Applied Mathematics and Computation最新文献

{"title":"A global approximation method for second-kind nonlinear integral equations","authors":"Luisa Fermo ,&nbsp;Anna Lucia Laguardia ,&nbsp;Concetta Laurita ,&nbsp;Maria Grazia Russo","doi":"10.1016/j.amc.2024.129094","DOIUrl":"10.1016/j.amc.2024.129094","url":null,"abstract":"<div><div>A global approximation method of Nyström type is explored for the numerical solution of a class of nonlinear integral equations of the second kind. The cases of smooth and weakly singular kernels are both considered. In the first occurrence, the method uses a Gauss-Legendre rule whereas in the second one resorts to a product rule based on Legendre nodes. Stability and convergence are proved in functional spaces equipped with the uniform norm and several numerical tests are given to show the good performance of the proposed method. An application to the interior Neumann problem for the Laplace equation with nonlinear boundary conditions is also considered.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421528","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}

{"title":"Component connectivity of wheel networks","authors":"Guozhen Zhang ,&nbsp;Xin Liu ,&nbsp;Dajin Wang","doi":"10.1016/j.amc.2024.129096","DOIUrl":"10.1016/j.amc.2024.129096","url":null,"abstract":"<div><div>The <em>r</em>-component connectivity <span><math><mi>c</mi><msub><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of a noncomplete graph <em>G</em> is the size of a minimum set of vertices, whose deletion disconnects <em>G</em> such that the remaining graph has at least <em>r</em> components. When <span><math><mi>r</mi><mo>=</mo><mn>2</mn></math></span>, <span><math><mi>c</mi><msub><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is reduced to the classic notion of connectivity <span><math><mi>κ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. So <span><math><mi>c</mi><msub><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is a generalization of <span><math><mi>κ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, and is therefore a more general and more precise measurement for the reliability of large interconnection networks. The <em>m</em>-dimensional wheel network <span><math><mi>C</mi><msub><mrow><mi>W</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> was first proposed by Shi and Lu in 2008 as a potential model for the interconnection network <span><span>[19]</span></span>, and has been getting increasing attention recently. It belongs to the category of Cayley graphs, and possesses some properties desirable for interconnection networks. In this paper, we determine the <em>r</em>-component connectivity of the wheel network for <span><math><mi>r</mi><mo>=</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn></math></span>. We prove that <span><math><mi>c</mi><msub><mrow><mi>κ</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>(</mo><mi>C</mi><msub><mrow><mi>W</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo><mo>=</mo><mn>4</mn><mi>m</mi><mo>−</mo><mn>7</mn></math></span> for <span><math><mi>m</mi><mo>≥</mo><mn>5</mn></math></span>, <span><math><mi>c</mi><msub><mrow><mi>κ</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>(</mo><mi>C</mi><msub><mrow><mi>W</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo><mo>=</mo><mn>6</mn><mi>m</mi><mo>−</mo><mn>13</mn></math></span> and <span><math><mi>c</mi><msub><mrow><mi>κ</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>(</mo><mi>C</mi><msub><mrow><mi>W</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>)</mo><mo>=</mo><mn>8</mn><mi>m</mi><mo>−</mo><mn>20</mn></math></span> for <span><math><mi>m</mi><mo>≥</mo><mn>6</mn></math></span>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421527","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}

{"title":"Two-disjoint-cycle-cover pancyclicity of split-star networks","authors":"Hao Li ,&nbsp;Liting Chen ,&nbsp;Mei Lu","doi":"10.1016/j.amc.2024.129085","DOIUrl":"10.1016/j.amc.2024.129085","url":null,"abstract":"<div><div>Pancyclicity is a stronger property than Hamiltonicity. In 1973, Bondy stated his celebrated meta-conjecture. Since then, problems related to pancyclicity have attracted a lot of attentions and interests of researchers. A connected graph <em>G</em> is two-disjoint-cycle-cover <span><math><mo>[</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo></math></span>-pancyclic or briefly 2-DCC <span><math><mo>[</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo></math></span>-pancyclic if for any positive integer <em>t</em> with <span><math><mi>t</mi><mo>∈</mo><mo>[</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo></math></span>, there are two vertex-disjoint cycles <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> in <em>G</em> satisfying <span><math><mo>|</mo><mi>V</mi><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo><mo>|</mo><mo>=</mo><mi>t</mi></math></span> and <span><math><mo>|</mo><mi>V</mi><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>)</mo><mo>|</mo><mo>=</mo><mo>|</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>|</mo><mo>−</mo><mi>t</mi></math></span>. In this paper, it is proved that the <em>n</em>-dimensional split-star network <span><math><msubsup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> is 2-DCC <span><math><mo>[</mo><mn>3</mn><mo>,</mo><mo>⌊</mo><mfrac><mrow><mi>n</mi><mo>!</mo></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌋</mo><mo>]</mo></math></span>-pancyclic when <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421885","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}

