T. Chtioui, A. Hajjaji, S. Mabrouk, Abdenacer Makhlouf
In this paper, first, we provide a graded Lie algebra whose Maurer–Cartan elements characterize Lie triple system structures. Then, we use it to study cohomology and deformations of O-operators on Lie triple systems by constructing a Lie 3-algebra whose Maurer–Cartan elements are O-operators. Furthermore, we define a cohomology of an O-operator T as the Lie–Yamaguti cohomology of a certain Lie triple system induced by T with coefficients in a suitable representation. Therefore, we consider infinitesimal and formal deformations of O-operators from a cohomological viewpoint. Moreover, we provide relationships between O-operators on Lie algebras and associated Lie triple systems.
{"title":"Cohomologies and deformations of O-operators on Lie triple systems","authors":"T. Chtioui, A. Hajjaji, S. Mabrouk, Abdenacer Makhlouf","doi":"10.1063/5.0118911","DOIUrl":"https://doi.org/10.1063/5.0118911","url":null,"abstract":"In this paper, first, we provide a graded Lie algebra whose Maurer–Cartan elements characterize Lie triple system structures. Then, we use it to study cohomology and deformations of O-operators on Lie triple systems by constructing a Lie 3-algebra whose Maurer–Cartan elements are O-operators. Furthermore, we define a cohomology of an O-operator T as the Lie–Yamaguti cohomology of a certain Lie triple system induced by T with coefficients in a suitable representation. Therefore, we consider infinitesimal and formal deformations of O-operators from a cohomological viewpoint. Moreover, we provide relationships between O-operators on Lie algebras and associated Lie triple systems.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"49 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79833123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we are concerned with a fractional Kirchhoff equation with a general coercive potential. First, we consider some existence and nonexistence of L2-constraint minimizers for related constrained minimization problems. Most importantly, by constructing appropriate trial functions for some delicate energy estimates and studying decay properties of solution sequences, we then establish the concentration behaviors of L2-constraint minimizers for related constrained minimization problems.
{"title":"Properties of minimizers for the fractional Kirchhoff energy functional","authors":"Lintao Liu, K. Teng, Jie Yang, Haibo Chen","doi":"10.1063/5.0157267","DOIUrl":"https://doi.org/10.1063/5.0157267","url":null,"abstract":"In this paper, we are concerned with a fractional Kirchhoff equation with a general coercive potential. First, we consider some existence and nonexistence of L2-constraint minimizers for related constrained minimization problems. Most importantly, by constructing appropriate trial functions for some delicate energy estimates and studying decay properties of solution sequences, we then establish the concentration behaviors of L2-constraint minimizers for related constrained minimization problems.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"5 10","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72466432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 1878, Hill found numerically, in his limiting case of the restricted three-body problem, the so-called Hill’s lunar problem, a planar direct periodic orbit with a period of one synodic month. By virtue of the spatial system’s invariance under a symplectic involution, whose fixed point set corresponds to the planar problem, we can assign to Hill’s orbit planar and spatial Floquet multipliers and planar and spatial Conley–Zehnder indices. We show that these have deep astronomical significance because, on the one hand, we relate the anomalistic month to the planar Floquet multipliers and the planar Conley–Zehnder index. On the other hand, we relate the draconitic month to the spatial Floquet multipliers and the spatial Conley–Zehnder index. Knowledge of this lunar month dates back to the Babylonians, who lived until around 500 BCE. In order to determine the indices, we analyze analytically the bifurcation procedure of the fundamental families of planar direct and retrograde periodic orbits (traditionally known as families g and f) from the rotating Kepler problem for very low energies.
{"title":"From Babylonian lunar observations to Floquet multipliers and Conley–Zehnder indices","authors":"Cengiz Aydin","doi":"10.1063/5.0156959","DOIUrl":"https://doi.org/10.1063/5.0156959","url":null,"abstract":"In 1878, Hill found numerically, in his limiting case of the restricted three-body problem, the so-called Hill’s lunar problem, a planar direct periodic orbit with a period of one synodic month. By virtue of the spatial system’s invariance under a symplectic involution, whose fixed point set corresponds to the planar problem, we can assign to Hill’s orbit planar and spatial Floquet multipliers and planar and spatial Conley–Zehnder indices. We show that these have deep astronomical significance because, on the one hand, we relate the anomalistic month to the planar Floquet multipliers and the planar Conley–Zehnder index. On the other hand, we relate the draconitic month to the spatial Floquet multipliers and the spatial Conley–Zehnder index. Knowledge of this lunar month dates back to the Babylonians, who lived until around 500 BCE. In order to determine the indices, we analyze analytically the bifurcation procedure of the fundamental families of planar direct and retrograde periodic orbits (traditionally known as families g and f) from the rotating Kepler problem for very low energies.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"60 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87048412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we systematically study the high-order stability of the stochastic reaction-diffusion equation driven by additive noise as the noise intensity vanishes. First, with a general assumption on the nonlinear term, we obtain the convergence of solutions and upper semi-continuity of random attractors in L2(RN). Second, by using the nonlinear decomposition method, we technically establish the convergence of solutions in Lp(RN)∩H1(RN)(p>2), and therefore, the upper semi-continuity of random attractors is proved, where p is the growth exponent of the nonlinearity. Finally, by induction argument, we prove that the solution is uniformly bounded near the initial time in Lδ(RN) for arbitrary δ > p, in which space the convergence of solutions and the upper semi-continuity of random attractors are also established.
