A facile approach for the first total synthesis of naturally occurring geranylated flavanoids sepicanin A has been obtained with total yield 16%starting from 2,4,6-trihydroxyacetophenone after four steps.The key step ...A facile approach for the first total synthesis of naturally occurring geranylated flavanoids sepicanin A has been obtained with total yield 16%starting from 2,4,6-trihydroxyacetophenone after four steps.The key step was the protic acids（HCl or p-TsOH）-catalyzed benzopyrone formation in a protic polar solvent by deprotection and cycUzation of chalcone in one step.展开更多
Volume-preserving field X on a 3-manifold is the one that satisfies LxΩ = 0 for some volume Ω. The Reeb vector field of a contact form is of volume-preserving, but not conversely. On the basis of Geiges-Gonzalo＇s p...Volume-preserving field X on a 3-manifold is the one that satisfies LxΩ = 0 for some volume Ω. The Reeb vector field of a contact form is of volume-preserving, but not conversely. On the basis of Geiges-Gonzalo＇s parallelization results, we obtain a volume-preserving sphere, which is a triple of everywhere linearly independent vector fields such that all their linear combinations with constant coefficients are volume-preserving fields. From many aspects, we discuss the distinction between volume-preserving fields and Reeb-like fields. We establish a duality between volume-preserving fields and h-closed 2-forms to understand such distinction. We also give two kinds of non-Reeb-like but volume-preserving vector fields to display such distinction.展开更多
基金supported by the National Natural Science Foundation(No20962016)Ningxia Natura Science Foundation(NoNZ1006)Program for New Century Excellent Talents in University(NoNCET- 09-0860)
文摘A facile approach for the first total synthesis of naturally occurring geranylated flavanoids sepicanin A has been obtained with total yield 16%starting from 2,4,6-trihydroxyacetophenone after four steps.The key step was the protic acids（HCl or p-TsOH）-catalyzed benzopyrone formation in a protic polar solvent by deprotection and cycUzation of chalcone in one step.
文摘Volume-preserving field X on a 3-manifold is the one that satisfies LxΩ = 0 for some volume Ω. The Reeb vector field of a contact form is of volume-preserving, but not conversely. On the basis of Geiges-Gonzalo＇s parallelization results, we obtain a volume-preserving sphere, which is a triple of everywhere linearly independent vector fields such that all their linear combinations with constant coefficients are volume-preserving fields. From many aspects, we discuss the distinction between volume-preserving fields and Reeb-like fields. We establish a duality between volume-preserving fields and h-closed 2-forms to understand such distinction. We also give two kinds of non-Reeb-like but volume-preserving vector fields to display such distinction.
