Pub Date : 2025-05-01DOI: 10.1016/j.rinam.2025.100586
Bazar Babajanov , Fakhriddin Abdikarimov
In this paper we investigate the fractional modified Korteweg de Vries-sine-Gordon equation and show the inverse scattering transform method can also be used to obtain soliton solutions of fractional modified Korteweg de Vries-sine-Gordon equation. It is illustrated the relationship between the wave velocity and the parameter for the fractional modified Korteweg de Vries-sine-Gordon equation in the case of one soliton solution, then this result was compared with fractional modified Korteweg de Vries equation, fractional sine-Gordon equation and the modified Korteweg de Vries-sine-Gordon equation.
本文研究了分数阶修正Korteweg - de vries -sin - gordon方程，并证明了逆散射变换方法也可以用于得到分数阶修正Korteweg - de vries -sin - gordon方程的孤子解。给出了单孤子解情况下分数阶修正Korteweg de Vries-sin - gordon方程的波速与柱形参数的关系，并与分数阶修正Korteweg de Vries方程、分数阶修正sin - gordon方程和修正Korteweg de Vries-sin - gordon方程进行了比较。
{"title":"Integration of the fractional modified Korteweg de Vries-sine-Gordon equation by the inverse scattering method","authors":"Bazar Babajanov , Fakhriddin Abdikarimov","doi":"10.1016/j.rinam.2025.100586","DOIUrl":"10.1016/j.rinam.2025.100586","url":null,"abstract":"<div><div>In this paper we investigate the fractional modified Korteweg de Vries-sine-Gordon equation and show the inverse scattering transform method can also be used to obtain soliton solutions of fractional modified Korteweg de Vries-sine-Gordon equation. It is illustrated the relationship between the wave velocity and the <span><math><mi>ϵ</mi></math></span> parameter for the fractional modified Korteweg de Vries-sine-Gordon equation in the case of one soliton solution, then this result was compared with fractional modified Korteweg de Vries equation, fractional sine-Gordon equation and the modified Korteweg de Vries-sine-Gordon equation.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100586"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144220976","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 : 2025-05-01DOI: 10.1016/j.rinam.2025.100580
Khaled Kefi
This paper investigates multiplicity results of weak solutions to a degenerate weighted elliptic problem involving Leray–Lions operators with indefinite nonlinearity and variable exponents. Using critical point theory, we establish the existence of at least one, respectively three weak solutions under suitable assumptions. The results extend to a wide range of nonlinear problems in mathematical physics, addressing the complications arising from degeneracy, Hardy-type singularities, and indefinite source terms.
{"title":"Existence of weak solutions to degenerate Leray–Lions operators in weighted quasilinear elliptic equations with variable exponents, indefinite nonlinearity, and Hardy-type term","authors":"Khaled Kefi","doi":"10.1016/j.rinam.2025.100580","DOIUrl":"10.1016/j.rinam.2025.100580","url":null,"abstract":"<div><div>This paper investigates multiplicity results of weak solutions to a degenerate weighted elliptic problem involving Leray–Lions operators with indefinite nonlinearity and variable exponents. Using critical point theory, we establish the existence of at least one, respectively three weak solutions under suitable assumptions. The results extend to a wide range of nonlinear problems in mathematical physics, addressing the complications arising from degeneracy, Hardy-type singularities, and indefinite source terms.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100580"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143895723","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 : 2025-05-01DOI: 10.1016/j.rinam.2025.100577
Yue Shan, Yibin Lu
In traditional integral equation methods, the calculation of singular integrals often leads to numerical difficulties, especially when dealing with complex regions containing slits. To address the problems of mapping distortion and integration difficulties, this paper proposes a novel method that combines a premap function with the generalized Neumann kernel integral equation method, aimed at simulating irrotational planar flow with arc-shaped obstacles. Using a premap function based on the Joukowski transformation, a complex region is mapped to a regular region with smooth boundaries, significantly improving numerical stability and solution accuracy. An iterative algorithm is developed in conjunction with the integral equation method to simulate the flow characteristics in complex regions. Numerical simulations show that the method efficiently and stably handles flow fields in multi-connected regions, providing a reliable tool for applications in engineering and physical sciences.
