Pub Date : 2023-03-30DOI: 10.22363/2658-4670-2023-31-1-5-26
M. Gevorkyan, A. Korolkova, D. Kulyabov
The Julia programming language is a specialized language for scientific computing. It is relatively new, so most of the libraries for it are in the active development stage. In this article, the authors consider the possibilities of the language in the field of mathematical statistics. Special emphasis is placed on the technical component, in particular, the process of installing and configuring the software environment is described in detail. Since users of the Julia language are often not professional programmers, technical issues in setting up the software environment can cause difficulties that prevent them from quickly mastering the basic features of the language. The article also describes some features of Julia that distinguish it from other popular languages used for scientific computing. The third part of the article provides an overview of the two main libraries for mathematical statistics. The emphasis is again on the technical side in order to give the reader an idea of the general possibilities of the language in the field of mathematical statistics.
{"title":"Julia language features for processing statistical data","authors":"M. Gevorkyan, A. Korolkova, D. Kulyabov","doi":"10.22363/2658-4670-2023-31-1-5-26","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-1-5-26","url":null,"abstract":"The Julia programming language is a specialized language for scientific computing. It is relatively new, so most of the libraries for it are in the active development stage. In this article, the authors consider the possibilities of the language in the field of mathematical statistics. Special emphasis is placed on the technical component, in particular, the process of installing and configuring the software environment is described in detail. Since users of the Julia language are often not professional programmers, technical issues in setting up the software environment can cause difficulties that prevent them from quickly mastering the basic features of the language. The article also describes some features of Julia that distinguish it from other popular languages used for scientific computing. The third part of the article provides an overview of the two main libraries for mathematical statistics. The emphasis is again on the technical side in order to give the reader an idea of the general possibilities of the language in the field of mathematical statistics.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"16 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41286962","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 : 2023-03-30DOI: 10.22363/2658-4670-2023-31-1-64-74
Nikolay A. Kolpakov, A. Molodchenkov, Anton V. Lukin
This article proposes an algorithm for solving the problem of extracting information from biomedical patents and scientific publications. The introduced algorithm is based on machine learning methods. Experiments were carried out on patents from the USPTO database. Experiments have shown that the best extraction quality was achieved by a model based on BioBERT.
{"title":"Methods of extracting biomedical information from patents and scientific publications (on the example of chemical compounds)","authors":"Nikolay A. Kolpakov, A. Molodchenkov, Anton V. Lukin","doi":"10.22363/2658-4670-2023-31-1-64-74","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-1-64-74","url":null,"abstract":"This article proposes an algorithm for solving the problem of extracting information from biomedical patents and scientific publications. The introduced algorithm is based on machine learning methods. Experiments were carried out on patents from the USPTO database. Experiments have shown that the best extraction quality was achieved by a model based on BioBERT.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43755383","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 : 2023-03-30DOI: 10.22363/2658-4670-2023-31-1-75-86
N. Kravchenko, S. Kovtunov
The article gives a description of the history of the development of research of electric explosion of metal conductors, the authors offer a modern view on the physics of the process of electric explosion. The result of such an explosion can be, in particular, the production of nanopowders, which today have found the widest application in industry, agriculture, medicine, and so on.
{"title":"Studying the mechanism of electric explosion of metal conductors","authors":"N. Kravchenko, S. Kovtunov","doi":"10.22363/2658-4670-2023-31-1-75-86","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-1-75-86","url":null,"abstract":"The article gives a description of the history of the development of research of electric explosion of metal conductors, the authors offer a modern view on the physics of the process of electric explosion. The result of such an explosion can be, in particular, the production of nanopowders, which today have found the widest application in industry, agriculture, medicine, and so on.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46370603","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 : 2023-01-01DOI: 10.22363/2658-4670-2023-31-2-164-173
M. Malykh, Polina S. Chusovitina
This work is devoted to the implementation and testing of the Adams method for solving ordinary differential equations in the Sage computer algebra system. The Sage computer algebra system has, to some extent, trivial means for numerical integration of ordinary differential equations, but at the same time, it is worth noting that this environment is convenient and practical for conducting computer experiments related to symbolic numerical calculations in it. The article presents the FDM package developed on the basis of the RUDN, which contains the developments of recent years, performed by M. D. Malykh and his students, for numerical integration of differential equations. In this package, attention is paid to the visualization of the calculation results, including the construction of various kinds of auxiliary diagrams, such as Richardson diagrams, as well as graphs of dependence, for example, the value of a function or step from a moment in time. The implementation of the Adams method will be considered from this package. In this article, this implementation of the Adams method will be tested on various examples of input data, and the method will also be compared with the Jacobi system. Exact and approximate values will be found and compared, and an estimate for the error will be obtained.