{"title":"Stability of stochastic reaction-diffusion equation under random influences in high regular spaces","authors":"Zhi Li, Wenqiang Zhao","doi":"10.1063/5.0148290","DOIUrl":"https://doi.org/10.1063/5.0148290","url":null,"abstract":"In this paper, we systematically study the high-order stability of the stochastic reaction-diffusion equation driven by additive noise as the noise intensity vanishes. First, with a general assumption on the nonlinear term, we obtain the convergence of solutions and upper semi-continuity of random attractors in L2(RN). Second, by using the nonlinear decomposition method, we technically establish the convergence of solutions in Lp(RN)∩H1(RN)(p>2), and therefore, the upper semi-continuity of random attractors is proved, where p is the growth exponent of the nonlinearity. Finally, by induction argument, we prove that the solution is uniformly bounded near the initial time in Lδ(RN) for arbitrary δ > p, in which space the convergence of solutions and the upper semi-continuity of random attractors are also established.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"11 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82003733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper focuses on the dynamics of the non-autonomous stochastic p-Laplacian parabolic problems defined on unbounded thin domains. We first show that the tails of solutions of the equation are uniformly small outside a bounded domain, which is utilized to overcome the non-compactness of Sobolev embeddings on unbounded domains. We then prove the existence and uniqueness of random attractors for the equations defined on (n + 1)-dimensional unbounded thin domains and further establish the upper semi-continuity of attractors as the thin domains collapse onto the space Rn.
{"title":"Dynamics of the non-autonomous stochastic p-Laplacian parabolic problems on unbounded thin domains","authors":"Zhengguo Pu, Dingshi Li","doi":"10.1063/5.0154808","DOIUrl":"https://doi.org/10.1063/5.0154808","url":null,"abstract":"This paper focuses on the dynamics of the non-autonomous stochastic p-Laplacian parabolic problems defined on unbounded thin domains. We first show that the tails of solutions of the equation are uniformly small outside a bounded domain, which is utilized to overcome the non-compactness of Sobolev embeddings on unbounded domains. We then prove the existence and uniqueness of random attractors for the equations defined on (n + 1)-dimensional unbounded thin domains and further establish the upper semi-continuity of attractors as the thin domains collapse onto the space Rn.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"26 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77332848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stimulated by improved oscillation estimates of the potential function and the scalar curvature on compact gradient Ricci solitons introduced in a recent study by Cheng, Ribeiro, and Zhou [Proc. Am. Math. Soc. Ser. B 10, 33–45 (2023)], we give several new sufficient conditions for compact four-dimensional normalized shrinking Ricci solitons to satisfy the Hitchin–Thorpe inequality. Our new conditions refine the validity of the Hitchin–Thorpe inequality obtained by Tadano [J. Math. Phys. 58, 023503 (2017)], Tadano [J. Math. Phys. 59, 043507 (2018)], and Tadano [Differ. Geom. Appl. 66, 231–241 (2019)].
