Pub Date : 2024-11-01DOI: 10.1016/j.rinam.2024.100513
Tuan Anh Pham , Nhat Huy Vu , Minh Tuan Nguyen
This paper presents a new approach to the norm decay rates of the Fourier oscillatory integral operators for some classes of degenerate phases. In particular, the sharp norm decay rates of the Fourier oscillatory integral operators for homogeneous-type polynomial phases, and those for a class of nonsmooth polynomial hybrid phase functions are obtained.
{"title":"Norm decay rates of the Fourier oscillatory integral operators for a class of homogeneous-type polynomial hybrid phases","authors":"Tuan Anh Pham , Nhat Huy Vu , Minh Tuan Nguyen","doi":"10.1016/j.rinam.2024.100513","DOIUrl":"10.1016/j.rinam.2024.100513","url":null,"abstract":"<div><div>This paper presents a new approach to the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> norm decay rates of the Fourier oscillatory integral operators for some classes of degenerate phases. In particular, the sharp norm decay rates of the Fourier oscillatory integral operators for homogeneous-type polynomial phases, and those for a class of nonsmooth polynomial hybrid phase functions are obtained.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100513"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, a class of nonlinear Volterra delay integral equations of the third kind (VDIEs) is approximated by an efficient manner. At first, by using some conditions the existence and uniqueness of the solution is discussed based on the nonlinear cordial Volterra integral operators. Moreover, its convergence analysis is shown by using interpolation properties through some theorems and lemmas. Also, some examples are given and the results are compared with their exact solutions to demonstrate the reliability and capability of this algorithm.
{"title":"A capable numerical scheme for solving nonlinear Volterra delay integral equations of the third kind","authors":"Rohollah Ghaedi Ghalini , Esmail Hesameddini , Hojatollah Laeli Dastjerdi","doi":"10.1016/j.rinam.2024.100512","DOIUrl":"10.1016/j.rinam.2024.100512","url":null,"abstract":"<div><div>In this paper, a class of nonlinear Volterra delay integral equations of the third kind (VDIEs) is approximated by an efficient manner. At first, by using some conditions the existence and uniqueness of the solution is discussed based on the nonlinear cordial Volterra integral operators. Moreover, its convergence analysis is shown by using interpolation properties through some theorems and lemmas. Also, some examples are given and the results are compared with their exact solutions to demonstrate the reliability and capability of this algorithm.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100512"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-01DOI: 10.1016/j.rinam.2024.100516
Yuntong Li, Lina Liu
Dictionary learning (DL) has been widely used for seismic data denoising. However, it is associated with the following challenges. First, learning a dictionary from one dataset cannot be applied to another dataset and requires setting learning and denoising parameters, which is not adaptive. Second, the DL method based on sparse constraints adds sparse regularization terms to the coefficients, while seismic data only has many coefficients close to zero, which can be approximated as sparse. To overcome these challenges, we propose a seismic data denoising approach using deep convolutional dictionary learning(DCDL) that integrates the explanatory power of DL with the robust learning capacity of deep neural networks. The proposed approach replaces sparse priors with coefficient priors learned from the training dataset and system learns adaptive dictionaries for each seismic datapoint to maintain the data structure. Synthetic and field data in the experiment demonstrate that our method effectively suppresses random noise and maintains seismic data events.