{"title":"Implementation of the Adams method for solving ordinary differential equations in the Sage computer algebra system","authors":"M. Malykh, Polina S. Chusovitina","doi":"10.22363/2658-4670-2023-31-2-164-173","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-2-164-173","url":null,"abstract":"This work is devoted to the implementation and testing of the Adams method for solving ordinary differential equations in the Sage computer algebra system. The Sage computer algebra system has, to some extent, trivial means for numerical integration of ordinary differential equations, but at the same time, it is worth noting that this environment is convenient and practical for conducting computer experiments related to symbolic numerical calculations in it. The article presents the FDM package developed on the basis of the RUDN, which contains the developments of recent years, performed by M. D. Malykh and his students, for numerical integration of differential equations. In this package, attention is paid to the visualization of the calculation results, including the construction of various kinds of auxiliary diagrams, such as Richardson diagrams, as well as graphs of dependence, for example, the value of a function or step from a moment in time. The implementation of the Adams method will be considered from this package. In this article, this implementation of the Adams method will be tested on various examples of input data, and the method will also be compared with the Jacobi system. Exact and approximate values will be found and compared, and an estimate for the error will be obtained.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68282925","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 : 2023-01-01DOI: 10.22363/2658-4670-2023-31-2-105-119
E. Polin, S. Moiseeva, A. Moiseev
In the proposed work, we consider a heterogeneous queueing system with a Markov renewal process and an unlimited number of servers. The service time for requests on the servers is a positive random variable with an exponential probability distribution. The service parameters depend on the state of the Markov chain nested over the renewal moments. It should be noted that these parameters do not change their values until the end of maintenance. Thus, the devices in the system under consideration are heterogeneous. The object of the study is a multidimensional random process - the number of servers of each type being served with different intensities in the stationary regime. The method of asymptotic analysis under the condition of equivalent growing of service times in the units of servers is applied for the study. The method of asymptotic analysis is implemented in the construction of a sequence of asymptotic of increasing order, in which the asymptotic of the first order determines the asymptotic mean value of the number of occupied servers. The second-order asymptotic allows one to construct a Gaussian approximation of the probability distribution of the number of occupied servers in the system. It is shown that this approximation coincides with the Gaussian distribution.
{"title":"Heterogeneous queueing system with Markov renewal arrivals and service times dependent on states of arrival process","authors":"E. Polin, S. Moiseeva, A. Moiseev","doi":"10.22363/2658-4670-2023-31-2-105-119","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-2-105-119","url":null,"abstract":"In the proposed work, we consider a heterogeneous queueing system with a Markov renewal process and an unlimited number of servers. The service time for requests on the servers is a positive random variable with an exponential probability distribution. The service parameters depend on the state of the Markov chain nested over the renewal moments. It should be noted that these parameters do not change their values until the end of maintenance. Thus, the devices in the system under consideration are heterogeneous. The object of the study is a multidimensional random process - the number of servers of each type being served with different intensities in the stationary regime. The method of asymptotic analysis under the condition of equivalent growing of service times in the units of servers is applied for the study. The method of asymptotic analysis is implemented in the construction of a sequence of asymptotic of increasing order, in which the asymptotic of the first order determines the asymptotic mean value of the number of occupied servers. The second-order asymptotic allows one to construct a Gaussian approximation of the probability distribution of the number of occupied servers in the system. It is shown that this approximation coincides with the Gaussian distribution.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68283049","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 : 2023-01-01DOI: 10.22363/2658-4670-2023-31-2-128-138
A. Belov, Maxim A. Tintul, V. S. Khokhlachev
The calculation of quadratures arises in many physical and technical applications. The replacement of integration variables is proposed, which dramatically increases the accuracy of the formula of averages. For infinitely smooth integrand functions, the convergence law becomes super power. It is significantly faster than the power law and is close to exponential one. For integrals with bounded smoothness, power convergence is realized with the maximum achievable order of accuracy.