{"title":"An integral equation method in conformal mapping of regions with circular slit","authors":"Yue Shan, Yibin Lu","doi":"10.1016/j.rinam.2025.100577","DOIUrl":"10.1016/j.rinam.2025.100577","url":null,"abstract":"<div><div>In traditional integral equation methods, the calculation of singular integrals often leads to numerical difficulties, especially when dealing with complex regions containing slits. To address the problems of mapping distortion and integration difficulties, this paper proposes a novel method that combines a premap function with the generalized Neumann kernel integral equation method, aimed at simulating irrotational planar flow with arc-shaped obstacles. Using a premap function based on the Joukowski transformation, a complex region is mapped to a regular region with smooth boundaries, significantly improving numerical stability and solution accuracy. An iterative algorithm is developed in conjunction with the integral equation method to simulate the flow characteristics in complex regions. Numerical simulations show that the method efficiently and stably handles flow fields in multi-connected regions, providing a reliable tool for applications in engineering and physical sciences.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100577"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143891245","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 : 2025-05-01DOI: 10.1016/j.rinam.2025.100579
Liuqing Hua , Wei Ma
In this paper, based on two-step Newton iterative procedure, we propose a two-step inexact Newton-like method for generalized inverse eigenvalue problems. Under some mild assumptions, our results show that the two-step inexact Newton-like method is super quadratically convergent. Numerical implementations demonstrate the effectiveness of the new method.
{"title":"Two-step inexact Newton-like method for solving generalized inverse eigenvalue problems","authors":"Liuqing Hua , Wei Ma","doi":"10.1016/j.rinam.2025.100579","DOIUrl":"10.1016/j.rinam.2025.100579","url":null,"abstract":"<div><div>In this paper, based on two-step Newton iterative procedure, we propose a two-step inexact Newton-like method for generalized inverse eigenvalue problems. Under some mild assumptions, our results show that the two-step inexact Newton-like method is super quadratically convergent. Numerical implementations demonstrate the effectiveness of the new method.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100579"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143911665","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 : 2025-05-01DOI: 10.1016/j.rinam.2025.100587
Suixin He , Shuangping Tao
An RD-space is a space of homogeneous type in the sense of Coifman and Weiss with the extra property that a reverse doubling property holds in . The authors establish the boundedness of the bilinear -type Calderón–Zygmund operator and its commutator in this setting. These are generated by the function and on generalized weighted Morrey space and generalized weighted weak Morrey space over RD-spaces.
{"title":"Bilinear θ-type Calderón–Zygmund operators and its commutator on generalized weighted Morrey spaces over RD-spaces","authors":"Suixin He , Shuangping Tao","doi":"10.1016/j.rinam.2025.100587","DOIUrl":"10.1016/j.rinam.2025.100587","url":null,"abstract":"<div><div>An RD-space <span><math><mi>X</mi></math></span> is a space of homogeneous type in the sense of Coifman and Weiss with the extra property that a reverse doubling property holds in <span><math><mi>X</mi></math></span>. The authors establish the boundedness of the bilinear <span><math><mi>θ</mi></math></span>-type Calderón–Zygmund operator <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>θ</mi></mrow></msub></math></span> and its commutator <span><math><mrow><mo>[</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>θ</mi></mrow></msub><mo>]</mo></mrow></math></span> in this setting. These are generated by the function <span><math><mrow><msub><mrow><mi>b</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>B</mi><mi>M</mi><mi>O</mi><mrow><mo>(</mo><mi>μ</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>θ</mi></mrow></msub></math></span> on generalized weighted Morrey space <span><math><mrow><msup><mrow><mi>M</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>ϕ</mi></mrow></msup><mrow><mo>(</mo><mi>ω</mi><mo>)</mo></mrow></mrow></math></span> and generalized weighted weak Morrey space <span><math><mrow><mi>W</mi><msup><mrow><mi>M</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>ϕ</mi></mrow></msup><mrow><mo>(</mo><mi>ω</mi><mo>)</mo></mrow></mrow></math></span> over RD-spaces.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100587"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116024","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 : 2025-05-01DOI: 10.1016/j.rinam.2025.100600
Yayoi Abe, Auna Setoh, Gen Yoneda
The vertex coloring problem to find chromatic numbers is known to be unsolvable in polynomial time. Although various algorithms have been proposed to efficiently compute chromatic numbers, they tend to take an enormous amount of time for large graphs. In this paper, we propose a recurrence relation to rapidly obtain the expected value of the chromatic number of random graphs. Then we compare the results obtained using this recurrence relation with other methods using an exact investigation of all graphs, the Monte Carlo method, the iterated random color matching method, and the method presented in Bollobás’ previous studies.
