APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19最新文献

{"title":"Strong topology on the set of persistence diagrams","authors":"V. Kiosak, A. Savchenko, M. Zarichnyi","doi":"10.1063/1.5130798","DOIUrl":"https://doi.org/10.1063/1.5130798","url":null,"abstract":"We endow the set of persistence diagrams with the strong topology (the topology of countable direct limit of increasing sequence of bounded subsets considered in the bottleneck distance). The topology of the obtained space is described. \u0000Also, we prove that the space of persistence diagrams with the bottleneck metric has infinite asymptotic dimension in the sense of Gromov.","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121865323","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}

{"title":"On the approximation of estimation problems for controlled systems","authors":"B. Ananyev, P. A. Yurovskih","doi":"10.1063/1.5130846","DOIUrl":"https://doi.org/10.1063/1.5130846","url":null,"abstract":"","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125370211","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}

{"title":"On the stability of a steady convective flow due to nonlinear heat sources in a magnetic field","authors":"A. Kolyshkin, V. Koliškina","doi":"10.1063/1.5130832","DOIUrl":"https://doi.org/10.1063/1.5130832","url":null,"abstract":"Consider a layer of a viscous incompressible fluid bounded by two vertical planes. There exists a steady flow in the vertical layer caused by internal heat generation. The heat sources are distributed within the fluid in accordance with the Arrhenius law. A magnetic field of constant strength is applied in the direction perpendicular to the planes. The flow is characterized by four dimensionless parameters: the Grashof number, the Prandtl number, the Hartmann number and the Frank-Kamenetsky parameter. This problem is important in applications such as biomass thermal conversion. The objective of the study is to determine the factors that enhance mixing and lead to more efficient energy conversion. The problem is described by a system of magnetohydrodynamic equations under the Boussinesq approximation. The nonlinear system of ordinary differential equations describing the steady flow is solved numerically. Linear stability of the steady flow is investigated using the method of normal modes. The corresponding linear stability problem is solved numerically by means of a collocation method. The solution is found for different values of the parameters characterizing the problem. It is found that the increase of the Frank-Kamenetsky parameter destabilizes the flow. On the other hand, the increase of the Hartmann number stabilizes the flow.","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114910825","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}

{"title":"Machine learning based EEG classification by diagnosis: Approach to EEG morphological feature extraction","authors":"A. V. M. Misiunas, T. Meškauskas, Rūta Samaitienė","doi":"10.1063/1.5130828","DOIUrl":"https://doi.org/10.1063/1.5130828","url":null,"abstract":"A hypothesis that spike morphological features contain information that can be used for epilepsy type detection by machine learning methods is discussed. Investigation of approach to EEG (electroencephalogram) spike morphological feature definition in relation to machine learning based EEG classification by diagnosis is presented in this study. Two approaches of defining EEG spike morphological features are investigated: A) numerically evaluating EEG spike geometric features, e.g., upslope, downslope; B) using 300 ms of spike (without additional features extracted) for classification. Lists of spikes are used for the classification. Before start of the algorithm some basic preprocessing steps are taken: electric utility frequency (50Hz) is removed. The EEG classification by diagnosis algorithm consists of these main steps: 1) EEG spike detection by morphological filter; 2) EEG classification employing spike morphological features (employing discussed approaches) by diagnosis using machine learning based classification algorithms. Various classification algorithms (e.g., artificial neural network based classifier, AdaBoost, decision tree, random forest, extremely randomized tree, etc.) and their quality metrics are considered (e.g., accuracy, true positive rate, true negative rate, etc.) as well as results of k-fold cross-validation are investigated in this work. EEGs from children (3-17 years old) are classified in this work. The EEGs under classification are patients diagnosed with: I) benign childhood epilepsy, II) structural focal epilepsy. Current results show that best performance (87% ± 1%) is exhibited by Extremely randomized tree based EEG classifier employing spike upslope and downslope data.A hypothesis that spike morphological features contain information that can be used for epilepsy type detection by machine learning methods is discussed. Investigation of approach to EEG (electroencephalogram) spike morphological feature definition in relation to machine learning based EEG classification by diagnosis is presented in this study. Two approaches of defining EEG spike morphological features are investigated: A) numerically evaluating EEG spike geometric features, e.g., upslope, downslope; B) using 300 ms of spike (without additional features extracted) for classification. Lists of spikes are used for the classification. Before start of the algorithm some basic preprocessing steps are taken: electric utility frequency (50Hz) is removed. The EEG classification by diagnosis algorithm consists of these main steps: 1) EEG spike detection by morphological filter; 2) EEG classification employing spike morphological features (employing discussed approaches) by diagnosis using machine learning based c...","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"322 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122704398","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}

