The Hopf dual H~? of any Poisson Hopf algebra H is proved to be a co-Poisson Hopf algebra provided H is noetherian. Without noetherian assumption, unlike it is claimed in literature, the statement does not hold. It is...The Hopf dual H~? of any Poisson Hopf algebra H is proved to be a co-Poisson Hopf algebra provided H is noetherian. Without noetherian assumption, unlike it is claimed in literature, the statement does not hold. It is proved that there is no nontrivial Poisson Hopf structure on the universal enveloping algebra of a non-abelian Lie algebra. So the polynomial Hopf algebra, viewed as the universal enveloping algebra of a finite-dimensional abelian Lie algebra, is considered. The Poisson Hopf structures on polynomial Hopf algebras are exactly linear Poisson structures. The co-Poisson structures on polynomial Hopf algebras are characterized.Some correspondences between co-Poisson and Poisson structures are also established.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
在卫星拒止下,配备低成本单通道相控阵天线的无人集群通过波达方向(Direction of Arrival,DOA)估计进行波束对准,是其定向低截获传输任务数据的前提。现有研究中通常采用多波束扫描算法实现DOA估计,存在需要预知节点数、算法复杂度高等...在卫星拒止下,配备低成本单通道相控阵天线的无人集群通过波达方向(Direction of Arrival,DOA)估计进行波束对准,是其定向低截获传输任务数据的前提。现有研究中通常采用多波束扫描算法实现DOA估计,存在需要预知节点数、算法复杂度高等问题。针对上述问题,建模分析空域协方差矩阵估计误差分布,研究估计误差约束下扫描次数与节点数的关系,并据此推导基于无人集群泊松分布先验的估计误差分布,提出一种估计误差约束下的低复杂度DOA估计方法。通过理论与仿真分析,与多波束扫描方法相比,所提方法在保证DOA估计精度的前提下波束数量减少了约30.16%,提升了低成本单通道相控阵无人集群的实用性。展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11331006 and 11171067)
文摘The Hopf dual H~? of any Poisson Hopf algebra H is proved to be a co-Poisson Hopf algebra provided H is noetherian. Without noetherian assumption, unlike it is claimed in literature, the statement does not hold. It is proved that there is no nontrivial Poisson Hopf structure on the universal enveloping algebra of a non-abelian Lie algebra. So the polynomial Hopf algebra, viewed as the universal enveloping algebra of a finite-dimensional abelian Lie algebra, is considered. The Poisson Hopf structures on polynomial Hopf algebras are exactly linear Poisson structures. The co-Poisson structures on polynomial Hopf algebras are characterized.Some correspondences between co-Poisson and Poisson structures are also established.
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.
文摘在卫星拒止下,配备低成本单通道相控阵天线的无人集群通过波达方向(Direction of Arrival,DOA)估计进行波束对准,是其定向低截获传输任务数据的前提。现有研究中通常采用多波束扫描算法实现DOA估计,存在需要预知节点数、算法复杂度高等问题。针对上述问题,建模分析空域协方差矩阵估计误差分布,研究估计误差约束下扫描次数与节点数的关系,并据此推导基于无人集群泊松分布先验的估计误差分布,提出一种估计误差约束下的低复杂度DOA估计方法。通过理论与仿真分析,与多波束扫描方法相比,所提方法在保证DOA估计精度的前提下波束数量减少了约30.16%,提升了低成本单通道相控阵无人集群的实用性。
