Pub Date : 2022-12-06DOI: 10.32626/2308-5916.2022-23.31-36
A. Verlan, Jo Sterten
Over the last decades there has been substantial progress on the development of theory and numerical methods for singular systems (known also as descriptor systems, semistate systems, differential alge-braic systems, generalized state-space systems, etc.). The need for such methodsarisen primarily from the increased practical interest for a more general system description which takes the intrinsic physical sys-tem model structure into account. Besides that, many physical process-es are most naturally and easily modelled as mixed systems of differen-tial and algebraic equations (DAE). As the title implies the paper de-scribes the singular systems theory application in power systems dy-namics simulation, particularly considered an alternative method for energy systems’ mathematical models formulation based on the singu-lar systems theory elements with some indicative examples illustrating feasibility and efficiency of this approach
{"title":"Approach to Energy Objects’ Dynamics Modelling Based on Singular Systems’ Elements","authors":"A. Verlan, Jo Sterten","doi":"10.32626/2308-5916.2022-23.31-36","DOIUrl":"https://doi.org/10.32626/2308-5916.2022-23.31-36","url":null,"abstract":"Over the last decades there has been substantial progress on the development of theory and numerical methods for singular systems (known also as descriptor systems, semistate systems, differential alge-braic systems, generalized state-space systems, etc.). The need for such methodsarisen primarily from the increased practical interest for a more general system description which takes the intrinsic physical sys-tem model structure into account. Besides that, many physical process-es are most naturally and easily modelled as mixed systems of differen-tial and algebraic equations (DAE). As the title implies the paper de-scribes the singular systems theory application in power systems dy-namics simulation, particularly considered an alternative method for energy systems’ mathematical models formulation based on the singu-lar systems theory elements with some indicative examples illustrating feasibility and efficiency of this approach","PeriodicalId":375537,"journal":{"name":"Mathematical and computer modelling. Series: Technical sciences","volume":"159 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115690919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.32626/2308-5916.2022-23.5-19
Serhii Baranovsky, A. Bomba
A number of very different mathematical models are used to predict the response of the immune system to pathogenic microorganisms detected in the body and the corresponding course of viral disease. Usually,such models are based on the assumption that the body is a homogeneous envi-ronment in which all factors are evenly distributed.The article presents a generalized discrete model of Marchuk's infectious disease for the complex accounting of small diffusion «redistributions», con-centrated effects and the body's temperature response. The introduction of such additional terms into the basic model significantly complicates the orig-inal problem and aggravates the problem of constructing efficient algorithms for the numerical solution of such systems of differential equations with de-lays. It is noted that as a result of discretization of the original model problem using an implicit scheme, a nonlinear system of equations is obtained, the so-lution of which must be sought at each time step by iterations. Thus, the use of the corresponding classical Runge-Kutta schemes is very uneconomical from the point of view of calculations.The authors propose a step-by-step procedure for numerically asymp-totic approximation of the solution of the corresponding singularly per-turbed discrete problem with delay, which allows to combine the ad-vantages of implicit schemes and the cost-effectiveness of explicit schemes. The results of computer simulations are presented, which illus-trate the influence of diffuse «scattering»of antigens, delays and concen-trated sources of antigens on the nature of the infectious disease. It is em-phasized that the complex action of these factors can lead to a reduction of the initially supercritical concentration of antigens to a more acceptable level, which is important in forming a rational program of decision-making on the use of external «therapeutic»effects.
