The small Lipschitz is a generalization of the Lipschitz condition. The Lipschitz condition guarantees the uniqueness of the solution of the initial value problems. A special Lipschitz condition in the small is a contraction in the small. Based on the small Lipschitz in this paper, fixed-point theorems involving contraction in the small will be presented. The results will be applied to develop Picard’s theorem.
{"title":"Fixed-Point Theorems Involving Small Lipschitz","authors":"C. R. Indrati","doi":"10.1155/2023/5236150","DOIUrl":"https://doi.org/10.1155/2023/5236150","url":null,"abstract":"The small Lipschitz is a generalization of the Lipschitz condition. The Lipschitz condition guarantees the uniqueness of the solution of the initial value problems. A special Lipschitz condition in the small is a contraction in the small. Based on the small Lipschitz in this paper, fixed-point theorems involving contraction in the small will be presented. The results will be applied to develop Picard’s theorem.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49665984","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}
In this article, a singularly perturbed convection-diffusion problem with a small time lag is examined. Because of the appearance of a small perturbation parameter, a boundary layer is observed in the solution of the problem. A hybrid scheme has been constructed, which is a combination of the cubic spline method in the boundary layer region and the midpoint upwind scheme in the outer layer region on a piecewise Shishkin mesh in the spatial direction. For the discretization of the time derivative, the Crank-Nicolson method is used. Error analysis of the proposed method has been performed. We found that the proposed scheme is second-order convergent. Numerical examples are given, and the numerical results are in agreement with the theoretical results. Comparisons are made, and the results of the proposed scheme give more accurate solutions and a higher rate of convergence as compared to some previous findings available in the literature.
{"title":"Hybrid Fitted Numerical Scheme for Singularly Perturbed Convection-Diffusion Problem with a Small Time Lag","authors":"M. Ayele, A. Tiruneh, G. A. Derese","doi":"10.1155/2023/4382780","DOIUrl":"https://doi.org/10.1155/2023/4382780","url":null,"abstract":"In this article, a singularly perturbed convection-diffusion problem with a small time lag is examined. Because of the appearance of a small perturbation parameter, a boundary layer is observed in the solution of the problem. A hybrid scheme has been constructed, which is a combination of the cubic spline method in the boundary layer region and the midpoint upwind scheme in the outer layer region on a piecewise Shishkin mesh in the spatial direction. For the discretization of the time derivative, the Crank-Nicolson method is used. Error analysis of the proposed method has been performed. We found that the proposed scheme is second-order convergent. Numerical examples are given, and the numerical results are in agreement with the theoretical results. Comparisons are made, and the results of the proposed scheme give more accurate solutions and a higher rate of convergence as compared to some previous findings available in the literature.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41408738","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}
The main purposes of this study are to propose the modified radial basis function (RBF) collocation method using a hybrid radial basis function to solve the convection-diffusion problems numerically and to choose the optimal shape parameter of radial basis functions. The modified numerical scheme is tested on a benchmark problem with varying shape parameters. The root mean square error and maximum error are used to validate the accuracy and efficiency of the method. The proposed method can be a good alternative to the radial basis function collocation method to improve accuracy and results.
{"title":"A Modified RBF Collocation Method for Solving the Convection-Diffusion Problems","authors":"N. Chuathong","doi":"10.1155/2023/8727963","DOIUrl":"https://doi.org/10.1155/2023/8727963","url":null,"abstract":"The main purposes of this study are to propose the modified radial basis function (RBF) collocation method using a hybrid radial basis function to solve the convection-diffusion problems numerically and to choose the optimal shape parameter of radial basis functions. The modified numerical scheme is tested on a benchmark problem with varying shape parameters. The root mean square error and maximum error are used to validate the accuracy and efficiency of the method. The proposed method can be a good alternative to the radial basis function collocation method to improve accuracy and results.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46270156","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}
In this paper, we explore a generalised solution of the Cauchy problems for the q -heat and q -wave equations which are generated by Jackson’s and the q -Sturm-Liouville operators with respect to t and x , respectively. For this, we use a new method, where a crucial tool is used to represent functions in the Fourier series expansions in a Hilbert space on quantum calculus. We show that these solutions can be represented by explicit formulas generated by the q -Mittag-Leffler function. Moreover, we prove the unique existence and stability of the weak solutions.
