Pub Date : 2021-12-01DOI: 10.32523/2306-6172-2021-9-4-26-50
K. Sabitov, I.A. Burkhanova (Haji)
In this paper, we study the inverse problem for a mixed-type equation with power degeneracy on a transition line by definition of its right-hand side, depending on the spatial coordinate. The theory of identity has been proved. In the case of degree degeneracy, the uniqueness criterion for the solution of the problem is proved, and the solution itself is con- structed in the form of a sum of orthogonal series. The consistency of series in the class of solutions of the given equation is justified and the validity of the solution with respect to the boundary conditions is proved.
{"title":"THE BOUNDARY VALUE PROBLEM OF FINDING A RIGHT-HAND SIDE FOR MIXED TYPE EQUATION WITH CHAPLYGIN’S TYPE OPERATOR","authors":"K. Sabitov, I.A. Burkhanova (Haji)","doi":"10.32523/2306-6172-2021-9-4-26-50","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-4-26-50","url":null,"abstract":"In this paper, we study the inverse problem for a mixed-type equation with power degeneracy on a transition line by definition of its right-hand side, depending on the spatial coordinate. The theory of identity has been proved. In the case of degree degeneracy, the uniqueness criterion for the solution of the problem is proved, and the solution itself is con- structed in the form of a sum of orthogonal series. The consistency of series in the class of solutions of the given equation is justified and the validity of the solution with respect to the boundary conditions is proved.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44102872","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 : 2021-12-01DOI: 10.32523/2306-6172-2021-9-4-100-114
O. Ulianchuk-Martyniuk, O. Michuta, N. Ivanchuk
The distribution of an organic chemical and the filtration process in the soil which contains a thin geochemical barrier are considered. Microorganism colonies develop in the presence of organic chemicals in the soil which leads to the so-called phenomenon of bioclogging of the pore space. As a result, the conductivity characteristics of both the soil as a whole and the geochemical barrier change. Conjugation conditions as a component of the mathematical model of chemical filtration in the case of inhomogeneity of porous media and the presence of fine inclusions were modified for the case of bioclogging. The numerical solution of the corresponding nonlinear boundary value problem with modified conjugation conditions was found by the finite element method. The conditions of the existence of a generalized solution of the corresponding boundary value problem are indicated. The results on the theoretical accuracy of finite element solutions are presented. Differences in the value of pressure jumps at a thin geochemical barrier were analyzed for the case considered in the article and the classical case on a model example of filtration consolidation of the soil in the base of solid waste storage. The excess pressure in 600 days after the start of the process reaches 25 % of the initial value when taking into account the effect of bioclogging, while is only 6 % for the test case disregarding the specified effect.
{"title":"FINITE ELEMENT ANALYSIS OF THE DIFFUSION MODEL OF THE BIOCLOGGING OF THE GEOBARRIER","authors":"O. Ulianchuk-Martyniuk, O. Michuta, N. Ivanchuk","doi":"10.32523/2306-6172-2021-9-4-100-114","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-4-100-114","url":null,"abstract":"The distribution of an organic chemical and the filtration process in the soil which contains a thin geochemical barrier are considered. Microorganism colonies develop in the presence of organic chemicals in the soil which leads to the so-called phenomenon of bioclogging of the pore space. As a result, the conductivity characteristics of both the soil as a whole and the geochemical barrier change. Conjugation conditions as a component of the mathematical model of chemical filtration in the case of inhomogeneity of porous media and the presence of fine inclusions were modified for the case of bioclogging. The numerical solution of the corresponding nonlinear boundary value problem with modified conjugation conditions was found by the finite element method. The conditions of the existence of a generalized solution of the corresponding boundary value problem are indicated. The results on the theoretical accuracy of finite element solutions are presented. Differences in the value of pressure jumps at a thin geochemical barrier were analyzed for the case considered in the article and the classical case on a model example of filtration consolidation of the soil in the base of solid waste storage. The excess pressure in 600 days after the start of the process reaches 25 % of the initial value when taking into account the effect of bioclogging, while is only 6 % for the test case disregarding the specified effect.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42451741","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 : 2021-12-01DOI: 10.32523/2306-6172-2021-9-4-51-62
D. Satybaldina, V. Zolotarev, G. Ovechkin, Zhuldyz Sailau kyzy
New serial concatenation schemes based on the multithreshold decoders and di- vergent principle for the convolutional self-orthogonal codes under Gaussian channels are proposed. Using both binary and symbolic decoders on the second decoding stage of the convolutional codes are considered. Simulation results are indicated the higher performance characteristics of the proposed cascade schemes on majority decoders in comparison with clas- sical schemes based on the Viterbi algorithm and Reed-Solomon codes. A moderate increase in decoding delay during concatenation is revealed. It is determined by the absence of the need to use traditional two-dimensional concatenated structures.