{"title":"Radio labelling of two-branch trees","authors":"Devsi Bantva ,&nbsp;Samir Vaidya ,&nbsp;Sanming Zhou","doi":"10.1016/j.amc.2024.129097","DOIUrl":"10.1016/j.amc.2024.129097","url":null,"abstract":"<div><div>A radio labelling of a graph <em>G</em> is a mapping <span><math><mi>f</mi><mo>:</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>→</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>}</mo></math></span> such that <span><math><mo>|</mo><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>−</mo><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>|</mo><mo>≥</mo><mrow><mi>diam</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo><mo>+</mo><mn>1</mn><mo>−</mo><mi>d</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span> for every pair of distinct vertices <span><math><mi>u</mi><mo>,</mo><mi>v</mi></math></span> of <em>G</em>, where <span><math><mrow><mi>diam</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is the diameter of <em>G</em> and <span><math><mi>d</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></span> is the distance between <em>u</em> and <em>v</em> in <em>G</em>. The radio number <span><math><mrow><mi>rn</mi></mrow><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of <em>G</em> is the smallest integer <em>k</em> such that <em>G</em> admits a radio labelling <em>f</em> with <span><math><mi>max</mi><mo>⁡</mo><mo>{</mo><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>:</mo><mi>v</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>}</mo><mo>=</mo><mi>k</mi></math></span>. The weight of a tree <em>T</em> from a vertex <span><math><mi>v</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>T</mi><mo>)</mo></math></span> is the sum of the distances in <em>T</em> from <em>v</em> to all other vertices, and a vertex of <em>T</em> achieving the minimum weight is called a weight centre of <em>T</em>. It is known that any tree has one or two weight centres. A tree is called a two-branch tree if the removal of all its weight centres results in a forest with exactly two components. In this paper we obtain a sharp lower bound for the radio number of two-branch trees which improves a known lower bound for general trees. We also give a necessary and sufficient condition for this improved lower bound to be achieved. Using these results, we determine the radio number of two families of level-wise regular two-branch trees.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421872","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}

{"title":"A FFT-based DDSIIM solver for elliptic interface problems with discontinuous coefficients on arbitrary domains and its error analysis","authors":"Jianjun Chen ,&nbsp;Yuxuan Wang ,&nbsp;Weiyi Wang ,&nbsp;Zhijun Tan","doi":"10.1016/j.amc.2024.129086","DOIUrl":"10.1016/j.amc.2024.129086","url":null,"abstract":"<div><div>In this study, we propose a fast FFT-based domain decomposition simplified immersed interface method (DDSIIM) solver for addressing elliptic interface problems characterized by fully discontinuous coefficients on arbitrary domains. The method involves decomposing the original elliptic interface problem along the interfaces, resulting in sub-problems defined on subdomains embedded within larger regular domains. By utilizing a variety of novel solution extension schemes and augmented variable strategies, each sub-problem is transformed into a straightforward elliptic interface problem with constant coefficients on a regular domain, interconnected through augmented equations. The interconnected sub-interface problems are initially resolved by solving for the augmented variables using GMRES, which does not depend on mesh size, followed by the application of the fast FFT-based SIIM in each GMRES iteration. Rigorous error estimates are derived to ensure global second-order accuracy in both the discrete <span><math><msup><mrow><mtext>L</mtext></mrow><mrow><mn>2</mn></mrow></msup></math></span>-norm and the maximum norm. A large number of numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed DDSIIM solver.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421884","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}

{"title":"Relaxed conditions for parameterized linear matrix inequality in the form of nested fuzzy summations","authors":"Do Wan Kim ,&nbsp;Donghwan Lee","doi":"10.1016/j.amc.2024.129079","DOIUrl":"10.1016/j.amc.2024.129079","url":null,"abstract":"<div><div>The aim of this study is to investigate less conservative conditions for parameterized linear matrix inequalities (PLMIs) that are formulated as nested fuzzy summations. Such PLMIs are commonly encountered in stability analysis and control design problems for Takagi-Sugeno (T-S) fuzzy systems. Utilizing the weighted inequality of arithmetic and geometric means (AM-GM inequality), we develop new, less conservative linear matrix inequalities for the PLMIs. This methodology enables us to efficiently handle the product of membership functions that have intersecting indices. Through empirical case studies, we demonstrate that our proposed conditions produce less conservative results compared to existing approaches in the literature.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421522","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}

