Pub Date : 2025-01-07DOI: 10.1016/j.cam.2025.116486
Qingjie Hu, Ruyun Li, Yanyan Zhang
Vector optimization problems are a critical class of optimization problems that find extensive application in fields such as engineering design, space exploration, and management science. Currently, the investigation into methodologies for addressing these issues forms an active area of research. In this paper, we propose a modified Hestenes–Stiefel (HS) conjugate gradient method for solving unconstrained vector optimization problems. It can be viewed as the generalization of the vector version of the HS+ conjugate gradient method. At each iteration of the algorithm, a search direction that satisfy the sufficient descent condition is generated without any line search or convexity. Global convergence of the algorithm is proved under the standard vector Wolfe line search. Numerical results show that the proposed method is effective. In particular, this method can properly generate the Pareto fronts for the test problems.
{"title":"A vector restricted variant MVHS+ CG method based algorithm for unconstrained vector optimization problems","authors":"Qingjie Hu, Ruyun Li, Yanyan Zhang","doi":"10.1016/j.cam.2025.116486","DOIUrl":"10.1016/j.cam.2025.116486","url":null,"abstract":"<div><div>Vector optimization problems are a critical class of optimization problems that find extensive application in fields such as engineering design, space exploration, and management science. Currently, the investigation into methodologies for addressing these issues forms an active area of research. In this paper, we propose a modified Hestenes–Stiefel (HS) conjugate gradient method for solving unconstrained vector optimization problems. It can be viewed as the generalization of the vector version of the HS+ conjugate gradient method. At each iteration of the algorithm, a search direction that satisfy the sufficient descent condition is generated without any line search or convexity. Global convergence of the algorithm is proved under the standard vector Wolfe line search. Numerical results show that the proposed method is effective. In particular, this method can properly generate the Pareto fronts for the test problems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"463 ","pages":"Article 116486"},"PeriodicalIF":2.1,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-07DOI: 10.1016/j.cam.2024.116448
Mohammadreza Jahangiri, Alireza Nazemi
In this study, the solution of the fuzzy nonlinear optimization problems is achieved by a recurrent neural network model. Since there are a few researches for solving fuzzy optimization problems by neural networks, we introduce a new model with reduced complexity to solve the problem. By reformulating the original program to an interval problem and then a weighting problem, the Karush–Kuhn–Tucker optimality conditions are stated. Moreover, we employ the optimality conditions into a neural network as a basic tool to solve the problem. Besides, the global convergence and the Lyapunov stability analysis of the system are debated in this study. Finally, different numerical examples allow to validate our algorithm with the proposed neural network compared to some other alternative networks.
{"title":"An efficient RNN based algorithm for solving fuzzy nonlinear constrained programming problems with numerical experiments","authors":"Mohammadreza Jahangiri, Alireza Nazemi","doi":"10.1016/j.cam.2024.116448","DOIUrl":"10.1016/j.cam.2024.116448","url":null,"abstract":"<div><div>In this study, the solution of the fuzzy nonlinear optimization problems is achieved by a recurrent neural network model. Since there are a few researches for solving fuzzy optimization problems by neural networks, we introduce a new model with reduced complexity to solve the problem. By reformulating the original program to an interval problem and then a weighting problem, the Karush–Kuhn–Tucker optimality conditions are stated. Moreover, we employ the optimality conditions into a neural network as a basic tool to solve the problem. Besides, the global convergence and the Lyapunov stability analysis of the system are debated in this study. Finally, different numerical examples allow to validate our algorithm with the proposed neural network compared to some other alternative networks.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"463 ","pages":"Article 116448"},"PeriodicalIF":2.1,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-07DOI: 10.1016/j.cam.2025.116489
Wenxiu Guo , Jianqing Li , Yongyao Li , Xiaoping Lu , Hua Zheng
In this work, a modulus-based inner–outer iteration method for solving a class of large sparse nonlinear complementarity problems with weak nonlinearity is constructed. The convergence of the proposed method is analyzed when the system matrix is assumed to be an -matrix. Some numerical examples are presented to show that the proposed method can converge faster than the existing modulus-based matrix splitting iteration method.
