Tag Archives: mathematical model

DEVELOPMENT OF A MATHEMATICAL MODEL OF THE PROCESS OF PROVIDING HIDDEN INFORMATION EXCHANGE IN RADIO SECURITY SYSTEMS AND A COMPUTATIONAL METHOD FOR ASSESSING THE STEALTH FOR THEM

UDC 004.94
DOI:10.26102/2310-6018/2019.27.4.022

A.A. Gavrishev


To control large areas, radio security systems are currently being used that provide information collection from radio-distributed sensors distributed throughout the facility. When a person or a foreign object enters the sensor’s coverage area, the sensor detects the occurrence of an emergency and sends an alarm signal via radio channel to the system control panel. At the same time, it is known from the literature that radio security systems themselves are subject to destructive influences aimed at disrupting their performance. In this work, the author, based on the previously proposed mathematical model and generalization of the known literature, developed a mathematical model of the process of providing hidden information exchange in radio security systems, taking into account the destabilizing effects (for example, imposing false data or suppressing interference) on the transmitted signals in the communication channel. A computational method has also been developed for assessing the stealth of information exchange in radio security systems based on fuzzy logic, the use of which under conditions of poorly structured and difficult formalizability of the source data and also in the conditions of a complex of destructive influences, can potentially help to more adequately assess the stealth of radio security systems. The results can be used to study the stealth of known and promising radio security systems. It is also possible to use the results obtained to increase the stealth of known and promising radio security systems.

Keywords: mathematical model, computational method, stealth, radio channel, radio security systems.

Full text:
Gavrishev_4_19_1.pdf

TWO-DIMENSIONAL MODEL OF STATIONARY TRANSFER OF BINARY ELECTROLYTE IN GALVANOSTATIC MODE

UDC 519.87+004.421
DOI:10.26102/2310-6018/2019.27.4.009

A.M. Uzdenova, M.Kh. Urtenov, N.O. Chubyr, A.V. Kovalenko


In electromembrane systems, the transfer of the binary electrolyte in the stationary case may be realized either in potentiostatic (PSR) (given the potential drop, ) or in galvanostatic (GSR) modes (given the average current density, ). These modes are alternative to each other. At theoretical and experimental researches it is convenient to work in GSR. However, the system of Nernst-Planck-Poisson equations (NPP) is convenient for simulating transfer in the PSR, but inconvenient for simulating in the GSR, due to the lack of an equation for the current density. Using the method of mathematical transformations from the original system of equations of the NPP transfer model to the PSR, a system of equations modeling the transfer to the GSR is obtained. The numerical analysis is given using finite element methods. In work: a new equation for the current density is obtained from the NPP by transformations; the boundary conditions required to determine the current density are derived; an algorithm for calculating the current-voltage characteristic is developed. We performed a numerical analysis of the boundary value problem and showed that there is a complete correspondence between the current-voltage characteristics (CVC) calculated in the PSR and GSR at pre-limit densities and a slight difference at exorbitant current densities. This shows the adequacy of the proposed mathematical model of transfer in galvanostatic mode and the algorithm for calculating the CVC. The paper proposes a model of transfer in the GSR, numerical analysis of the boundary value problem and shows that there is a complete correspondence between the CVC calculated in the PSR and GSR at pre-limit densities and a slight difference at exorbitant current densities. This confirms the adequacy of the proposed mathematical model of transfer in the galvanostatic mode and the algorithm for calculating the CVC. The proposed model of GSR transfer can serve as a mathematical tool for processing the results of experimental studies of GSR transfer.

Keywords: numerical methods, membrane systems, ion exchange membrane, galvanostatic mode, potentiostatic mode, mathematical model.