{"title":"Step by Step Perturbation of Discrete Models of Immunology","authors":"Serhii Baranovsky, A. Bomba","doi":"10.32626/2308-5916.2022-23.5-19","DOIUrl":"https://doi.org/10.32626/2308-5916.2022-23.5-19","url":null,"abstract":"A number of very different mathematical models are used to predict the response of the immune system to pathogenic microorganisms detected in the body and the corresponding course of viral disease. Usually,such models are based on the assumption that the body is a homogeneous envi-ronment in which all factors are evenly distributed.The article presents a generalized discrete model of Marchuk's infectious disease for the complex accounting of small diffusion «redistributions», con-centrated effects and the body's temperature response. The introduction of such additional terms into the basic model significantly complicates the orig-inal problem and aggravates the problem of constructing efficient algorithms for the numerical solution of such systems of differential equations with de-lays. It is noted that as a result of discretization of the original model problem using an implicit scheme, a nonlinear system of equations is obtained, the so-lution of which must be sought at each time step by iterations. Thus, the use of the corresponding classical Runge-Kutta schemes is very uneconomical from the point of view of calculations.The authors propose a step-by-step procedure for numerically asymp-totic approximation of the solution of the corresponding singularly per-turbed discrete problem with delay, which allows to combine the ad-vantages of implicit schemes and the cost-effectiveness of explicit schemes. The results of computer simulations are presented, which illus-trate the influence of diffuse «scattering»of antigens, delays and concen-trated sources of antigens on the nature of the infectious disease. It is em-phasized that the complex action of these factors can lead to a reduction of the initially supercritical concentration of antigens to a more acceptable level, which is important in forming a rational program of decision-making on the use of external «therapeutic»effects.","PeriodicalId":375537,"journal":{"name":"Mathematical and computer modelling. Series: Technical sciences","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114629688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.32626/2308-5916.2022-23.91-106
V. Pavlenko, Tetyana Shamanina, Vladyslav Chori
The information technology of biometric identification of a person has re-ceived further development due to the use as a source of primary data of infor-mation models of the oculo-motor system (OMS) of the «input-output» type based on the Volterra series. Eye-tracking technology is used to build models. Experimental studies of the OMS of two respondents were carried out. Based on the data obtained with the Tobii Pro TX300 eye-tracker, the transient func-tions of the first, second and third orders of the OMS when applying the Volter-ra series model were determined. This makes it possible to increase the accura-cy of OMS modeling and, as a result, to increase the reliability of recognition in the space of the proposed heuristic features, which are determined using inte-gral and differential transformations of multidimensional transient functions of OMS, which greatly simplifies the identification of features and the practical implementation of the Bayesian classifier.A high variability of the transient functions of the second and third or-ders for two respondents was revealed. Thus, it seems appropriate to use multidimensional transient functions for biometric identification.A set of heuristic features are proposed, which are determined on the basis of multidimensional transient functions obtained from eye-tracking data. The informativeness of individual features and their combinations in pairswas investigated. Two-dimensional feature spaces with the maximum value of the probability of correct recognition indicator when solving the problem of biometric identification of a person were found (Pmax=0.974). The research results were obtained using the construction of Bayesian clas-sifiers in different spaces of the proposed features by means of machine learning based on the data of the formed trainingsamples
由于使用基于Volterra系列的“输入-输出”型眼动系统(OMS)信息模型作为主要数据来源，人体生物特征识别的信息技术得到了进一步发展。眼球追踪技术被用来建立模型。对两名被调查者的OMS进行了实验研究。基于Tobii Pro TX300眼动仪获得的数据，确定了应用Volter-ra系列模型时，OMS的一、二、三阶瞬态功能。这使得提高OMS建模的准确性成为可能，从而提高在所提出的启发式特征空间中识别的可靠性，这些特征是使用OMS的多维瞬态函数的积分和微分变换确定的，这大大简化了特征的识别和贝叶斯分类器的实际实现。一个高变异性的瞬态函数的第二个和第三个或两个受访者被揭示。因此，使用多维瞬态函数进行生物识别似乎是合适的。提出了一组启发式特征，该特征是基于眼动追踪数据获得的多维瞬态函数确定的。研究了个体特征及其成对组合的信息量。找到了解决人的生物特征识别问题时，识别指标正确概率最大的二维特征空间(Pmax=0.974)。基于形成的训练样本数据，通过机器学习在所提出的特征的不同空间中构造贝叶斯分类器，获得研究结果
{"title":"Identification of the Human Oculo-Motor System Based on the Volterra Series: Application in the Information Security System","authors":"V. Pavlenko, Tetyana Shamanina, Vladyslav Chori","doi":"10.32626/2308-5916.2022-23.91-106","DOIUrl":"https://doi.org/10.32626/2308-5916.2022-23.91-106","url":null,"abstract":"The information technology of biometric identification of a person has re-ceived further development due to the use as a source of primary data of infor-mation models of the oculo-motor system (OMS) of the «input-output» type based on the Volterra series. Eye-tracking technology is used to build models. Experimental studies of the OMS of two respondents were carried out. Based on the data obtained with the Tobii Pro TX300 eye-tracker, the transient func-tions of the first, second and third orders of the OMS when applying the Volter-ra series model were determined. This makes it possible to increase the accura-cy of OMS modeling and, as a result, to increase the reliability of recognition in the space of the proposed heuristic features, which are determined using inte-gral and differential transformations of multidimensional transient functions of OMS, which greatly simplifies the identification of features and the practical implementation of the Bayesian classifier.A high