Pub Date : 2024-01-09DOI: 10.3103/s1066369x23100080
M. Rehman, T. Rasulov, B. Aminov
Abstract
In this article, we present new results for the computation of structured singular values of nonnegative matrices subject to pure complex perturbations. We prove the equivalence of structured singular values and spectral radius of perturbed matrix ((Mvartriangle )). The presented new results on the equivalence of structured singular values, nonnegative spectral radius and nonnegative determinant of ((Mvartriangle )) is presented and analyzed. Furthermore, it has been shown that for a unit spectral radius of ((Mvartriangle )), both structured singular values and spectral radius are exactly equal. Finally, we present the exact equivalence between structured singular value and the largest singular value of ((Mvartriangle )).
{"title":"Nonnegative Matrices and Their Structured Singular Values","authors":"M. Rehman, T. Rasulov, B. Aminov","doi":"10.3103/s1066369x23100080","DOIUrl":"https://doi.org/10.3103/s1066369x23100080","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this article, we present new results for the computation of structured singular values of nonnegative matrices subject to pure complex perturbations. We prove the equivalence of structured singular values and spectral radius of perturbed matrix <span>((Mvartriangle ))</span>. The presented new results on the equivalence of structured singular values, nonnegative spectral radius and nonnegative determinant of <span>((Mvartriangle ))</span> is presented and analyzed. Furthermore, it has been shown that for a unit spectral radius of <span>((Mvartriangle ))</span>, both structured singular values and spectral radius are exactly equal. Finally, we present the exact equivalence between structured singular value and the largest singular value of <span>((Mvartriangle ))</span>.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"18 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139411378","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 : 2024-01-09DOI: 10.3103/s1066369x23100067
A. R. Khalmukhamedov, E. I. Kuchkorov
Abstract
We study a nonlocal problem for a differential Boussinesq-type equations in a multidimensional domain. Conditions for the existence and uniqueness of the solution are established, and a spectral decomposition of the solution is obtained.
{"title":"On the Solvability of a Nonlocal Problem for a Boussinesq-Type Differential Equation","authors":"A. R. Khalmukhamedov, E. I. Kuchkorov","doi":"10.3103/s1066369x23100067","DOIUrl":"https://doi.org/10.3103/s1066369x23100067","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We study a nonlocal problem for a differential Boussinesq-type equations in a multidimensional domain. Conditions for the existence and uniqueness of the solution are established, and a spectral decomposition of the solution is obtained.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139411435","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 : 2024-01-09DOI: 10.3103/s1066369x23100055
M. E. Gnedko, D. N. Oskorbin, E. D. Rodionov
Abstract
A natural generalization of Killing vector fields is conformally Killing vector fields, which play an important role in the study of the group of conformal transformations of manifolds, Ricci flows on manifolds, and the theory of Ricci solitons. In this paper, conformally Killing vector fields are studied on 2-symmetric indecomposable Lorentzian manifolds. It is established that the conformal factor of the conformal analogue of the Killing equation on them depends on the behavior of the Weyl tensor. In addition, in the case when the Weyl tensor is equal to zero, nontrivial examples of conformally Killing vector fields with a variable conformal factor are constructed using the Airy functions.
{"title":"On Conformally Killing Vector Fields on a 2-Symmetric Indecomposable Lorentzian Manifold","authors":"M. E. Gnedko, D. N. Oskorbin, E. D. Rodionov","doi":"10.3103/s1066369x23100055","DOIUrl":"https://doi.org/10.3103/s1066369x23100055","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A natural generalization of Killing vector fields is conformally Killing vector fields, which play an important role in the study of the group of conformal transformations of manifolds, Ricci flows on manifolds, and the theory of Ricci solitons. In this paper, conformally Killing vector fields are studied on 2-symmetric indecomposable Lorentzian manifolds. It is established that the conformal factor of the conformal analogue of the Killing equation on them depends on the behavior of the Weyl tensor. In addition, in the case when the Weyl tensor is equal to zero, nontrivial examples of conformally Killing vector fields with a variable conformal factor are constructed using the Airy functions.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"113 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139411463","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 : 2024-01-09DOI: 10.3103/s1066369x2310002x
A. V. Banshchikov, A. V. Lakeev, V. A. Rusanov
Abstract
A characteristic criterion (and its modifications) of the solvability of differential realization of the bundle of controlled trajectory curves of deterministic chaotic dynamic processes in the class of higher order bilinear nonautonomous ordinary differential equations (with and without delay) in the separable Hilbert space has been found. This formulation refers to inverse problems for the additive combination of higher order nonstationary linear and bilinear operators of the evolution equation in the Hilbert space. This theory is based on constructs of tensor products of Hilbert spaces, structures of lattices with an orthocomplement, the theory of extension of M2 operators, and the functional apparatus of the Rayleigh–Ritz nonlinear entropy operator. It has been shown that, in the case of a finite bundle of controlled trajectory curves, the property of sublinearity of the given operator allows one to obtain sufficient conditions for the existence of such realizations. The results obtained in this study are partly of a review nature and can become the basis for the development (in terms of Fock spaces) of a qualitative theory of inverse problems of higher order polylinear evolution equations with generalized delay operators describing, for example, the modeling of nonlinear oscillators of the Van der Pol type or Lorentz strange attractors.