{"title":"Quadratures with super power convergence","authors":"A. Belov, Maxim A. Tintul, V. S. Khokhlachev","doi":"10.22363/2658-4670-2023-31-2-128-138","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-2-128-138","url":null,"abstract":"The calculation of quadratures arises in many physical and technical applications. The replacement of integration variables is proposed, which dramatically increases the accuracy of the formula of averages. For infinitely smooth integrand functions, the convergence law becomes super power. It is significantly faster than the power law and is close to exponential one. For integrals with bounded smoothness, power convergence is realized with the maximum achievable order of accuracy.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68282706","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 : 2023-01-01DOI: 10.22363/2658-4670-2023-31-2-120-127
A. Belov
The paper describes a grid method for solving an ill-posed problem for the Fredholm equation of the first kind using the A. N. Tikhonov regularizer. The convergence theorem for this method was formulated and proved. A procedure for thickening grids with a simultaneous increase in digit capacity of calculations is proposed.
本文描述了用a . N. Tikhonov正则化器求解第一类Fredholm方程不适定问题的网格方法。构造并证明了该方法的收敛性定理。提出了一种增厚网格同时增加数字计算容量的方法。
{"title":"Convergence of the grid method for the Fredholm equation of the first kind with Tikhonov regularization","authors":"A. Belov","doi":"10.22363/2658-4670-2023-31-2-120-127","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-2-120-127","url":null,"abstract":"The paper describes a grid method for solving an ill-posed problem for the Fredholm equation of the first kind using the A. N. Tikhonov regularizer. The convergence theorem for this method was formulated and proved. A procedure for thickening grids with a simultaneous increase in digit capacity of calculations is proposed.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68283149","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 : 2023-01-01DOI: 10.22363/2658-4670-2023-31-2-150-163
K. Lovetskiy, D. Kulyabov, L. Sevastianov, Stepan V. Sergeev
The spectral collocation method for solving two-point boundary value problems for second order differential equations is implemented, based on representing the solution as an expansion in Chebyshev polynomials. The approach allows a stable calculation of both the spectral representation of the solution and its pointwise representation on any required grid in the definition domain of the equation and additional conditions of the multipoint problem. For the effective construction of SLAE, the solution of which gives the desired coefficients, the Chebyshev matrices of spectral integration are actively used. The proposed algorithms have a high accuracy for moderate-dimension systems of linear algebraic equations. The matrix of the system remains well-conditioned and, with an increase in the number of collocation points, allows finding solutions with ever-increasing accuracy.
{"title":"Chebyshev collocation method for solving second order ODEs using integration matrices","authors":"K. Lovetskiy, D. Kulyabov, L. Sevastianov, Stepan V. Sergeev","doi":"10.22363/2658-4670-2023-31-2-150-163","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-2-150-163","url":null,"abstract":"The spectral collocation method for solving two-point boundary value problems for second order differential equations is implemented, based on representing the solution as an expansion in Chebyshev polynomials. The approach allows a stable calculation of both the spectral representation of the solution and its pointwise representation on any required grid in the definition domain of the equation and additional conditions of the multipoint problem. For the effective construction of SLAE, the solution of which gives the desired coefficients, the Chebyshev matrices of spectral integration are actively used. The proposed algorithms have a high accuracy for moderate-dimension systems of linear algebraic equations. The matrix of the system remains well-conditioned and, with an increase in the number of collocation points, allows finding solutions with ever-increasing accuracy.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68282820","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 : 2023-01-01DOI: 10.22363/2658-4670-2023-31-2-174-188
V. Chistyakov, Sergey M. Soloviev
The method of numerical integration of Euler problem of buckling of a homogeneous console with symmetrical cross section in regime of plastic deformation using Maple18 is presented. The ordinary differential equation for a transversal coordinate (y) was deduced which takes into consideration higher geometrical momenta of cross section area. As an argument in the equation a dimensionless console slope (p=tg theta) is used which is linked in mutually unique manner with all other linear displacements. Real strain-stress diagram of metals (steel, titan) and PTFE polymers were modelled via the Maple nonlinear regression with cubic polynomial to provide a conditional yield point ((t),(sigma_f)). The console parameters (free length (l_0), (m), cross section area (S) and minimal gyration moment (J_x)) were chosen so that a critical buckling forces (F_text{cr}) corresponded to the stresses (sigma) close to the yield strength (sigma_f). To find the key dependence of the final slope (p_f) vs load (F) needed for the shape determination the equality for restored console length was applied. The dependences (p_f(F)) and shapes (y(z)), (z) being a longitudinal coordinate, were determined within these three approaches: plastic regime with cubic strain-stress diagram, tangent modulus (E_text{tang}) approximations and Hook’s law. It was found that critical buckling load (F_text{cr}) in plastic range nearly two times less of that for an ideal Hook’s law. A quasi-identity of calculated console shapes was found for the same final slope (p_f) within the three approaches especially for the metals.