Full text:
UzdenovaSoavtors_4_19_1.pdf

MODEL OF PRODUCTION QUALITY CONTROL AND PREDICTION UNDER THE CONDITIONS OF A POTENTIALLY HAZARDOUS AUTOMOBILE TIRE VULCANIZATION PROCESS

UDC (681.3)
DOI:10.26102/2310-6018/2019.26.3.020

B. Yahiaoui, A.A. Mitrokhin, V.L. Burkovsky


Quality of products is one of the most important criteria of efficiency of any production. Control systems of potentially dangerous technological processes should be subject to constant development and improvement in connection with the indisputable importance of ensuring proper quality control, as potentially dangerous technological processes are complex formalized systems that operate under conditions of uncertainty, incomplete knowledge and fuzzy descriptions of both the system itself and the signals acting on it. In this paper, a potentially hazardous technological process of vulcanizing automobile tires is considered a subject of study. The paper presents a generalized structure of the control object, as well as a mathematical model of the control object, organized in the form of a set of values that describe the processes in the real system, analyzes the parameters that affect product quality. In order to improve the quality of the final product, a model for controlling and predicting the functioning of a dangerous technological process of vulcanization is proposed. The paper presents a generalized structure of the control model and the prediction of the quality of the finished product, the implementation of the model in relation to the vulcanization process.

Keywords: potentially dangerous objects, mathematical model, technological process, vulcanization.

Full text:
Yahiaoui_3_19_1.pdf

FORMALIZATION OF THE ACCESS CONTROL AUDIT PROCEDURE IN THE INFORMATION SYSTEM

UDC 004.56
DOI:10.26102/2310-6018/2019.26.3.018

V.S. Oladko


The article discusses current problems and tools for ensuring information security in information systems. The author analyzes the current trends in information security breaches in 2018-2019, concludes about the relevance of countering threats related to unauthorized access. The basic tools for protecting an information system from unauthorized access are many rights and rules for access control between objects and subjects. Therefore, to ensure the necessary level of security, the adequacy and consistency of the distribution of access rights is important. The methodology and conceptual scheme for conducting an audit of the access control subsystem based on ACL lists, consisting of procedures for initiating audits, collecting and analyzing audit data has been developed. The mathematically model of audit procedure is automation in the form of an audit software tool for the access control subsystem using the Windows operating system as an example. The main advantage of the proposed audit procedure is that it does not require complex testing procedures, calculation of probabilities, involvement and selection of experts. The main purpose of the program is to assess the compliance of the existing settings of the access control policy in the system with the security policy of the system under investigation.

Keywords: access rights, information protection, operating system, access control model, mathematical model, cybersecurity.

Full text:
Oladko_3_19_1.pdf

PREDICTION OF THE CONSEQUENCES OF THE PROPAGATION OF THE VIRUS IN A COMPUTER NETWORK USING A BASIC REPRODUCTION NUMBER

UDC 004.942
DOI:10.26102/2310-6018/2019.26.3.012

N.A. Semykina


Today, Internet is considered to be one of the most useful tools for people to communicate, find information and to buy goods and services. Most computers are connected to each other in some way. The Internet is the primary medium used by attackers to commit computer crimes. They share the same operating system software and communicate with all other computers using the standard set of protocols. This has spawned a new generation of criminals. The similarity between the spread of a biological virus and worm propagation encourages researchers to adopt an epidemic model to the network environment. This approach is most effective for describing the computer viruses propagation on the network. The article uses the results of the theory of mathematical epidemiology to analyze the SIRS model. The dynamics of the virus propagation to the computer network is described using a system of differential equations. The stability of the network to the spread of malware is investigated. An equilibrium position is found. The basic reproduction number is determined. The dependence of the virus attack evolution on the basic reproduction number is analyzed. Numerical simulations are provided to support our theoretical conclusions.

Keywords: mathematical model, computer virus, virus dynamics, basic reproduction number, nonlinear system of differential equations, stability of the system.

Full text:
Semykina_3_19_1.pdf

MATHEMATICAL MODEL TO ASSESS THE INFLUENCE OF ELECTROMAGNETIC FIELDS ON THE EMERGENCE AND DEVELOPMENT OF OCCUPATIONAL DISEASES IN THE ELECTRICITY SECTOR