variability of the transient functions of the second and third or-ders for two respondents was revealed. Thus, it seems appropriate to use multidimensional transient functions for biometric identification.A set of heuristic features are proposed, which are determined on the basis of multidimensional transient functions obtained from eye-tracking data. The informativeness of individual features and their combinations in pairswas investigated. Two-dimensional feature spaces with the maximum value of the probability of correct recognition indicator when solving the problem of biometric identification of a person were found (Pmax=0.974). The research results were obtained using the construction of Bayesian clas-sifiers in different spaces of the proposed features by means of machine learning based on the data of the formed trainingsamples","PeriodicalId":375537,"journal":{"name":"Mathematical and computer modelling. Series: Technical sciences","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128936084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.32626/2308-5916.2022-23.45-55
K. Klyuchka, A. Verlan, Lidiya Mitʹko, V. Fedorchuk, Jo Sterten
The article proposes an approach to solving actual problem of the obtained results’ control in the construction and implementation of al-gorithms for identifying energy objects based on integral dynamic models. The considered method based on the use of quadrature algo-rithms and splines for approximation of the kernel, with the transition to solving equations with a degenerate kernel using recurrent formulas, showed sufficiently high efficiency in solving the problems of obtain-ing high performance at provided control over the accuracy of the inte-gral dynamic model parameters’ calculation, as well as providing re-sistance to the experimental data errors. The proposed method makes it possible to solve the problem of accumulating calculations, which, in turn, leads the numerical implementation algorithm to a form in which it is feasible to obtain solutions in real-time. The obtained integrated models have a sufficient level of adequacy and can be usedin integrat-ed computing control systems for energy objects
{"title":"On the Control of Numerical Results in the Problems of Identification of Dynamic Energy Objects","authors":"K. Klyuchka, A. Verlan, Lidiya Mitʹko, V. Fedorchuk, Jo Sterten","doi":"10.32626/2308-5916.2022-23.45-55","DOIUrl":"https://doi.org/10.32626/2308-5916.2022-23.45-55","url":null,"abstract":"The article proposes an approach to solving actual problem of the obtained results’ control in the construction and implementation of al-gorithms for identifying energy objects based on integral dynamic models. The considered method based on the use of quadrature algo-rithms and splines for approximation of the kernel, with the transition to solving equations with a degenerate kernel using recurrent formulas, showed sufficiently high efficiency in solving the problems of obtain-ing high performance at provided control over the accuracy of the inte-gral dynamic model parameters’ calculation, as well as providing re-sistance to the experimental data errors. The proposed method makes it possible to solve the problem of accumulating calculations, which, in turn, leads the numerical implementation algorithm to a form in which it is feasible to obtain solutions in real-time. The obtained integrated models have a sufficient level of adequacy and can be usedin integrat-ed computing control systems for energy objects","PeriodicalId":375537,"journal":{"name":"Mathematical and computer modelling. Series: Technical sciences","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115487932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.32626/2308-5916.2022-23.36-44
A. Demchyshyn, Ganna Smakovska
The article analyzes membrane (awning) structures, which become relevant due to their cost-effectiveness and the creation of original forms. The characteristics of awning structures, the possibilities of molding, the use of various materials and combined options for com-bining an awning with other materials are considered. Due to their cost-effectiveness, tent structures are becoming increasingly popular today, because in modern socio-economic conditions there is a need for the rapid construction of low-cost buildings to overcome the shortage of mobile housing and structures for other purposes. In the conditions of restoration of the lost objects of buildings and structures, the use of tent coverings is important. Their development was held back for a long time due to the non-compliance of domestic tent materials with the high requirements for tent coverings of this type, namely: strength, durability, color diversity, light fastness, etc. The use of hinged struc-tures allows you to create small architectural forms and mobile build-ingsthat are not only quickly erected, but also easilytransformed in accordance with a change in functionality. This allows you to create new types of objects, such as stadiums, airports, giant greenhouses, bo-tanical gardens, warehouses, etc. Modern technologies combine the advantages of industrial construction methods with the individualiza-tion of form and open the way to the use of various awning structures. Membrane coatings, as one of the modern trends in the presentation of a new form of roofing, create new spatial characteristics of architectur-al objects. They form expanses freed from bulky internal structures. The freedom of space determines the flexibility and functionality of its use, a high degree of adaptation and, as a result, the durability of the space and structure. Having a wide variety of forms, this type of coat-ing has broad prospects for use along with other architectural and struc-tural systems. To ensure such characteristics, the article proposes an in-formation model of the proportionality of the elements of the architec-tural form, established on the basis of the information modularity of the relations of the elements for the volumetric structure.