{"title":"Polylinear Differential Realization of Deterministic Dynamic Chaos in the Class of Higher Order Equations with Delay","authors":"A. V. Banshchikov, A. V. Lakeev, V. A. Rusanov","doi":"10.3103/s1066369x2310002x","DOIUrl":"https://doi.org/10.3103/s1066369x2310002x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A characteristic criterion (and its modifications) of the solvability of differential realization of the bundle of controlled trajectory curves of deterministic chaotic dynamic processes in the class of higher order bilinear nonautonomous ordinary differential equations (with and without delay) in the separable Hilbert space has been found. This formulation refers to inverse problems for the additive combination of higher order nonstationary linear and bilinear operators of the evolution equation in the Hilbert space. This theory is based on constructs of tensor products of Hilbert spaces, structures of lattices with an orthocomplement, the theory of extension of <i>M</i><sub>2</sub> operators, and the functional apparatus of the Rayleigh–Ritz nonlinear entropy operator. It has been shown that, in the case of a finite bundle of controlled trajectory curves, the property of sublinearity of the given operator allows one to obtain sufficient conditions for the existence of such realizations. The results obtained in this study are partly of a review nature and can become the basis for the development (in terms of Fock spaces) of a qualitative theory of inverse problems of higher order polylinear evolution equations with generalized delay operators describing, for example, the modeling of nonlinear oscillators of the Van der Pol type or Lorentz strange attractors.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"19 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139411551","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 : 2024-01-09DOI: 10.3103/s1066369x23100043
D. K. Durdiev, J. J. Jumaev
Abstract
In this paper, an inverse problem of determining a kernel in a one-dimensional integro-differential time-fractional diffusion equation with initial-boundary and overdetermination conditions is investigated. An auxiliary problem equivalent to the problem is introduced first. By Fourier method this auxilary problem is reduced to equivalent integral equations. Then, using estimates of the Mittag–Leffler function and successive aproximation method, an estimate for the solution of the direct problem is obtained in terms of the norm of the unknown kernel which will be used in study of inverse problem. The inverse problem is reduced to the equivalent integral equation. For solving this equation the contracted mapping principle is applied. The local existence and global uniqueness results are proven.
{"title":"Inverse Problem of Determining the Kernel of Integro-Differential Fractional Diffusion Equation in Bounded Domain","authors":"D. K. Durdiev, J. J. Jumaev","doi":"10.3103/s1066369x23100043","DOIUrl":"https://doi.org/10.3103/s1066369x23100043","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, an inverse problem of determining a kernel in a one-dimensional integro-differential time-fractional diffusion equation with initial-boundary and overdetermination conditions is investigated. An auxiliary problem equivalent to the problem is introduced first. By Fourier method this auxilary problem is reduced to equivalent integral equations. Then, using estimates of the Mittag–Leffler function and successive aproximation method, an estimate for the solution of the direct problem is obtained in terms of the norm of the unknown kernel which will be used in study of inverse problem. The inverse problem is reduced to the equivalent integral equation. For solving this equation the contracted mapping principle is applied. The local existence and global uniqueness results are proven.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"56 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139411431","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 : 2023-12-15DOI: 10.3103/s1066369x23090074
S. Khodjiev
Abstract
A compressible gas in plane channels of constant and variable cross sections is numerically simulated using two-dimensional parabolized Navier–Stokes equations. The system of equations is solved numerically using the narrow-channel approximation model. A number of transformations, such as nondimensionalization of the system of equations to reduce the given domain to a square and refinement of computational points with large gradients of gas-dynamic parameters, are described in detail. Pressure gradient is determined from the flow-rate conservation condition. An efficient method is given for simultaneously determining the pressure gradient and longitudinal velocity, followed by other gas-dynamic parameters of stability for subsonic and supersonic flows, as well as a method for determining the critical flow rate for solving Laval nozzle problems. The results of methodical calculations are presented to validate the calculation methodology and confirm the reliability of the results by comparing them with data obtained by other authors.