{"title":"NEW CONCATENATION SCHEMES BASED ON THE MULTITHRESHOLD DECODERS OF CONVOLUTIONAL SELF-ORTHOGONAL CODES FOR GAUSSIAN CHANNELS","authors":"D. Satybaldina, V. Zolotarev, G. Ovechkin, Zhuldyz Sailau kyzy","doi":"10.32523/2306-6172-2021-9-4-51-62","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-4-51-62","url":null,"abstract":"New serial concatenation schemes based on the multithreshold decoders and di- vergent principle for the convolutional self-orthogonal codes under Gaussian channels are proposed. Using both binary and symbolic decoders on the second decoding stage of the convolutional codes are considered. Simulation results are indicated the higher performance characteristics of the proposed cascade schemes on majority decoders in comparison with clas- sical schemes based on the Viterbi algorithm and Reed-Solomon codes. A moderate increase in decoding delay during concatenation is revealed. It is determined by the absence of the need to use traditional two-dimensional concatenated structures.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42935917","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 : 2021-12-01DOI: 10.32523/2306-6172-2021-9-4-63-75
V. Vasin, F. Toussaint
In the paper, the method suggested in [5] for solving the pressure–rate deconvo- lution problem was modified with implementation for the synthetic (quasi-real) oil and gas data. Modification of the method is based on using the additional a priori information on the function v(t) = tg(t) in the logarithmic scale. On the initial time interval, the function is concave and its final interval is monotone. Here, g(t) is the solution of the basis equation (1). To take into account these properties in the Tikhonov algorithm, the penalty function method is used. It allowed one to increase the precision of the numerical solution and to improve quality of identification of the wellbore–reservoir system. Numerical experiments are provided.
{"title":"A MODIFIED METHOD OF SOLVING THE PRESSURE–RATE DECONVOLUTION PROBLEM FOR IDENTIFICATION OF WELLBORE–RESERVOIR SYSTEM","authors":"V. Vasin, F. Toussaint","doi":"10.32523/2306-6172-2021-9-4-63-75","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-4-63-75","url":null,"abstract":"In the paper, the method suggested in [5] for solving the pressure–rate deconvo- lution problem was modified with implementation for the synthetic (quasi-real) oil and gas data. Modification of the method is based on using the additional a priori information on the function v(t) = tg(t) in the logarithmic scale. On the initial time interval, the function is concave and its final interval is monotone. Here, g(t) is the solution of the basis equation (1). To take into account these properties in the Tikhonov algorithm, the penalty function method is used. It allowed one to increase the precision of the numerical solution and to improve quality of identification of the wellbore–reservoir system. Numerical experiments are provided.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44751868","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 : 2021-12-01DOI: 10.32523/2306-6172-2021-9-4-89-99
A. Tikhonravov, I. Lagutin, A. Lagutina, D. Lukyanenko, I. Kochikov, A. Yagola
The reverse engineering problem of determining the layer thicknesses of deposited optical coatings from on-line monochromatic measurements is considered. To solve this inverse problem, non-local algorithms are proposed that use all the data accumulated during the deposition process. For the proposed algorithms, the accuracy of solving the inverse problem is compared in the presence of random and systematic errors. It is shown that in the case when the measured data contains only random errors, the best accuracy is provided by the algorithm based on minimizing the discrepancy functional. In the case of systematic errors, the advantage of one the algorithms based on minimizing the variance functionals is demonstrated. Key words: inverse problems, reverse engineering, optical coatings, thin films.