{"title":"Research of Geometric and Information Models for Awning Structures","authors":"A. Demchyshyn, Ganna Smakovska","doi":"10.32626/2308-5916.2022-23.36-44","DOIUrl":"https://doi.org/10.32626/2308-5916.2022-23.36-44","url":null,"abstract":"The article analyzes membrane (awning) structures, which become relevant due to their cost-effectiveness and the creation of original forms. The characteristics of awning structures, the possibilities of molding, the use of various materials and combined options for com-bining an awning with other materials are considered. Due to their cost-effectiveness, tent structures are becoming increasingly popular today, because in modern socio-economic conditions there is a need for the rapid construction of low-cost buildings to overcome the shortage of mobile housing and structures for other purposes. In the conditions of restoration of the lost objects of buildings and structures, the use of tent coverings is important. Their development was held back for a long time due to the non-compliance of domestic tent materials with the high requirements for tent coverings of this type, namely: strength, durability, color diversity, light fastness, etc. The use of hinged struc-tures allows you to create small architectural forms and mobile build-ingsthat are not only quickly erected, but also easilytransformed in accordance with a change in functionality. This allows you to create new types of objects, such as stadiums, airports, giant greenhouses, bo-tanical gardens, warehouses, etc. Modern technologies combine the advantages of industrial construction methods with the individualiza-tion of form and open the way to the use of various awning structures. Membrane coatings, as one of the modern trends in the presentation of a new form of roofing, create new spatial characteristics of architectur-al objects. They form expanses freed from bulky internal structures. The freedom of space determines the flexibility and functionality of its use, a high degree of adaptation and, as a result, the durability of the space and structure. Having a wide variety of forms, this type of coat-ing has broad prospects for use along with other architectural and struc-tural systems. To ensure such characteristics, the article proposes an in-formation model of the proportionality of the elements of the architec-tural form, established on the basis of the information modularity of the relations of the elements for the volumetric structure.","PeriodicalId":375537,"journal":{"name":"Mathematical and computer modelling. Series: Technical sciences","volume":"130 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128496604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.32626/2308-5916.2022-23.116-129
A. Prokofiev
One of the main qualitative indicators of computing tools is the accura-cy of the results of solving applied problems by them, in particular, prob-lems of modeling and control of dynamic systems. However, despite the widespread use of computer technology (CT), the problem of assessing the accuracy of calculations cannot be considered solved, and its relevance is growing due to the rapid development and spread of cybernetic tools for various purposes. The severity of the problem lies in the complexity of the analysis of calculation errors, which leads to the cumbersomeness of ana-lytical justifications and the large volume of calculations required to obtain specific numerical data.To solve many technical and research problems, both universal and specialized OT tools are widely used. The characteristic difference of the latter from universal tools of OT is a deliberately narrow class of algo-rithms that are implemented, oriented (class) to solving a limited range of applied problems. At the same time, it is naturally expected to achieve a number of certain (compared to universal OT tools) advantages, which usually include one or a group of factors, such as:increased speed, a non-analytical method of solving problems (for analog specialized OT tools), reduced mass-dimensional characteristics and cost, etc. It should be noted that the problem of accuracy is relevant for both universal and specialized OT tools, being somewhat transformed, depending on the type of tool and the principle of its action, for example, the originality of primary errors.
