Mathematical Methods in the Applied Sciences最新文献

{"title":"Learning Rates of Multioutput Regression With Kernel Methods and ℓp-Regularization","authors":"Haoming Sun","doi":"10.1002/mma.11217","DOIUrl":"https://doi.org/10.1002/mma.11217","url":null,"abstract":"<div>\u0000 \u0000 <p>Multioutput learning aims at learning multiple outputs simultaneously from a given input. It has been extensively studied in the literature on machine learning. Among them, how to estimate learning rates for various learning problems remains a fundamental theoretical problem. By far, most of the existing research only focuses on single-output learning. To strengthen the theoretical support of multioutput learning, we study the learning rates of multioutput regression with kernel methods and \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℓ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {ell}&amp;amp;#x0005E;p $$</annotation>\u0000 </semantics></math>-regularization. We obtain an explicit learning rate, which reveals the quantitative dependency on both the output dimensions and the sample size. Our results cover a broader scope than previous works and improve upon them in certain special cases. To the best of our knowledge, this is the first work to provide learning rate estimates for this scheme.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"14846-14856"},"PeriodicalIF":1.8,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242969","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":"Meta-Metamodelling of Engineering Systems by Help of Abstract Mathematics","authors":"Daniel Luckey,&nbsp;Dmitrii Legatiuk","doi":"10.1002/mma.11215","DOIUrl":"https://doi.org/10.1002/mma.11215","url":null,"abstract":"<p>The growing trend of automation in engineering significantly increases the complexity of engineering systems and necessitates a deeper understanding of the coupling of physical and cyber components interacting within the systems. A typical example of such a highly coupled system is an autonomous construction site, where robotic systems aim to enhance the efficiency of the construction process. To adequately address, define, and model the structure of such engineering systems, it is essential to use the tools of abstract mathematics, which provide a sufficient level of abstraction to describe entire systems as well as interactions between their components. Moreover, the use of abstract mathematics enables conceptual modelling at different levels of details and abstraction, and, thus, providing possibilities to work not only on a meta-level, but also on the meta-meta-level. In this context, a meta-metamodelling approach to the formal description of engineering systems via the coupling of categorical ontology logs and abstract definitions for individual components has been proposed in recent years. The goal of this paper is to further develop the meta-metamodelling approach, emphasizing its practical applicability for engineering systems by considering practical problems on autonomous construction sites. In particular, a connection between the meta-meta-level and the meta-level is discussed as well as the advantages of using the tools of abstract mathematics are underlined.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"14815-14827"},"PeriodicalIF":1.8,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.11215","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242968","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":"Dynamics of the Wave Equation With Double Critical Exponents","authors":"Feng Zhou,&nbsp;Hongfang Li,&nbsp;Kaixuan Zhu","doi":"10.1002/mma.11209","DOIUrl":"https://doi.org/10.1002/mma.11209","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the dynamics of a wave model with nonlinear damping \u0000<span></span><math>\u0000 <mrow>\u0000 <mi>𝒥</mi>\u0000 <mo>(</mo>\u0000 <mo>‖</mo>\u0000 <mi>u</mi>\u0000 <msup>\u0000 <mrow>\u0000 <mo>‖</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 <mi>g</mi>\u0000 <mfenced>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>∂</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mi>u</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow></math> and a nonlinear term \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 <mo>(</mo>\u0000 <mi>u</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$$ f(u) $$</annotation>\u0000 </semantics></math>, assuming that the growth rates of both \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>f</mi>\u0000 </mrow>\u0000 <annotation>$$ f $$</annotation>\u0000 </semantics></math> and \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 </mrow>\u0000 <annotation>$$ g $$</annotation>\u0000 </semantics></math> are governed by a quintic critical exponent. In this framework, we establish the existence and structural properties of weak and strong attractors for the solution semigroup associated with this equation. Our results extend and refine previous work in the literature, which focuses only on subquintic exponents.