{"title":"A motion correction of stochastic evolutionary systems with uncertainties","authors":"B. Ananyev","doi":"10.1063/1.5130803","DOIUrl":"https://doi.org/10.1063/1.5130803","url":null,"abstract":"In this paper, evolutionary control systems in Hilbert space are considered, which subject to random and uncertain disturbances. The state of the system is unknown, but there is an equation of measurement in discrete instants. The initial state and uncertain disturbances are restricted by joint integral constraints. According to measurements, the best linear minimax estimate is calculated. The preliminary aim of control consists in minimization of the terminal criterion that equals to expectation of the squared final state. We suggest some statements of the problem based on the separation of control and observation processes. The optimal instants of transition from estimation to control are found on the base of the theory of optimal stopping. The approach is applied to systems with the deviation of time of retarded and neutral types. It can be applied to parabolic and hyperbolic partial differential equations as well. An example with numerical results is given.In this paper, evolutionary control systems in Hilbert space are considered, which subject to random and uncertain disturbances. The state of the system is unknown, but there is an equation of measurement in discrete instants. The initial state and uncertain disturbances are restricted by joint integral constraints. According to measurements, the best linear minimax estimate is calculated. The preliminary aim of control consists in minimization of the terminal criterion that equals to expectation of the squared final state. We suggest some statements of the problem based on the separation of control and observation processes. The optimal instants of transition from estimation to control are found on the base of the theory of optimal stopping. The approach is applied to systems with the deviation of time of retarded and neutral types. It can be applied to parabolic and hyperbolic partial differential equations as well. An example with numerical results is given.","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"66 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114133609","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}

{"title":"Probabilities for p-outside values – General properties","authors":"P. Jordanova","doi":"10.1063/1.5130789","DOIUrl":"https://doi.org/10.1063/1.5130789","url":null,"abstract":"Probability distributions are uncountably many. The task for a general and useful their classification still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be described via many characteristics. Index of regular variation is a good characteristic, but it puts too many distributions with very different tail behavior in one and the same class. One can consider for example Stable(α) and Hill-horror(α) laws with one and the same fixed parameter α > 0. When analyzing the tail behavior of the observed distribution we need some characteristic which does not depend on the moments because in the most important cases of the heavy-tailed distributions theoretical moments do not exist and the corresponding empirical moments fluctuate too much. In this paper, we show that probabilities for different types of outside values can be very appropriate characteristics of the tails of the observed distribution. They do not depend on increasing affine transformations and do not need the existence of the moments. The idea origins from Tukey’s box plots, and allows us to obtain one and the same characteristic of the tail behavior of the observed distribution within the whole distributional type with respect to all increasing affine transformations. These characteristics answer the question: “At what extent we can observe “unexpected” values?”.Probability distributions are uncountably many. The task for a general and useful their classification still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be described via many characteristics. Index of regular variation is a good characteristic, but it puts too many distributions with very different tail behavior in one and the same class. One can consider for example Stable(α) and Hill-horror(α) laws with one and the same fixed parameter α > 0. When analyzing the tail behavior of the observed distribution we need some characteristic which does not depend on the moments because in the most important cases of the heavy-tailed distributions theoretical moments do not exist and the corresponding empirical moments fluctuate too much. In this paper, we show that probabilities for different types of outside values can be very appropriate characteristics of the tails of the observed distribution. They do not depend on increasing affin...","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127890157","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}

{"title":"A direct simulation Monte Carlo approach on the Riemann problem for gas mixtures","authors":"S. Meskos, S. Stefanov","doi":"10.1063/1.5130855","DOIUrl":"https://doi.org/10.1063/1.5130855","url":null,"abstract":"The Direct Simulation Monte Carlo method is employed to solve the “1D - Sod-Shock tube problem”, a special case of Riemann problems, for gas mixtures. Initially, two different gas species are distributed separately in the high and low pressure sides of the tube without interacting with each other. For time greater than zero the species start mixing and shock and rarefaction waves are formed moving in opposite directions. In this work, the mixing process between different kinds of gas species was investigated by observing differences in waves’ formation. The influence of the mass and diameter ratio between the species was studied in detail. It was found that greater mass differences had a very strong effect on the mixing process, while the effects due to diameter differences were relatively small. Finally, it is shown that in the case of single species the interaction molecular models of the hard sphere, the variable hard sphere and the variable soft sphere gave the same results, while for gas mixtures the variable hard sphere and variable soft sphere models gave slightly different results.The Direct Simulation Monte Carlo method is employed to solve the “1D - Sod-Shock tube problem”, a special case of Riemann problems, for gas mixtures. Initially, two different gas species are distributed separately in the high and low pressure sides of the tube without interacting with each other. For time greater than zero the species start mixing and shock and rarefaction waves are formed moving in opposite directions. In this work, the mixing process between different kinds of gas species was investigated by observing differences in waves’ formation. The influence of the mass and diameter ratio between the species was studied in detail. It was found that greater mass differences had a very strong effect on the mixing process, while the effects due to diameter differences were relatively small. Finally, it is shown that in the case of single species the interaction molecular models of the hard sphere, the variable hard sphere and the variable soft sphere gave the same results, while for gas mixtures the...","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132554838","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}

