performance is maximum, and the size depends on the number of cores and the size of graph.
Conclusion. It has been shown that dataflow networks of actors are an effective means to parallelize computationally intensive algorithms that describe a partial order of computations over decomposed data. The results obtained on the blocked algorithm of shortest paths search prove that the parallelism of dataflow networks gives higher performance of software implementations on multicore processors in comparison with the fork-join parallelism of OpenMP.

Objectives. The problem of mathematical modeling and algorithmization of the processes of correction of requests in the system of information support for decision-making is being solved. At the same time, three main goals are pursued: building of a generalized information retrieval model, development of algorithms for pre-search query correction and development of algorithms for post-search query correction.
Methods. Methods of set theory and probability theory are used.
Results. A generalized information retrieval model has been developed. Within the framework of the model, the concepts of search function, issuance criterion, relevance and pertinence of search results are formalized. Algorithms for pre-search and post-search correction of queries in the information decision support system are proposed.
Conclusion. A mathematical model for correcting user requests in the information decision support system has been developed. Within the framework of the model, the efficiency of search processes in terms of the relevance and pertinence of the information found has been studied. Necessary and sufficient optimality of search functions are proved.

Objectives. In connection with the increase in the number of solar power plants, the automation of monitoring their performance becomes an urgent task. The search for anomalies in the operation of solar power plants is one of the main components of monitoring. The purpose of the study is to develop new methods and software algorithms for finding anomalies in the operation of solar panels based on the results of a digital twin created and trained according to the telemetry data of a solar power plant.
Methods. The developed technique is based on statistical studies of deviations of power values at the point of maximum efficient operation of the solar panel calculated by the digital twin. In addition, a normalized value of the power in the maximum efficient operation of the solar panel was introduced for more accurate clustering and anomaly search.
Results. Using the developed method of static search for half a year of observations, 18 anomalies were detected in the operation of the solar panels of the power plant. All cases are analyzed for the causes of anomalies in the operation of solar panels.
Conclusion. It has been established that when using normalized power values in the analysis of deviations at the point of maximum power PN, it is possible to detect abnormal operation of individual panels. The level of deviation of the normalized values at the point of maximum power was calculated, indicating the presence of an anomaly in the operation of solar panel.

Objectives. A finite-difference computational algorithm is proposed for solving a mixed boundary-value problem for the Poisson equation given in two-dimensional irregular domains.
Methods. To solve the problem, generalized curvilinear coordinates are used. The physical domain is mapped to the computational domain (unit square) in the space of generalized coordinates. The original problem is written in curvilinear coordinates and approximated on a uniform grid in the computational domain.
The obtained results are mapped on non-uniform boundary-fitted difference grid in the physical domain.
Results. The second order approximations of mixed Neumann-Dirichlet boundary conditions for the Poisson equation in the space of generalized curvilinear coordinate are constructed. To increase the order of Neumann condition approximations, an approximation of the Poisson equation on the boundary of the domain is used.
Conclusions. To solve a mixed boundary value problem for the Poisson equation in two-dimensional irregular domains, the computational algorithm of second-order accuracy is constructed. The generalized curvilinear coordinates are used. The results of numerical experiments, which confirm the second order accuracy of the computational algorithm, are presented.