{"title":"Chromatic number of random graphs: An approach using a recurrence relation","authors":"Yayoi Abe, Auna Setoh, Gen Yoneda","doi":"10.1016/j.rinam.2025.100600","DOIUrl":"10.1016/j.rinam.2025.100600","url":null,"abstract":"<div><div>The vertex coloring problem to find chromatic numbers is known to be unsolvable in polynomial time. Although various algorithms have been proposed to efficiently compute chromatic numbers, they tend to take an enormous amount of time for large graphs. In this paper, we propose a recurrence relation to rapidly obtain the expected value of the chromatic number of random graphs. Then we compare the results obtained using this recurrence relation with other methods using an exact investigation of all graphs, the Monte Carlo method, the iterated random color matching method, and the method presented in Bollobás’ previous studies.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100600"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144253792","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 : 2025-05-01DOI: 10.1016/j.rinam.2025.100584
Somayeh Nemati , Salameh Sedaghat , Sajedeh Arefi
In this paper, a numerical method for solving space–time fractional Schrödinger equations is proposed. The method employs fractional-order Chelyshkov functions and their properties to derive the remainders associated with the main problem. The Riemann–Liouville fractional integral operator is applied to the basis functions, yielding exact results through the analytical representation of Chelyshkov polynomials. The real and imaginary parts of the functions involved in the problem are separated, transforming the Schrödinger equation into two equations. By approximating the fractional derivative of the unknown function and using a set of collocation points, the problem is reduced to a system of algebraic equations, the solution of which provides the numerical solution to the problem. Additionally, an error analysis is presented. Finally, numerical examples and their results demonstrate the efficiency and accuracy of the proposed scheme.
{"title":"A new numerical approach for solving space–time fractional Schrödinger differential equations via fractional-order Chelyshkov functions","authors":"Somayeh Nemati , Salameh Sedaghat , Sajedeh Arefi","doi":"10.1016/j.rinam.2025.100584","DOIUrl":"10.1016/j.rinam.2025.100584","url":null,"abstract":"<div><div>In this paper, a numerical method for solving space–time fractional Schrödinger equations is proposed. The method employs fractional-order Chelyshkov functions and their properties to derive the remainders associated with the main problem. The Riemann–Liouville fractional integral operator is applied to the basis functions, yielding exact results through the analytical representation of Chelyshkov polynomials. The real and imaginary parts of the functions involved in the problem are separated, transforming the Schrödinger equation into two equations. By approximating the fractional derivative of the unknown function and using a set of collocation points, the problem is reduced to a system of algebraic equations, the solution of which provides the numerical solution to the problem. Additionally, an error analysis is presented. Finally, numerical examples and their results demonstrate the efficiency and accuracy of the proposed scheme.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100584"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071845","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}
This paper uses the HCT finite element method and mesh adaptation technology to solve the nonlinear plate bending problem and conducts error analysis on the iterative method, including a priori and a posteriori error estimates. Our investigation exploits Hermite finite elements such as BELL and HSIEH-CLOUGH-TOCHER (HCT) triangles for conforming finite element discretization. We use an iterative resolution algorithm to linearize the associated discrete problem and study the convergence of this algorithm towards the solution of the approximate problem. An optimal a priori error estimation has been established. We construct a posteriori error indicators by distinguishing between discretization and linearization errors and prove their reliability and optimality. A numerical test is carried out and the results obtained confirm those established theoretically.
{"title":"Numerical solution and errors analysis of iterative method for a nonlinear plate bending problem","authors":"Akakpo Amoussou Wilfried , Houédanou Koffi Wilfrid","doi":"10.1016/j.rinam.2025.100576","DOIUrl":"10.1016/j.rinam.2025.100576","url":null,"abstract":"<div><div>This paper uses the HCT finite element method and mesh adaptation technology to solve the nonlinear plate bending problem and conducts error analysis on the iterative method, including a priori and a posteriori error estimates. Our investigation exploits Hermite finite elements such as BELL and HSIEH-CLOUGH-TOCHER (HCT) triangles for conforming finite element discretization. We use an iterative resolution algorithm to linearize the associated discrete problem and study the convergence of this algorithm towards the solution of the approximate problem. An optimal a priori error estimation has been established. We construct a posteriori error indicators by distinguishing between discretization and linearization errors and prove their reliability and optimality. A numerical test is carried out and the results obtained confirm those established theoretically.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100576"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143947210","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 : 2025-05-01DOI: 10.1016/j.rinam.2025.100592
Jingwei Li, Thomas G. Robertazzi
This paper explores the distribution of indistinguishable balls into distinct urns with varying capacity constraints, a foundational issue in combinatorial mathematics with applications across various disciplines. We present a comprehensive theoretical framework that addresses both upper and lower capacity constraints under different distribution conditions, elaborating on the combinatorial implications of such variations. Through rigorous analysis, we derive analytical solutions that cater to different constrained environments, providing a robust theoretical basis for future empirical and theoretical investigations. These solutions are pivotal for advancing research in fields that rely on precise distribution strategies, such as physics and parallel processing. The paper not only generalizes classical distribution problems but also introduces novel methodologies for tackling capacity variations, thereby broadening the utility and applicability of distribution theory in practical and theoretical contexts.