{"title":"A modulus-based inner–outer iteration method for nonlinear complementarity problems","authors":"Wenxiu Guo , Jianqing Li , Yongyao Li , Xiaoping Lu , Hua Zheng","doi":"10.1016/j.cam.2025.116489","DOIUrl":"10.1016/j.cam.2025.116489","url":null,"abstract":"<div><div>In this work, a modulus-based inner–outer iteration method for solving a class of large sparse nonlinear complementarity problems with weak nonlinearity is constructed. The convergence of the proposed method is analyzed when the system matrix is assumed to be an <span><math><msub><mrow><mi>H</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>-matrix. Some numerical examples are presented to show that the proposed method can converge faster than the existing modulus-based matrix splitting iteration method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"463 ","pages":"Article 116489"},"PeriodicalIF":2.1,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-06DOI: 10.1016/j.cam.2024.116476
Siyang Wang
The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth’s crust, taking into account of both the elastic properties of rocks and the dissipative effects due to internal friction and viscosity; acoustic waves propagating through biological tissues, where both elastic and viscous effects play a significant role. We propose a stable and high-order finite difference method for solving the governing equations. By designing the spatial discretization with the summation-by-parts property, we prove stability by deriving a discrete energy estimate. In addition, we derive error estimates for problems with constant coefficients using the normal mode analysis and for problems with variable coefficients using the energy method. Numerical examples are presented to demonstrate the stability and accuracy properties of the developed method.
{"title":"Stable and high-order accurate finite difference methods for the diffusive viscous wave equation","authors":"Siyang Wang","doi":"10.1016/j.cam.2024.116476","DOIUrl":"10.1016/j.cam.2024.116476","url":null,"abstract":"<div><div>The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth’s crust, taking into account of both the elastic properties of rocks and the dissipative effects due to internal friction and viscosity; acoustic waves propagating through biological tissues, where both elastic and viscous effects play a significant role. We propose a stable and high-order finite difference method for solving the governing equations. By designing the spatial discretization with the summation-by-parts property, we prove stability by deriving a discrete energy estimate. In addition, we derive error estimates for problems with constant coefficients using the normal mode analysis and for problems with variable coefficients using the energy method. Numerical examples are presented to demonstrate the stability and accuracy properties of the developed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"463 ","pages":"Article 116476"},"PeriodicalIF":2.1,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-05DOI: 10.1016/j.cam.2025.116505
Qiqi Zhou , Huiming Duan , Derong Xie
The Intelligent Transport System (ITS) has been proven to be an effective way to solve urban traffic congestion and improve road capacity, the traffic guidance system is an important part of ITS, and short-time traffic flow prediction is the key issue for the traffic guidance system. In this paper, a second-order multivariate partial grey prediction model based on traffic flow kinematics equation is constructed from the traffic flow kinematics equations to study the spatio-temporal and partial grey prediction model mechanism of complex road networks. The structure of this new model has good interpretability and can capture some nonlinear features of the data, which can portray the dynamic evolution law of traffic flow in two-dimensional road networks. Meanwhile, the least squares technique is used to estimate the parameters of this model, and the model is solved by the Runge-Kutta formula, which solves the problem of solving the multivariate nonlinear system of equations and ensures the high efficiency and accuracy of the model computation. The spatiotemporal and cyclical nature of traffic flow data was considered, and traffic flow data from multiple road sections were selected by the grey correlation analysis method. Finally, the traffic flow data at the same time of different road sections and the traffic flow data at different times of the same road sections are selected to analyze the effectiveness of the new model using four cases, and it is illustrated through the experimental results that the new model has a higher fitting accuracy, which is better than the other five grey prediction models. At the same time, the new model effectively predicts the traffic flow of the two road sections in different periods, and can accurately insight into the trend of traffic flow, the results can provide real-time and accurate traffic flow data for the traffic guidance system, and can also improve the overall operational efficiency of the urban transport system.
