Pub Date : 2025-11-13DOI: 10.1016/j.geomphys.2025.105709
Manuel Gutiérrez , Raymond A. Hounnonkpe
We study the influence of the existence of totally geodesic null hypersurface on the properties of a Lorentzian manifold. By coupling the rigging technique with the existence of a null foliation we prove the existence of a Riemann flow structure which allows us to use some powerful results to show how curvature conditions on the spacetime restrict its causal structure. We also study the existence of periodic null or spacelike geodesic.
{"title":"Riemannian flow techniques on totally geodesic null hypersurfaces","authors":"Manuel Gutiérrez , Raymond A. Hounnonkpe","doi":"10.1016/j.geomphys.2025.105709","DOIUrl":"10.1016/j.geomphys.2025.105709","url":null,"abstract":"<div><div>We study the influence of the existence of totally geodesic null hypersurface on the properties of a Lorentzian manifold. By coupling the rigging technique with the existence of a null foliation we prove the existence of a Riemann flow structure which allows us to use some powerful results to show how curvature conditions on the spacetime restrict its causal structure. We also study the existence of periodic null or spacelike geodesic.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105709"},"PeriodicalIF":1.2,"publicationDate":"2025-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579504","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}
Consider a Lie subalgebra and an -invariant open submanifold . We demonstrate that any smooth dynamical twist on V, valued in , establishes a twistor on the associated quantum groupoid when combined with the Gutt star product on the cotangent bundle of a Lie group L that integrates . This result provides a framework for constructing equivariant star products from smooth dynamical twists on those Poisson homogeneous spaces arising from nondegenerate polarized Lie algebras, leveraging the structure of twistors of quantum groupoids.
{"title":"From smooth dynamical twists to twistors of quantum groupoids","authors":"Jiahao Cheng , Zhuo Chen , Yu Qiao , Maosong Xiang","doi":"10.1016/j.geomphys.2025.105708","DOIUrl":"10.1016/j.geomphys.2025.105708","url":null,"abstract":"<div><div>Consider a Lie subalgebra <span><math><mi>l</mi><mo>⊂</mo><mi>g</mi></math></span> and an <span><math><mi>l</mi></math></span>-invariant open submanifold <span><math><mi>V</mi><mo>⊂</mo><msup><mrow><mi>l</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. We demonstrate that any smooth dynamical twist on <em>V</em>, valued in <span><math><mi>U</mi><mo>(</mo><mi>g</mi><mo>)</mo><mo>⊗</mo><mi>U</mi><mo>(</mo><mi>g</mi><mo>)</mo><mo>〚</mo><mi>ħ</mi><mo>〛</mo></math></span>, establishes a twistor on the associated quantum groupoid when combined with the Gutt star product on the cotangent bundle <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>L</mi></math></span> of a Lie group <em>L</em> that integrates <span><math><mi>l</mi></math></span>. This result provides a framework for constructing equivariant star products from smooth dynamical twists on those Poisson homogeneous spaces arising from nondegenerate polarized Lie algebras, leveraging the structure of twistors of quantum groupoids.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105708"},"PeriodicalIF":1.2,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579508","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}
Pub Date : 2025-11-10DOI: 10.1016/j.geomphys.2025.105705
Shun Xu
In [8], [5], [11], (generalized) Zhu's algebras are realized as subquotients of the universal enveloping algebras of vertex operator (super)algebras. In this paper, we provide a unified and concise proof of these results. As applications, we show that (generalized) Zhu's algebras [3], [10] associated with vertex operator (super)algebras over an arbitrary algebraically closed field with can all be realized as subquotients of their universal enveloping algebras.
{"title":"Bimodules and associative algebras associated to SVOAs over an arbitrary field","authors":"Shun Xu","doi":"10.1016/j.geomphys.2025.105705","DOIUrl":"10.1016/j.geomphys.2025.105705","url":null,"abstract":"<div><div>In <span><span>[8]</span></span>, <span><span>[5]</span></span>, <span><span>[11]</span></span>, (generalized) Zhu's algebras are realized as subquotients of the universal enveloping algebras of vertex operator (super)algebras. In this paper, we provide a unified and concise proof of these results. As applications, we show that (generalized) Zhu's algebras <span><span>[3]</span></span>, <span><span>[10]</span></span> associated with vertex operator (super)algebras over an arbitrary algebraically closed field <span><math><mi>F</mi></math></span> with <span><math><mi>char</mi><mspace></mspace><mi>F</mi><mo>≠</mo><mn>2</mn></math></span> can all be realized as subquotients of their universal enveloping algebras.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"220 ","pages":"Article 105705"},"PeriodicalIF":1.2,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145486134","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}
Pub Date : 2025-11-10DOI: 10.1016/j.geomphys.2025.105706
Dadi Ni
In analogy to the classical holomorphic setting, Lang, Jia and Liu introduced the notion of the Atiyah class for a generalized holomorphic vector bundle using three different approaches: leveraging Čech cohomology, employing the first jet short exact sequence, and adopting the perspective of Lie algebroid pairs. The purpose of this note is to establish the equivalence among these diverse definitions of the Atiyah class.