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"14722-14735"},"PeriodicalIF":1.8,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145243091","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":"Some New Results on Robustness for Impulsive Differential Equations","authors":"Yuwei Li,&nbsp;Zhichun Yang,&nbsp;Jiafa Xu","doi":"10.1002/mma.11204","DOIUrl":"https://doi.org/10.1002/mma.11204","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we investigate the robustness of impulsive differential equations in Banach spaces. We establish sufficient conditions to ensure that nonuniform exponential contractions, nonuniform exponential expansions and nonuniform exponential dichotomies of impulsive differential equations persist within a wider range of perturbations. It is worth emphasizing that the new results provide some significant improvements of existing results in the case where the perturbations are not required to be sufficiently small. Moreover, the conditions of our conclusions even for differential equations without impulse are more relaxed. Finally, we illustrate our results with a concrete example.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14640-14654"},"PeriodicalIF":1.8,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145011999","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":"The Rota-Baxter Algebra Structures on Split Semiquaternion Algebra","authors":"Quanguo Chen,&nbsp;Yong Deng","doi":"10.1002/mma.11218","DOIUrl":"https://doi.org/10.1002/mma.11218","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we shall describe all the Rota-Baxter operators with any weight on split semiquaternion algebra. Firstly, we give the matrix characterization of the Rota-Baxter operator on split semiquaternion algebra. Then we give the corresponding matrix representations of all the Rota-Baxter operators with any weight on split semiquaternion algebra. Finally, we shall prove that the Ma et al. results about the Rota-Baxter operators on Sweedler algebra are just special cases of our results.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"14857-14867"},"PeriodicalIF":1.8,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242853","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":"Kantorovich-Type Sampling Operators and Approximation","authors":"Vijay Gupta,&nbsp;Vaibhav Sharma","doi":"10.1002/mma.11192","DOIUrl":"https://doi.org/10.1002/mma.11192","url":null,"abstract":"<div>\u0000 \u0000 <p>In this article, we investigate the convergence behavior of generalized sampling operators of Kantorovich-type. By combining the generalized sampling operators and Kantorovich sampling operators, we obtain the new composition operators and estimate the order of approximation. Then, we establish quantitative estimates for convergence in terms of the first-order modulus of continuity and \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 </mrow>\u0000 <annotation>$$ K $$</annotation>\u0000 </semantics></math>-functional. We also estimate the difference of these operators with generalized sampling operators. Moreover, we examine the order of approximation in the weighted space of continuity. Illustrative examples of kernels that meet the necessary assumptions are provided. We also demonstrate the performance of the proposed operators through graphical examples and numerical tables. Finally, we explore their potential applications in digital image processing.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14488-14504"},"PeriodicalIF":1.8,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012037","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 Multivalued Feedback Approach to Stabilization of Linear Multivariable Systems Under Switching Control Constraint","authors":"Larbi Berrahmoune","doi":"10.1002/mma.11207","DOIUrl":"https://doi.org/10.1002/mma.11207","url":null,"abstract":"<div>\u0000 \u0000 <p>We consider a class of finite-dimensional linear autonomous control systems with controls subject to possible saturation. The aim is to study the stabilization under the additional switching control constraint which means that only one actuator is active. The appropriate feedback turns out to be multivalued and the existence of the solution to the resulting differential inclusion is established by using nonlinear semigroup theory. The switching control property occurs whenever the set of instants at which the trajectory intersects some specified submanifolds is of null measure. In the multivalued feedback framework, asymptotic stability and asymptotic output stability are obtained from LaSalle invariance principle. We establish also other stabilization results by constructing suitable state-dependent switched systems where only one control is activated in each subsystem.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 16","pages":"14690-14704"},"PeriodicalIF":1.8,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145242907","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":"Some New Nonlinear Hyperbolic Waves in Macroscopic Production Model","authors":"Zhijian Wei,&nbsp;Lihui Guo","doi":"10.1002/mma.11202","DOIUrl":"https://doi.org/10.1002/mma.11202","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this paper, the Riemann solutions and their asymptotic limits for the macroscopic production model with modified Chaplygin gas are investigated. Due to this model belonging to the Temple class and the curve of this rarefaction wave lying between the one of shock and uncertain waves in the phase plane, the Riemann solutions we constructed differ from those of