In this paper, we show that there exists a twisted duality symmetry between the Maurer-Cartan equations and the equations of motion in the hybrid formalism for the type liB superstring in an AdS2 ×S2 background w...In this paper, we show that there exists a twisted duality symmetry between the Maurer-Cartan equations and the equations of motion in the hybrid formalism for the type liB superstring in an AdS2 ×S2 background with Ramond-Ramond flux. As a result, from the twisted duality transformation, we construct the Lax connection with the spectral parameter, which ensures the integrability of the system.展开更多
By using the linear independent solutions of the linear variational equation along the homoclinic loop as the demanded local coordinates to construct the Poincaré map,the bifurcations of twisted homoclinic loop f...By using the linear independent solutions of the linear variational equation along the homoclinic loop as the demanded local coordinates to construct the Poincaré map,the bifurcations of twisted homoclinic loop for higher dimensional systems are studied.Under the nonresonant and resonant conditions,the existence,number and existence regions of the 1-homoclinic loop,1-periodic orbit,2-homoclinic loop,2-periodic orbit and 2-fold 2-periodic orbit were obtained.Particularly,the asymptotic repressions of related bifurcation surfaces were also given.Moreover, the stability of homoclinic loop for higher dimensional systems and nontwisted homoclinic loop for planar systems were studied.展开更多
Arbitrary polarized vortex beam induced by polarization singularity offers a new platform for both classical optics and quantum entanglement applications.Bound states in the continuum(BICs)have been demonstrated to be...Arbitrary polarized vortex beam induced by polarization singularity offers a new platform for both classical optics and quantum entanglement applications.Bound states in the continuum(BICs)have been demonstrated to be associated with topological charge and vortex polarization singularities in momentum space.For conventional symmetric photonic crystal slabs(PhCSs),BIC is enclosed by linearly polarized far fields with winding angle of 2π,which is unfavorable for high-capacity and multi-functionality integration-optics applications.Here,we show that by breakingσz-symmetry of the PhCS,asymmetry in upward and downward directions and arbitrarily polarized BIC can be realized with a bilayer-twisted PhCS.It exhibits elliptical polarization states with constant ellipticity angle at every point in momentum space within the vicinity of BIC.The topological nature of BIC reflects on the orientation angle of polarization state,with a topological charge of 1 for any value of ellipticity angle.Full coverage of Poincarésphere(i.e.,-π/4≤X≤4 and-π/2≤ψ≤π/2)and higher-order Poincarésphere can be realized by tailoring the twist angles.Our findings may open up new avenues for applications in structured light,quantum optics,and twistronics for photons.展开更多
In this paper, we study the truncated polynomial algebra L in n variables, and discuss the following four problems in detail: 1) Homology complex and homology group of Poisson algebra L;2) Given a new Poisson bracket ...In this paper, we study the truncated polynomial algebra L in n variables, and discuss the following four problems in detail: 1) Homology complex and homology group of Poisson algebra L;2) Given a new Poisson bracket by calculation modular derivation of Frobenius Poisson algebra;3) Calculate the twisted homology group of Poisson algebra L;4) Verify the theorem of twisted Poincaré duality between twisted Poisson homology and Poisson Cohomology.展开更多
Over any smooth algebraic variety over a p-adic local field k,we construct the deRham comparison isomorphisms for theétale cohomology with partial compact support of de Rham Z_(p)-local systems,and show that they...Over any smooth algebraic variety over a p-adic local field k,we construct the deRham comparison isomorphisms for theétale cohomology with partial compact support of de Rham Z_(p)-local systems,and show that they are compatible with Poincaréduality and with the canonical morphisms among such cohomology.We deduce these results from their analogues for rigid analytic varieties that are Zariski open in some proper smooth rigid analytic varieties over k.In particular,we prove finiteness ofétale cohomology with partial compact support of any Z_(p)-local systems,and establish the Poincaréduality for such cohomology after inverting p.展开更多
In this article we show that any embedded graph has a checkerboard colourable twual,which is equivalent to having a bipartite twual.We also obtain that any Eulerian embedded graph has a checkerboard colourable partial...In this article we show that any embedded graph has a checkerboard colourable twual,which is equivalent to having a bipartite twual.We also obtain that any Eulerian embedded graph has a checkerboard colourable partial Petrial,answering questions posed by Ellis-Monaghan and Moffatt[Trans.Amer.Math.Soc.,364,1529–1569(2012)].展开更多
on Double Vector Bundles Zhuo CHEN Zhang Ju LIU Yun He SHENG Abstract In this paper,we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector b...on Double Vector Bundles Zhuo CHEN Zhang Ju LIU Yun He SHENG Abstract In this paper,we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles.Moreover,operations on double vector bundles can be transferred to operations on the corresponding short exact sequences.In particular,we study the duality theory of double vector bundles in term展开更多
This paper deals with the existence and multiplicity of periodic solutions of Duffing equations x + g(x) = p(t). The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equatio...This paper deals with the existence and multiplicity of periodic solutions of Duffing equations x + g(x) = p(t). The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided that g(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 90403019 Acknowledgments We would like to thank Prof. Kang-Jie Shi for many stimulating discussions. Xie is also grateful to Zhan-Yun Wang, Xiao-Lin Cai, Pei Song, and Jun Feng for their helpful discussions, and especially A-Ping Yang＇s encouragements.
