Mathematical Machines and Systems. 2020 #3



UDC 621.3

Reznik O.M. The concept of an open dynamic system. Mathematical machines and systems. 2020. N 3. P. 3–22.

The concept of an open dynamical system as a general model of the development of systems and processes of various nature is proposed
. It is based on a new interpretation of M. Mesarovichs theorem on the decomposition of the Universum, and the concept of observation as an asymmetric relation corresponding to the movement of basis elements of a set of states of a dynamical system between its external and internal space. The element of the basis, according to the concept of geometrodynamics, exists as a vortex in an empty curved internal space of a dynamical system, or as an elementary particle that transfers a quantum of energy when observed. An open dynamical system is defined as a finite dynamical system exchanging observations with the environment, divided into local, representing an inverse dynamical system, and external, where external observations come from. In the intervals between external observations, it exists as a conservative dynamical system. It is regarded the evolution of dynamic systems in the process of expansion and cooling of the Universe: the appearance of elementary particles and atoms, the formation of complex molecules and chain macromolecules, the appearance of living cells, the formation of multicellular organisms, the nervous system and the brain, the appearance of a human and the intellect, the development of society and civilization. With the emergence of life, open dynamic systems became distributed and perform the functions of natural selection of members of the population, and after the appearance of intelligence and the formation of society, they realize social intelligence and become virtual. Threats of uncontrolled behavior of virtual systems, in particular digital artificial intelligence systems, which can neglect the discreteness of space-time due to the use in their design of the classical model of infinitesimal, which do not exist due to the discreteness of space-time, are considered. The incompatibility of the classical model with the discrete model of an open dynamic system is an urgent scientific problem that requires further study. Figs.: 5. Refs.: 37 titles.


Sapaty P.S. Symbiosis of Distributed Simulation and Control under Spatial Grasp Technology. Mathematical machines and systems. 2020. N 3. P. 23–48. 

We are witnessing rapidly growing world dynamics caused by climate change, military, religious and ethnic conflicts, terrorism, refugee flows and weapons proliferation, political and industrial restructuring too. Dealing with frequently emerging crises may need rapid integration of scattered heterogeneous resources into capable operational forces pursuing goals which may not be known in advance. Proper understanding and managing of unpredictable and crisis situations may need their detailed simulation at runtime and even ahead of it. The current paper aims at deep integration, actually symbiosis, of advanced simulation with live system control and management, which can be effectively organized in nationwide and world scale. It will be presenting the latest version of Spatial Grasp Technology (SGT) which is not based on traditional communicating parts or agents, as usual, but rather using self-spreading, self-replicating, and self-modifying higher-level code covering and matching distributed systems at runtime while providing global integrity, goal-orientation, and finding effective solutions. These spatial solutions are often hundreds of times shorter and simpler than with other approaches due to special recursive scenario language hiding traditional system management routines inside its parallel and distributed interpretation. The paper provides basics for deep integration, actually symbiosis, of different worlds allowing us to unite advanced distributed simulation with spatial parallel and fully distributed control, while doing all this within the same high-level and very simple Spatial Grasp formalism and its basic Spatial Grasp Language (SGL). It will also mention various SGT applications including economy, ecology, space research & conquest and security, where effective symbiosis of distributed interactive simulation with live control and management may provide a real breakthrough. SGL can be quickly implemented even within standard university environments by a group of system programmers, similar to its previous versions in different countries under the author’s supervision. The technology can be installed in numerous copies worldwide and deeply integrated with any other systems, actually acquiring unlimited power throughout the world. Figs.: 35. Refs.: 62 titles.

UDC 528.06

Alpert S.I. The basic arithmetic operations on fuzzy numbers and new approaches to the theory of fuzzy numbers under the classification of space images. Mathematical machines and systems. 2020. N 3. P. 49–59.