{"title":"On the Heat and Wave Equations with the Sturm-Liouville Operator in Quantum Calculus","authors":"S. Shaimardan, L. Persson, N. Tokmagambetov","doi":"10.1155/2023/2488165","DOIUrl":"https://doi.org/10.1155/2023/2488165","url":null,"abstract":"In this paper, we explore a generalised solution of the Cauchy problems for the \u0000 \u0000 q\u0000 \u0000 -heat and \u0000 \u0000 q\u0000 \u0000 -wave equations which are generated by Jackson’s and the \u0000 \u0000 q\u0000 \u0000 -Sturm-Liouville operators with respect to \u0000 \u0000 t\u0000 \u0000 and \u0000 \u0000 x\u0000 \u0000 , respectively. For this, we use a new method, where a crucial tool is used to represent functions in the Fourier series expansions in a Hilbert space on quantum calculus. We show that these solutions can be represented by explicit formulas generated by the \u0000 \u0000 q\u0000 \u0000 -Mittag-Leffler function. Moreover, we prove the unique existence and stability of the weak solutions.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47203272","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}
In this article, we mainly discuss the existence and uniqueness of fixed point satisfying integral type contractions in complete metric spaces via rational expression using real-valued functions. We improve and unify many widely known results from the literature. Among these, the work of Rakotch (1962), Branciari (2002), and Liu et al. (2013) is extended. Finally, we conclude with an example presented graphically in favour of our work.
本文主要利用实值函数的有理表达式，讨论了完备度量空间中满足整型压缩的不动点的存在唯一性。我们改进和统一了文献中许多广为人知的结果。其中，扩展了Rakotch(1962)、Branciari(2002)和Liu et al.(2013)的工作。最后，我们用一个图形化的例子来说明我们的工作。
{"title":"Fixed Point Results via Real-Valued Function Satisfying Integral Type Rational Contraction","authors":"Naveen Mani, Amit Sharma, Rahul Shukla","doi":"10.1155/2023/2592507","DOIUrl":"https://doi.org/10.1155/2023/2592507","url":null,"abstract":"In this article, we mainly discuss the existence and uniqueness of fixed point satisfying integral type contractions in complete metric spaces via rational expression using real-valued functions. We improve and unify many widely known results from the literature. Among these, the work of Rakotch (1962), Branciari (2002), and Liu et al. (2013) is extended. Finally, we conclude with an example presented graphically in favour of our work.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44169410","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}
By combining the notions of -metric space and -metric space, in this paper, we present coincidence fixed-point theorems for -hybrid mappings in -metric spaces. An example is given to demonstrate the novelty of our main results. Henceforth, the illustrative applications are given by using nonlinear fractional differential equations.
本文结合G -度量空间和b -度量空间的概念，给出了G - b -度量空间中p -混合映射的重合不动点定理。最后给出了一个例子来说明我们的主要结果的新颖性。此后，本文通过非线性分数阶微分方程给出了该方法的说明应用。
{"title":"Coincidence Fixed-Point Theorems for <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mi>p</mi>\u0000 </math>-Hybrid Contraction Mappings in <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <msub>\u0000 <mrow>","authors":"Lucas Wangwe","doi":"10.1155/2022/7688168","DOIUrl":"https://doi.org/10.1155/2022/7688168","url":null,"abstract":"<jats:p>By combining the notions of <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>G</mi>\u0000 </math>\u0000 </jats:inline-formula>-metric space and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <mi>b</mi>\u0000 </math>\u0000 </jats:inline-formula>-metric space, in this paper, we present coincidence fixed-point theorems for <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M5\">\u0000 <mi>p</mi>\u0000 </math>\u0000 </jats:inline-formula>-hybrid mappings in <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M6\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>b</mi>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula>-metric spaces. An example is given to demonstrate the novelty of our main results. Henceforth, the illustrative applications are given by using nonlinear fractional differential equations.</jats:p>","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42535658","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}
P. Sozhaeswari, R. Sowrirajan, K. Loganathan, Sonam Gyeltshen
In this work, we study the effect of nonlinear source term in Black-Scholes model by finding the solution of it. We use the mathematical concepts of existence and uniqueness to arrive the conclusion. The transformation of the nonlinear equation into heat equation leads to the existence of solution through fixed-point theorems, semigroup theory, and certain regularity conditions imposed on variables.