{"title":"Multiscale flow simulations of dilute polymeric solutions with bead-rod chains using Brownian configuration fields","authors":"Andreas Meier,&nbsp;Eberhard Bänsch,&nbsp;Florian Frank","doi":"10.1016/j.amc.2024.129091","DOIUrl":"10.1016/j.amc.2024.129091","url":null,"abstract":"<div><div>We couple the momentum and mass balance equations with the bead-rod chain model (Kramers chain) to simulate non-Newtonian polymeric fluids using finite elements and the Brownian configuration field method. A suitable rod-length preserving discretization is presented, which is based on the ideas of Liu's algorithm <span><span>[28]</span></span> and generalized into the finite-element context. Additional details concerning the parallelization of the Brownian configuration field part of the simulation are discussed to achieve outstanding code runtimes on large computation clusters. The novel coupling enables the investigation of how the bead-rod chains influence the fluid flow. This is done with proof-of-concept simulations for the start-up shear flow and flow around a cylinder scenario in 2D that serve as a reference for future research. In the start-up shear flow scenario, the velocity overshoot effect, which is typical for polymeric fluids, is successfully demonstrated. In the more challenging flow around a cylinder scenario, we numerically confirm the viscoelastic drag reduction phenomenon by comparing the drag coefficients with a purely Newtonian Navier–Stokes solution.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421882","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}

{"title":"Superconvergence results for hypersingular integral equation of first kind by Chebyshev spectral projection methods","authors":"Saloni Gupta,&nbsp;Arnab Kayal,&nbsp;Moumita Mandal","doi":"10.1016/j.amc.2024.129093","DOIUrl":"10.1016/j.amc.2024.129093","url":null,"abstract":"<div><div>In this article, we propose Chebyshev spectral projection methods to solve the hypersingular integral equation of first kind. The presence of strong singularity in Hadamard sense in the first part of the integral equation makes it challenging to get superconvergence results. To overcome this, we transform the first kind hypersingular integral equation into a second kind integral equation. This is achieved by defining a bounded inverse of the hypersingular integral operator in some suitable Hilbert space. Using iterated Chebyshev spectral Galerkin method on the equivalent second kind integral equation, we obtain improved convergence of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mn>2</mn><mi>r</mi></mrow></msup><mo>)</mo></math></span>, where <span><math><mi>N</mi></math></span> is the highest degree of Chebyshev polynomials employed in the approximation space and <em>r</em> is the smoothness of the solution. Further, using commutativity of projection operator and inverse of the hypersingular integral operator, we are able to obtain superconvergence of <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mn>3</mn><mi>r</mi></mrow></msup><mo>)</mo></math></span> and <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>−</mo><mn>4</mn><mi>r</mi></mrow></msup><mo>)</mo></math></span>, by Chebyshev spectral multi-Galerkin method (CSMGM) and iterated CSMGM, respectively. Finally, numerical examples are presented to verify our theoretical results.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421529","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}

{"title":"Stokes phenomenon for the M-Wright function of order 1n","authors":"Hassan Askari,&nbsp;Alireza Ansari","doi":"10.1016/j.amc.2024.129088","DOIUrl":"10.1016/j.amc.2024.129088","url":null,"abstract":"<div><div>In this paper, using the higher-order differential equation of M-Wright function (Mainardi function) of order <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac><mo>,</mo><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, we get the integral representations for this function and other linear independent functions on the Laplace contours. The Stokes phenomenon and the Stokes/anti-Stokes rays for different domains in the complex plane are also investigated. Our approach is based on the steepest descent method for analyzing and drawing the steepest descent curves/directions for the initial values of <em>n</em>.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421867","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}

{"title":"Integral transforms for explicit source estimation in non-linear advection-diffusion problems","authors":"André J.P. de Oliveira ,&nbsp;Diego C. Knupp ,&nbsp;Luiz A.S. Abreu","doi":"10.1016/j.amc.2024.129092","DOIUrl":"10.1016/j.amc.2024.129092","url":null,"abstract":"<div><div>In many engineering problems non-linear mathematical models are needed to accurately describe the physical phenomena involved. In such cases, the inverse problems related to those models bring additional challenges. In this scenario, this work provides a novel general regularized methodology based on integral transforms for obtaining explicit solutions to inverse problems related to source term estimation in non-linear advection-diffusion models. Numerical examples demonstrate the application of the methodology for some cases of the one- and two-dimensional versions of the non-linear Burgers' equation. An uncertainty analysis for the proposed inverse problem is also conducted using the Monte Carlo Method, in order to illustrate the reliability of the estimates. The results reveal accurate estimates for different functional forms of the sought source term and varying noise levels, for both diffusion-dominated and advection-dominated scenarios.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421530","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}