Classification in remote sensing is a very difficult procedure, because it involves a lot of steps and data preprocessing. Fuzzy Set Theory plays a very important role in classification problems, because the fuzzy approach can capture the structure of the image. Most concepts are fuzzy in nature. Fuzzy sets allow to deal with uncertain and imprecise data. Many classification problems are formalized by using fuzzy concepts, because crisp classes represent an oversimplification of reality, leading to wrong results of classification. Fuzzy Set Theory is an important mathematical tool to process complex and fuzzy data. This theory is suitable for high resolution remote sensing image classification. Fuzzy sets and fuzzy numbers are used to determine basic probability assignment. Fuzzy numbers are used for detection of the optimal number of clusters in Fuzzy Clustering Methods. Image is modeled as a fuzzy graph, when we represent the dissimilitude between pixels in some classification tasks. Fuzzy sets are also applied in different tasks of processing digital optical images. It was noted, that fuzzy sets play an important role in analysis of results of classification, when different agreement measures between the reference data and final classification are considered. In this work arithmetic operations of fuzzy numbers using alpha-cut method were considered. Addition, subtraction, multiplication, division of fuzzy numbers and square root of fuzzy number were described in this paper. Moreover, it was illustrated examples with different arithmetic operations of fuzzy numbers. Fuzzy Set Theory and fuzzy numbers can be applied for analysis and classification of hyperspectral satellite images, solving ecological tasks, vegetation classification, in remote searching for minerals. Refs.: 11 titles.



UDC 004.7

Oksanych I.M., Grechaninov V.F., Lopushansky A.V. Information interaction in disparate information systems of situational centers. Mathematical machines and systems. 2020. N 3. P. 60–68. 

The article is devoted to the problem of information exchange between automated systems of situational centers (SC) of the government authorities of the Security and Defence Sector (SDS) of Ukraine. The problem is extremely topical today, since in the event of nationwide threats (military intervention, terrorism, emergencies), the SDS should work as a single well-coordinated mechanism. Therefore, the creation of the SC SDS system and the establishment of information exchange between them is a prerequisite for this. The paper assesses the most common types of data integration in information systems (IS), such as data warehouses, data federation and service-oriented approach. As the most modern approach to information interaction of disparate ISs, a service-oriented approach is proposed. It is noted that for data exchange it is inappropriate to get access to “other” IS and independently search for the necessary information there. Alternatively, it is proposed to isolate the data exchange subject area (SbA) from the IS subject areas of various SCs and to determine the topics necessary for the exchange. Next, for each topic, to build a thematic view of grouped, analytical data by the type of data mart. Such views will become a data source for the corresponding services in SOA and can be used in Publish/Subscribe and Request/Response modes. The paper considers a method and proposes an algorithm for the interaction of ISs of disparate SCs based on the use of the ontology of SbA data exchange and SOA. The MIP4-IES family of data exchange specifications of the NATO Multilateral Interoperability Program (MIP) is taken as an example. On the basis of legislative documents in the field of emergency response, an ontology of data exchange between the IS of the SC in response to emergency situations has been built. Examples of topics and thematic views are given that can be constructed on the basis of the constructed SbA ontology for data exchange. Tabl.: 1. Figs.: 2. Refs.: 12 titles.

 UDC 004.89

Lyakhov O.L., Cherevatenko O.V., Shostak I.V. Information system for dispatcherization of territorial municipal electric transport. Mathematical machines and systems. 2020. N 3. P. 69–79.

The paper deals with the topical problem of the large cities development – to improve the quality of service for the population by electric municipal transport and to solve this problem by informatization of the management system. Currently, various information systems are widely used to support the work of dispatch services. The paper provides an overview of such systems. It is shown that dispatchers are provided with real-time data on the technical condition and position of transport units on the route. Thus, the main means of ensuring the high-quality work of urban transport by dispatch services is the drawing up of traffic schedules based on some statistical data and heuristics, monitoring the implementation of this schedule and making decisions based on these data. At the same time, data on the current value of passenger traffic are not known and are not taken into account. Passenger traffic is a value of a complex nature, the current value of which may differ significantly from the provided traffic schedule. The paper provides data of model studies on real data (for Kharkiv city). It is shown that in large cities the probability of denied boarding can be critically high even with small deviations in occupying and intervals from the provided values by the traffic schedule. The concept of an information system is proposed, which in real time visualizes on the dispatcher’s screen not only the position, but also the degree of loading of transport units on the route. It is proposed to determine the occupancy rate of the vehicle by the power consumed by the electric motors while driving. The fundamental possibility of such approach is shown on the example of simple model. It is indicated how this model can be improved as well. It is essential for the practical implementation of the system that modern trams are equipped with all the necessary devices: a speedometer, an inclinometer, a wattmeter and GPS sensors. The basic principles of building the architecture of such an information system are given. The current data of the devices is read and sent to the server for processing. The processed data is divided into two streams. One stream is intended for online visualization of the situation on the routes on the dispatcher’s monitor. Another stream is data that is transferred to the repository for storage and further processing. Таbl.: 1. Figs.: 11. Refs.: 17 titles.