{"title":"A Study on the Impact of Nonlinear Source Term in Black-Scholes Option Pricing Model","authors":"P. Sozhaeswari, R. Sowrirajan, K. Loganathan, Sonam Gyeltshen","doi":"10.1155/2022/6385401","DOIUrl":"https://doi.org/10.1155/2022/6385401","url":null,"abstract":"In this work, we study the effect of nonlinear source term in Black-Scholes model by finding the solution of it. We use the mathematical concepts of existence and uniqueness to arrive the conclusion. The transformation of the nonlinear equation into heat equation leads to the existence of solution through fixed-point theorems, semigroup theory, and certain regularity conditions imposed on variables.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45589240","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}
N. Opoku, R. Borkor, Andrews Frimpong Adu, H. Nyarko, Albert Doughan, Edwin Moses Appiah, Biigba Yakubu, Isabel Mensah, S. P. Salifu
Meningitis is an inflammation of the meninges, which covers the brain and spinal cord. Every year, most individuals within sub-Saharan Africa suffer from meningococcal meningitis. Moreover, tens of thousands of these cases result in death, especially during major epidemics. The transmission dynamics of the disease keep changing, according to health practitioners. The goal of this study is to exploit robust mechanisms to manage and prevent the disease at a minimal cost due to its public health implications. A significant concern found to aid in the transmission of meningitis disease is the movement and interaction of individuals from low-risk to high-risk zones during the outbreak season. Thus, this article develops a mathematical model that ascertains the dynamics involved in meningitis transmissions by partitioning individuals into low- and high-risk susceptible groups. After computing the basic reproduction number, the model is shown to exhibit a unique local asymptotically stability at the meningitis-free equilibrium E † , when the effective reproduction number R 0 < 1 , and the existence of two endemic equilibria for which R 0 † < R 0 < 1 and exhibits the phenomenon of backward bifurcation, which shows the difficulty of relying only on the reproduction number to control the disease. The effective reproductive number estimated in real time using the exponential growth method affirmed that the number of secondary meningitis infections will continue to increase without any intervention or policies. To find the best strategy for minimizing the number of carriers and infected individuals, we reformulated the model into an optimal control model using Pontryagin’s maximum principles with intervention measures such as vaccination, treatment, and personal protection. Although Ghana’s most preferred meningitis intervention method is via treatment, the model’s simulations demonstrated that the best strategy to control meningitis is to combine vaccination with treatment. But the cost-effectiveness analysis results show that vaccination and treatment are among the most expensive measures to implement. For that reason, personal protection which is the most cost-effective measure needs to be encouraged, especially among individuals migrating from low- to high-risk meningitis belts.
{"title":"Modelling the Transmission Dynamics of Meningitis among High and Low-Risk People in Ghana with Cost-Effectiveness Analysis","authors":"N. Opoku, R. Borkor, Andrews Frimpong Adu, H. Nyarko, Albert Doughan, Edwin Moses Appiah, Biigba Yakubu, Isabel Mensah, S. P. Salifu","doi":"10.1155/2022/9084283","DOIUrl":"https://doi.org/10.1155/2022/9084283","url":null,"abstract":"Meningitis is an inflammation of the meninges, which covers the brain and spinal cord. Every year, most individuals within sub-Saharan Africa suffer from meningococcal meningitis. Moreover, tens of thousands of these cases result in death, especially during major epidemics. The transmission dynamics of the disease keep changing, according to health practitioners. The goal of this study is to exploit robust mechanisms to manage and prevent the disease at a minimal cost due to its public health implications. A significant concern found to aid in the transmission of meningitis disease is the movement and interaction of individuals from low-risk to high-risk zones during the outbreak season. Thus, this article develops a mathematical model that ascertains the dynamics involved in meningitis transmissions by partitioning individuals into low- and high-risk susceptible groups. After computing the basic reproduction number, the model is shown to exhibit a unique local asymptotically stability at the meningitis-free equilibrium \u0000 \u0000 \u0000 \u0000 E\u0000 \u0000 \u0000 †\u0000 \u0000 \u0000 \u0000 , when the effective reproduction number \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 <\u0000 1\u0000 \u0000 , and the existence of two endemic