{"title":"Atiyah classes in the context of generalized complex geometry","authors":"Dadi Ni","doi":"10.1016/j.geomphys.2025.105706","DOIUrl":"10.1016/j.geomphys.2025.105706","url":null,"abstract":"<div><div>In analogy to the classical holomorphic setting, Lang, Jia and Liu introduced the notion of the Atiyah class for a generalized holomorphic vector bundle using three different approaches: leveraging Čech cohomology, employing the first jet short exact sequence, and adopting the perspective of Lie algebroid pairs. The purpose of this note is to establish the equivalence among these diverse definitions of the Atiyah class.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"220 ","pages":"Article 105706"},"PeriodicalIF":1.2,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145486286","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}
Pub Date : 2025-11-10DOI: 10.1016/j.geomphys.2025.105704
Apurba Das, Ramkrishna Mandal, Anupam Sahoo
This paper provides some applications of the Poisson cohomology groups introduced by Flato, Gerstenhaber and Voronov. Given an abelian extension of a Poisson algebra by a representation, we first investigate the inducibility of a pair of Poisson algebra automorphisms and show that the corresponding obstruction lies in the second Poisson cohomology group. Consequently, we obtain the Wells exact sequence connecting various automorphism groups and the second Poisson cohomology group. Subsequently, we also consider the inducibility for a pair of Poisson algebra derivations, obtain the obstruction and construct the corresponding Wells-type exact sequence. To get another application, we introduce the notion of a ‘deformation map’ in a proto-twilled Poisson algebra. A deformation map unifies various well-known operators such as Poisson homomorphisms, Poisson derivations, crossed homomorphisms, Rota-Baxter operators of any weight, twisted Rota-Baxter operators, Reynolds operators and modified Rota-Baxter operators on Poisson algebras. We show that a deformation map r induces a new Poisson algebra structure and a suitable representation of it. The corresponding Poisson cohomology is defined to be the cohomology of the deformation map r. Finally, we study the formal deformations of the operator r in terms of the cohomology.
{"title":"Applications of Poisson cohomology to the inducibility problems and study of deformation maps","authors":"Apurba Das, Ramkrishna Mandal, Anupam Sahoo","doi":"10.1016/j.geomphys.2025.105704","DOIUrl":"10.1016/j.geomphys.2025.105704","url":null,"abstract":"<div><div>This paper provides some applications of the Poisson cohomology groups introduced by Flato, Gerstenhaber and Voronov. Given an abelian extension of a Poisson algebra by a representation, we first investigate the inducibility of a pair of Poisson algebra automorphisms and show that the corresponding obstruction lies in the second Poisson cohomology group. Consequently, we obtain the Wells exact sequence connecting various automorphism groups and the second Poisson cohomology group. Subsequently, we also consider the inducibility for a pair of Poisson algebra derivations, obtain the obstruction and construct the corresponding Wells-type exact sequence. To get another application, we introduce the notion of a ‘deformation map’ in a proto-twilled Poisson algebra. A deformation map unifies various well-known operators such as Poisson homomorphisms, Poisson derivations, crossed homomorphisms, Rota-Baxter operators of any weight, twisted Rota-Baxter operators, Reynolds operators and modified Rota-Baxter operators on Poisson algebras. We show that a deformation map <em>r</em> induces a new Poisson algebra structure and a suitable representation of it. The corresponding Poisson cohomology is defined to be the cohomology of the deformation map <em>r</em>. Finally, we study the formal deformations of the operator <em>r</em> in terms of the cohomology.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"220 ","pages":"Article 105704"},"PeriodicalIF":1.2,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145529266","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}
Pub Date : 2025-11-07DOI: 10.1016/j.geomphys.2025.105701
Loïc Marsot, Yuzhang Liu
This article aims to derive equations of motion for dynamical systems with angular momentum on Finsler geometries. To this end, we apply Souriau's Principle of General Covariance, which is a geometrical framework to derive diffeomorphism invariant equations of motion. The equations we obtain are the generalization of that of Mathisson-Papapetrou-Dixon (MPD) on Finsler geometries, and we give their conserved quantities which turn out to be formally identical to the Riemannian case.