UDC 004.7

Ternavskyi V.O., Kalbazov D.Y., Lysetskyi Yu.M. Automation of the processing of emergency operations in the information and technology and infrastructure organizations. Mathematical machines and systems. 2020. N 3. P. 80–86. 

Telecommunication and internet providers manage IT infrastructures consisting of tens of thousands of various devices. Monitoring and managing such infrastructure is quite a complicated task demanding professional and coherent job from technical support teams. One of key tasks for monitoring service is prompt detection of equipment faults and quick engagement of corresponding experts to restore normal operation of equipment and systems. Corresponding tools are required to automate this process, which is quite labour-consuming. Orion CRL is offered as a tool with such functionality. It is integrated with the systems for monitoring, incident management, network management, inventories, CRM, Service Desk, IVR, contact center. It accelerates addressing critical faults giving additional opportunities for basic diagnostics. False diagnostics or mistaken incident registration leads to time losses, delays elimination of problems and distracts specialist from handling other urgent issues and tasks. To increase diagnostics efficiency there has been developed an original algorithm of analysis and search for root cause of fault; so called Root Cause Analysis (RCA). Algorithm is based on network topology analysis and faults which are detected by monitoring system such as Host Down, Host Up, Link Down. Algorithm provides for basic diagnostics, typical fault check operations on restore procedures which are typical for organization's IT infrastructure. Due to integration with monitoring system the RCA discovers root cause and symptomatic events. At the same time Orion CRL disguises faults that are symptomatic and highlights the root cause in monitoring system. The developed Orion CRL tool set increases efficiency of monitoring service. Automation of typical basic diagnostics operations and fault detection, in its turn, accelerates restoration of normal operation of equipment and saves operators’ work time. Figs.: 4. Refs.: 8 titles.

                                   SIMULATION AND MANAGEMENT

UDC (628.52.011.56:621.771.23-413):620.179.1

Ievlev M.G., Grabovsky G.G. Mathematical models of stand deformation for ACS TP for plate rolling mills. Mathematical machines and systems. 2020. N 3. P. 87–92. 

One of the most important indicators of the plate mill operation is the accuracy of implementation of the specified geometric dimensions of rolled products. To a large extent, this indicator depends on the accuracy of predicting rolling parameters using mathematical models. The mathematical model of the stand deformation, along with the rolling force model, is the most important in controlling the geometric dimensions of rolled products on thick-plate mills: thickness, width, profile and flatness of the sheet. The paper discusses the well-known methods of calculating the deformation of the stand elements, it is shown that they give significantly different results and are suitable only for a qualitative assessment of the deformation of the stand, and those of them that have sufficient accuracy are cumbersome and unsuitable for implementation in control computer used in the automation of rolling processes in real time. From the above, it follows that the most correct method for obtaining a model of stand deformation suitable for use in ACS TP is experimental. The paper considers the stand deformation model developed by the authors, obtained by conducting “active” experiments with minimal disruption of the technological process. The experimental technique provides for the redistribution of reductions between passes during rolling of various billets in the entire range of widths rolled on the mill. Another method for determining the deformation characteristics of the stand, developed by the authors, is considered and makes it possible to determine these characteristics in the process of automatic rolling control without redistributing reductions between passes. The mathematical models of the stand deformation described in the paper, developed by the authors, were used in a number of automated control systems for rolling modes on the rolling mill. Tabl.: 1. Fig.: 1. Refs.: 8 titles.

