Objectives. The problem of reducing the dynamic range of infrared images for their reproduction on display devices with a narrow dynamic range is considered. The method of local image histogram equalization based on the integral distribution function of brightness is investigated. To transform the brightness of a pixel, this method uses an approximation of the local alignment values of the nearest blocks of pixels of original image. This in-creases the local contrast of the image, but leads to high computational complexity, which is increasing while block size decreases. The aim of the work is to reduce the computational complexity of adaptive equalization and compression of infrared image histograms while reducing their dynamic range.

Methods. Image processing methods are used.

Results. To reduce the computational complexity of transforming the dynamic range of infrared images, a block-priority modification of the adaptive histogram equalization method is proposed. The modification is based on the division of the set of image blocks into two subsets of high-priority and low-priority blocks depend-ing on their brightness statistical properties. When interpolating pixel values, high-priority blocks use local alignment values, and low-priority blocks use global alignment values. As a result, the total number of alignment vectors is reduced in proportion to the ratio of subsets sizes and the computational complexity of the dynamic range transformation is reduced.

Conclusion. When changing the ratio of the number of high-priority blocks of infrared image pixels to the number of all blocks in the range of 0.25–0.75, the proposed algorithm is more efficient than global and adaptive histogram equalization algorithms.

Objectives. Methods, algorithms and programs for solving problems of minimizing the DNF representations of Boolean functions are widely used in the design of digital systems to reduce the complexity (crystal area) of functional combinational blocks of digital systems placed into digital VLSI.

The objective of the work is experimental comparison of domestic programs for minimizing Boolean functions in the DNF class included in the FLC-2 with two well-known foreign freely distributed programs for minimizing DNF known as Espresso IIC and ABC.

Methods. Four sets sample of input data were used to compare the programs – there are widely known examples on which the effectiveness of the Espresso IIC program was tested and two sets of industrial examples from the practice of designing the logic circuits. Algorithms and programs for parallelization of calculations when separate functions of minimizing have been developed. Software tools for the application of joint minimization programs with separate minimization of functions are proposed.

Results. The areas of preferred use and the execution time of programs for the source systems of functions (for minimization) characterized by large parameter values of dozens of arguments and functions, tens of thousands of elementary conjunctions are revealed. The efficiency of application of minimization programs for various forms of input data assignment is investigated – DNF, orthogonalized DNF, BDD (Binary Decision Diagrams) representations for systems of functions, truth tables and perfect DNF systems.

Conclusion. The experimental results show the effectiveness of parallel programs – reducing the calculation time and increasing the dimensions of solved problems of separate minimization of Boolean function systems.

Objectives. The problem of constructing and investigating a mathematical model of a stochastic system with processor sharing, repeated calls, and customer impatience is considered. This system is formalized in the form of a queueing system. The operation of the queue is described in terms of multi-dimensional Markov chain. A condition for the existence of a stationary distribution is found, and algorithms for calculating the stationary distribution and stationary performance characteristics of the system are proposed.

Methods. Methods of probability theory, queueing theory and matrix theory are used.

Results. The steady state operation of a queueing system with repeated calls, processor sharing and two types of customers arriving in a marked Markovian arrival process is studied. The channel bandwidth is divided between two types of customers in a certain proportion, and the number of customers of each type simultaneously located on the server is limited. Customers of one of the types that have made all the channels assigned to them busy leave the system unserved with some probability and, with an additional probability, go to the orbit of infinite size, from where they make attempts to get service at random time intervals. Customers of the second type, which caused all the channels assigned to them to be busy, are lost. Customers in orbit show impatience: each of them can leave orbit forever if the time of its stay in orbit exceeds some random time distributed according to an exponential law. Service times of customers of different types are distributed according to the phase law with different parameters. The operation of the system is described in terms of a multi-dimensional Markov chain. It is proved that for any values of the system parameters this chain has a stationary distribution. Algorithms for calculating the stationary distribution and a number of performance measures of the system are proposed. The results of the study can be used to simulate the operation of a fixed capacity cell in a wireless cellular communication network and other real systems operating in the processor sharing mode.