These equations share the same properties as the MPD equations, and we mention different choices possible for supplementary conditions to close this system of equations. These equations have an additional requirement, which is the choice of what defines the tangent direction of the Finsler manifold, since the velocity and momentum are not parallel in general. After choosing the momentum as the Finsler direction and to define the center of mass, we give the complete equations of motion in 3 spatial dimensions, which we find coincide to previously known equations for Finsler spinoptics, and novel equations in 4 dimensions for massive and massless dynamical systems.
{"title":"Equations of motion for dynamical systems with angular momentum on Finsler geometries","authors":"Loïc Marsot, Yuzhang Liu","doi":"10.1016/j.geomphys.2025.105701","DOIUrl":"10.1016/j.geomphys.2025.105701","url":null,"abstract":"<div><div>This article aims to derive equations of motion for dynamical systems with angular momentum on Finsler geometries. To this end, we apply Souriau's Principle of General Covariance, which is a geometrical framework to derive diffeomorphism invariant equations of motion. The equations we obtain are the generalization of that of Mathisson-Papapetrou-Dixon (MPD) on Finsler geometries, and we give their conserved quantities which turn out to be formally identical to the Riemannian case.</div><div>These equations share the same properties as the MPD equations, and we mention different choices possible for supplementary conditions to close this system of equations. These equations have an additional requirement, which is the choice of what defines the tangent direction of the Finsler manifold, since the velocity and momentum are not parallel in general. After choosing the momentum as the Finsler direction and to define the center of mass, we give the complete equations of motion in 3 spatial dimensions, which we find coincide to previously known equations for Finsler spinoptics, and novel equations in 4 dimensions for massive and massless dynamical systems.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105701"},"PeriodicalIF":1.2,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145529319","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}
Pub Date : 2025-11-05DOI: 10.1016/j.geomphys.2025.105693
Marco Castrillón López , Álvaro Rodríguez Abella
We develop a reduction theory for G-invariant Lagrangian field theories defined on the higher-order jet bundle of a principal G-bundle, thus obtaining the higher-order Euler–Poincaré field equations. To that end, we transfer the Hamilton's principle to the reduced configuration bundle, which is identified with the bundle of flat connections (up to a certain order) of the principal G-bundle. As a result, the reconstruction condition is always satisfied and, hence, every solution of the reduced field equations locally comes from a solution of the original (unreduced) equations. Furthermore, the reduced equations are shown to be equivalent to the conservation of the Noether current. Lastly, we illustrate the theory by investigating multivariate higher-order splines on Lie groups.
{"title":"Higher-order Euler–Poincaré field equations","authors":"Marco Castrillón López , Álvaro Rodríguez Abella","doi":"10.1016/j.geomphys.2025.105693","DOIUrl":"10.1016/j.geomphys.2025.105693","url":null,"abstract":"<div><div>We develop a reduction theory for <em>G</em>-invariant Lagrangian field theories defined on the higher-order jet bundle of a principal <em>G</em>-bundle, thus obtaining the higher-order Euler–Poincaré field equations. To that end, we transfer the Hamilton's principle to the reduced configuration bundle, which is identified with the bundle of flat connections (up to a certain order) of the principal <em>G</em>-bundle. As a result, the reconstruction condition is always satisfied and, hence, every solution of the reduced field equations locally comes from a solution of the original (unreduced) equations. Furthermore, the reduced equations are shown to be equivalent to the conservation of the Noether current. Lastly, we illustrate the theory by investigating multivariate higher-order splines on Lie groups.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105693"},"PeriodicalIF":1.2,"publicationDate":"2025-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145529318","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}
Pub Date : 2025-11-04DOI: 10.1016/j.geomphys.2025.105692
Shuping Huang , Xiaoming Zhu
This paper presents multi-component integrable generalizations of both the positive and negative (2+1)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) hierarchies, associated with the A.III, BD.I, C.I, and D.III classes of irreducible Hermitian symmetric spaces. Utilizing recursive operators and symmetric reductions, it is demonstrated that, with two exceptions, the -flow of each (2+1)-dimensional multi-component AKNS hierarchy, corresponding to an irreducible Hermitian symmetric space, can be decomposed into the - and -flows of the respective (1+1)-dimensional multi-component AKNS hierarchy. These results reveal the structural connections between (1+1)- and (2+1)-dimensional integrable hierarchies, offering a rigorous basis for further investigations of multi-component hierarchies arising from Hermitian symmetric spaces.