{"title":"Three-dimensional seismic denoising based on deep convolutional dictionary learning","authors":"Yuntong Li, Lina Liu","doi":"10.1016/j.rinam.2024.100516","DOIUrl":"10.1016/j.rinam.2024.100516","url":null,"abstract":"<div><div>Dictionary learning (DL) has been widely used for seismic data denoising. However, it is associated with the following challenges. First, learning a dictionary from one dataset cannot be applied to another dataset and requires setting learning and denoising parameters, which is not adaptive. Second, the DL method based on sparse constraints adds sparse regularization terms to the coefficients, while seismic data only has many coefficients close to zero, which can be approximated as sparse. To overcome these challenges, we propose a seismic data denoising approach using deep convolutional dictionary learning(DCDL) that integrates the explanatory power of DL with the robust learning capacity of deep neural networks. The proposed approach replaces sparse priors with coefficient priors learned from the training dataset and system learns adaptive dictionaries for each seismic datapoint to maintain the data structure. Synthetic and field data in the experiment demonstrate that our method effectively suppresses random noise and maintains seismic data events.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100516"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-01DOI: 10.1016/j.rinam.2024.100504
Haneen Badawi , Omar Abu Arqub , Nabil Shawagfeh
In this paper, the existence and uniqueness of a specific class of fractional stochastic integro-differential equations considering the stochastic Brownian motion equipped with an appropriate form of a random initial condition is introduced regarding the Hilfer fractional derivative. The proofs of the existence and uniqueness of the solution are presented utilizing sensible constraints upon the deterministic and stochastic coefficients, Schauder's fixed point theorem, and some stochastic theories. Moreover, to get approximations of the exact paths solving such equations we introduce a numerical technique based upon the time-dependent spectral collocation technique considering the shifted Legendre polynomials as a basis. The underlying concept of this technique involves transforming complex equations into a set of algebraic ones by selecting an appropriate set of collocation points within the specified domain where collocation is applied. Herein, the values of the stochastic Brownian motion are calculated using the Mathematica program. For approximating the integrals, the Gauss–Legendre integration scheme is implemented. In addition, we establish the convergence concerning the presented scheme with the error estimate in detail. For this purpose, we present the graphs of maximum errors under the log-log scale. The utilized procedure is leveraged to tackle a variety of stochastic examples encompassing various types to confirm the effectiveness of the obtained theoretical and numerical results. The acquired upshots expose the efficiency and applicability of the presented methodology in the fractional stochastic field.
{"title":"Existence, uniqueness, and collocation solutions using the shifted Legendre spectral method for the Hilfer fractional stochastic integro-differential equations regarding stochastic Brownian motion","authors":"Haneen Badawi , Omar Abu Arqub , Nabil Shawagfeh","doi":"10.1016/j.rinam.2024.100504","DOIUrl":"10.1016/j.rinam.2024.100504","url":null,"abstract":"<div><div>In this paper, the existence and uniqueness of a specific class of fractional stochastic integro-differential equations considering the stochastic Brownian motion equipped with an appropriate form of a random initial condition is introduced regarding the Hilfer fractional derivative. The proofs of the existence and uniqueness of the solution are presented utilizing sensible constraints upon the deterministic and stochastic coefficients, Schauder's fixed point theorem, and some stochastic theories. Moreover, to get approximations of the exact paths solving such equations we introduce a numerical technique based upon the time-dependent spectral collocation technique considering the shifted Legendre polynomials as a basis. The underlying concept of this technique involves transforming complex equations into a set of algebraic ones by selecting an appropriate set of collocation points within the specified domain where collocation is applied. Herein, the values of the stochastic Brownian motion are calculated using the Mathematica program. For approximating the integrals, the Gauss–Legendre integration scheme is implemented. In addition, we establish the convergence concerning the presented scheme with the error estimate in detail. For this purpose, we present the graphs of maximum errors under the log-log scale. The utilized procedure is leveraged to tackle a variety of stochastic examples encompassing various types to confirm the effectiveness of the obtained theoretical and numerical results. The acquired upshots expose the efficiency and applicability of the presented methodology in the fractional stochastic field.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100504"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-01DOI: 10.1016/j.rinam.2024.100509
Soufiane Moussaten
The present paper deals with the study of the cross-variation of two-dimensional stochastic process defined using the Young integral with respect to a continuous, -self-similar Gaussian process that does not necessarily have stationary increments, with increment exponent some . We analyze the limit, in probability, of the so-called cross-variation when in , and we finish by providing some examples of known processes that satisfy the required assumptions.
{"title":"On the cross-variation of a class of stochastic processes","authors":"Soufiane Moussaten","doi":"10.1016/j.rinam.2024.100509","DOIUrl":"10.1016/j.rinam.2024.100509","url":null,"abstract":"<div><div>The present paper deals with the study of the cross-variation of two-dimensional stochastic process defined using the Young integral with respect to a continuous, <span><math><mi>α</mi></math></span>-self-similar Gaussian process that does not necessarily have stationary increments, with increment exponent some <span><math><mrow><mi>β</mi><mo>></mo><mn>0</mn></mrow></math></span>. We analyze the limit, in probability, of the so-called cross-variation when <span><math><mi>β</mi></math></span> in <span><math><mfenced><mrow><mn>0</mn><mo>,</mo><mn>2</mn><mi>α</mi></mrow></mfenced></math></span>, and we finish by providing some examples of known processes that satisfy the required assumptions.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100509"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-01DOI: 10.1016/j.rinam.2024.100517
M.J. Huntul
This paper focuses on the backward problem related to an integro-differential equation with a general convolutional derivative in time and nonlinear source terms. The existence, uniqueness, and regularity of the mild solution to the proposed problem are established under certain assumptions in a suitable space. The proposed problem is ill-posed in the sense of Hadamard. Moreover, the Fourier truncation method is used to construct a regularized solution. Finally, the convergence rate between the regularized solution and the exact solution is determined.