{"title":"A multivariate partial grey prediction model based on second-order traffic flow kinematics equation and its application","authors":"Qiqi Zhou , Huiming Duan , Derong Xie","doi":"10.1016/j.cam.2025.116505","DOIUrl":"10.1016/j.cam.2025.116505","url":null,"abstract":"<div><div>The Intelligent Transport System (ITS) has been proven to be an effective way to solve urban traffic congestion and improve road capacity, the traffic guidance system is an important part of ITS, and short-time traffic flow prediction is the key issue for the traffic guidance system. In this paper, a second-order multivariate partial grey prediction model based on traffic flow kinematics equation is constructed from the traffic flow kinematics equations to study the spatio-temporal and partial grey prediction model mechanism of complex road networks. The structure of this new model has good interpretability and can capture some nonlinear features of the data, which can portray the dynamic evolution law of traffic flow in two-dimensional road networks. Meanwhile, the least squares technique is used to estimate the parameters of this model, and the model is solved by the Runge-Kutta formula, which solves the problem of solving the multivariate nonlinear system of equations and ensures the high efficiency and accuracy of the model computation. The spatiotemporal and cyclical nature of traffic flow data was considered, and traffic flow data from multiple road sections were selected by the grey correlation analysis method. Finally, the traffic flow data at the same time of different road sections and the traffic flow data at different times of the same road sections are selected to analyze the effectiveness of the new model using four cases, and it is illustrated through the experimental results that the new model has a higher fitting accuracy, which is better than the other five grey prediction models. At the same time, the new model effectively predicts the traffic flow of the two road sections in different periods, and can accurately insight into the trend of traffic flow, the results can provide real-time and accurate traffic flow data for the traffic guidance system, and can also improve the overall operational efficiency of the urban transport system.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"463 ","pages":"Article 116505"},"PeriodicalIF":2.1,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.cam.2024.116482
Chunming Tang , Wancheng Tan , Yongshen Zhang , Zhixian Liu
The conjugate gradient (CG) method and its accelerated variants are an efficient class of methods for solving unconstrained optimization problems in Euclidean space. This paper aims to develop an accelerated spectral CG (SCG) method for solving optimization problems on Riemannian manifolds. A general algorithmic framework for the accelerated Riemannian SCG (ARSCG) method is presented, in which a general transport mapping is introduced and the Riemannian spectral parameter ensures that the search direction is always a descent direction of the objective function. By adjusting the stepsize of the Riemannian CG method, we enhance the rate of descent of the objective function. The global convergence of the algorithm is established under the assumption that the absolute value of the CG parameter does not exceed the Fletcher–Reeves CG parameter. Moreover, a linear convergence rate is demonstrated under the assumption that the objective function is geodesically strongly convex. Finally, some preliminary numerical results are reported, indicating the proposed algorithm ARSCG performs well numerically compared to some related Riemannian CG methods.
{"title":"An accelerated spectral CG based algorithm for optimization techniques on Riemannian manifolds and its comparative evaluation","authors":"Chunming Tang , Wancheng Tan , Yongshen Zhang , Zhixian Liu","doi":"10.1016/j.cam.2024.116482","DOIUrl":"10.1016/j.cam.2024.116482","url":null,"abstract":"<div><div>The conjugate gradient (CG) method and its accelerated variants are an efficient class of methods for solving unconstrained optimization problems in Euclidean space. This paper aims to develop an accelerated spectral CG (SCG) method for solving optimization problems on Riemannian manifolds. A general algorithmic framework for the accelerated Riemannian SCG (ARSCG) method is presented, in which a general transport mapping is introduced and the Riemannian spectral parameter ensures that the search direction is always a descent direction of the objective function. By adjusting the stepsize of the Riemannian CG method, we enhance the rate of descent of the objective function. The global convergence of the algorithm is established under the assumption that the absolute value of the CG parameter does not exceed the Fletcher–Reeves CG parameter. Moreover, a linear convergence rate is demonstrated under the assumption that the objective function is geodesically strongly convex. Finally, some preliminary numerical results are reported, indicating the proposed algorithm ARSCG performs well numerically compared to some related Riemannian CG methods.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"462 ","pages":"Article 116482"},"PeriodicalIF":2.1,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.cam.2024.116478
Ondřej Bublík , Václav Heidler , Jan Vimmr
This paper aims to design a computational model for simulating the unsteady flow field in a cascade of oscillating blades. The core of the new model is a convolutional neural network, which is trained on a simplified cascade consisting of three blades. The primary advantage lies in significantly reducing the computational cost, as the new model is several orders of magnitude faster than traditional CFD methods for evaluations, though training the model remains computationally intensive. The convolutional neural network can accurately predict the unsteady flow field, as demonstrated in validation examples. In the next step, a composition algorithm is proposed to combine several simplified cases, enabling the solution of a cascade with any number of blades.
{"title":"Convolution neural network for fluid flow simulations in cascade with oscillating blades","authors":"Ondřej Bublík , Václav Heidler , Jan Vimmr","doi":"10.1016/j.cam.2024.116478","DOIUrl":"10.1016/j.cam.2024.116478","url":null,"abstract":"<div><div>This paper aims to design a computational model for simulating the unsteady flow field in a cascade of oscillating blades. The core of the new model is a convolutional neural network, which is trained on a simplified cascade consisting of three blades. The primary advantage lies in significantly reducing the computational cost, as the new model is several orders of magnitude faster than traditional CFD methods for evaluations, though training the model remains computationally intensive. The convolutional neural network can accurately predict the unsteady flow field, as demonstrated in validation examples. In the next step, a composition algorithm is proposed to combine several simplified cases, enabling the solution of a cascade with any number of blades.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"462 ","pages":"Article 116478"},"PeriodicalIF":2.1,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.cam.2024.116480
Marcio Antônio de Andrade Bortoloti
In this paper, we perform an analysis of the Descent Gradient Method (DGM) within the context of the conformable fractional derivatives. We explore the mathematical properties of functions with continuous Lipschitz gradients. Notably, this fractional derivative approach significantly reduced computational effort when compared to the conventional DGM. Additionally, we present a detailed numerical example to prove the high performance of this generalized DGM algorithm.