previous studies. More specifically, a special structure \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;‾&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ Roverline{J}&amp;amp;#x0002B;J $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is found in the construction of the Riemann solution. \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;‾&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ Roverline{J} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is formed by a rarefaction wave \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ R $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and a discontinuity \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;‾&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ overline{J} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; attached to the wavefront of this rarefaction wave. It should be stressed that the rarefaction wave and the shock wave share the same wave velocity on this discontinuity \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;‾&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ overline{J} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In the asymptotic limits of the Riemann solutions, not all solutions converge to those of the conservation law equations when the perturbation parameters tend to 0 with the same initial data. What is interesting is that the vacuum and delta shock wave solutions are obtained by the small Riemann solution \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14611-14631"},"PeriodicalIF":1.8,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012588","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":"Qualitative Stochastic Homogenization of Elliptic Equations With Random Coefficients and Convolutional Potentials","authors":"Xiaofeng Jin,&nbsp;Lingwei Ma,&nbsp;Zhenqiu Zhang","doi":"10.1002/mma.11182","DOIUrl":"https://doi.org/10.1002/mma.11182","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper deals with the homogenization problem for elliptic equations with random statistically homogeneous ergodic coefficients and convolutional potentials in bounded domains. Assuming that the potential has a small absolute expectation, we prove the almost sure qualitative homogenization results in the weak topology in \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation>$$ {H}_0&amp;amp;amp;#x0005E;1 $$</annotation>\u0000 </semantics></math> by Tartar's perturbed test function method. Moreover, for bounded \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>C</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {C}&amp;amp;amp;#x0005E;{2,alpha } $$</annotation>\u0000 </semantics></math>-domains, with the aid of the sublinear growth properties of correctors, we also prove the qualitative stochastic homogenization results in the strong \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {H}&amp;amp;amp;#x0005E;1 $$</annotation>\u0000 </semantics></math>-topology via two-scale expansion method.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14342-14352"},"PeriodicalIF":1.8,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012586","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":"Bogdanov-Takens Bifurcation of Codimension 4 in a Leslie-Gower Predator-Prey Model With Allee Effect and Intraspecific Competition","authors":"Chenyu Liang,&nbsp;Yancong Xu,&nbsp;Libin Rong","doi":"10.1002/mma.11200","DOIUrl":"https://doi.org/10.1002/mma.11200","url":null,"abstract":"<div>\u0000 \u0000 <p>Predator-prey models, such as the Leslie-Gower model, are essential for understanding population dynamics and stability within ecosystems. These models help explain the balance between species under natural conditions, but the inclusion of factors like the Allee effect and intraspecific competition adds complexity and realism to these interactions, enhancing our ability to predict system behavior under stress. To detect early indicators of population collapse, this study investigates the intricate dynamics of a modified Leslie-Gower predator-prey model with both Allee effect and intraspecific competition. We analyze the existence and stability of equilibria, as well as bifurcation phenomena, including saddle-node bifurcations of codimension 2, Hopf bifurcations of codimension 2, and Bogdanov-Takens bifurcations of codimension at least 4. Detailed transitions between bifurcation curves–specifically saddle-node, Hopf, homoclinic, and limit cycle bifurcations–are also examined. We observe a novel transition phenomenon, where a system jumps from saddle-node bifurcation to homoclinic and limit cycle bifurcations. This suggests that burst oscillations may serve as an early warning of system collapse rather than simply a tipping point. Our findings indicate that moderate levels of intraspecific competition or Allee effect support coexistence of both populations, while excessive levels may destabilize the entire biological system, leading to collapse. These insights offer valuable implications for ecological management and the early detection of risks in population dynamics.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 15","pages":"14575-14596"},"PeriodicalIF":1.8,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145012587","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}