UDC 004.891.2

Kovalenko O.Ye., Kosolapov V.L. Stability model of agent-based situational control system. Mathematical machines and systems. 2020. N 3. P. 93–104.

While managing complex systems, it is advisable to use mathematical models adequate to real systems, which can be used for generalized model analysis of different solutions in systems of situational management (SSM). Such mathematical models are an important component of the SSM in the process of supporting the adoption of important strategic and operational decisions at various levels of government. Implementation of SSM in the form of a multi-agent system, due to its characteristics, is an adequate approach to solving the problems of situational management (SM). According to the context of SM, the behavior of the SSM is described as the dynamics of movement from a certain point in the phase space, that corresponds to some state of the managed system under the influence of the ensemble of SSM agents. During the operation of the SSM, its agents use knowledge that corresponds to the context of the situation. The agent's knowledge is a fragment of the field of knowledge on the target problem of SM. Knowledge of the problem area of the SM is a key element of the SM model. The convergent agents’ ensemble of SSM is characterized by a certain level of intelligence, which is represented as an entropic force that uses the free energy of the dissipative system to maintain its stability. An agent-oriented approach to the study of the stability of a dynamic stochastic system in the process of situational management as a target project activity is proposed. Within the scope of the proposed approach, the stability model of agent SSM as a dynamic stochastic system is considered using the Lyapunov stability criterion in the form of a system of ordinary differential equations. Support of modeling functions by agents of agent-oriented system allows to form adequate behavior in the process of situational management in the conditions of changes in the environment. Developed models for integrating behavioral and coordination aspects of knowledge-based agents can be used in the development of situational management systems and technologies. Fig.: 1. Refs.: 30 titles.

UDC 004.942; 04.383.4

Yakovlev Yu.S., Tymashov O.O., Yelysieva O.V., Kurzantseva L.I. A system of semi-natural modeling using Smart-technologies. Mathematical machines and systems. 2020. N 3. P. 105–114.

A new type of semi-natural modeling system is proposed. This type differs from the existing ones by the presence of a human-machine Smart interface, that maintains a comfortable environment for the user due to sensors of various functional purposes, providing opportunities for conducting experiments and other user actions, as well as a subsystem of converters and switching circuits that have its functionality, which generally improves the performance and efficiency of the system. The main components of the proposed system of semi-natural modeling and the workstation of the experimenter, as well as the block diagram of the block of converters and the switching circuit are presented. Modeling is used to study the designed automatic system in order to determine its reliability, stability, sensitivity and behavior in the event of failure of certain elements, under various, including emergency, effects. In addition, in the process of semi-natural modeling, the advantages of mathematical and natural modeling are successfully combined, and an optimal interaction between computational and natural experiments can be achieved. The use of a computer with all the attributes creates the necessary prerequisites for checking the parameters within various limits. Test verification complements the entire process that allows you to find errors in the computational process, while the content of the model adequately reflects the object itself, and the sequential (parallel) build-up of models and their processing provides the following features: reducing the time and cost of testing, increasing the reliability and survivability of the designed objects and other quality criteria typical for semi-natural modeling. Furthermore, great importance is attached to the use of systems with ring buses, which greatly increases the performance of the system due to parallelization in each sector of the ring bus. Figs.: 4. Refs.: 14 titles.

UDC 517.958:519.63

Berdnyk M.G. New finite integral transform for the Laplace equation in an arbitrary domain. Mathematical machines and systems. 2020. N 3. P. 115–124.