{"title":"Computational performance of a generalized descent gradient method based algorithm with conformable fractional-order derivatives","authors":"Marcio Antônio de Andrade Bortoloti","doi":"10.1016/j.cam.2024.116480","DOIUrl":"10.1016/j.cam.2024.116480","url":null,"abstract":"<div><div>In this paper, we perform an analysis of the Descent Gradient Method (DGM) within the context of the conformable fractional derivatives. We explore the mathematical properties of functions with continuous Lipschitz gradients. Notably, this fractional derivative approach significantly reduced computational effort when compared to the conventional DGM. Additionally, we present a detailed numerical example to prove the high performance of this generalized DGM algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"462 ","pages":"Article 116480"},"PeriodicalIF":2.1,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-03DOI: 10.1016/j.cam.2024.116484
Hailun Xu, Hongmei Kang
Quasi-interpolation based on analysis-suitable T-splines (AS T-splines) has been considered by Kang et al. (2022), but the provided method is only able to reproduce polynomial spaces. In this paper, we consider quasi-interpolation constructed from the local tensor product of linear functionals in univariate B-spline projectors. Thanks to the dual-compatibility property of AS T-splines, such quasi-interpolation leads to AS T-spline projectors. For practical applications, we provide explicit expressions and norm estimates for the projections of quadratic and cubic AS T-splines. We also present a comparison between the proposed AS T-spline projectors and several existing AS T-spline quasi-interpolations.
{"title":"Local spline projectors of analysis-suitable T-splines","authors":"Hailun Xu, Hongmei Kang","doi":"10.1016/j.cam.2024.116484","DOIUrl":"10.1016/j.cam.2024.116484","url":null,"abstract":"<div><div>Quasi-interpolation based on analysis-suitable T-splines (AS T-splines) has been considered by Kang et al. (2022), but the provided method is only able to reproduce polynomial spaces. In this paper, we consider quasi-interpolation constructed from the local tensor product of linear functionals in univariate B-spline projectors. Thanks to the dual-compatibility property of AS T-splines, such quasi-interpolation leads to AS T-spline projectors. For practical applications, we provide explicit expressions and norm estimates for the projections of quadratic and cubic AS T-splines. We also present a comparison between the proposed AS T-spline projectors and several existing AS T-spline quasi-interpolations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"462 ","pages":"Article 116484"},"PeriodicalIF":2.1,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The generalized alternating direction method of multipliers (GADMM) has attracted considerable attention due to its versatile applications. This study introduces an innovative adaptation called the linearized GADMM (L-GADMM), which is specifically tailored for solving convex optimization problems. The objective function of the problems under consideration encompasses three distinct convex components with no interdependencies among variables or linear constraints. We establish a set of sufficient conditions ensuring the global convergence of the proposed L-GADMM technique for the three-block separable convex minimization problem. Moreover, a series of numerical experiments are conducted to showcase the effectiveness of L-GADMM in tasks such as image compression and calibration of correlation matrices.
{"title":"A three-block linearized generalized ADMM based iterative algorithm for separable convex programming with application to an image compression problem","authors":"Xueqing Zhang , Jianwen Peng , Debdas Ghosh , Jen-Chih Yao","doi":"10.1016/j.cam.2024.116483","DOIUrl":"10.1016/j.cam.2024.116483","url":null,"abstract":"<div><div>The <em>generalized alternating direction method of multipliers</em> (GADMM) has attracted considerable attention due to its versatile applications. This study introduces an innovative adaptation called the linearized GADMM (L-GADMM), which is specifically tailored for solving convex optimization problems. The objective function of the problems under consideration encompasses three distinct convex components with no interdependencies among variables or linear constraints. We establish a set of sufficient conditions ensuring the global convergence of the proposed L-GADMM technique for the three-block separable convex minimization problem. Moreover, a series of numerical experiments are conducted to showcase the effectiveness of L-GADMM in tasks such as image compression and calibration of correlation matrices.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"462 ","pages":"Article 116483"},"PeriodicalIF":2.1,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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