{"title":"Numerical Simulation of Compressible Gas Flow in Flat Channels in the Narrow Channel Approximation","authors":"S. Khodjiev","doi":"10.3103/s1066369x23090074","DOIUrl":"https://doi.org/10.3103/s1066369x23090074","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A compressible gas in plane channels of constant and variable cross sections is numerically simulated using two-dimensional parabolized Navier–Stokes equations. The system of equations is solved numerically using the narrow-channel approximation model. A number of transformations, such as nondimensionalization of the system of equations to reduce the given domain to a square and refinement of computational points with large gradients of gas-dynamic parameters, are described in detail. Pressure gradient is determined from the flow-rate conservation condition. An efficient method is given for simultaneously determining the pressure gradient and longitudinal velocity, followed by other gas-dynamic parameters of stability for subsonic and supersonic flows, as well as a method for determining the critical flow rate for solving Laval nozzle problems. The results of methodical calculations are presented to validate the calculation methodology and confirm the reliability of the results by comparing them with data obtained by other authors.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"71 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138682608","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 : 2023-12-15DOI: 10.3103/s1066369x23090013
J. I. Abdullaev, A. M. Khalkhuzhaev, T. H. Rasulov
Abstract
We consider three-particle Schrödinger operator ({{H}_{{mu ,gamma }}}({mathbf{K}})), ({mathbf{K}} in {{mathbb{T}}^{3}}), associated to a system of three particles (two of them are bosons with mass 1 and one is an arbitrary with mass (m = {text{1/}}gamma < 1)), interacting via zero-range pairwise potentials (mu > 0) and λ > 0 on the three dimensional lattice ({{mathbb{Z}}^{3}}). It is proved that there exist critical value of ratio of mass γ = γ1 and γ = γ2 such that the operator ({{H}_{{mu ,gamma }}}(mathbf{0}))0 = (0, 0, 0), has a unique eigenvalue for (gamma in (0,{{gamma }_{1}})), has two eigenvalues for (gamma in ({{gamma }_{1}},{{gamma }_{2}})) and four eigenvalues for (gamma in ({{gamma }_{2}}, + infty )), located on the left-hand side of the essential spectrum for large enough µ > 0 and fixed λ > 0.
Abstract We consider three-particle Schrödinger operator ({{H}_{mu ,gamma }}}({mathbf{K}})), ({mathbf{K}} in {{mathbb{T}}^{3}}), associated to a system of three particles (two of them are bosons with mass 1 and one is an arbitrary with mass (m = {text{1/}}gamma <；1）），在三维晶格({{mathbb{Z}}^{3}})上通过零距离对偶势（(mu > 0) and λ > 0）相互作用。研究证明，存在质量比临界值 γ = γ1 和 γ = γ2，使得算子 ({{H}_{mu ,gamma }}}(mathbf{0}))0 = (0, 0, 0), (gamma in (0,{{gamma }_{1}})) 有一个唯一的特征值, (gamma in ({{gamma }_{1}}、({{gamma}_{2}})有两个特征值，而(gamma in ({{gamma }_{2}}, + infty )) 有四个特征值，位于足够大的 µ >；0 和固定的 λ > 0.