{"title":"Analyzing inverse backward problem in nonlinear integro-differential equation with memory kernel","authors":"M.J. Huntul","doi":"10.1016/j.rinam.2024.100517","DOIUrl":"10.1016/j.rinam.2024.100517","url":null,"abstract":"<div><div>This paper focuses on the backward problem related to an integro-differential equation with a general convolutional derivative in time and nonlinear source terms. The existence, uniqueness, and regularity of the mild solution to the proposed problem are established under certain assumptions in a suitable space. The proposed problem is ill-posed in the sense of Hadamard. Moreover, the Fourier truncation method is used to construct a regularized solution. Finally, the convergence rate between the regularized solution and the exact solution is determined.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100517"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-01DOI: 10.1016/j.rinam.2024.100515
Abdelbaki Choucha , Salah Boulaaras , Fares Yazid , Rashid Jan , Ibrahim Mekawy
The nonlinear wave equation with acoustic and fractional boundary conditions, coupled with logarithmic source and delay terms, is notable for its capacity to model complex systems, contribute to the advancement of mathematical theory, and exhibit wide-ranging applicability to real-world problems. This paper investigates the global existence and general decay of solutions to a wave equation characterized by the inclusion of logarithmic source and delay terms, governed by both fractional and acoustic boundary conditions. The global existence of solutions is analyzed under various hypotheses, and the general decay behavior is established through the construction and application of a suitable Lyapunov function.
{"title":"Results on a nonlinear wave equation with acoustic and fractional boundary conditions coupling by logarithmic source and delay terms: Global existence and asymptotic behavior of solutions","authors":"Abdelbaki Choucha , Salah Boulaaras , Fares Yazid , Rashid Jan , Ibrahim Mekawy","doi":"10.1016/j.rinam.2024.100515","DOIUrl":"10.1016/j.rinam.2024.100515","url":null,"abstract":"<div><div>The nonlinear wave equation with acoustic and fractional boundary conditions, coupled with logarithmic source and delay terms, is notable for its capacity to model complex systems, contribute to the advancement of mathematical theory, and exhibit wide-ranging applicability to real-world problems. This paper investigates the global existence and general decay of solutions to a wave equation characterized by the inclusion of logarithmic source and delay terms, governed by both fractional and acoustic boundary conditions. The global existence of solutions is analyzed under various hypotheses, and the general decay behavior is established through the construction and application of a suitable Lyapunov function.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100515"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142655288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-01DOI: 10.1016/j.rinam.2024.100507
Alicia Cordero , Renso V. Rojas-Hiciano , Juan R. Torregrosa , Maria P. Vassileva
We present three new approaches for solving first-order quasi-linear partial differential equations (PDEs) with iterative methods of high stability and low cost. The first is a new numerical version of the method of characteristics that converges efficiently, under certain conditions. The next two approaches initially apply the unconditionally stable Crank–Nicolson method, which induces a system of nonlinear equations. In one of them, we solve this system by using the first optimal schemes for systems of order four (Ermakov’s Hyperfamily). In the other approach, using a new technique called JARM decoupling, we perform a modification that significantly reduces the complexity of the scheme, which we solve with scalar versions of the aforementioned iterative methods. This is a substantial improvement over the conventional way of solving the system. The high numerical performance of the three approaches is checked when analyzing the resolution of some examples of nonlinear PDEs.