本文给出了与不可约密尔对称空间的A.III， BD.I, c.i.和D.III类相关的正（2+1）维ablowitz - kap - newwell - segur （AKNS）层次的多分量可积推广。利用递归算子和对称约简，证明了在两个例外情况下，对应于不可约厄米对称空间的每个（2+1）维多分量AKNS层次的(n2−n1+1)-流可以分解为各自（1+1）维多分量AKNS层次的n1-流和n2-流。这些结果揭示了(1+1)-和（2+1）维可积层次之间的结构联系，为进一步研究厄米对称空间中产生的多分量层次提供了严格的基础。
{"title":"Positive and negative (2+1)-dimensional multi-component AKNS hierarchies associated with Hermitian symmetric spaces and their integrable decompositions","authors":"Shuping Huang , Xiaoming Zhu","doi":"10.1016/j.geomphys.2025.105692","DOIUrl":"10.1016/j.geomphys.2025.105692","url":null,"abstract":"<div><div>This paper presents multi-component integrable generalizations of both the positive and negative (2+1)-dimensional Ablowitz-Kaup-Newell-Segur (AKNS) hierarchies, associated with the A.III, BD.I, C.I, and D.III classes of irreducible Hermitian symmetric spaces. Utilizing recursive operators and symmetric reductions, it is demonstrated that, with two exceptions, the <span><math><mo>(</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>−</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-flow of each (2+1)-dimensional multi-component AKNS hierarchy, corresponding to an irreducible Hermitian symmetric space, can be decomposed into the <span><math><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>- and <span><math><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-flows of the respective (1+1)-dimensional multi-component AKNS hierarchy. These results reveal the structural connections between (1+1)- and (2+1)-dimensional integrable hierarchies, offering a rigorous basis for further investigations of multi-component hierarchies arising from Hermitian symmetric spaces.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105692"},"PeriodicalIF":1.2,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145442560","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}
Pub Date : 2025-11-03DOI: 10.1016/j.geomphys.2025.105690
Alexander Flamant , Bram Mesland , Adam Rennie
We compare the constructions of Levi-Civita connections for noncommutative algebras developed in [2], [8], [15]. The assumptions in these various constructions differ, but when they are all defined, we provide direct translations between them. An essential assumption is that the (indefinite) Hermitian inner product on differential forms/vector fields provides an isomorphism with the module dual. By exploiting our translations and clarifying the simplifications that occur for centred bimodules, we extend the existence results for Hermitian torsion-free connections in [2], [8].
{"title":"Comparison of Levi-Civita connections in noncommutative geometry","authors":"Alexander Flamant , Bram Mesland , Adam Rennie","doi":"10.1016/j.geomphys.2025.105690","DOIUrl":"10.1016/j.geomphys.2025.105690","url":null,"abstract":"<div><div>We compare the constructions of Levi-Civita connections for noncommutative algebras developed in <span><span>[2]</span></span>, <span><span>[8]</span></span>, <span><span>[15]</span></span>. The assumptions in these various constructions differ, but when they are all defined, we provide direct translations between them. An essential assumption is that the (indefinite) Hermitian inner product on differential forms/vector fields provides an isomorphism with the module dual. By exploiting our translations and clarifying the simplifications that occur for centred bimodules, we extend the existence results for Hermitian torsion-free connections in <span><span>[2]</span></span>, <span><span>[8]</span></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"219 ","pages":"Article 105690"},"PeriodicalIF":1.2,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475850","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}
Pub Date : 2025-10-31DOI: 10.1016/j.geomphys.2025.105691
Mohamed Tahar Kadaoui Abbassi, Khadija Boulagouaz
We characterize Siklos space-times which satisfy the quasi-Einstein equation, both in the gradient and the non-gradient cases. Then, we prove that several homogeneous Siklos space-times are quasi-Einstein, and finally we provide a classification of locally conformally flat quasi-Einstein Siklos space-times.
{"title":"Quasi-Einstein Siklos space-times","authors":"Mohamed Tahar Kadaoui Abbassi, Khadija Boulagouaz","doi":"10.1016/j.geomphys.2025.105691","DOIUrl":"10.1016/j.geomphys.2025.105691","url":null,"abstract":"<div><div>We characterize Siklos space-times which satisfy the quasi-Einstein equation, both in the gradient and the non-gradient cases. Then, we prove that several homogeneous Siklos space-times are quasi-Einstein, and finally we provide a classification of locally conformally flat quasi-Einstein Siklos space-times.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"218 ","pages":"Article 105691"},"PeriodicalIF":1.2,"publicationDate":"2025-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145466559","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}
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