{"title":"Invariant Subspaces and Eigenvalues of the Three-Particle Discrete Schrödinger Operators","authors":"J. I. Abdullaev, A. M. Khalkhuzhaev, T. H. Rasulov","doi":"10.3103/s1066369x23090013","DOIUrl":"https://doi.org/10.3103/s1066369x23090013","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider three-particle Schrödinger operator <span>({{H}_{{mu ,gamma }}}({mathbf{K}}))</span>, <span>({mathbf{K}} in {{mathbb{T}}^{3}})</span>, associated to a system of three particles (two of them are bosons with mass 1 and one is an arbitrary with mass <span>(m = {text{1/}}gamma < 1)</span>), interacting via zero-range pairwise potentials <span>(mu > 0)</span> and λ > 0 on the three dimensional lattice <span>({{mathbb{Z}}^{3}})</span>. It is proved that there exist critical value of ratio of mass γ = γ<sub>1</sub> and γ = γ<sub>2</sub> such that the operator <span>({{H}_{{mu ,gamma }}}(mathbf{0}))</span> <b>0</b> = (0, 0, 0), has a unique eigenvalue for <span>(gamma in (0,{{gamma }_{1}}))</span>, has two eigenvalues for <span>(gamma in ({{gamma }_{1}},{{gamma }_{2}}))</span> and four eigenvalues for <span>(gamma in ({{gamma }_{2}}, + infty ))</span>, located on the left-hand side of the essential spectrum for large enough µ > 0 and fixed λ > 0. </p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"68 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138682887","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 : 2023-12-15DOI: 10.3103/s1066369x23090025
G. E. Abduragimov
Abstract
The paper considers a two-point boundary value problem with homogeneous boundary conditions for a single 4nth-order nonlinear ordinary differential equation. Using the well-known Krasnoselskii theorem on the expansion (compression) of a cone, sufficient conditions for the existence of a positive solution to the problem under consideration are obtained. To prove the uniqueness of a positive solution, the principle of compressed operators was invoked. In conclusion, an example is given that illustrates the fulfillment of the obtained sufficient conditions for the unique solvability of the problem under study.
{"title":"On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a 4nth-Order Nonlinear Ordinary Differential Equation","authors":"G. E. Abduragimov","doi":"10.3103/s1066369x23090025","DOIUrl":"https://doi.org/10.3103/s1066369x23090025","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper considers a two-point boundary value problem with homogeneous boundary conditions for a single 4<i>n</i>th-order nonlinear ordinary differential equation. Using the well-known Krasnoselskii theorem on the expansion (compression) of a cone, sufficient conditions for the existence of a positive solution to the problem under consideration are obtained. To prove the uniqueness of a positive solution, the principle of compressed operators was invoked. In conclusion, an example is given that illustrates the fulfillment of the obtained sufficient conditions for the unique solvability of the problem under study.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"68 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138682726","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 : 2023-12-15DOI: 10.3103/s1066369x23090050
M. M. Alimov
Abstract
An attempt was made to reproduce, using the Schwartz function method, the well-known exact solution of Kinnersley to the problem of capillary waves on the surface of a liquid of finite depth. However, as a result, a new exact solution was obtained, which does not coincide with the solution of Kinnersley, although it is expressed in the same terms of Jacobi elliptic functions. The results of an independent numerical verification of the new solution are presented, confirming its reliability. The parametric analysis of the solution revealed, in particular, a nonmonotonic dependence of the wavelength and its amplitude on the Weber number.
{"title":"Exact Solution for Capillary Waves on the Surface of a Liquid of Finite Depth","authors":"M. M. Alimov","doi":"10.3103/s1066369x23090050","DOIUrl":"https://doi.org/10.3103/s1066369x23090050","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An attempt was made to reproduce, using the Schwartz function method, the well-known exact solution of Kinnersley to the problem of capillary waves on the surface of a liquid of finite depth. However, as a result, a new exact solution was obtained, which does not coincide with the solution of Kinnersley, although it is expressed in the same terms of Jacobi elliptic functions. The results of an independent numerical verification of the new solution are presented, confirming its reliability. The parametric analysis of the solution revealed, in particular, a nonmonotonic dependence of the wavelength and its amplitude on the Weber number.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138682804","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 : 2023-12-15DOI: 10.3103/s1066369x23090049
D. I. Akramova
Abstract
The second initial-boundary value problem in a bounded domain for a fractional-diffusion equation with the Bessel operator and the Gerasimov–Caputo derivative is investigated. Theorems of existence and uniqueness of the solution to the inverse problem of determining the lowest coefficient in a one-dimensional fractional-diffusion equation under the condition of integral observation are obtained. The Schauder principle was used to prove the existence of the solution.
{"title":"Inverse Coefficient Problem for a Fractional-Diffusion Equation with a Bessel Operator","authors":"D. I. Akramova","doi":"10.3103/s1066369x23090049","DOIUrl":"https://doi.org/10.3103/s1066369x23090049","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The second initial-boundary value problem in a bounded domain for a fractional-diffusion equation with the Bessel operator and the Gerasimov–Caputo derivative is investigated. Theorems of existence and uniqueness of the solution to the inverse problem of determining the lowest coefficient in a one-dimensional fractional-diffusion equation under the condition of integral observation are obtained. The Schauder principle was used to prove the existence of the solution.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138682666","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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