{"title":"The Method of Precision Calibration in the Implementation of Mathematical Models of Dynamic Systems in Modeling and Control Problems","authors":"A. Prokofiev","doi":"10.32626/2308-5916.2022-23.116-129","DOIUrl":"https://doi.org/10.32626/2308-5916.2022-23.116-129","url":null,"abstract":"One of the main qualitative indicators of computing tools is the accura-cy of the results of solving applied problems by them, in particular, prob-lems of modeling and control of dynamic systems. However, despite the widespread use of computer technology (CT), the problem of assessing the accuracy of calculations cannot be considered solved, and its relevance is growing due to the rapid development and spread of cybernetic tools for various purposes. The severity of the problem lies in the complexity of the analysis of calculation errors, which leads to the cumbersomeness of ana-lytical justifications and the large volume of calculations required to obtain specific numerical data.To solve many technical and research problems, both universal and specialized OT tools are widely used. The characteristic difference of the latter from universal tools of OT is a deliberately narrow class of algo-rithms that are implemented, oriented (class) to solving a limited range of applied problems. At the same time, it is naturally expected to achieve a number of certain (compared to universal OT tools) advantages, which usually include one or a group of factors, such as:increased speed, a non-analytical method of solving problems (for analog specialized OT tools), reduced mass-dimensional characteristics and cost, etc. It should be noted that the problem of accuracy is relevant for both universal and specialized OT tools, being somewhat transformed, depending on the type of tool and the principle of its action, for example, the originality of primary errors.","PeriodicalId":375537,"journal":{"name":"Mathematical and computer modelling. Series: Technical sciences","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126454192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.32626/2308-5916.2022-23.55-72
A. Kobozieva, D. Maevsky, Olena Simonova
One of the most common representations of information today are digi-tal images, unauthorized changes of which can lead to negative conse-quences for an individual, institution, firm, and the state as a whole, which makes the detection of digital image integrity violation one of the most ur-gent tasks of information security. The main drawback of the existing ex-pert methods is their focus on detecting the results of a specific disruptive action, but in practice the expert often does not have information about the specifics of an attack on a digital image, while his set of tools is always limited, which can lead to a situation where the investigated digital image is erroneously recognized as original. The first «defense line» here should be methods that are effective regardless of the type of disruptiveaction, i.e. universal. At present, there are a very small number of such methods in open sources; most of them are not free from shortcomings, the main of which is a significant decrease in efficiency in conditions of minor disturb-ances. The aim of the paper is to develop a theoretical basis for an effective universal method of detection of digital image integrity violation, in par-ticular, in conditions of minor disturbances. In the course of achieving the aim of the paper: the justified expediency of using a block approach when organizing an examination of the integrity of a digital image; the area of discrete cosine transformation (DCP) of the block is chosen as the area of examination; justified selection of specific DCP coefficients for organizing the detection of violations of the integrity of digital images, the values of which do not depend on the value of the quality coefficient used when ob-taining the original image, as well as on the specific type of digital images; the difference in the nature ofchanges in the selected formal parameters during re-saving of lossy digital images, depending on whether it is origi-nal or non-original, is investigated. The obtained results of theoretical stud-ies, which are confirmed by the results of computational experiments, con-stitute the theoretical basis for the development of an effective universal method of examination of the integrity of digital images, in particular, in conditions of minor disturbances.