文摘In this paper, we show that there exists a twisted duality symmetry between the Maurer-Cartan equations and the equations of motion in the hybrid formalism for the type liB superstring in an AdS2 ×S2 background with Ramond-Ramond flux. As a result, from the twisted duality transformation, we construct the Lax connection with the spectral parameter, which ensures the integrability of the system.
文摘By using the linear independent solutions of the linear variational equation along the homoclinic loop as the demanded local coordinates to construct the Poincaré map,the bifurcations of twisted homoclinic loop for higher dimensional systems are studied.Under the nonresonant and resonant conditions,the existence,number and existence regions of the 1-homoclinic loop,1-periodic orbit,2-homoclinic loop,2-periodic orbit and 2-fold 2-periodic orbit were obtained.Particularly,the asymptotic repressions of related bifurcation surfaces were also given.Moreover, the stability of homoclinic loop for higher dimensional systems and nontwisted homoclinic loop for planar systems were studied.
基金support from the National Natural Science Foundation of China(no.12204264)the Shenzhen Stability Support Program(no.WDZC20220810152404001)+2 种基金the Cross-Disciplinary Research Fund of Tsinghua Shenzhen International Graduate School(SIGS),Tsinghua University(JC2022001),and the startup funding in Tsinghua Shenzhen International Graduate School(SIGS),Tsinghua University(no.01030100006)support from the National Natural Science Foundation of China(No.62205246)the Fundamental Research Funds for the Central Universities.C-W.Q.acknowledges financial support from the NRF,Prime Minister's Office,Singapore under the Competitive Research Program Award(NRF-CRP26-2021-0063).
文摘Arbitrary polarized vortex beam induced by polarization singularity offers a new platform for both classical optics and quantum entanglement applications.Bound states in the continuum(BICs)have been demonstrated to be associated with topological charge and vortex polarization singularities in momentum space.For conventional symmetric photonic crystal slabs(PhCSs),BIC is enclosed by linearly polarized far fields with winding angle of 2π,which is unfavorable for high-capacity and multi-functionality integration-optics applications.Here,we show that by breakingσz-symmetry of the PhCS,asymmetry in upward and downward directions and arbitrarily polarized BIC can be realized with a bilayer-twisted PhCS.It exhibits elliptical polarization states with constant ellipticity angle at every point in momentum space within the vicinity of BIC.The topological nature of BIC reflects on the orientation angle of polarization state,with a topological charge of 1 for any value of ellipticity angle.Full coverage of Poincarésphere(i.e.,-π/4≤X≤4 and-π/2≤ψ≤π/2)and higher-order Poincarésphere can be realized by tailoring the twist angles.Our findings may open up new avenues for applications in structured light,quantum optics,and twistronics for photons.
文摘In this paper, we study the truncated polynomial algebra L in n variables, and discuss the following four problems in detail: 1) Homology complex and homology group of Poisson algebra L;2) Given a new Poisson bracket by calculation modular derivation of Frobenius Poisson algebra;3) Calculate the twisted homology group of Poisson algebra L;4) Verify the theorem of twisted Poincaré duality between twisted Poisson homology and Poisson Cohomology.
文摘Over any smooth algebraic variety over a p-adic local field k,we construct the deRham comparison isomorphisms for theétale cohomology with partial compact support of de Rham Z_(p)-local systems,and show that they are compatible with Poincaréduality and with the canonical morphisms among such cohomology.We deduce these results from their analogues for rigid analytic varieties that are Zariski open in some proper smooth rigid analytic varieties over k.In particular,we prove finiteness ofétale cohomology with partial compact support of any Z_(p)-local systems,and establish the Poincaréduality for such cohomology after inverting p.
基金Supported by NSFC(Grant Nos.12171402,12101600)the Fundamental Research Funds for the Central Universities(Grant Nos.20720190062,2021QN1037)。
文摘In this article we show that any embedded graph has a checkerboard colourable twual,which is equivalent to having a bipartite twual.We also obtain that any Eulerian embedded graph has a checkerboard colourable partial Petrial,answering questions posed by Ellis-Monaghan and Moffatt[Trans.Amer.Math.Soc.,364,1529–1569(2012)].
文摘on Double Vector Bundles Zhuo CHEN Zhang Ju LIU Yun He SHENG Abstract In this paper,we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles.Moreover,operations on double vector bundles can be transferred to operations on the corresponding short exact sequences.In particular,we study the duality theory of double vector bundles in term
文摘This paper deals with the existence and multiplicity of periodic solutions of Duffing equations x + g(x) = p(t). The author proves an infinity of periodic solutions to the periodically forced nonlinear Duffing equations provided that g(x) satisfies the globally lipschitzian condition and the time-mapping satisfies the weaker oscillating property.