UDC 615.47
doi:10.26102/2310-6018/2019.25.2.013

M. A. Myasoedova, N. A. Korenevskiy, L. V. Starodubtseva,
M. V. Pisarev


The aim of the study is to develop mathematical models for assessing the impact of electromagnetic fields of different modality and intensity on the human body providing a solution to the problems of assessing the health of people employed in the electric power industry with acceptable accuracy for medical practice.The technology of soft computing and, in particular, is chosen as the basic mathematical apparatus, the methodology of synthesis of hybrid fuzzy decision models developed in the South-West state University has proven itself in the synthesis of mathematical models of forecasting, early and differential diagnosis of diseases with a similar structure of the studied classes of States. As an example, a mathematical model for predicting the appearance and development of immune system diseases in employees of electric power enterprises of the Kursk region is described. Fuzzy mathematical models use membership functions with basic variables that take into account the intensity of the electromagnetic field of industrial frequency, work experience in the power industry and individual risk factors that provoke the appearance and development of diseases of the nervous system. In the course of mathematical modeling and expert evaluation it was shown that the use of the chosen methodology of synthesis of hybrid fuzzy mathematical models allowed to obtain a mathematical model of forecasting and development of diseases of the immune system in employees of the electric power complex with confidence exceeding 0.9.

Keywords: :mathematical model, fuzzy logic, occupational diseases, immune system, power engineering, forecasting

Full text:
MyasoedovaSoavtori_2_19_1.pdf

A MATHEMATICAL MODEL OF THE ASSESSMENT OF THE SEVERITY OF GENITAL HERPES ON THE BASIS OF FUZZY LOGIC

UDC 615.47
doi: 10.26102/2310-6018/2019.24.1.009

M.I. Lukashov, E.V Pismennaya, O.Y. Olisova, L.V. Starodubtseva, L.V. Shulga


The work is devoted to the urgent problem of improving the quality of medical care for the population suffering from genital herpes due to the timely and qualitative assessment of the severity of the disease under study. In the course of the research, a fuzzy mathematical model was obtained, which allows to distinguish four classes of patient’s conditions: patients with clinically undetectable genital herpes; patients with detected traces of herpes; patients with detected herpes; patients with clinically observed herpes. The methodology used in the synthesis of hybrid fuzzy decision rules allows to reliably separate the selected classes of States in the conditions of incomplete and fuzzy representation of the original data with a strongly overlapping structure of classes. The chosen classification system allows to rationalize the choice of treatment regimens depending on the individual condition of patients. As a result of the research it was found that the use of fuzzy logic of decision-making, can improve the quality of decision-making, according to the stages of disease by 10,…, 15% and reduce the duration of treatment by 5,…10%, which allows us to recommend the results for use in medical practice.

Keywords: : mathematical model, genital herpes, fuzzy logic of decision – making, laboratory indicators.

Full text:
LukashovSoavtori_1_19_1.pdf

MATHEMATICAL MODEL FOR SECURE INFORMATION EXCHANGE FOR WIRELESS SECURITY SYSTEMS

UDC 004.056

A.A. Gavrishev


Currently, there is a rapid increase in technical equipment and training of persons who commit illegal acts. In this regard, the number of attempts to carry out criminal attacks on objects of high importance has increased dramatically. For perimeter protection of sites of high categories of significance from unlawful attacks using different security system. A great development is a variety of security systems built on the basis of wireless communication lines. At the same time, it is known that wireless security systems themselves are subject to destructive actions aimed at disrupting their performance. Protection against unauthorized access of alarm and service messages in security systems when they are transmitted over a wireless communication channel is an urgent task. One of the main technologies to protect the radio channel of security systems from unauthorized access is the use of noise-like signals. A promising technology for improving the security of information exchange based on noise-like signals is the use of chaotic signals. However, there are very few algorithms for secure information exchange based on chaotic signals for wireless security systems. One of the known algorithms of protected information exchange based on chaotic signals is presented. It is noted that there is no formalized mathematical description of this algorithm of protected information exchange, which allows to understand more clearly the process of its functioning, in the known literature. In this regard, the author, partly on the basis of the well-known literature, for this algorithm of secure information exchange developed a mathematical model, an explanatory block diagram of the developed mathematical model. With the help of a well-known algorithm of secure information exchange and a mathematical model developed on its basis, it is potentially possible to increase the security of transmitted messages from unauthorized access to various wireless security systems. Also, the proposed example on the mathematical description of the algorithm of secure information exchange, due to its simplicity, may be extended to a wider class of algorithms for secure information exchange.