{"title":"Investigation of the Properties of the Coefficients of the Discrete Cosine Transformation as the Basis of the Method of Detection of Digital Image Integrity Violation","authors":"A. Kobozieva, D. Maevsky, Olena Simonova","doi":"10.32626/2308-5916.2022-23.55-72","DOIUrl":"https://doi.org/10.32626/2308-5916.2022-23.55-72","url":null,"abstract":"One of the most common representations of information today are digi-tal images, unauthorized changes of which can lead to negative conse-quences for an individual, institution, firm, and the state as a whole, which makes the detection of digital image integrity violation one of the most ur-gent tasks of information security. The main drawback of the existing ex-pert methods is their focus on detecting the results of a specific disruptive action, but in practice the expert often does not have information about the specifics of an attack on a digital image, while his set of tools is always limited, which can lead to a situation where the investigated digital image is erroneously recognized as original. The first «defense line» here should be methods that are effective regardless of the type of disruptiveaction, i.e. universal. At present, there are a very small number of such methods in open sources; most of them are not free from shortcomings, the main of which is a significant decrease in efficiency in conditions of minor disturb-ances. The aim of the paper is to develop a theoretical basis for an effective universal method of detection of digital image integrity violation, in par-ticular, in conditions of minor disturbances. In the course of achieving the aim of the paper: the justified expediency of using a block approach when organizing an examination of the integrity of a digital image; the area of discrete cosine transformation (DCP) of the block is chosen as the area of examination; justified selection of specific DCP coefficients for organizing the detection of violations of the integrity of digital images, the values of which do not depend on the value of the quality coefficient used when ob-taining the original image, as well as on the specific type of digital images; the difference in the nature ofchanges in the selected formal parameters during re-saving of lossy digital images, depending on whether it is origi-nal or non-original, is investigated. The obtained results of theoretical stud-ies, which are confirmed by the results of computational experiments, con-stitute the theoretical basis for the development of an effective universal method of examination of the integrity of digital images, in particular, in conditions of minor disturbances.","PeriodicalId":375537,"journal":{"name":"Mathematical and computer modelling. Series: Technical sciences","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121813965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.32626/2308-5916.2022-23.83-90
Dmytro Myroniuk, B. Blagitko, Ihor Zaiachuk
Modern object detection methods in the image recognition process us-ing transformer technology are analyzed.The various methods advantages and disadvantages are identified. An own network was created based on the DETR transformer from the FAIR team, and its operation was analyzed. A comparison of the transformer networks perfor-mance with optimized architectures of convolutional neural networks is made.The cloud computing tools, graphics processors, Internet of Things clusters or embedded microprocessor systems were used in the research process.To ensure high object detector accuracy and real-time detection results on different types of devices, an efficient object detector and model scaling technique are required.The transformer model learning is illustrated step-by-step process.
{"title":"Object Detection in the Image Recognition Process Using Transformers","authors":"Dmytro Myroniuk, B. Blagitko, Ihor Zaiachuk","doi":"10.32626/2308-5916.2022-23.83-90","DOIUrl":"https://doi.org/10.32626/2308-5916.2022-23.83-90","url":null,"abstract":"Modern object detection methods in the image recognition process us-ing transformer technology are analyzed.The various methods advantages and disadvantages are identified. An own network was created based on the DETR transformer from the FAIR team, and its operation was analyzed. A comparison of the transformer networks perfor-mance with optimized architectures of convolutional neural networks is made.The cloud computing tools, graphics processors, Internet of Things clusters or embedded microprocessor systems were used in the research process.To ensure high object detector accuracy and real-time detection results on different types of devices, an efficient object detector and model scaling technique are required.The transformer model learning is illustrated step-by-step process.","PeriodicalId":375537,"journal":{"name":"Mathematical and computer modelling. Series: Technical sciences","volume":"188 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116105153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.32626/2308-5916.2022-23.73-82
A. Kunynets, R. Pelekh
One of the modern scientific methods of researching phenomena and pro-cesses is mathematical modeling, which in many cases allows replacing the real process and makes it possible to obtain both a qualitative and a quantitative pic-ture of the process. Since the exact solutions of such models can be found in very individual cases, it is necessary to use approximate methods. In applied mathematics, fractional-rational approximations, which under appropriate con-ditions give a high rate of convergence of algorithms, bilateral and monotonic approximations have become widely used.In this work, using the technique of constructing one-step methods for solv-ing the initial problem for ordinary differential equations and developing the sought solution into a finite continued fraction, a numerical method for solving the Cauchy problem for nonlinear integro-differential equations of the Volterra type is proposed. The values of the parameters at which the nonlinear method of the first and second order of accuracy is obtained are found.Computational formulas are proposed, which at each integration step allow obtaining an upper and lower approximation to the exact solution without additional references to the right-hand side of the integro-differential equation. Calculation formulas, in which the main terms of the local error differ only in sign, form a two-sided method. We take the half-sum of bilateral approximations to the exact solution as the approximate solution at the given integration point, and the absolute value of the half-difference determines the error of the obtained result.The modular nature of the proposed algorithms makes it possible to ob-tain several approximations to the exact solution of the initial problem for the nonlinear integro-differential equation at each point of integration. The comparison of these approximations gives useful information in the matter of choosing the integration step or in assessing the accuracy of the result