{"title":"An algorithm for estimating reachable set of control system under uncertainties","authors":"O. G. Matviychuk, A. R. Matviychuk","doi":"10.1063/1.5130854","DOIUrl":"https://doi.org/10.1063/1.5130854","url":null,"abstract":"","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134355168","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}

{"title":"Some analytical solutions for magnetic flux distribution in long Josephson junction with second harmonic in the current phase relation","authors":"H. Dimov, P. Atanasova, S. A. Panayotova","doi":"10.1063/1.5130838","DOIUrl":"https://doi.org/10.1063/1.5130838","url":null,"abstract":"In the current work long Josephson junctions are being studied. Magnetic flux distribution is the physical measure for phase difference of the wave functions in the superconducting layers of the junction. The current phase relation, in most cases, can be considered as an odd strict 2π-periodic function, and hence, it can be presented in Fourier series of sinuses. It is well-known from the physical experiment that with a sufficient degree of precision, a number of physical systems are reliably described with the contribution of only first two harmonics. The adequate mathematical model for the distribution of the magnetic flux is then the double sine-Gordon equation with Neumann boundary conditions at the ends of the junction. Even in the stationary case, the boundary problem is highly nonlinear and the only tool for its comprehensive study is numerical methods. The aim of the present work is to show that in the case of zero external current, the stationary equation turns out to be a fully integrable model, derived from a variation principle with a cosine potential. In our work analytical solutions for the magnetic flux distributions described in the terms of Jacobi elliptic sinuses are derived. Analytical studies in this case serve to further numerically study of this multiparametric nonlinear boundary problem, which is so important in the applied nanophysics.In the current work long Josephson junctions are being studied. Magnetic flux distribution is the physical measure for phase difference of the wave functions in the superconducting layers of the junction. The current phase relation, in most cases, can be considered as an odd strict 2π-periodic function, and hence, it can be presented in Fourier series of sinuses. It is well-known from the physical experiment that with a sufficient degree of precision, a number of physical systems are reliably described with the contribution of only first two harmonics. The adequate mathematical model for the distribution of the magnetic flux is then the double sine-Gordon equation with Neumann boundary conditions at the ends of the junction. Even in the stationary case, the boundary problem is highly nonlinear and the only tool for its comprehensive study is numerical methods. The aim of the present work is to show that in the case of zero external current, the stationary equation turns out to be a fully integrable model,...","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133285540","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}

{"title":"Rarefied gas between two coaxial cylinders - Transient heat transfer: The effect of pulsating radial motion of the outer cylinder. Acoustic waves modeling","authors":"P. Gospodinov, D. Dankov, V. Roussinov, M. Mironova","doi":"10.1063/1.5130831","DOIUrl":"https://doi.org/10.1063/1.5130831","url":null,"abstract":"On the basis of our previous studies in the flow modeling of rarefied gas between coaxial cylinders under different temperature and kinematic boundary conditions, the energy transfer in the system of gas - surrounding cylinders is studied in the radius pulsating of one of the cylinders. The energy transfer is modeled with continuous model based on Navier-Stokes-Fourier equations of motion and a statistical DSMC model. The obtained results show that the external mechanical disturbances in the radial direction influence more significantly the operation of the Pirani gauge when there is a difference in the temperature of the thread and the wall of the outer cylinder. These results make it possible to assess the gauge sensitivity under external mechanical disturbances.On the basis of our previous studies in the flow modeling of rarefied gas between coaxial cylinders under different temperature and kinematic boundary conditions, the energy transfer in the system of gas - surrounding cylinders is studied in the radius pulsating of one of the cylinders. The energy transfer is modeled with continuous model based on Navier-Stokes-Fourier equations of motion and a statistical DSMC model. The obtained results show that the external mechanical disturbances in the radial direction influence more significantly the operation of the Pirani gauge when there is a difference in the temperature of the thread and the wall of the outer cylinder. These results make it possible to assess the gauge sensitivity under external mechanical disturbances.","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"138 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124669871","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}