Mathematical Methods in the Applied Sciences最新文献

{"title":"Efficient Methods for Solving Equilibrium and Fixed-Point Problems Using Accelerated Viscosity-Based Approximations","authors":"Habib ur Rehman,&nbsp;Kanokwan Sitthithakerngkiet,&nbsp;Ioannis Argyros,&nbsp;Thidaporn Seangwattana","doi":"10.1002/mma.70010","DOIUrl":"https://doi.org/10.1002/mma.70010","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we proposed enhanced extragradient methods for solving equilibrium problems in Hilbert spaces. The constraint set is defined as the solution set for a fixed-point problem with demicontractive mappings. The proposed methodologies center on a subgradient extragradient approach that combines an inertial technique, a self-adaptive procedure, and a viscosity approximation scheme. These algorithms use variable step sizes that are dynamically updated in accordance with previous iteration outcomes. A key advantage of the proposed methods is their ability to function eliminating the need for prior knowledge of Lipschitz constants or line search techniques. Instead, the step sizes are determined through simple calculations at each iteration. The convergence analysis is established under relaxed assumptions. Furthermore, we present a numerical study that compares the effectiveness of the proposed techniques to existing approaches.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15219-15235"},"PeriodicalIF":1.8,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Periodic Solutions in Distribution of Stratonovich Stochastic Lattice Differential Equations With Markovian Switching and Jumps","authors":"Xinping Zhou,&nbsp;Xiaomeng Jiang,&nbsp;Jiamin Xing","doi":"10.1002/mma.70031","DOIUrl":"https://doi.org/10.1002/mma.70031","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we study the Stratonovich stochastic lattice differential equations with the Markovian switching and jumps. The strong well-posedness and weak uniqueness of solutions for such equations are shown under locally Lipschitz conditions. The comparison principle for solutions is established. Furthermore, the existence of periodic solutions in distribution is obtained by utilizing this result and the method of upper and lower solutions.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15506-15522"},"PeriodicalIF":1.8,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Octonionic Hyperbolic Fourier Transform","authors":"Youssef El Haoui","doi":"10.1002/mma.70027","DOIUrl":"https://doi.org/10.1002/mma.70027","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;The three-dimensional octonionic hyperbolic Fourier transform (OHFT) is introduced as a hypercomplex integral Fourier transform associated with three-dimensional octonion-valued signals defined within an open rectangular prism \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ left(-{t}_1,{t}_1right)times left(-{t}_2,{t}_2right)times left(-{t}_3,{t}_3right) $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15433-15451"},"PeriodicalIF":1.8,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantitative Estimates for Generalized Bernstein–Kantorovich Operators","authors":"Behar Baxhaku,&nbsp;P. N. Agrawal","doi":"10.1002/mma.70030","DOIUrl":"https://doi.org/10.1002/mma.70030","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper introduces a Kantorovich-type modification of the generalized Bernstein polynomials proposed by Cao (J Math Anal Appl 209:140–146, 1997). We investigate the convergence properties of these operators, establishing necessary and sufficient conditions for uniform convergence and deriving quantitative estimates for the rate of convergence in terms of the Ditzian–Totik unified modulus of smoothness. Furthermore, we establish an inverse approximation theorem that characterizes the smoothness of the function based on the rate of convergence of the operators. We extend our analysis to the \u0000<span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math>-norm setting, proving the convergence of the operators for functions in \u0000<span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>[</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>]</mo>\u0000 <mo>,</mo>\u0000 <mspace></mspace>\u0000 <mn>1</mn>\u0000 <mo>≤</mo>\u0000 <mi>p</mi>\u0000 <mo>&lt;</mo>\u0000 <mi>∞</mi>\u0000 </mrow></math> and providing quantitative estimates for the rate of convergence in the \u0000<span></span><math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow></math>-norm, utilizing the integral modulus of smoothness. Numerical simulations demonstrate the effectiveness of the proposed operators. We observe rapid convergence in practical examples, with significant error reduction as the number of basis functions (\u0000<span></span><math>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow></math>) increases. These findings are supported by detailed numerical experiments and visual representations, showcasing the practical applicability of the operators.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15493-15505"},"PeriodicalIF":1.8,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A New Approach to the Accretive Growth of Surfaces Via Hyperbolical Kinematics","authors":"Gül Tuğ,&nbsp;Zehra Özdemir","doi":"10.1002/mma.70020","DOIUrl":"https://doi.org/10.1002/mma.70020","url":null,"abstract":"<p>In the current work, we introduce the accretive growth of surfaces by using hyperbolical geometry. First, we describe hyperbolical kinematics along a generating curve to construct accretive surfaces having a hyperbolical cross-section. The obtained surfaces are not only the ones having hyperbolical cross-sections but also their material points follow a hyperbolic trajectory during the formation. Additionally, we explain the process by using hyperbolical split quaternions as an alternative perspective. This shows a remarkable simplicity in the construction of the mentioned surfaces. Then we investigate the connection between velocity and eccentricity of such surfaces together with a comparison to the circular motion. We present visualizations of several examples with the help of a programming language to support the theoretical results.