{"title":"Methods of Solving the Initial Value Problem for Nonlinear Integro-Differential Equations with Local Error Estimation","authors":"A. Kunynets, R. Pelekh","doi":"10.32626/2308-5916.2022-23.73-82","DOIUrl":"https://doi.org/10.32626/2308-5916.2022-23.73-82","url":null,"abstract":"One of the modern scientific methods of researching phenomena and pro-cesses is mathematical modeling, which in many cases allows replacing the real process and makes it possible to obtain both a qualitative and a quantitative pic-ture of the process. Since the exact solutions of such models can be found in very individual cases, it is necessary to use approximate methods. In applied mathematics, fractional-rational approximations, which under appropriate con-ditions give a high rate of convergence of algorithms, bilateral and monotonic approximations have become widely used.In this work, using the technique of constructing one-step methods for solv-ing the initial problem for ordinary differential equations and developing the sought solution into a finite continued fraction, a numerical method for solving the Cauchy problem for nonlinear integro-differential equations of the Volterra type is proposed. The values of the parameters at which the nonlinear method of the first and second order of accuracy is obtained are found.Computational formulas are proposed, which at each integration step allow obtaining an upper and lower approximation to the exact solution without additional references to the right-hand side of the integro-differential equation. Calculation formulas, in which the main terms of the local error differ only in sign, form a two-sided method. We take the half-sum of bilateral approximations to the exact solution as the approximate solution at the given integration point, and the absolute value of the half-difference determines the error of the obtained result.The modular nature of the proposed algorithms makes it possible to ob-tain several approximations to the exact solution of the initial problem for the nonlinear integro-differential equation at each point of integration. The comparison of these approximations gives useful information in the matter of choosing the integration step or in assessing the accuracy of the result","PeriodicalId":375537,"journal":{"name":"Mathematical and computer modelling. Series: Technical sciences","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124271944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-06DOI: 10.32626/2308-5916.2022-23.107-115
Serhii Polozhaenko, F. Garaschenko, L. Prokofieva
Theorems of existence and uniqueness of the decision of system of the equations in the private derivatives, representing the generalized mathematical model of processes and devices of preprocessing of crude hydrocarbons are formulated and proved. Generalization gives the chance to apply the principle of unification and typification when de-veloping a method of numerical realization of mathematical models of a class of processes (devices) of preprocessing of crude hydrocarbons, and the proof of the corresponding theorems (an essence —the qua-litative analysis) provides a correctness of application of the generalized model in applied problems of mathematical modeling of studied pro-cesses (devices). Proofs of the formulated theorems are strict, logically true and are consistently executed within terms of the functional ana-lysis. Practical applicability of theorems of existence and uniqueness of the decision as component of the qualitative analysis, is defined by pos-sibility of research on their basis of adequacy of algorithmic means of mathematical modeling of a studied class of processes (devices).
{"title":"Mathematical Models of Technological Processes of Oil Refining and Their Qualitative Analysis Based on the General Concept Of Models","authors":"Serhii Polozhaenko, F. Garaschenko, L. Prokofieva","doi":"10.32626/2308-5916.2022-23.107-115","DOIUrl":"https://doi.org/10.32626/2308-5916.2022-23.107-115","url":null,"abstract":"Theorems of existence and uniqueness of the decision of system of the equations in the private derivatives, representing the generalized mathematical model of processes and devices of preprocessing of crude hydrocarbons are formulated and proved. Generalization gives the chance to apply the principle of unification and typification when de-veloping a method of numerical realization of mathematical models of a class of processes (devices) of preprocessing of crude hydrocarbons, and the proof of the corresponding theorems (an essence —the qua-litative analysis) provides a correctness of application of the generalized model in applied problems of mathematical modeling of studied pro-cesses (devices). Proofs of the formulated theorems are strict, logically true and are consistently executed within terms of the functional ana-lysis. Practical applicability of theorems of existence and uniqueness of the decision as component of the qualitative analysis, is defined by pos-sibility of research on their basis of adequacy of algorithmic means of mathematical modeling of a studied class of processes (devices).","PeriodicalId":375537,"journal":{"name":"Mathematical and computer modelling. Series: Technical sciences","volume":"45 24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115398447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：