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61.
Harald Biller 《Transactions of the American Mathematical Society》2003,355(1):407-432
Essential results about actions of compact Lie groups on connected manifolds are generalized to proper actions of arbitrary groups on connected cohomology manifolds. Slices are replaced by certain fiber bundle structures on orbit neighborhoods. The group dimension is shown to be effectively finite. The orbits of maximal dimension form a dense open connected subset. If some orbit has codimension at most , then the group is effectively a Lie group.
62.
Sergey Antonyan 《Transactions of the American Mathematical Society》2003,355(8):3379-3404
Let be a compact Lie group, a metric -space, and the hyperspace of all nonempty compact subsets of endowed with the Hausdorff metric topology and with the induced action of . We prove that the following three assertions are equivalent: (a) is locally continuum-connected (resp., connected and locally continuum-connected); (b) is a -ANR (resp., a -AR); (c) is an ANR (resp., an AR). This is applied to show that is an ANR (resp., an AR) for each compact (resp., connected) Lie group . If is a finite group, then is a Hilbert cube whenever is a nondegenerate Peano continuum. Let be the hyperspace of all centrally symmetric, compact, convex bodies , , for which the ordinary Euclidean unit ball is the ellipsoid of minimal volume containing , and let be the complement of the unique -fixed point in . We prove that: (1) for each closed subgroup , is a Hilbert cube manifold; (2) for each closed subgroup acting non-transitively on , the -orbit space and the -fixed point set are Hilbert cubes. As an application we establish new topological models for tha Banach-Mazur compacta and prove that and have the same -homotopy type.
63.
Let (Xn,dn) be a sequence of finite metric spaces of uniformlybounded diameter. An equivalence relation D on the product defined by if and only if is a c0-equality.A systematic study is made of c0-equalities and Borel reductionsbetween them. Necessary and sufficient conditions, expressedin terms of combinatorial properties of metrics dn, are obtainedfor a c0-equality to be effectively reducible to the isomorphismrelation of countable structures. It is proved that every Borelequivalence relation E reducible to a c0-equality D either reducesa c0-equality D' additively reducible to D, or is Borel-reducibleto the equality relation on countable sets of reals. An appropriatelydefined sequence of metrics provides a c0-equality which isa turbulent orbit equivalence relation with no minimum turbulentequivalence relation reducible to it. This answers a questionof Hjorth. It is also shown that, whenever E is an F-equivalencerelation and D is a c0-equality, every Borel equivalence relationreducible to both D and to E has to be essentially countable.2000 Mathematics Subject Classification: 03E15. 相似文献
64.
Driss Drissi Mostafa Mbekhta 《Proceedings of the American Mathematical Society》2001,129(7):2011-2016
For a pair of linear bounded operators and on a complex Banach space , if commutes with then the orbits of under are uniformly bounded. The study of the converse implication was started in the 1970s by J. A. Deddens. In this paper, we present a new approach to this type of question using two localization theorems; one is an operator version of a theorem of tauberian type given by Katznelson-Tzafriri and the second one is on power-bounded operators by Gelfand-Hille. This improves former results of Deddens-Stampfli-Williams. 相似文献
65.
Let G be a complex semisimple group with real form G
. For the action of G
× G
on G by left and right translation, we define and study an orbit-type stratification of G. In particular, we compute the dimension of an arbitrary stratum; we identify certain strata of low codimension in G, the union of whose closures contains every nonprincipal stratum; and we describe the boundaries and adjacency relations of the maximal connected domains in G that contain only principal orbits. 相似文献
66.
Cecí lia Ferreira Armando Machado 《Proceedings of the American Mathematical Society》2000,128(7):2181-2186
Let denote the set of all -roots of the identity in a Lie group . We show that is always an embedded submanifold of , having the conjugacy classes of its elements as open submanifolds. These conjugacy classes are examples of -symmetric spaces and we show, more generally, that every -symmetric space of a Lie group is a covering manifold of an embedded submanifold of . We compute also the Hessian of the inclusions of and into , relative to the natural connection on the domain and to the symmetric connection on .
67.
68.
基于稳定性理论,提出了一种状态反馈控制混沌的方法。介绍了该方法的控制原理以及各个预期的周期轨道反馈系数的选取原则。以Gibbs光学双稳系统为例,验证了该方法的有效性。数值结果表明,通过调节反馈系数,可以将系统控制在所需的目标轨道上。 相似文献
69.
地球同步轨道二维扫描像移补偿技术建模与分析 总被引:2,自引:0,他引:2
在建立二维扫描观测模型的基础上,提出了基于椭球体地球模型的二维扫描像移补偿方案,给出了任意空间观测到的目标位置的快速迭代算法,并以真实轨道和仿真姿态数据验证了像移补偿模型的实际性能。仿真结果表明,对于长周期(大于一个东西方向扫描行周期)轨道和姿态偏差,可以通过调整仪器坐标系内的扫描轨迹来实现像移补偿;同时,在现有轨道测量和控制条件下,轨道因素引起的瞬时方位角和俯仰角补偿量在0.01°~0.1°量级,且随轨道位置不同而变化。FY-2C卫星在轨偏航轴姿态失配修正实例证实了上述模型的有效性。 相似文献
70.
The problem of orbit determination using one or two GPS satellites is discussed. Methods of getting initial values based on
linear translation is presented; the Secant method and the descend Newton iterative procedure and the continuation algorithm
are used synthetically to solve the nonlinear equations. Computer simulation shows that this algorithm can give preliminary
state of satellite orbit with a certain precision in short time. 相似文献