{"title":"COMPARISON OF ALGORITHMS FOR DETERMINING THE THICKNESS OF OPTICAL COATING LAYERS BASED ON THE MONOCHROMATIC MONITORING DATA","authors":"A. Tikhonravov, I. Lagutin, A. Lagutina, D. Lukyanenko, I. Kochikov, A. Yagola","doi":"10.32523/2306-6172-2021-9-4-89-99","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-4-89-99","url":null,"abstract":"The reverse engineering problem of determining the layer thicknesses of deposited optical coatings from on-line monochromatic measurements is considered. To solve this inverse problem, non-local algorithms are proposed that use all the data accumulated during the deposition process. For the proposed algorithms, the accuracy of solving the inverse problem is compared in the presence of random and systematic errors. It is shown that in the case when the measured data contains only random errors, the best accuracy is provided by the algorithm based on minimizing the discrepancy functional. In the case of systematic errors, the advantage of one the algorithms based on minimizing the variance functionals is demonstrated. Key words: inverse problems, reverse engineering, optical coatings, thin films.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48802546","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 : 2021-12-01DOI: 10.32523/2306-6172-2021-9-4-76-88
Y. Smirnov, V. Martynova, M. Moskaleva, A. Tikhonravov
A modified method of separation of variables is proposed for solving the direct problem of diffraction of electromagnetic wave by multilayer dielectric gratings (MDG). To apply this method, it is necessary to solve a one-dimensional eigenvalue problem for a 2nd- order differential equation on a segment with piecewise constant coefficients. The accuracy of the method is verified by comparison with the results obtained by the commercially available RCWA method. It is demonstrated that the method can be applied not only to commonly used MDG elements with one line in a grating period but also to potentially promising MDG elements with several different lines in a grating period.
{"title":"MODIFIED METHOD OF SEPARATION OF VARIABLES FOR SOLVING DIFFRACTION PROBLEMS ON MULTILAYER DIELECTRIC GRATINGS","authors":"Y. Smirnov, V. Martynova, M. Moskaleva, A. Tikhonravov","doi":"10.32523/2306-6172-2021-9-4-76-88","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-4-76-88","url":null,"abstract":"A modified method of separation of variables is proposed for solving the direct problem of diffraction of electromagnetic wave by multilayer dielectric gratings (MDG). To apply this method, it is necessary to solve a one-dimensional eigenvalue problem for a 2nd- order differential equation on a segment with piecewise constant coefficients. The accuracy of the method is verified by comparison with the results obtained by the commercially available RCWA method. It is demonstrated that the method can be applied not only to commonly used MDG elements with one line in a grating period but also to potentially promising MDG elements with several different lines in a grating period.","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42657887","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 : 2021-09-25DOI: 10.32523/2306-6172-2021-9-3-4-13
Sarah Baimukhametova, Dana Alina, A. Shomanov
{"title":"IMAGE SEGMENTATION ALGORITHM FOR FILAMENTARY STRUCTURES DETECTION","authors":"Sarah Baimukhametova, Dana Alina, A. Shomanov","doi":"10.32523/2306-6172-2021-9-3-4-13","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-3-4-13","url":null,"abstract":"","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49316432","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 : 2021-09-25DOI: 10.32523/2306-6172-2021-9-3-53-67
V. Kamynin, A. Kostin
{"title":"THE INVERSE PROBLEM OF DETERMINING THE LOWEST COEFFICIENT IN A HIGHER-ORDER PARABOLIC EQUATION WITH WEAK DEGENERACY","authors":"V. Kamynin, A. Kostin","doi":"10.32523/2306-6172-2021-9-3-53-67","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-3-53-67","url":null,"abstract":"","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45490225","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 : 2021-09-25DOI: 10.32523/2306-6172-2021-9-3-39-52
V. Filimonov, O. Lovtskaya, A. Zinoviev
{"title":"DIFFUSE POLLUTION OF SMALL RIVERS. FEATURES OF DISTRIBUTION OF DISSOLVED POLLUTANT CONCENTRATIONS","authors":"V. Filimonov, O. Lovtskaya, A. Zinoviev","doi":"10.32523/2306-6172-2021-9-3-39-52","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-3-39-52","url":null,"abstract":"","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46434798","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 : 2021-09-25DOI: 10.32523/2306-6172-2021-9-3-68-81
V. Romanov
{"title":"EXPANSIONS OF SOLUTIONS OF ELECTRODYNAMIC EQUATIONS IN A VICINITY OF CHARACTERISTIC SURFACES","authors":"V. Romanov","doi":"10.32523/2306-6172-2021-9-3-68-81","DOIUrl":"https://doi.org/10.32523/2306-6172-2021-9-3-68-81","url":null,"abstract":"","PeriodicalId":42910,"journal":{"name":"Eurasian Journal of Mathematical and Computer Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42810427","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}
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