Reliability, survivability, as well as the optimal operating mode of operation of the supercomputer will depend on the architecture and efficiency of the cooling system of the hot components of the supercomputer. That is why the number of problems, of great theoretical and practical interest, is the problem of studying the temperature fields arising in elements of arbitrary configuration, cooling a supercomputer. To solve this class of heat conduction problems, the method of finite integral transformations turned out to be the most convenient. This article is the first to construct a new finite integral transformation for the Laplace equation in an arbitrary domain bounded by several closed piecewise-smooth contours. An inverse transformation formula is given. Finding the core of the constructed new finite integral transformation by the finite element method in the Galerkin form for simplex first-order elements reduces to solving a system of algebraic equations. To test the operability of the new integral transformation, calculations were carried out of solutions of the boundary value problem for the Laplace equation obtained using the developed new integral transformation and the well-known analytical solution. The results of
comparison the calculations of the solution of the Laplace equation are presented. In the case of a square with a side length equal to one and on one side of the square, the temperature is unity, and on the other, the temperature is zero, with a well-known analytical solution and a solution obtained using the new integral transformation. These results were obtained for 228 simplex first-order elements and 135 nodes. The maximum deviation modulo of these solutions is 0,096, the mathematical expectation of deviations is 0,009, and the variance of the type is 0,001. The developed integral transformation makes it possible to obtain a solution to complex boundary value problems of mathematical physics. Figs.: 8. Refs.: 4 titles.

UDC 519.8

Brovarets O.O., Chovniuk Yu.V. Analysis of the possibilities of self-adaptive neural networks with search behavior in agro-ecological systems. Mathematical machines and systems. 2020. N 3. P. 125–133.

The complexity of environmental problems facing modern science in connection with the deterioration of the environmental situation on the planet and the growing dynamics of ongoing processes are constantly growing (this primarily concerns agro-ecological systems). At the same time, the flexibility and accuracy of ecological models created by traditional mathematical methods, as well as the speed of their construction, in practice often does not live up to expectations. The same can be said about the engineering management of agro-ecological facilities. Among the most flexible and effective ways to solve such problems, neural network models and neurocomputers are highlighted. However, the concepts underlying the construction of modern neural network training algorithms impose serious limitations on the potential range of application of neuroinformatics achievements in solving environmental problems of agricultural systems. The number of scientific publications with radically new results is steadily decreasing and existing developments are beginning to spread across applications. The manifestation of such trends indicates that the main potential of the ideas that caused the next progress in this most important bionic direction and the creation of the 6th generation of computers neurocomputers are exhausted. Modern advances in neuroinformatics, based on the use of supervisor algorithms, are mainly associated with the possibility of using hidden layers of neurons (not connected to the input and output), which provided high adaptive capabilities of neural networks, and universality based on the ability to train a neural network to solve a precisely posed problem. In this paper, the main limitations inherent in modern approaches to limiting neural networks are indicated, and the concep of constructing a new type of training neural network and network algorithms is proposed. Some non-traditional opportunities provided by the proposed concept are described. The conceptual foundations of the development of the neuroinformation system for controlling the electrotechnical complex of the information and technical system for local operational monitoring are proposed. Figs.: 3. Refs.: 18 titles.

UDC 004.9

Malyshev O.V., Kalmykov V.G., Lysytskyi I.V. Maintenance accounting and usage of  organizational capabilities. Mathematical machines and systems. 2020. N 3. P. 134–145. 

One approach to improving an organization’s activities is an approach aimed at regulating its capabilities. This approach is applied in many fields of activity, but most extensively and consistently in the defense sphere of developed countries, NATO, and recently in Ukraine. The scale and complexity of the tasks that need to be addressed within the capability-based approach make it necessary to support these activities with appropriate tools. In this paper, we propose a conceptual model of accounting and use of capabilities. This model, the principal feature of which is the distinction between nominal and actual activity plans, has two components: static and dynamic. The static component of the model is a set of entities, relationships between them, as well as attributes of entities and relationships between entities. The main entities are capability and carrier of capability. There are nominal carriers of capabilities (exist only on paper) and actual carriers (instances of nominal carrier, for which, at a minimum, the coordinates of their location can be specified). The division into types, as well as the use of metamodels for describing capabilities and carriers of capabilities are supposed. The requirements to both the capability and the carrier of the capability can be advanced. Both actual carriers of capabilities as a whole and their (actual) capabilities are subject to assessment. Dynamic component of the model – the activity supported by the model – breaks up into accounting and use of capabilities. The model is supplemented by a component that allows to record the requirements and assessments of the capability carrier with distribution to various components of its resource (DOTMLPF-distribution). The proposed model can be used as the basis for creating the appropriate information technology. Таbl.: 1. Figs.: 5. Refs.: 21 titles.




       Last modified: Oct 27, 2020