{"title":"Capacity constraints in ball and urn distribution problems","authors":"Jingwei Li, Thomas G. Robertazzi","doi":"10.1016/j.rinam.2025.100592","DOIUrl":"10.1016/j.rinam.2025.100592","url":null,"abstract":"<div><div>This paper explores the distribution of indistinguishable balls into distinct urns with varying capacity constraints, a foundational issue in combinatorial mathematics with applications across various disciplines. We present a comprehensive theoretical framework that addresses both upper and lower capacity constraints under different distribution conditions, elaborating on the combinatorial implications of such variations. Through rigorous analysis, we derive analytical solutions that cater to different constrained environments, providing a robust theoretical basis for future empirical and theoretical investigations. These solutions are pivotal for advancing research in fields that rely on precise distribution strategies, such as physics and parallel processing. The paper not only generalizes classical distribution problems but also introduces novel methodologies for tackling capacity variations, thereby broadening the utility and applicability of distribution theory in practical and theoretical contexts.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100592"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144231525","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 : 2025-05-01DOI: 10.1016/j.rinam.2025.100589
Ali Baheri , Marzieh Amiri Shahbazi
We propose a multi-scale extension of conformal prediction, an approach that constructs prediction sets with finite-sample coverage guarantees under minimal statistical assumptions. Classic conformal prediction relies on a single notion of “conformity” overlooking the multi-level structures that arise in applications such as image analysis, hierarchical data exploration, and multi-resolution time series modeling. In contrast, the proposed framework defines a distinct conformity function at each relevant scale or resolution, producing multiple conformal predictors whose prediction sets are then intersected to form the final multi-scale output. We establish theoretical results confirming that the multi-scale prediction set retains the marginal coverage guarantees of the original conformal framework and can, in fact, yield smaller or more precise sets in practice. By distributing the total miscoverage probability across scales in proportion to their informative power, the method further refines the set sizes. We also show that the dependence between scales can lead to conservative coverage, ensuring that the actual coverage exceeds the nominal level. Numerical experiments in a synthetic classification setting demonstrate that multi-scale conformal prediction achieves or surpasses the nominal coverage level while generating smaller prediction sets compared to single-scale conformal methods.
{"title":"Conformal prediction across scales: Finite-sample coverage with hierarchical efficiency","authors":"Ali Baheri , Marzieh Amiri Shahbazi","doi":"10.1016/j.rinam.2025.100589","DOIUrl":"10.1016/j.rinam.2025.100589","url":null,"abstract":"<div><div>We propose a multi-scale extension of conformal prediction, an approach that constructs prediction sets with finite-sample coverage guarantees under minimal statistical assumptions. Classic conformal prediction relies on a single notion of “conformity” overlooking the multi-level structures that arise in applications such as image analysis, hierarchical data exploration, and multi-resolution time series modeling. In contrast, the proposed framework defines a distinct conformity function at each relevant scale or resolution, producing multiple conformal predictors whose prediction sets are then intersected to form the final multi-scale output. We establish theoretical results confirming that the multi-scale prediction set retains the marginal coverage guarantees of the original conformal framework and can, in fact, yield smaller or more precise sets in practice. By distributing the total miscoverage probability across scales in proportion to their informative power, the method further refines the set sizes. We also show that the dependence between scales can lead to conservative coverage, ensuring that the actual coverage exceeds the nominal level. Numerical experiments in a synthetic classification setting demonstrate that multi-scale conformal prediction achieves or surpasses the nominal coverage level while generating smaller prediction sets compared to single-scale conformal methods.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100589"},"PeriodicalIF":1.4,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166906","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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