{"title":"High-efficiency implicit scheme for solving first-order partial differential equations","authors":"Alicia Cordero , Renso V. Rojas-Hiciano , Juan R. Torregrosa , Maria P. Vassileva","doi":"10.1016/j.rinam.2024.100507","DOIUrl":"10.1016/j.rinam.2024.100507","url":null,"abstract":"<div><div>We present three new approaches for solving first-order quasi-linear partial differential equations (PDEs) with iterative methods of high stability and low cost. The first is a new numerical version of the method of characteristics that converges efficiently, under certain conditions. The next two approaches initially apply the unconditionally stable Crank–Nicolson method, which induces a system of nonlinear equations. In one of them, we solve this system by using the first optimal schemes for systems of order four (Ermakov’s Hyperfamily). In the other approach, using a new technique called JARM decoupling, we perform a modification that significantly reduces the complexity of the scheme, which we solve with scalar versions of the aforementioned iterative methods. This is a substantial improvement over the conventional way of solving the system. The high numerical performance of the three approaches is checked when analyzing the resolution of some examples of nonlinear PDEs.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100507"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this paper is to determine a new discussion on trajectory-(T) controllability of time variant impulsive neutral stochastic functional integrodifferential equations (INSFIDEs) driven by fractional Brownian motion (fBm) via noncompact semigroup in a Hilbert space. Initially, with the help of the Hausdorff measure of noncompactness (HMN), the Mönch fixed point theorem and some inequality techniques, some new standards to guarantee the mild solution for INSFIDEs are obtained. The system’s T-controllability is then examined using Gronwall’s inequality. An example is given to validate the results at the end. This work is applicable to the heart disease biological system using parametric smoothing technique with modifying time variable. Our work extends the work of Boufoussi and Hajji (2012), Chen (2010), Caraballoa et al., (2011), Boudaoui et al., (2015).
{"title":"New discussion on trajectory controllability of time-variant impulsive neutral stochastic functional integrodifferential equations via noncompact semigroup","authors":"Dhanalakshmi Kasinathan , Ravikumar Kasinathan , Ramkumar Kasinathan , Dimplekumar Chalishajar","doi":"10.1016/j.rinam.2024.100518","DOIUrl":"10.1016/j.rinam.2024.100518","url":null,"abstract":"<div><div>The purpose of this paper is to determine a new discussion on trajectory-(T) controllability of time variant impulsive neutral stochastic functional integrodifferential equations (INSFIDEs) driven by fractional Brownian motion (fBm) via noncompact semigroup in a Hilbert space. Initially, with the help of the Hausdorff measure of noncompactness (HMN), the Mönch fixed point theorem and some inequality techniques, some new standards to guarantee the mild solution for INSFIDEs are obtained. The system’s T-controllability is then examined using Gronwall’s inequality. An example is given to validate the results at the end. This work is applicable to the heart disease biological system using parametric smoothing technique with modifying time variable. Our work extends the work of Boufoussi and Hajji (2012), Chen (2010), Caraballoa et al., (2011), Boudaoui et al., (2015).</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100518"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142759536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-01DOI: 10.1016/j.rinam.2024.100503
José Fernández Goycoolea , Luis H. Herrera , Pablo Pérez-Lantero , Carlos Seara
The coarseness of a set of points in the plane colored red and blue is a measure of how well the points are mixed together. It has appealing theoretical properties, including a connection to the set of points tendency to accept a good clustering partition. Yet, it is computationally expensive to compute exactly. In this paper, the notion of computing the coarseness using a guillotine partition approach is introduced, and efficient algorithms for computing this guillotine coarseness are presented: a top-down approach and a dynamic programming approach, both of them achieving polynomial time and space complexities. Finally, an even faster polynomial-time algorithm to compute a reduced version of the measurement named two-level guillotine coarseness is presented using geometric data structures for faster computations. These restrictions establish lower bounds for the general guillotine coarseness that allow the development of more efficient algorithms for computing it.
{"title":"Computing the coarseness measure of a bicolored point set over guillotine partitions","authors":"José Fernández Goycoolea , Luis H. Herrera , Pablo Pérez-Lantero , Carlos Seara","doi":"10.1016/j.rinam.2024.100503","DOIUrl":"10.1016/j.rinam.2024.100503","url":null,"abstract":"<div><div>The coarseness of a set of points in the plane colored red and blue is a measure of how well the points are mixed together. It has appealing theoretical properties, including a connection to the set of points tendency to accept a good clustering partition. Yet, it is computationally expensive to compute exactly. In this paper, the notion of computing the coarseness using a guillotine partition approach is introduced, and efficient algorithms for computing this guillotine coarseness are presented: a top-down approach and a dynamic programming approach, both of them achieving polynomial time and space complexities. Finally, an even faster <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mo>log</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>n</mi><mo>)</mo></mrow></mrow></math></span> polynomial-time algorithm to compute a reduced version of the measurement named two-level guillotine coarseness is presented using geometric data structures for faster computations. These restrictions establish lower bounds for the general guillotine coarseness that allow the development of more efficient algorithms for computing it.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"24 ","pages":"Article 100503"},"PeriodicalIF":1.4,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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