equilibria for which \u0000 \u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 †\u0000 \u0000 \u0000 <\u0000 \u0000 \u0000 R\u0000 \u0000 \u0000 0\u0000 \u0000 \u0000 <\u0000 1\u0000 \u0000 and exhibits the phenomenon of backward bifurcation, which shows the difficulty of relying only on the reproduction number to control the disease. The effective reproductive number estimated in real time using the exponential growth method affirmed that the number of secondary meningitis infections will continue to increase without any intervention or policies. To find the best strategy for minimizing the number of carriers and infected individuals, we reformulated the model into an optimal control model using Pontryagin’s maximum principles with intervention measures such as vaccination, treatment, and personal protection. Although Ghana’s most preferred meningitis intervention method is via treatment, the model’s simulations demonstrated that the best strategy to control meningitis is to combine vaccination with treatment. But the cost-effectiveness analysis results show that vaccination and treatment are among the most expensive measures to implement. For that reason, personal protection which is the most cost-effective measure needs to be encouraged, especially among individuals migrating from low- to high-risk meningitis belts.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44609769","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}
The paper deals with a coupling algorithm using shape and topological derivatives of a given cost functional and a problem governed by nonstationary Maxwell’s equations in 3D. To establish the shape and topological derivatives, an adjoint method is used. For the topological asymptotic expansion, two examples of cost functionals are considered with the perturbation of the electric permittivity and magnetic permeability. We combine the shape derivative and topological one to propose an algorithm. The proposed algorithm allows to insert a small inhomogeneity (electric or magnetic) in a given shape.
{"title":"Coupling Shape Optimization and Topological Derivative for Maxwell Equations","authors":"SY Alassane","doi":"10.1155/2022/2425990","DOIUrl":"https://doi.org/10.1155/2022/2425990","url":null,"abstract":"The paper deals with a coupling algorithm using shape and topological derivatives of a given cost functional and a problem governed by nonstationary Maxwell’s equations in 3D. To establish the shape and topological derivatives, an adjoint method is used. For the topological asymptotic expansion, two examples of cost functionals are considered with the perturbation of the electric permittivity and magnetic permeability. We combine the shape derivative and topological one to propose an algorithm. The proposed algorithm allows to insert a small inhomogeneity (electric or magnetic) in a given shape.","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43359957","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}
In this work, we shall derive a new subclass of univalent analytic functions denoted by in the open unit disk which is defined by multiplier transformation. Coefficient inequalities, growth and distortion theorem, extreme points, and radius of starlikeness and convexity of functions belonging to the subclass are obtained.
{"title":"New Subclass of \u0000 K\u0000 -Uniformly Univalent Analytic Functions with Negative Coefficients Defined by Multiplier Transformation","authors":"Ma’moun I. Y. Alharayzeh, F. Ghanim","doi":"10.1155/2022/4593799","DOIUrl":"https://doi.org/10.1155/2022/4593799","url":null,"abstract":"<jats:p>In this work, we shall derive a new subclass of univalent analytic functions denoted by <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>H</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>α</mi>\u0000 <mo>,</mo>\u0000 <mi>β</mi>\u0000 <mo>,</mo>\u0000 <mi>γ</mi>\u0000 <mo>,</mo>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>λ</mi>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> in the open unit disk <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mi>D</mi>\u0000 <mo>=</mo>\u0000 <mfenced open=\"{\" close=\"}\">\u0000 <mrow>\u0000 <mi>z</mi>\u0000 <mo>∈</mo>\u0000 <mi>ℂ</mi>\u0000 <mo>:</mo>\u0000 <mfenced open=\"|\" close=\"|\">\u0000 <mrow>\u0000 <mi>z</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo><</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> which is defined by multiplier transformation. Coefficient inequalities, growth and distortion theorem, extreme points, and radius of starlikeness and convexity of functions belonging to the subclass are obtained.</jats:p>","PeriodicalId":7061,"journal":{"name":"Abstract and Applied Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45538933","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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