Objectives. When transition from a fleet of diesel buses to a fleet of electric buses, it is important to optimize the charging infrastructure, which combines the slow-charging technologies at the depot overnight and fast recharging at the terminals of the routes. The purpose of the study is to create models and methods for developing the cost-effective solutions for selecting this type of charging infrastructure for a fleet of electric buses serving the city route system, taking into account a number of specific conditions. The operation of the fleet and charging infrastructure is modeled both for the depot at night and for the terminal stops in the most representative period of the day, characterized by the highest intensity of passenger traffic and maximum power consumption.

Methods. Methods of set theory, graph theory and linear approximation are used.

Results. A mathematical model has been developed for the problem of optimizing a mixed-type charging infrastructure for an electric bus fleet. The total daily cost of charging stations, degradation of electric bus batteries and consumed electricity was chosen as the objective function. The model is formulated as a mixed integer linear programming problem.

Conclusion. To solve the formulated problem, standard solvers like IBM ILOG CPLEX can be used. The solution of the problem lies in the choice of durations and schedules for charging electric buses at low-capacity charging stations in the depot at night and at high-capacity charging stations of terminal stops in a given range of peak hours.

Objectives. The creation of ontologies of subject areas is considered. The goal is to develop a mathematical model of ontology and the information system for ontological modeling. The task is to reduce the complexity of ontological modeling.

Methods. As research methods, the theory of hybrid intelligence systems, the theory of sets, elements of mathematical logic, methods for developing the information systems, comparative analysis of information systems, informal analysis of information system were used.

Results. Mathematical model of ontology using the concept of metaobject is developed. Ontological modelling based on this model involves specification, conceptualization and formalization. A glossary of terms is being built at the specification stage. At the conceptualization stage, objects in the subject area and their hierarchy are defined, and then connections between objects are identified. In the formalization stage, the metaobjects and the relationships between metaobjects that correspond to objects and the relationships between objects were defined. This is considered as the ontology of the subject area. During the actualization stage, the parameters of subject area objects and their values, classes, subclasses, and instances of classes were defined. Parameters, parameter values, classes, subclasses, and instances of classes are implemented in ontology as metaobjects of relative types. An information system with a unique architecture has been developed, namely a hybrid intelligence system for the automation of ontological modelling.

Conclusion. The article conducts a comparative analysis of the developed information system with the systems used today for creation of ontologies. The analysis showed that the information system developed by paper author in most parameters is not inferior to considered systems and at the same time easier to use and expand. The mathematical model of ontology and the information system for ontological modeling of subject areas, developed by author, are tested in practical creation of ontology on ecology. On the basis of the conducted comparative analysis and informal analysis of practical use, it is concluded that ontological modeling with the help of the information system developed by author reduces the labor intensity and decreases the time of ontologies creation.

Objectives. The purpose of the analytical and research work was to develop and perform an initial assessment of the capabilities of simulation environment for modeling the Internet of Things (IoT) components and applications. The relevance of the problem is associated with the need to simplify research and testing of such systems as the field is growing. In the implementation of the simulation environment, the following goals were pursued: building a mathematical model; implementation of software, capable of running experiments on that model; providing the user with the ability to analyze results and adjust the model.

Methods. Methods of simulation modeling were used.

Results. Analysis of the relevance and impact of the research results has led to an appropriate example for demonstrating methods and means of solving the problem of IoT subsystems, components, and applications simulation in the proposed environment. This example has been implemented in the part of the Smart Home application model responsible for the energy efficiency optimization in residential buildings enclosed in a simulation environment based on an integrated software package consisting of the Node-RED visual tool for flow-based programming and the Yandex Cloud / Yandex IoT Core cloud service.

Conclusion. A simulation model for managing energy consumption of a "smart home" was developed and implemented using the previously specified software package, including modeling time, environmental conditions, heat loss, operating modes of heating equipment and the behavior of house residents. Based on the implemented model, an initial series of simulation experiments were also carried out, on the one hand, aimed at checking some characteristics of the functionality of the developed simulation environment and the selected example for simulation of residential premises energy management. As a result of the initial experiments, the basic functionality of the integrated software package was proven and demonstrated based on the use of Node-RED and the Yandex Cloud / Yandex IoT Core cloud service for solving problems of simulation modeling of components, subsystems and applications of the Internet of things.