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15349-15363"},"PeriodicalIF":1.8,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.70020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Criteria for Blow-Up Phenomena for Solutions to Nonlinear Reaction–Diffusion Equations on Cones","authors":"Soon-Yeong Chung,&nbsp;Jaeho Hwang","doi":"10.1002/mma.70017","DOIUrl":"https://doi.org/10.1002/mma.70017","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates the global and nonglobal existence of solutions to nonlinear reaction-diffusion equations with a general nonlinearity and time-dependent sources defined on cones of Euclidean spaces. More precisely, the purpose of this work is to give a necessary and sufficient condition for the equations to have only blow-up solutions. As a matter of fact, this problem has been left open for about 30 years, since the work by P. Meier.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15300-15310"},"PeriodicalIF":1.8,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Closed-Form Meromorphic Solution to Fractional Whitham–Broer–Kaup System and Its Real-Valued Characterization","authors":"Heqing Sun,&nbsp;Yezhou Li,&nbsp;Jian-Guo Liu","doi":"10.1002/mma.70015","DOIUrl":"https://doi.org/10.1002/mma.70015","url":null,"abstract":"<div>\u0000 \u0000 <p>The coupled Whitham–Broer–Kaup system can be used to describe the propagation of shallow water waves in fluid dynamics. In this paper, we investigate the nonlinear conformable fractional-order Whitham–Broer–Kaup system by complex analytic method and obtain plentiful new closed-form meromorphic solutions. These derived meromorphic solutions include rational solutions, simply periodic solutions, and elliptic function solutions. At the same time, we give the real-valued characterizations of such meromorphic solutions and illustrate the dynamic behaviors of these solutions with some graphs.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15278-15288"},"PeriodicalIF":1.8,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal Control Analysis of Onchocerciasis Through Multiple Integrated Control Measures","authors":"Mohamedi S. Manjenga,&nbsp;Joshua A. Mwasunda,&nbsp;Jacob I. Irunde","doi":"10.1002/mma.70028","DOIUrl":"https://doi.org/10.1002/mma.70028","url":null,"abstract":"<div>\u0000 \u0000 <p>Onchocerciasis, also known as river blindness, is a vector-borne disease caused by <i>Onchocerca volvulus</i> and transmitted by infected female blackflies. It affects millions of people globally, with the greatest impact in sub-Saharan Africa. In this study, we develop a deterministic mathematical model that integrates multiple control measures, including sterile insect technique (SIT), mechanical control, chemical control, public health education, and ivermectin treatment, to manage the transmission of onchocerciasis. We employ the next-generation matrix method to calculate the blackfly offspring reproduction number \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {N}_0 $$</annotation>\u0000 </semantics></math> and the basic reproduction number \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {R}_0 $$</annotation>\u0000 </semantics></math>. Sensitivity analysis, conducted using the normalized forward sensitivity index, highlights the biting rate as the most positive influence on driving onchocerciasis dynamics, while the mortality rate of female blackflies has a significant negative impact on disease containment. To identify the optimal control strategy for onchocerciasis infections, we apply optimal control theory, considering five time-dependent controls which are public health education, treatment, mechanical control, SIT, and chemical control. Using Pontryagin's maximum principle, we derive the optimality system for controlling onchocerciasis. By implementing forward-backward Runge–Kutta method in Matlab, we identify the most optimal strategy for controlling, preventing, and treating onchocerciasis in both human and blackfly populations. The results suggest that a combined strategy focusing on public health education, treatment, and chemical control offers the most effective approach for combating onchocerciasis.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15452-15473"},"PeriodicalIF":1.8,"publicationDate":"2025-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Upper and Lower Solution Method for a Singular k-Hessian System With Augmented Gradient Term","authors":"Xinguang Zhang,&nbsp;Peng Chen,&nbsp;Lishuang Li,&nbsp;Yonghong Wu,&nbsp;Benchawan Wiwatanapataphee,&nbsp;Ying Wang","doi":"10.1002/mma.70024","DOIUrl":"https://doi.org/10.1002/mma.70024","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we focus on the existence of solutions for a singular \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation>$$ k $$</annotation>\u0000 </semantics></math>-Hessian system with augmented gradient term. By using a radial symmetric transformation and constructing a pair of suitable upper and lower solutions of the singular \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation>$$ k $$</annotation>\u0000 </semantics></math>-Hessian system, the existence and the asymptotic estimate of the solution for the system are established under the case where the nonlinearities \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>,</mo>\u0000 <mi>g</mi>\u0000 </mrow>\u0000 <annotation>$$ f,g $$</annotation>\u0000 </semantics></math> are allowed to have stronger singularity on the space variables. In particular, the nonsingular case is also considered and a sharp result is derived.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15400-15412"},"PeriodicalIF":1.8,"publicationDate":"2025-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantized Projective Synchronization of Delayed Fractional Order Uncertain Quaternion-Valued Neural Networks Via Direct Method","authors":"Wewei Zhang,&nbsp;Hongyong Zhao,&nbsp;Chunlin Sha,&nbsp;Jinde Cao","doi":"10.1002/mma.70019","DOIUrl":"https://doi.org/10.1002/mma.70019","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper treats the projective synchronization (PS) in finite time for a class of delayed fractional order uncertain quaternion-valued neural networks (DFOUQVNNs) based on event triggered quantized control (ETQC). In addition, to consider more general models, uncertainty and time delay terms are introduced into the FOQVNNs. Different from using decomposition method, the considered model is treated as a single entity. By designing a suitable Lyapunov function and applying inequality skills, sufficient criteria are derived to ensure PS in finite time of DFOUQVNNs. Furthermore, the setting time is estimated and the Zeno behavior of the system is excluded under the proposed scheme. Finally, the effectiveness of the theoretical results is validated by using a numerical example.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"15338-15348"},"PeriodicalIF":1.8,"publicationDate":"2025-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}