{"title":"Improved oscillation estimates and the Hitchin–Thorpe inequality on compact Ricci solitons","authors":"H. Tadano","doi":"10.1063/5.0152174","DOIUrl":"https://doi.org/10.1063/5.0152174","url":null,"abstract":"Stimulated by improved oscillation estimates of the potential function and the scalar curvature on compact gradient Ricci solitons introduced in a recent study by Cheng, Ribeiro, and Zhou [Proc. Am. Math. Soc. Ser. B 10, 33–45 (2023)], we give several new sufficient conditions for compact four-dimensional normalized shrinking Ricci solitons to satisfy the Hitchin–Thorpe inequality. Our new conditions refine the validity of the Hitchin–Thorpe inequality obtained by Tadano [J. Math. Phys. 58, 023503 (2017)], Tadano [J. Math. Phys. 59, 043507 (2018)], and Tadano [Differ. Geom. Appl. 66, 231–241 (2019)].","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"20 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80506137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let Q(n) be the queer Lie superalgebra. We determine conditions under which two one-dimensional modules over the super-Yangian of Q(1) can be extended nontrivially, and thus belong to the same block of the subcategory of finite-dimensional YQ(1)-modules admitting generalized central character χ = 0. We use these results to determine conditions under which two one-dimensional modules over the finite W-algebra for Q(n) can be extended nontrivially. We describe blocks in the category of finite-dimensional modules over the finite W-algebra for Q(2). In certain cases, we determine conditions under which two simple finite-dimensional YQ(1)-modules admitting central character χ ≠ 0 can be extended nontrivially and propose a conjecture in the general case.
{"title":"On linked modules over the super-Yangian of the superalgebra Q(1)","authors":"E. Poletaeva","doi":"10.1063/5.0153942","DOIUrl":"https://doi.org/10.1063/5.0153942","url":null,"abstract":"Let Q(n) be the queer Lie superalgebra. We determine conditions under which two one-dimensional modules over the super-Yangian of Q(1) can be extended nontrivially, and thus belong to the same block of the subcategory of finite-dimensional YQ(1)-modules admitting generalized central character χ = 0. We use these results to determine conditions under which two one-dimensional modules over the finite W-algebra for Q(n) can be extended nontrivially. We describe blocks in the category of finite-dimensional modules over the finite W-algebra for Q(2). In certain cases, we determine conditions under which two simple finite-dimensional YQ(1)-modules admitting central character χ ≠ 0 can be extended nontrivially and propose a conjecture in the general case.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"131 10 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91026278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is concerned with the asymptotic stability of a planar stationary solution to an initial-boundary value problem for a two-dimensional hyperbolic–elliptic coupled system of the radiating gas on half space. We show that the solution to the problem converges to the corresponding planar stationary solution as time tends to infinity under small initial perturbation. This result is proved by the standard L2-energy method and the div–curl decomposition. Moreover, we prove that the solution (u, q) converges to the corresponding planar stationary solution at the rate t−α/2−1/4 for the non-degenerate case and t−1/4 for the degenerate case. The proof is based on the time and space weighted energy method.
{"title":"Convergence rates to the planar stationary solution to a 2D model of the radiating gas on half space","authors":"Minyi Zhang, Changjiang Zhu","doi":"10.1063/5.0150233","DOIUrl":"https://doi.org/10.1063/5.0150233","url":null,"abstract":"This paper is concerned with the asymptotic stability of a planar stationary solution to an initial-boundary value problem for a two-dimensional hyperbolic–elliptic coupled system of the radiating gas on half space. We show that the solution to the problem converges to the corresponding planar stationary solution as time tends to infinity under small initial perturbation. This result is proved by the standard L2-energy method and the div–curl decomposition. Moreover, we prove that the solution (u, q) converges to the corresponding planar stationary solution at the rate t−α/2−1/4 for the non-degenerate case and t−1/4 for the degenerate case. The proof is based on the time and space weighted energy method.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"21 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87259664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For an affine Lie algebra ĝ, the coefficients of certain vertex operators that annihilate level k standard ĝ-modules are the defining relations for level k standard modules. In this paper, we study a combinatorial structure of the leading terms of these relations for level k = 2 standard ĝ-modules for affine Lie algebras of type Cn(1) and the main result is the construction of combinatorially parameterized relations among the coefficients of annihilating fields. It is believed that the constructed relations among relations will play a key role in the construction of Gröbner-like basis of the maximal ideal of the universal vertex operator algebra Vgk for k = 2.
{"title":"Combinatorial relations among relations for level 2 standard Cn(1)-modules","authors":"M. Primc, Tomislav Šikić","doi":"10.1063/5.0145719","DOIUrl":"https://doi.org/10.1063/5.0145719","url":null,"abstract":"For an affine Lie algebra ĝ, the coefficients of certain vertex operators that annihilate level k standard ĝ-modules are the defining relations for level k standard modules. In this paper, we study a combinatorial structure of the leading terms of these relations for level k = 2 standard ĝ-modules for affine Lie algebras of type Cn(1) and the main result is the construction of combinatorially parameterized relations among the coefficients of annihilating fields. It is believed that the constructed relations among relations will play a key role in the construction of Gröbner-like basis of the maximal ideal of the universal vertex operator algebra Vgk for k = 2.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"28 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81647457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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