{"title":"Buckling in inelastic regime of a uniform console with symmetrical cross section: computer modeling using Maple 18","authors":"V. Chistyakov, Sergey M. Soloviev","doi":"10.22363/2658-4670-2023-31-2-174-188","DOIUrl":"https://doi.org/10.22363/2658-4670-2023-31-2-174-188","url":null,"abstract":"The method of numerical integration of Euler problem of buckling of a homogeneous console with symmetrical cross section in regime of plastic deformation using Maple18 is presented. The ordinary differential equation for a transversal coordinate (y) was deduced which takes into consideration higher geometrical momenta of cross section area. As an argument in the equation a dimensionless console slope (p=tg theta) is used which is linked in mutually unique manner with all other linear displacements. Real strain-stress diagram of metals (steel, titan) and PTFE polymers were modelled via the Maple nonlinear regression with cubic polynomial to provide a conditional yield point ((t),(sigma_f)). The console parameters (free length (l_0), (m), cross section area (S) and minimal gyration moment (J_x)) were chosen so that a critical buckling forces (F_text{cr}) corresponded to the stresses (sigma) close to the yield strength (sigma_f). To find the key dependence of the final slope (p_f) vs load (F) needed for the shape determination the equality for restored console length was applied. The dependences (p_f(F)) and shapes (y(z)), (z) being a longitudinal coordinate, were determined within these three approaches: plastic regime with cubic strain-stress diagram, tangent modulus (E_text{tang}) approximations and Hook’s law. It was found that critical buckling load (F_text{cr}) in plastic range nearly two times less of that for an ideal Hook’s law. A quasi-identity of calculated console shapes was found for the same final slope (p_f) within the three approaches especially for the metals.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68282991","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 : 2022-12-26DOI: 10.22363/2658-4670-2022-30-4-342-356
E. Laneev, O. Baaj
The paper considers mathematical methods of correction of thermographic images (thermograms) in the form of temperature distribution on the surface of the object under study, obtained using a thermal imager. The thermogram reproduces the image of the heat-generating structures located inside the object under study. This image is transmitted with distortions, since the sources are usually removed from its surface and the temperature distribution on the surface of the object transmits the image as blurred due to the processes of thermal conductivity and heat exchange. In this paper, the continuation of the temperature function as a harmonic function from the surface deep into the object under study in order to obtain a temperature distribution function near sources is considered as a correction principle. This distribution is considered as an adjusted thermogram. The continuation is carried out on the basis of solving the Cauchy problem for the Laplace equation - an ill-posed problem. The solution is constructed using the Tikhonov regularization method. The main part of the constructed approximate solution is presented as a Fourier series by the eigenfunctions of the Laplace operator. Discretization of the problem leads to discrete Fourier series. A modification of the Hamming method for summing Fourier series and calculating their coefficients is proposed.
{"title":"On a modification of the Hamming method for summing discrete Fourier series and its application to solve the problem of correction of thermographic images","authors":"E. Laneev, O. Baaj","doi":"10.22363/2658-4670-2022-30-4-342-356","DOIUrl":"https://doi.org/10.22363/2658-4670-2022-30-4-342-356","url":null,"abstract":"The paper considers mathematical methods of correction of thermographic images (thermograms) in the form of temperature distribution on the surface of the object under study, obtained using a thermal imager. The thermogram reproduces the image of the heat-generating structures located inside the object under study. This image is transmitted with distortions, since the sources are usually removed from its surface and the temperature distribution on the surface of the object transmits the image as blurred due to the processes of thermal conductivity and heat exchange. In this paper, the continuation of the temperature function as a harmonic function from the surface deep into the object under study in order to obtain a temperature distribution function near sources is considered as a correction principle. This distribution is considered as an adjusted thermogram. The continuation is carried out on the basis of solving the Cauchy problem for the Laplace equation - an ill-posed problem. The solution is constructed using the Tikhonov regularization method. The main part of the constructed approximate solution is presented as a Fourier series by the eigenfunctions of the Laplace operator. Discretization of the problem leads to discrete Fourier series. A modification of the Hamming method for summing Fourier series and calculating their coefficients is proposed.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46949584","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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