Keywords: : mathematical model, radio channel, security systems, security, information exchange.

Full text:
Gavrishev_4_18_1.pdf

MATHEMATICAL MODELS OF THE CHOICE OF THE PATTERNS OF PREVENTION OF THE RECURRENCE OF GANGRENE OF THE LOWER LIMBS

UDC 615.47

A.V. Bykov, N.A. Korenevsky, S.A. Parkhomenko, A.V. Boytsov, E.V. Cymbal, L.V. Starodubtseva


The work is devoted to the actual problem of improving the quality of care for patients suffering from critical ischemia of the lower extremities, turning into gangrene, which may result in amputation and even death. In the course of the research it was shown that the task of predicting the recurrence of lower extremity gangrene belongs to the class of poor results, which was the basis for choosing the method of synthesis of hybrid fuzzy decision rules as the basic method for studying the methodological synthesis. During the synthesis of fuzzy decision rules, the choice of informative features obtained during surveys and inspections, instrumental and laboratory research methods was justified. As the basic elements of fuzzy decision rules applied to a class of high risk of gangrene recurrence, which are aggregated into a fuzzy rule for assessing the confidence that the patient will have a relapse of the lower extremities. : Scale of confidence in the development of gangrene: – confidence in the recurrence of gangrene; II-medium confidence in the recurrence of gangrene; III – high confidence in the recurrence of gangrene; IV – very high confidence in the recurrence of gangrene. The classification decision is made based on the maximum value of the prediction functions. For each of the selected classes, the appropriate scheme for the prevention of lower extremity gangrene recurrence, whose effectiveness was tested using measurement theory, as well as the analyzed mathematical model of their choice depending on the degree of lower extremity gangrene recurrence. In the course of statistical tests, it was shown that, compared with traditional schemes to prevent the use of the proposed technologies, increase the rate of positive results by 2.4 times (58%) and reduce the risk of limb amputation by 2.5 times (73%). The results obtained guarantee the proposed mathematical models for use in the practice of vascular surgeons and angiologists.

 

Keywords: : gangrene, lower limbs, prediction, mathematical model, fuzzy logic, prevention, model G. Rush.

Full text:
BykovSoavtors_4_18_1.pdf

FORECASTING OF THE GENERATION OF THE LOWER LIMBS ON THE BASIS OF HYBRID FUZZY MODELS

UDC 616.31

N.A. Korenevskiy, T.I. Subbotina, I.I. Khripina, S.A. Parkhomenko,
S.N. Rodionova


The work is devoted to the urgent problem of improving the quality of care for patients suffering from critical ischemia of the lower limbs, passing into gangrene, which can result in amputation and even death. In the course of the studies, it was shown that the task of predicting the origin and development of gangrene of the lower limbs belongs to the class of poorly formalizable problems with an indistinct data structure, which served as the basis for choosing as a basic research apparatus the methodology for the synthesis of hybrid fuzzy decision rules. During the synthesis of fuzzy decisive rules, the selection of informative signs obtained during surveys and examinations, instrumental and laboratory methods of investigation was justified. As the basic elements of fuzzy decision rules, the functions of belonging to the class of high risk of gangrene development are obtained, which are aggregated into an unclear rule of confidence assessment that the patient will develop gangrene of the lower limbs. On a scale of confidence in the development of gangrene, experts determined the secondary functions of belonging to such predictable classes of patient conditions as: I – low confidence in gangrene development; II – moderate confidence in the development of gangrene; III – high confidence in the development of gangrene; IV – very high confidence in the development of gangrene. The decision to classify is taken based on the maximum value of prognostic membership functions.The performed mathematical modeling and expert evaluation of the fuzzy models obtained showed that their predictive confidence is at least 0.9. The same quality of forecasting was confirmed during statistical tests on control samples of 100 persons per class for such indicators as diagnostic specificity, sensitivity and efficiency, as well as prognostic significance of positive and negative results.
The results obtained make it possible to recommend the proposed mathematical models for use in the practice of cardiovascular surgeons and angiologists.

Keywords: : gangrene, lower extremities, prediction, mathematical model, fuzzy logic.

Full text:
KorenevskiySoavtori_4_18_1.pdf